 
#  **Table of Contents**

  1.  Cover
  2.  Title Page
  3.  Preface
  4.  1 Study on Method for Relative Fidelity Preservation of Seismic Data
    1.  1.1 Introduction
    2.  1.2 Discussion on Impact on Processing of High‐resolution, High SNR for Seismic Acquisition and Observation Mode
    3.  1.3 Discussion on the Cause of Notching
    4.  1.4 Discussion of Impact on Processing of Relative Fidelity Preservation Seismic Data for Seismic Acquisition and Observation Mode
    5.  1.5 Comparison of Results of High‐resolution, High SNR Processing and Relative Fidelity Preservation Processing
    6.  1.6 Elastic Wave Forward Modeling
    7.  1.7 Conclusions
    8.  References
  5.  2 Method and Principle for Seismic Migration and Imaging
    1.  2.1 Kirchhoff Integral Prestack Depth Migration
    2.  2.2 Amplitude Preservation Fourier Finite Difference Prestack Depth Migration Method
    3.  2.3 Reverse Time Migration
    4.  References
  6.  3 Study of Reverse Time Migration Method for Areas With Complicated Structures Based on the GPU/CPU System
    1.  3.1 Introduction
    2.  3.2 The GPU/CPU High‐performance Calculation and Its Application in Seismic Exploration
    3.  3.3 Study on the Two‐way Wave Extrapolation Operator and Its Boundary Conditions
    4.  3.4 Study on the Imaging Condition and Low‐frequency Noise Suppression Method
    5.  3.5 Study and Application of RTM Prestack Imaging Algorithm based on the GPU/CPU System
    6.  3.6 Conclusions
    7.  References
  7.  4 Study and Application of Velocity Model Building Method for the Areas with Complicated Structures
    1.  4.1 Introduction
    2.  4.2 Status Quo and the Development of the Velocity Model Building Method
    3.  4.3 Impacting Factors for the Velocity Model Building
    4.  4.4 Study and Application of the Seismic Velocity Model Building Method
    5.  4.5 Quality Monitoring and Accuracy Discussion of the Seismic Velocity Model Building
    6.  4.6 Velocity Analysis Method for Reverse Time Migration in Angle Domain
    7.  4.7 Study of the Full Waveform Inversion Method
    8.  References
  8.  5 Case Study
    1.  5.1 Application of 3D Prestack Reverse Time Migration in Subsalt Imaging
    2.  5.2 Application of High‐density All‐round Seismic Data Processing in the Carbonatite Region
    3.  5.3 Application of Seismic Imaging Method for Complicated Structures in the Tuha and Jiuquan Basins
    4.  5.4 Application of the Seismic Prestack Imaging Method in the Buried Hill Structural Zone in the Nanpu of Jidong Oilfield
    5.  References
  9.  Index
  10.  End User License Agreement

##  **List of Tables**

  1.  Chapter 02
    1.   Table 2.1 Spatial location of quasi‐P wavefield components and elastic parameters. 

##  **List of Illustrations**

  1.  Chapter 01
    1.   Figure 1.1 Comparison between (a) conventional seismic profile and (b) relative fidelity seismic profile through wells S302 and S303. 
    2.   Figure 1.2 The t0 contour of the sand bottom boundary in Cretaceous Qinshuihe Formation of Shidong area. 
    3.   Figure 1.3 Seismic data high resolution and high SNR processing. 
    4.   Figure 1.4 Single shot records at same shot point of different seismic sources. ( a) Analysis on 0 ~ 20 Hz scanning. ( b) Analysis on 10 ~ 120 Hz scanning. 
    5.   Figure 1.5 Analysis results on single shot record and frequency spectrum of target layer processed by static correction of first arrival refraction. 
    6.   Figure 1.6 Analysis result on single shot record and frequency spectrum of target layer processed by prestack noise elimination. 
    7.   Figure 1.7 Analysis results on single shot record and frequency spectrum of target layer processed by prestack zero phase deconvolution. 
    8.   Figure 1.8 Seismic profile and frequency spectrum of target layers processed by high resolution and high SNR processing. 
    9.   Figure 1.9 Results comparison of random noise data processed two times with RNA method repeatedly. 
    10.   Figure 1.10 The location of notch frequency band in seismic frequency spectrum. 
    11.   Figure 1.11 Filter frequency spectrum comparison between pre‐pack and post‐pack deconvolutions in single deep well. 
    12.   Figure 1.12 Filter frequency spectrum comparison between prepack and post‐pack deconvolutions in combined well. 
    13.   Figure 1.13 The processing flow of relative fidelity preservation seismic data. 
    14.   Figure 1.14 Single shot record of single deep well and seismic spectrum of target layer (SD4). 
    15.   Figure 1.15 Single shot record of combined well and seismic spectrum of target layer (SD4). 
    16.   Figure 1.16 Single shot record of controllable seismic source excitation and seismic spectrum of target layer (SD4). 
    17.   Figure 1.17 Seismic profile and target layer spectrum processed by relative fidelity preservation. 
    18.   Figure 1.18 Spectrum comparison of single deep well prestack and poststack deconvolution filters. 
    19.   Figure 1.19 Spectrum comparison of both combined well prestack and poststack deconvolution filters. 
    20.   Figure 1.20 Sand interpretation based on results of high‐resolution (a1, b1) and relative fidelity (a2, b2) seismic data processing. ( a1,a2) single deep well, 1200 receiving channels, channel interval of 5 m; (b1,b2) combined well, 1200 receiving channels, channel interval of 5 m.
    21.   Figure 1.21 Forward model design. 
    22.   Figure 1.22 Forward model 1 (100 Hz, channel interval of 10 m) prestack time migration profile (depth domain). 
    23.   Figure 1.23 Forward model 2 (100 Hz, channel interval of 10 m) prestack time migration profile (depth domain). 
  2.  Chapter 02
    1.   Figure 2.1 Single shot illumination analysis results by Marmousi model. ( a) Based on conventional Fourier finite difference operator. ( b) Based on fidelity‐preserved amplitude Fourier finite difference operator. 
    2.   Figure 2.2 Illumination comparison results of all shots by Marmousi model. ( a) Based on conventional Fourier finite difference method. ( b) Based on preserved‐amplitude Fourier finite difference method. 
    3.  Figure 2.3 Migration comparison results of all shots records by Marmousi model. ( a) Based on conventional Fourier finite difference method. ( b) Based on fidelity‐preserved amplitude Fourier finite difference method. 
    4.   Figure 2.4 Test result of foothills model data migration method. ( a) Kirchhoff integral method. ( b) Preserved‐amplitude Fourier finite difference method. 
    5.   Figure 2.5 Test result of foothills actual seismic data migration method. ( a) Kirchhoff integral method. ( b) Preserved‐amplitude Fourier finite difference method. 
    6.   Figure 2.6 Diagram of PML absorbing boundary. 
    7.   Figure 2.7 Flowchart of excitation time imaging conditions. 
    8.   Figure 2.8 Flowchart of cross‐correlation imaging condition. 
    9.   Figure 2.9 NWGI velocity model. 
    10.   Figure 2.10 Reverse time migration results by NWGI model. 
    11.   Figure 2.11 Marmousi velocity model. 
    12.   Figure 2.12 Reverse time migration results by Marmousi model. 
    13.   Figure 2.13 Staggered grid diagram. 
    14.   Figure 2.14 Pulse response test data. 
    15.   Figure 2.15 Pulse response based on downward wave maximum energy method imaging condition. 
    16.   Figure 2.16 Pulse response based on cross‐correlation imaging condition. 
    17.   Figure 2.17 Pulse response based on normalized cross‐correlation imaging condition. 
    18.   Figure 2.18 Horizontally layered medium model and synthetic record. ( a) Horizontally layered medium model. ( b) Figure a model's synthetic record in every four groups. 
    19.  Figure 2.19 Migration results under two imaging conditions. ( a) Migration results by downward wave maximum energy method imaging condition. ( b) Migration results by the normalized cross‐correlation imaging conditions. 
    20.   Figure 2.20 η model. 
    21.   Figure 2.21 The reverse time migration profile of Quasi‐P wave equation in VTI media. ( a) Imaging condition migration profile by downward wave maximum energy method. ( b) Imaging condition migration profile by normalized cross‐correlation method. 
    22.   Figure 2.22 Krichhoff prestack time migration profile (from Alkhalifah, 1998). 
    23.  Figure 2.23 Prestack reverse time depth migration profile. 
    24.   Figure 2.24 Reverse time migration profile of isotropic medium acoustic wave equation. 
  3.  Chapter 03
    1.   Figure 3.1 Floating‐point computation efficiency development comparison between GPU and CPU from 2003 to 2007. 
    2.   Figure 3.2 Reverse time depth migration result of the Marmousi model on GT200 GPU (from Tongji University). 
    3.   Figure 3.3 Reverse time migration imaging result of 3D salt dome model on GT200 GPU (from Tongji University). 
    4.  Figure 3.4 Diagram of network subdivision. 
    5.   Figure 3.5 NWGI velocity model. 
    6.   Figure 3.6 Profile comparison before (a) and after (b) low‐frequency suppression of RTM imaging result (parameters [32, 0, 8], wavelet dominant frequency of 20 Hz). 
    7.   Figure 3.7 Profile comparison before (a) and after (b) low‐frequency suppression for RTM imaging result of SEG/EAGE Sigsbee model (parameters [32, 0, 8]). 
    8.   Figure 3.8 The Marmousi model RTM migration result. 
    9.   Figure 3.9 The Marmousi model RTM migration result by applying Laplace filtering. 
    10.   Figure 3.10 The Marmousi model RTM migration result by applying Muder noise elimination method, parameters [32, 0, 2]. 
    11.   Figure 3.11 Comparison of (a) the CPU structure features and (b) the GPU structure features. 
    12.   Figure 3.12 Architecture model of GPU hardware. 
    13.   Figure 3.13 Reverse time migration flowchart. 
    14.   Figure 3.14 GPU flowchart of reverse time depth migration. 
    15.  Figure 3.15a Inline velocity model. 
    16.  Figure 3.15b The CPU migration result. 
    17.   Figure 3.15c The CPU migration result. 
    18.   Figure 3.16a The GPU migration result. 
    19.   Figure 3.16b The CPU migration result. 
    20.   Figure 3.16c The GPU migration result. 
    21.   Figure 3.17a Depth slice velocity model. 
    22.   Figure 3.17b The CPU migration result. 
    23.   Figure 3.17c The GPU migration result. 
    24.   Figure 3.18 NWGI model (a) forward wavefield and (b) forwarded zero migration domain profile. 
    25.   Figure 3.19 Comparison between (a) NWGI velocity model and (b) imaging results of different migration methods. 
    26.   Figure 3.20 Velocity‐depth model of multi‐well restrained inversion. 
    27.   Figure 3.21 Imaging result comparison of (a) subsalt structure one‐way wave migration and (b) reverse time migration. 
  4.  Chapter 04
    1.  Figure 4.1 The coverage plat. 
    2.  Figure 4.2 Distribution of pre‐regularization offset. 
    3.  Figure 4.3 Distribution of post‐regularization offset. 
    4.  Figure 4.4 The migration effects comparison of pre/post‐regularizations. ( a) Pre‐regularization migration. ( b) Post‐regularization. 
    5.  Figure 4.5 The schematic map of subsurface media. 
    6.  Figure 4.6 Inversion coherence capacity of interval velocity. 
    7.  Figure 4.7 The inverted interval velocity spectrum. 
    8.  Figure 4.8 Schematic diagram of coherence inversion. 
    9.  Figure 4.9 Obtaining interval velocity with coherence inversion method. 
    10.  Figure 4.10 Interval velocity inversion of the first interval. ( a) Model data. ( b) Actual data (anisotropy assumption). 
    11.  Figure 4.11a Successive interval velocity inversion of the second interval. 
    12.  Figure 4.11b Interval velocity inversion of the second interval. 
    13.  Figure 4.12a Interval velocity inversion of the second interval. 
    14.  Figure 4.12b Successive interval velocity inversion of the second interval. 
    15.  Figure 4.13 Flow chart of prestack depth migration velocity analysis. 
    16.  Figure 4.14 Transformation from depth error to time error. 
    17.  Figure 4.15 Vertical slowness angle at reflection point. 
    18.  Figure 4.16 CRP gathers (a) before model optimization and (b) after model optimization. 
    19.  Figure 4.17 Comparison of horizontal delay before and after model optimization. 
    20.  Figure 4.18 Field example of CFP modeling and imaging, where (a) is the velocity field after CFP modeling, and (b) is the CFP prestack migration profile of the corresponding velocity field. 
    21.  Figure 4.19 Flow chart of comprehensive modeling combining first arrival wave with reflection wave. 
    22.  Figure 4.20 Inverted shallow layer velocity model Velocity unit:m/s.
    23.  Figure 4.21 (a) True velocity model and (b) depth migration result. 
    24.  Figure 4.22 (a) Velocity model of inversion shallow layer and (b) depth migration result. 
    25.  Figure 4.23 (a) Shallow layer velocity inversion model and (b) depth migration result. 
    26.  Figure 4.24 (a) Conventional velocity model and (b) velocity modeling integrating first arrival wave inversion with reflection wave inversion. 
    27.  Figure 4.25 (a) Velocity modeling migration integrating first arrival wave inversion with reflected wave inversion and (b) comparison of geological outcrop interpretation profile. 
    28.  Figure 4.26 Diagram of external drift Kriging principle. 
    29.  Figure 4.27 Multi‐model external drift Kriging interpolation. 
    30.  Figure 4.28 (a) Well constrained interval velocity inversion plane and (b) well velocity error. 
    31.  Figure 4.29 Inverted interval velocity model under multi‐well constraint. 
    32.  Figure 4.30 Well data constraint and velocity interface. 
    33.  Figure 4.31 Velocity modeling under geological structure constraint. 
    34.  Figure 4.32 (a) One‐way wave of PSDM profile and (b) reverse time migration. 
    35.  Figure 4.33 The relationship of incident angle, propagation angle and dip angle. 
    36.  Figure 4.34 The Marmousi II velocity model. 
    37.  Figure 4.35 Reverse time migration results of the model Marmousi II. 
    38.  Figure 4.36 Computation results of dip angle of the model Marmousi II. 
    39.  Figure 4.37 Reverse time migration results of the simple interval model. 
    40.  Figure 4.38 Computation results of the incident angle of the simple interval model. 
    41.  Figure 4.39 Computation results of the incident angle at CDP points of the model Marmousi II. ( a) CDP = 150. ( b) CDP = 350. ( c) CDP = 650. 
    42.  Figure 4.40 Single shot reverse time migration results of the model Marmousi II. ( a) Single shot reverse time migration before Laplace filtering. ( b) Single shot reverse time migration after Laplace filtering. 
    43.  Figure 4.41 Angle domain CIP gathers at different locations of the model Marmousi II.(a) CDP = 150. ( b) CDP = 650. 
    44.  Figure 4.42 The flat bed velocity model. 
    45.  Figure 4.43 Angle domain CIP gathers gained by flat bed velocity model at various velocities.(a) Accurate velocity. ( b) Lower velocity. ( c) Higher velocity. 
    46.  Figure 4.44 The real velocity model and parameters for numerical experiment of angle domain velocity analysis. 
    47.  Figure 4.45 Reverse migration results from the constant velocity initial velocity model. 
    48.  Figure 4.46 The velocity model updated through the angle domain velocity analysis method. 
    49.  Figure 4.47 Reverse time migration results obtained from the updated velocity model. 
    50.  Figure 4.48 Comparison of the updated velocity model and real velocity model. ( a) CDP = 200. ( b) CDP = 450. ( c) CDP = 600. ( d) CDP = 750. ( e) CDP = 1000. ( f) Locations of five CDPs in the velocity model. 
    51.  Figure 4.49 (a) Tomography inversion velocity. ( b) Inversion results after five times iteration with 2–10 Hz.; ( c) Inversion results after five times iteration with 2–3 Hz, 2–4 Hz, 2–6 Hz, 2–8 Hz. 
    52.  Figure 4.50 Flow chart of gradient full waveform inversion. 
    53.  Figure 4.51 The Marmousi real velocity model. 
    54.  Figure 4.52 Inversion results of the model Marmousi. ( a) The 100th iteration; (b) The 200th iteration. 
    55.  Figure 4.53 Velocity value of the 120th channel with various iterations. ( a) The 100th iteration. ( b) The 200th iteration.  The green line represents real value while the red line represents inversion results. 
  5.  Chapter 05
    1.  Figure 5.1 Seismic time profile through salt dome. 
    2.  Figure 5.2 Reflection wave characters of main geologic horizons on seismic profile. 
    3.  Figure 5.3 Geologic structural map of Pre‐Caspian Basin Region. 
    4.  Figure 5.4 Regional structure division map of the Middle Block. 
    5.  Figure 5.5 Quality of original single shots. ( a) Acquired in 2005. ( b) Acquired in 2007. 
    6.  Figure 5.6 Correlation of single shot at the same location acquired in different years. 
    7.  Figure 5.7 Profile correlation on the same CDP location in different years. 
    8.  Figure 5.8 Time domain‐velocity profile (anomalous subsalt velocity). 
    9.  Figure 5.9 Forward geological model. 
    10.  Figure 5.10 Relation between salt dome time thickness and upward pull height. 
    11.  Figure 5.11 Building time‐domain model with interval control method. 
    12.  Figure 5.12 Space carving of salt dome. 
    13.  Figure 5.13 Velocity‐depth model built on multiple‐well constraint. 
    14.  Figure 5.14 Correlation of (a) time migration and (b) depth migration crossing Well AL‐1 line (east‐west). 
    15.  Figure 5.15 Comparison of low frequency noises from RTM of Marmousi Model (a) before suppression and (b) after suppression. 
    16.  Figure 5.16 Comparison between (a) one‐way wave migration and (b) reverse time migration results of salt dome model. 
    17.  Figure 5.17 Comparison between (a) velocity slice and (b) reverse time migration velocity slice of salt dome model. 
    18.  Figure 5.18 Comparison of imaging results of subsalt structure by (a) one‐way wave migration and (b) reverse time migration. 
    19.  Figure 5.19 Comparison of imaging slices of subsalt structure by (a) one‐way wave migration and (b) reverse time migration. 
    20.  Figure 5.20 (a) Iso‐to graph and (b) structural map of the Lower Permian top in mid block. 
    21.  Figure 5.21 (a) Iso‐to graph and (b) structural map of KT‐I top in mid block. 
    22.  Figure 5.22 (a) Iso‐to graph and (b) structural map of the Carboniferous KT‐II top in mid block. 
    23.  Figure 5.23 (a) Iso‐to graph and (b) structural map of the Carboniferous MKT top in mid block. 
    24.  Figure 5.24 (a) Iso‐to graph and (b) structural map of the Carboniferous Visean top in mid block. 
    25.  Figure 5.25 Distribution map of traps on KT‐I and KT‐II tops in mid block. 
    26.  Figure 5.26 Deployment diagram for high‐density 3D seismic survey. 
    27.  Figure 5.27 Distribution map of high‐density 3D surface types. 
    28.  Figure 5.28 Plane variation diagram of high‐density 3D surface elevation. 
    29.  Figure 5.29 Thickness variation diagram of high‐density 3D low‐velocity belt. 
    30.  Figure 5.30 Analysis of interference wave. 
    31.  Figure 5.31 Analysis of spectrum. 
    32.  Figure 5.32 Comparison chart of (a) single shot and (b) spectrum of acquired data by conventional method and high‐density full azimuth method. 
    33.  Figure 5.33 (a) SNR attribute and (b) original stacked profile. 
    34.  Figure 5.34 Comparison of velocity spectrum and gather of high‐density full azimuth data at different azimuths. 
    35.  Figure 5.35 Attribute graph of folds, azimuth and offset in work zone. 
    36.  Figure 5.36 Single shot before and after frequency division anomalous amplitude processing. 
    37.  Figure 5.37 The profile before and after frequency division anomalous amplitude processing and noise profile. 
    38.  Figure 5.38 Cross‐array observation system chart. 
    39.  Figure 5.39 3D f‐kx‐ky before and after single shot prior to denoising on cross‐array gather. 
    40.  Figure 5.40 The figure of refracted wave about different arrays of lateral offset. 
    41.  Figure 5.41 Distribution of group interval before and after linear moveout correction. 
    42.  Figure 5.42 Implementation process schematic of linear moveout correction with 2D f‐k. 
    43.  Figure 5.43 Comparison of CMP gathers (a, b) before and after 3D prestack random noise attenuation. 
    44.  Figure 5.44 Comparison of profiles before and after serial deconvolution. 
    45.  Figure 5.45 Comparison of common offset folds before and after data regularization. 
    46.  Figure 5.46 Comparison of common offset folds before and after data regularization. 
    47.  Figure 5.47 Comparison of profiles (a) before and (b) after data regularization. 
    48.  Figure 5.48 Comparison of profiles (a) before and (b) after data regularization. 
    49.  Figure 5.49 Distribution map of fractures and cavities. 
    50.  Figure 5.50 Processing flow for PSTM.  
    51.  Figure 5.51 Criterion for velocity rationality in velocity analysis. ( a) Analysis of root mean square velocity on CRP gather. ( b) Residual delay analysis to perform fine tuning of velocity. 
    52.  Figure 5.52 Root mean square velocity model for final PSTM. 
    53.  Figure 5.53 Building the time interval model. 
    54.  Figure 5.54 Lateral delay spectrum of target zone. 
    55.  Figure 5.55 S/P velocity analysis and quality control. 
    56.  Figure 5.56 Velocity profiles of P‐velocity modeling and S‐velocity modeling. 
    57.  Figure 5.57 Comparison of P‐modeling and P‐joint modeling imaging profiles. ( a) Along‐interval lateral velocity adjustment result. ( b) Fine adjustment result of longitudinal velocity. 
    58.  Figure 5.58 Six azimuth folds and azimuth attribute chart. 
    59.  Figure 5.59 Comparison of fractures on different azimuth profiles. 
    60.  Figure 5.60 Remarkable amplitude difference of fractures on different azimuth gather. 
    61.  Figure 5.61 Velocity difference of "beads" at different azimuths. 
    62.  Figure 5.62 Plane graph of the obtained anisotropic parameter δ. 
    63.  Figure 5.63 Anisotropic parameters δ body and ε body. 
    64.  Figure 5.64 Comparison of (a) isotropic depth migration and (b) anisotropic depth migration. 
    65.  Figure 5.65 Reverse time flow chart. 
    66.  Figure 5.66 Comparison of (a) integral PSDM and (b) reverse time PSDM. 
    67.  Figure 5.67 Comparison of PSTM of (a) conventional data and (b) PSTM of high‐density full azimuth data. 
    68.  Figure 5.68 Comparison of (a) PSTM and (b) PSDM of high‐density full azimuth data. 
    69.  Figure 5.69 Bead profile superimposition map for PSTM and PSDM of high‐density full azimuth data. 
    70.  Figure 5.70 Comparison of (a) Kirchhoff depth migration and (b) reverse time migration. 
    71.  Figure 5.71 Comparison of (a) Kirchhoff depth migration and (b) reverse time migration. 
    72.  Figure 5.72 Comparison of (a) Kirchhoff depth migration and (b) reverse time migration. 
    73.  Figure 5.73 3D seismic survey deployment map for the north foothill of Turpan‐Hami Basin. 
    74.  Figure 5.74 Division of surface types in the research area. 
    75.  Figure 5.75 3D seismic survey deployment map for the Qingxi Depression of the Jiuquan Basin. 
    76.  Figure 5.76 Surface types division of the research area. 
    77.  Figure 5.77 Geomorphologic map of the research zone. 
    78.  Figure 5.78 Near‐surface inversion profile of the research area and original single shot record. 
    79.  Figure 5.79 Original single shots in different locations of Baka region (a) single shot in western work zone (b) single shot in middle work zone (c) single shot in eastern work zone. 
    80.  Figure 5.80 Profile comparison of static correction effect at different locations. ( a) Tomographic static correction profile. ( b) Refraction static correction profile. 
    81.  Figure 5.81 Comparison of near‐surface model for tomographic inversion. ( a) Constraint inversion model. ( b) Inversion model by conventional method. 
    82.  Figure 5.82 Comparison of tomographic inversion stacking profile effect. ( a) Model‐constrained stacking profile. ( b) Non‐model‐constrained stacking profile. 
    83.  Figure 5.83 Stacking results correlation of various static correction methods for northern Turpan‐Hami foothills. ( a) Stacking results of database static correction. ( b) Stacking result of integrated chromatographic static correction by fitted reconstruction. 
    84.  Figure 5.84 Stacking results comparison of various static correction methods for the Qingxi Region of Jiuquan. ( a) Profile prior to static correction. ( b) Static correction profile by field model. ( c) Tomographic static correction profile. ( d) Constrained integrated static correction profile. 
    85.  Figure 5.85 Application effects analysis of residual static correction in the Baka Region. ( a) Profile prior to residual static correction. ( b) Profile after residual static correction to reflected waves. ( c) Profile after global optimization static correction. 
    86.  Figure 5.86 Application effects analysis of constraint integrated static correction in the Qingxi Region of Jiuquan Basin. ( a) Original profile prior to static correction. ( b) Profile after constraint integrated basic static correction. ( c) Profile after integrated residual static correction. 
    87.  Figure 5.87 Single shot comparison before and after anomalous amplitude and surface wave suppression. ( a) Original single shot. ( b) Single shot after noise suppression. ( c) Suppressed noise. 
    88.  Figure 5.88 Single shot linear interference wave step suppression in the northern Turpan‐Hami foothills. ( a) Original single shot. ( b) Single shot after mid‐low velocity interference suppression. ( c) Single shot after high velocity suppression. 
    89.  Figure 5.89 Step suppression of 3D single shot linear interference in the Qingxi Region of Jiuquan. ( a) Original single shot. ( b) Single shot after mid‐low velocity interference suppression. ( c) Single shot after high velocity suppression. 
    90.  Figure 5.90 Step suppression of 3D single shot linear interference in the Qingxi Region of Jiuquan. ( a) Original single shot. ( b) Original single shot spectrum. ( c) Original single shot f‐k spectrum. ( d) Single shot after suppression. ( e) Single shot spectrum after suppression. ( f) Single shot f‐k spectrum after suppression. 
    91.  Figure 5.91 Suppressing of prestack domain noise. ( a) Original shot gather. ( b) Result after shot gather noise suppression. ( c) Gather of common geophone points. ( d) Results after geophone domain noise suppression. 
    92.  Figure 5.92 Noise suppression comparison of prestack multi‐domain and cross array domain. ( a) Original shot gather. ( b) Result after noise suppression. 
    93.  Figure 5.93 Comparison of prestack step‐by‐step and multi‐domain noise suppression. ( a) Original single shot. ( b) Result of shot‐domain noise suppression. ( c) Result of geophone‐domain noise suppression. ( d) Result of cross‐array surface wave suppression. ( e) Result of cross‐array domain anomalous energy suppression. ( f) Result of linear noise cross‐array domain suppression. 
    94.  Figure 5.94 Comparison of PSTM profiles for high precision root mean square velocity modeling. ( a) PSTM profile for conventional velocity modeling method. ( b) PSTM profile for high precision velocity modeling method. 
    95.  Figure 5.95 Final interval velocity‐depth model. ( a) Final interval velocity profile. ( b) Final interval velocity body. 
    96.  Figure 5.96 Final interval velocity‐depth model. ( a) PSTM profile. ( b) PSDM profile. 
    97.  Figure 5.97 PSDM effects comparison between floating datum and fixed datum of some survey line. ( a) PSDM of fixed surface. ( b) PSDM of float datum. 
    98.  Figure 5.98 Comparison of new and previous migration imaging results for highly steep structures. ( a) Previous migration result. ( b) New migration result. 
    99.  Figure 5.99 PSDM results comparison of different methods. ( a) Kirchhoff integral migration. ( b) One‐way wave migration. 
    100.  Figure 5.100 PSDM result comparison of different methods for the Qingxi area. ( a) Kirchhoff integral PSDM. ( b) Reverse time PSDM. 
    101.  Figure 5.101 PSDM result comparison of different methods for the Qingxi area. ( a) Kirchhoff integral PSDM. ( b) Reverse time PSDM. 
    102.  Figure 5.102 PSDM result comparison of different methods for the northern Turpan‐Hami mountain foothills. ( a) Kirchhoff integral PSDM. ( b) Reverse time PSDM. 
    103.  Figure 5.103 Comparison between new and previous PSTM results. ( a) Previous migration results. ( b) New migration results. 
    104.  Figure 5.104 Comparison between new and previous PSDM results (inline 644). ( a) Previous migration results. ( b) New migration results. 
    105.  Figure 5.105 Comparison between new and previous PSDM results. ( a) Previous migration results. ( b) New migration results. 
    106.  Figure 5.106 Representative profile of various structural patterns in the Baka region. ( a) Monoclinal structure. ( b) Fault structure. ( c) Fault anticline structure. 
    107.  Figure 5.107 Sand body forecast spread map of J1b interval. 
    108.  Figure 5.108 Multi‐attribute fusion plane spread map of J1b interval. 
    109.  Figure 5.109 Comparison between new and previous PSTM results (inline 740). ( a) Previous migration results. ( b) New migration results. 
    110.  Figure 5.110 Comparison between new and previous PSTM results (inline 420). ( a) Previous migration results. ( b) New migration results. 
    111.  Figure 5.111 Comparison between new and previous migration results (inline 410). ( a) Previous PSTM profile. ( b) New integral PSDM profile (depth domain). 
    112.  Figure 5.112 Comparison between new and previous PSDM results (inline 420). ( a) Previous integral PSDM profile. ( b) New reverse time PSDM profile. 
    113.  Figure 5.113 Structural map of coal bed top boundary in Badaowan Formation. 
    114.  Figure 5.114 Favorable reservoir distribution map forecasted by multi‐information fusion. 
    115.  Figure 5.115 Comparison between new and previous PSTM results. ( a) Previous PSTM profile. ( b) New PSTM profile. 
    116.  Figure 5.116 Comparison between new and previous PSTM results before and after the research (I). ( a) Previous PSTM profile. ( b) New PSTM profile. 
    117.  Figure 5.117 Comparison between new and previous PSTM results before and after the research (II). ( a) Previous PSTM profile. ( b) New PSTM profile. 
    118.  Figure 5.118 Comparison between new and previous PSTM results before and after the research (III). ( a) Previous PSTM profile. ( b) New PSTM profile. 
    119.  Figure 5.119 Comparison between PSTM and PSDM results after the research (I). ( a) PSTM profile. ( b) PSDM profile. 
    120.  Figure 5.120 Comparison between PSTM and PSDM well‐tie profiles after the research (II). ( a) PSTM profile. ( b) PSDM profile. 
    121.  Figure 5.121 Comparison of amplitude on prestack migration well‐time profile. 
    122.  Figure 5.122 Proposed well site map on sub‐depression in the Qingnan region. 
    123.  Figure 5.123 Seismic profile I of sub‐depression of the Qingnan Area. 
    124.  Figure 5.124 Seismic profile II of sub‐depression of the Qingnan Area. 
    125.  Figure 5.125 Schematic of work zone location. 
    126.  Figure 5.126 Stacked profile. 
    127.  Figure 5.127 Record of original single shot (development of high frequency noise). 
    128.  Figure 5.128 Spectrum of original single shot record (development of high frequency noise). 
    129.  Figure 5.129 f‐k spectrum of original single shot record (high frequency setting developed in tidal flat). 
    130.  Figure 5.130 Separation of high frequency noise and signal. 
    131.  Figure 5.131 Comparison between (a) shot gather sequencing as per trace number and (b) sequencing as per offset. 
    132.  Figure 5.132 Comparison of (a) high frequency noise before suppression, (b) after suppression and (c) after denoising. 
    133.  Figure 5.133 Effect graph of high frequency coherent noise suppression. 
    134.  Figure 5.134 Effect graph of air‐bubbled secondary source suppression. 
    135.  Figure 5.135 Folds comparison of (a) common‐offset profile bin and (b) after homogenization. 
    136.  Figure 5.136 PSDM profile comparison (a) before and (b) after bin homogenization. 
    137.  Figure 5.137 Folds comparison (a) before and (b) after bin homogenization. 
    138.  Figure 5.138 PSDM profile comparison (a) before and (b) after bin homogenization. 
    139.  Figure 5.139 Initial velocity model in depth domain obtained from longitudinal velocity modeling. 
    140.  Figure 5.140 Determining velocity interface as per log data. 
    141.  Figure 5.141 Building time horizon model. 
    142.  Figure 5.142 Comparison of Ed2 zone velocity before and after optimization. ( a) Velocity prior to correction. ( b) Depth domain residual moveout. ( c) The velocity after reflected wave tomography. 
    143.  Figure 5.143 P‐S velocity analysis and quality control. 
    144.  Figure 5.144 Final velocity model. ( a) Horizon depth. ( b) Layer velocity (c) Final velocity‐depth model. 
    145.  Figure 5.145 Flow chart for grid tomographic imaging. 
    146.  Figure 5.146 Various attribute chart for seismic data. 
    147.  Figure 5.147 Comparison of velocity profiles before and after grid tomographic imaging. 
    148.  Figure 5.148 Comparison of depth migration profiles (a) before and (b) after grid tomographic imaging. 
    149.  Figure 5.149 Comparison between (a) curved ray PSTM and (b) asymmetric travel time PSTM. 
    150.  Figure 5.150 Profile comparison between (a) Kirchhoff PSDM and (b) reverse time migration (I). 
    151.  Figure 5.151 Profiles comparison between (a) Kirchhoff PSDM and (b) reverse time migration (II). 
    152.  Figure 5.152 Profile comparison between (a) previous migration result and (b) new migration results (I). 
    153.  Figure 5.153 Profile comparison between (a) previous migration result and (b) new migration results (II). 
    154.  Figure 5.154 Time slices comparison between (a) previous PSDM result and (b) new reverse time migration result. 

## Guide

  1.  Cover
  2.  Table of Contents
  3.  Begin Reading

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#

## Wiley Series in Petroleum Industry Press series list

### Relative Fidelity Processing of Seismic Data

Xiwen Wang

March 2017

### Sand Production Management for Unconsolidated Sandstone Reservoirs

Shouwei Zhou and Fujie Sun

January 2016

# Relative Fidelity Processing of Seismic Data

## Methods and Applications

_Edited by Xiwen Wang et al_

_Petrochina_  
 _Lanzhou, Gansu_  
 _China_

This edition first published 2017  
© 2017 John Wiley & Sons Ltd

All rights reserved.  No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law.  Advice on how to obtain permission to reuse material from this title is available at <http://www.wiley.com/go/permissions>. 

The right of Xiwen Wang to be identified as the editor of this work has been asserted in accordance with law. 

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_Library of Congress Cataloging‐in‐Publication Data_

Names: Wang, Xiwen, 1956–  
Title: Relative fidelity processing of seismic data : methods and applications / Professor Xiwen Wang, Petrochina, Lanzhou, Gansu [Province], CH [China].   
Description: 1 edition.  | Hoboken, NJ : John Wiley & Sons, Inc., 2017.  | Series: Wiley series in petroleum industry press | Includes bibliographical references and index.   
Identifiers: LCCN 2016049496 (print) | LCCN 2016049872 (ebook) | ISBN 9781119052906 (cloth) | ISBN 9781119052937 (pdf) | ISBN 9781119052920 (epub)  
Subjects: LCSH: Seismic prospecting.  | Petroleum–Prospecting.  | Petroleum–Geology.  | Petrology.   
Classification: LCC TN271.P4 W344 2017 (print) | LCC TN271.P4 (ebook) | DDC 622/.1592–dc23  
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# Preface

In recent years, lithology reservoir has gradually become the major field of reservoir gain in China.  The lithology analysis poses high requirements for amplitude preservation of seismic migration results, but the previous prestack depth migration methods mainly focus on structural imaging.  Therefore, much study has been carried out in terms of the amplitude preservation prestack depth migration method using geophysics.  Meanwhile, the reservoir of lithology formation is under the control of multiple factors, such as regional structures and depositional facies belts.  It presents great exploration difficulties due to being complicated and concealed.  On seismic profile, the display reliability of response to lithology formation is subject to the fidelity of processing. 

Currently, it is difficult to realize absolute seismic fidelity preservation processing, but relative fidelity preservation processing is possible, which poses higher requirements for seismic data processing, requiring amplitude preservation.  It needs to avoid adopting the module that will damage the amplitude relationship of neighboring seismic channels in the processing procedure.  In view of the seismic processing problem of lithology reservoir exploration, the relative fidelity preservation processing method that is represented in this book has four critical principles for wide‐frequency relative fidelity preservation processing: (1) Protection of effective band.  The widening of effective band should be based on SNR of data, high‐frequency widening and be conducted for the low SNR seismic data; the bandwidth and dominant frequency of deconvolution operator should be controlled.  The main effect of deconvolution will be the elevation of energy of high‐frequency component within the effective band, to avoid the occurrence of serious notching in the high‐frequency end of effective band. ( 2) Protection of low frequency, especially that of 3 ~ 8 Hz.  The scenarios of low frequency information suppressed due to high resolution, high SNR processing or significant loss of low frequency end effective information with adoption of strong j‐k denoising, should be avoided. ( 3) Amplitude preservation.  Modification module such as RNA should not be applied, to avoid damaging the lateral relationship of seismic channel amplitude. ( 4) Phase preservation.  The module that will damage phase position should be avoided during processing.  Zero phase deconvolution and surface consistent deconvolution will not damage relationship of phases.  Compared with high‐resolution high SNR processed profile, relative fidelity preservation processed profile could reflect seismic response of subsurface sand reservoir quite genuinely.  While there is discussion on the processing method of relative fidelity preservation processing or high‐resolution high SNR, the impact on seismic processing by acquisition mode of seismic data is also elaborated in this book.  Seismic broadband acquisition is the basis for relative fidelity preservation processing.  Based on profile reflection traits and spectrum characteristics, the impact on the data processed with high‐resolution, high SNR method or data processed with relative fidelity preservation method by means of seismic acquisition source and observation approach is also analyzed and discussed. 

In the previous seismic exploration, in order to satisfy the requirements of structural interpretation, SNR was given much more attention for seismic data imaging and the consideration of fidelity and amplitude preservation of data was insufficient.  Nowadays, with the promotion of oil and gas exploration, the requirement for fidelity of seismic data processing is much higher.  In recent years, the author has done much in this respect and the research idea and methodology for fidelity preservation imaging have gradually been developed. 

The study of the relative fidelity preservation processing method, elaborates the method and principle of the Kirchhoff integral migration method based on ray theory, the one‐way wave equation migration based on wavefield extrapolation and two‐way wave equation reverse time migration.  Meanwhile, the study status of respective amplitude preservation migration algorithm is introduced.  The methods of critical technology, including reverse time migration imaging based on a GPU/CPU system for complicated structures and depth domain velocity modeling for complicated structural zone, are represented.  Also, the pertinent fidelity preservation imaging processing measures and application performance are applied in practice for different fields, including subsalt imaging of 3D prestack reverse time migration, high‐density, all‐round seismic data processing for carbonate region, seismic imaging for complicated structures in the Tuha and Ji‐uquan Basins, and seismic prestack imaging of buried hill structural zone in the Nanpu of Jidong Oilfield.  In view of the technical difficulties of seismic imaging and structural interpretation existing in these regions, in‐depth study on seismic prestack imaging and integrated interpretation has been carried out, with the formation of a pertinent technical series for seismic prestack imaging. 

In terms of imaging method, it is difficult for the current regular integral seismic method to delineate subsalt imaging, while the two‐way wave equation method (WEM) could generate premium image for complicated deep salt structure.  The reverse time migration imaging technology adopted in this book solves the problem of subsalt imaging, which significantly improves the imaging quality for the fairly large dip structure such as vertical fault, salt dome flank and salt domes, eliminating the distortion caused to the underlayer by abnormal velocity of salt dome, making the subsalt formation capable of being accurately imaged in depth field.  Study on high‐density all‐round imaging technology in terms of carbonate seismic data is described in this book, with the formation of prestack imaging technical flow for high‐density all‐round seismic data, of which the critical technologies are: high fidelity all‐round noise suppression technology, enhancing prestack vertical resolution technology, all‐round data regularization technology, all‐round high accuracy migration velocity modeling technology, sub‐azimuth prestack depth migration technology.  The result of prestack depth migration dominated by reverse time migration accurately delineates the subsurface structure pattern and location of fault for complicated block, and is especially capable of clearly delineating abdominal block of anticline, small displacement fault, and, consequently, provides a reliable basis of data for structural interpretation.  By utilizing results of prestack depth migration, comprehensive study such as fine structural interpretation and reservoir prediction is conducted, structural details in the study area are reconfirmed, and the fault characteristics as well as the regularity of formation distribution are further understood.  In this book, also, the asymmetrical travel time prestack time migration and prestack reverse time migration are combined, which solves the impact on imaging for lateral velocity variation.  Where the structures are complicated and the dip is large, the performance of imaging is much better than the previous results from studies and the final processing results represent various geological characteristics, which are worth sharing.  Currently, in theory, 3D reverse time depth migration is the most accurate imaging method, which is a surefire result of the development of prestack depth migration imaging technology and is the direction of development for accurate imaging when combined with FWI velocity estimation method. 

During the study for this book, the R&D was closely integrated with production, and pertinent technical series formed during study were applied in a timely way for oilfield exploration.  With the application of new study results, the overall structural pattern and local structural characteristics of a series of blocks were accurately confirmed and favorable targets of exploration and drilling were optimally selected with the achievement of excellent application performance. 

The preface is by Wang Xiwen et al.  Chapter 1 by Wang Xiwen; Chapter 2 by Lv Bin, Wang Yuchao and Han Linghe; Chapter 3 by Wang Yuchao, Liu Wenqing, Wang Xiaowei, Xu Xingrong, Lv Bin, Zeng Huahui, Lu Lieqin and Zhao Yulian; Chapter 4 by Liu Wenqing, Wang Xiwen and Lyu Bin; section 5.1 of Chapter 5 is by Lv Wenqing, Zhang Jing and Shao Xichun; section 5.2 of Chapter 5 is by Wang Xiaowei, Tian Yancan and Zhang Tao; section 5.3 of Chapter 5 is by Su Qin, Xiao Mingtu, Li Hailiang, Lv Bin and Shao Xichun; section 5.4 of Chapter 5 is by Tian Yancan, Zeng Huahui and Zhang Tao.  The whole book is modified and revised by Wang Xiwen. 

The study projects involved in this book are supported by PetroChina E & P Company, Tarim Oilfield Subsidiary, Yumen Oilfield Subsidiary, Tuha Oilfield Subsidiary, Jidong Oilfield Subsidiary, Mid‐Asia and Russia Research Branch of Research Institute of Petroleum Exploration and Development (RIPED) of CNPC.  The preparation of this book is supported and assisted by Director Yang Jie and other experts of Northwest Branch of Research Institute of Petroleum Exploration and Development (RIPED).  We would like to sincerely acknowledge their support in publishing this book. 

The authors would welcome comments and questions about the contents of the book. 

#  1   
Study on Method for Relative Fidelity Preservation of Seismic Data

## 1.1 Introduction

The reservoir of lithology formation, under the control of multiple factors such as regional structures and depositional facies belt, shows some distribution regularity and also has significant exploration potential.  However, the exploration challenge is relatively great due to their complex concealment.  In recent years, China has made great breakthroughs and discoveries in this field, proving favorable and huge remaining resource potential; this has gradually become the major field of reservoir gain in China [1–4]. 

The lithology analysis of these lithology reservoirs poses high requirements for the seismic data processing [5–7].  The first challenge is to increase the resolution of seismic data, so as to identify the geologic features like thin sand layers and sand body pinch‐out points, on the processed seismic data.  Second, to preserve the amplitude, and not damage the module of amplitude relation between adjacent seismic traces on processing flow.  However, previous study mainly focused on identifying thin layers, increasingly widening the frequency band of seismic data and improving the dominant frequency.  Therefore, a lot of high‐resolution seismic processes have been developed for the purpose of increasing seismic dominant frequency. 

Increasing the resolution of seismic data is mostly realized by deconvolution method [8–19], which is an important means in seismic data processing.  In order to increase the resolution of seismic data, an operator for high frequency deconvolution is devised to identify thin layers.  However, which principles should be used to determine the frequency bandwidth and dominant frequency of operator for high frequency deconvolution?  Is it possible to increase the dominant frequency of the operator for high frequency deconvolution without restriction?  These are the questions that remain to be discussed. 

Figure 1.1 presents the comparison of lithology reservoir seismic profiles through SN31 wellblock in the Luxi area of Junggar Basin.  In Figure 1.1a, a high‐resolution and high‐S/N seismic processing technology was adopted.  The lithology reservoir of J2t0 of SN31 wellblock was interpreted from the seismic profile shown in the figure (it also proved to be sand reservoir through drilling), but from the profile, the continuity of J2t0 reservoir was favorable (in the location of Well S302, the J2t0 extended for more than 1 km to the updip direction of the reservoir until the lithology reservoir pinched out).  For this purpose, a number of wells were planned for this complete lithology reservoir.  Wells S302 and S302 shown on the figure were among them, but their drilling effectiveness varied greatly.  The reservoir in Well S303 is very good and the well is a high oil producer, while reservoir in Well S302 is poor (lithology varied, and J2t0 reservoir is mainly mudstone). 

**Figure 1.1** Comparison between (a) conventional seismic profile and (b) relative fidelity seismic profile through wells S302 and S303. 

From the analysis of the data on Figure 1.1, it was believed that the over emphasizing on the high resolution and high SNR during processing deteriorated the fidelity of processed results, directly resulting in the distortion of lithology reservoir seismic response that was reflected on seismic profile. 

On seismic profile, the display reliability of seismic response on lithology reservoirs is subject to the fidelity of seismic processing.  Currently, it is very difficult to realize absolute seismic fidelity preservation processing, but relative fidelity preservation processing is possible.  Figure 1.1b shows the relative fidelity preservation profile that was reprocessed as per the flowchart in Figure 1.13, in 2006.  As clearly shown in the figure, the reflection of J2t0 reservoir in Well S302 is very weak, indicating that the reservoir is no longer present.  The pinch‐out point of J2t0 reservoir identified on seismic profile is nearly 300 m to downdip direction of lithology reservoir in Well S302, which matches with the data of Well S302 that has been completed. 

This has raised a question: the processing of seismic data is the key in exploration of lithology reservoirs.  Only when the seismic response of reservoir properties is truly reflected on the profile after seismic processing to the greatest extent can the seismic data be effectively used to identify the lithology reservoirs. 

In view of the above problems, we made analysis by selecting a 2D high‐resolution pilot line of 8 km from the Shidong area in the Junggar Basin across Wells Shidong‐2 and Shidong‐4, on the results of high resolution and high SNR processing and relative fidelity preservation processing.  Based on this, we came up with a processing method for relative fidelity of seismic data. 

Relative fidelity preservation processing[5] of seismic data should pay attention to the following items: (1) Protection of effective frequency band.  The widening of effective band should rely on SNR of seismic data.  In order to widen the low S/N seismic data to high frequency band, it is necessary to control the bandwidth and dominant frequency of the deconvolution operator.  The main function of deconvolution is to increase the energy of high frequency components within the effective band so as to prevent notch frequency at effective high frequency band. ( 2) Protection of low frequency, especially that of 3–8 Hz.  The scenarios that suppress low frequency data of 10 Hz and below in high resolution and high SNR processing, or give significant loss of effective low frequency information with adoption of strong f‐k noise elimination should be avoided. ( 3) Amplitude preservation.  Modification modules like RNA should not be applied to avoid damaging the lateral relationship of seismic channel amplitude. ( 4) Phase preservation.  The module should not be used as it may damage the phase position in processing, while the zero phase deconvolution and surface consistent deconvolution will not damage the phase relation.  Compared with the profile processed by high resolution and high SNR, the profile processed by relative fidelity preservation could reflect the seismic effect on subsurface sand reservoirs quite genuinely. 

While discussing the processing method of relative fidelity preservation processing or high‐resolution and high SNR processing, the effect of seismic acquisition manner on seismic data processing is also elaborated in this book.  Seismic broadband acquisition is the basis for relative fidelity preservation processing.  Based on the seismic pilot survey line, we analyzed and discussed the effects of seismic acquisition source and observation means on the data processed by high resolution and high SNR or by relative fidelity in terms of profile reflection features and spectrum features. 

## 1.2 Discussion on Impact on Processing of High‐resolution, High SNR for Seismic Acquisition and Observation Mode

Figure 1.2 is the t0 contour of the sand bottom boundary in the Cretaceous Qinshuihe Formation of the Shidong area in the Junggar Basin.  It is located in the distribution area of the oil layer of the Qingshuihe formation in Well Shidong No.  2 region and Well Shidong No.  4 region, which is highlighted by yellow in the figure.  But based on the previous seismic data, it is really difficult to explain the reservoir distribution characteristics of these two wells.  Therefore, in 2002, seismic pilot survey lines (blue line) across Wells Shidong No.  2 and Shidong No.  2 were deployed to study and find out a method for improving the quality of field seismic data acquisition, thus meeting the requirements of lithology reservoir exploration. 

**Figure 1.2** The t0 contour of the sand bottom boundary in Cretaceous Qinshuihe Formation of Shidong area. 

The seismic pilot survey lines across Well Shidong No.  2 and Shidong No.  4 is 8 km long, with acquisition factors including: (1) Single well excitation: excitation well depth is 85 ~ 139 m; the dosage of explosive per well is 4 kg and the number of wells is 1, so the total dosage for single well excitation is 4 kg.  The offset distance is 50 m. The number of receiving channels is 1200 and the distance between channels is 5 m (or 240 receiving channels with a 25 m interval). ( 2) Combined well excitation: excitation well depth is 6 m; the dosage of explosive per well is 2 kg and the number of wells is 10, so the total explosive dosage is 20 kg.  The offset distance is 50 m. The number of receiving channels is 1200 and the distance between channels is 5 m (or 240 receiving channels with a 25 m interval). ( 3) Controllable seismic source excitation: 4 seismic sources multiplied by 6 times and the scan frequency is 8 ~ 90 Hz.  The offset distance is 25 m. The number of receiving channels is 300 and the distance between channels is 25 m. High resolution and high SNR process (Figure 1.2) were used to increase the resolution of seismic data and find out the reservoir distribution characteristics in the Qingshuihe formation between Well Shidong No.  2 region and Well Shidong No.  4 region.  In data processing, zero phase deconvolution was used both at prestack and poststack in order to increase the resolution; additionally, the random noise attenuation modification was employed to improve the signal‐to‐noise ratio. 

We analyzed the processing progress based on the five control points shown in Figure 1.3: original single shot record frequency scan (control point ①, Figure 1.4); upon the completion of the first arrival refraction static correction process, we used the single shot record and spectrum analysis results of target layer (control point ②, Figure 1.5) to analyze the quality of data.  After completing prestack noise elimination, we used the single shot record and the spectrum analysis results of target layer (control point ③, Figure 1.6) to analyze the effect of noise elimination.  After finishing zero phase deconvolution process, we used the single shot record and the analysis results on spectrum of target layer (control point ④, Figure 1.7) to analyze the effect of zero phase deconvolution; after completing the migration process, we used the stacked migration profile and the spectrum analysis results of target layer (control point ⑤, Figure 1.8) to analyze the effect of increasing the resolution. 

**Figure 1.3** Seismic data high resolution and high SNR processing. 

**Figure 1.4** Single shot records at same shot point of different seismic sources. ( a) Analysis on 0 ~ 20 Hz scanning. ( b) Analysis on 10 ~ 120 Hz scanning. 

**Figure 1.5** Analysis results on single shot record and frequency spectrum of target layer processed by static correction of first arrival refraction. 

**Figure 1.6** Analysis result on single shot record and frequency spectrum of target layer processed by prestack noise elimination. 

**Figure 1.7** Analysis results on single shot record and frequency spectrum of target layer processed by prestack zero phase deconvolution. 

**Figure 1.8** Seismic profile and frequency spectrum of target layers processed by high resolution and high SNR processing. 

In Figure 1.4, the original single shot record frequency scan (control point ① in Figure 1.3) is used to analyze the quality of original seismic data, and to analyze the single shot record of 0 ~ 20 Hz scanning at the same shot point from different seismic source. 

A little signal (or noise) can be observed in the single shot record of 5 ~ 8 Hz scanning under single deep well excitation and in the single shot record of 3 ~ 6 Hz scanning under combined well excitation, while no signal (or noise) can be observed in the single shot record below 8 Hz scanning under controllable seismic source excitation, indicating the loss of low‐frequency component (the scanning frequency of controllable seismic source excitation is 8 ~ 90 Hz). 

Figure 1.4b shows the analysis on single shot records of 10 ~ 120 Hz scanning at the same shot point of different seismic sources.  Signals can be observed in the single shot record of 5 ~ 100 Hz scanning of single deep well excitation.  Signals can be observed in the single shot record of 4 ~ 80 Hz scanning under combined well excitation.  Signals can still be observed in the single shot record of 8 ~ 100 Hz scanning under controllable seismic source excitation. 

From the perspective of scanning signal, single deep well and controllable seismic source excitation have wide frequency bandwidth, while combined well excitation has narrow bandwidth; low frequency component below 8 Hz is missing in controllable seismic source excitation. 

Figure 1.5 shows the analysis results on the single shot record (control point ② in Figure 1.3, selects the same point for excitation and compares the original single shot records excited by different seismic sources) and seismic spectrum of target layer processed by static correction of first arrival refraction ((a) is single deep well excitation; (b) is combined well excitation; (c) is controllable seismic source excitation).  From this we can see that the frequency bandwidth of single shot record under single well excitation is 4 ~ 50 Hz, with the dominant frequency at 22 Hz (Figure 1.5a); the frequency bandwidth of single shot record under combined well excitation is 4 ~ 40 Hz, with the dominant frequency at 18 Hz (Figure 1.5b); the frequency bandwidth of single shot record under controllable seismic source excitation is 8 ~ 45 Hz, with the dominant frequency at 20 Hz (Figure 1.5c). 

Figure 1.6 shows the analysis results on single shot record (control point ③ in Figure 1.3, which eliminates low frequency surface wave mainly by f‐k; the high frequency component is enhanced for the high intensity of eliminating low frequency components) and frequency spectrum of target layer processed by prestack noise elimination ((a) is single deep well excitation; (b) is combined well excitation; (c) is controllable seismic source excitation).  From this we can see that the frequency bandwidth of single shot record under single well excitation is 10 ~ 50 Hz, with the dominant frequency at 30 Hz; the frequency bandwidth of single shot record under combined well excitation is 8 ~ 46 Hz, with the dominant frequency at 26 Hz; the frequency bandwidth of single shot record under controllable seismic source excitation is 8 ~ 50 Hz, with the dominant frequency at 30 Hz (Figure 1.6c). 

Figure 1.7 shows the analysis on the single shot record and frequency spectrum of target layer at the same point from different seismic resources, which is obtained after zero‐phase deconvolution (control point ④ in Figure 1.3) applied in the process stated in Figure 1.3 ((a) is single deep well excitation; (b) is combined well excitation; (c) is controllable seismic source excitation).  From this we can see that the frequency bandwidth of single shot record under single well excitation is 10 ~ 62 Hz, with the dominant frequency at 33 Hz; the frequency bandwidth of single shot record under combined well excitation is 8 ~ 46 Hz, with the dominant frequency at 28 Hz; the frequency bandwidth of single shot record under combined well excitation is 8 ~ 60 Hz, with the dominant frequency at 34 Hz. 

The zero phase deconvolution widens frequency bandwidth of target layer seismic record and improves the dominant frequency.  It is obvious that the single deep well excitation and controllable seismic source excitation have wide frequency bandwidth and high dominant frequency, compared to these of combined well excitation. 

From the analysis results on the frequency bandwidth and the dominant frequency of target layer recorded in single shot records in Figures from 1.4 to 1.7, the frequency bandwidth of single deep well excitation and controllable seismic source excitation are wide (low frequency component below 8 Hz is missed in controllable seismic source excitation) and the dominant frequencies are high, while those of combined well excitation are narrow and low.  Therefore, the performance of single deep well excitation and controllable seismic source excitation are better than that of combined well excitation. 

Figure 1.8 shows a final image in the form of migration profile based on the procedures presented in Figure 1.3 (control point ⑤ in Figure 1.3 uses poststack deconvolution parameters to widen the frequency bandwidth to the uniform bandwidth). 

Figure 1.8a1 is a final migration profile of single deep well excitation (channel interval of 5 m) obtained from processes indicated in Figure 1.3.  In Figure 1.8a1, the reflection event marked by red arrows refers to the reservoir of the Cretaceous Qingshuihe river sand formation.  This image clearly presents the geological phenomenon of lateral sand body variation.  Figure 1.8a2 is a frequency spectrum of the target layer(2050 ~ 2150 ms), with a frequency bandwidth of 8 ~ 65 Hz and a dominant frequency of 40 Hz. 

Figure 1.8b1 shows one final migration profile of a single deep well excitation (channel interval of 5 m) obtained from processes presented in Figure 1.3.  Obviously, the lateral resolution of the Cretaceous Qingshuihe river sand formation reflection marked by red arrows in this figure is lower than that of Figure 1.8a1.  Although different from the resolution, the spectrums (Figure 1.8a2, Figure 1.8b2) of the target layers (2050 ~ 2150 ms) are almost the same, which suggests that the longitudinal resolutions are the same.  The lateral resolution directly depends on the channel interval of the research samples; therefore, it is clear that the lateral resolution of a 5 m channel interval is higher than that of a 25 m interval. 

Figure 1.8c1 shows the final migration profile of combined well excitation (channel interval of 5 m) obtained from processes presented in Figure 1.3.  The Cretaceous Qingshuihe river sand formation reflection marked by red arrows in this figure is similar to that in Figure 1.8a1, while its energy is relatively weak and its lateral resolution is relatively high.  Figure 1.8c2 is a frequency spectrum of the target layer (2050 ~ 2150 ms), with a frequency bandwidth of 8 ~ 65 Hz and a dominant frequency of 35 Hz. 

Figure 1.8d1 shows a final migration profile of combined well excitation (channel interval of 25 m) obtained from processes presented in Figure 1.3.  It is obvious that its lateral resolution is lower than that of Figure 1.8c1.  The fact that the frequency characteristics presented in Figure 1.8c2 and Figure 1.8d2 are almost the same suggests that the lateral resolution directly depends on the channel interval of the research samples if the longitudinal resolutions are the same.  Accordingly, the lateral resolution of a 5 m channel interval is higher than that of a 25 m interval.  On comparison between Figure 1.8c2 (Figure 1.8d2) and Figure 1.8a2 (Figure 1.8b2), we can see segments of low frequency (marked by blue arrows) in the range of 35 Hz and 42 Hz.  This difference shows that the frequency components of combined well excitation are less abundant than that of single deep well excitation. 

Figure 1.8e1 shows a final migration profile of controllable seismic source excitation (channel interval of 25 m) obtained from processes presented in Figure 1.3.  Obviously, the Cretaceous Qingshuihe river sand formation reflection marked by red arrows in this figure can be regarded as a strong one, which is much worse in description of sand body details compared with Figures 1.8a1 to 1.8d1. 

Figure 1.8e2 is a frequency spectrum of the target layer (2050 ~ 2150 ms), with a frequency bandwidth of 8 ~ 65 Hz and a dominant frequency of 35 Hz.  Compared with Figures 1.8a2 (Figure 1.8b2), it has two segments of low frequency (marked by blue arrows) and a lack of frequency components blow 8Hz. 

The frequency bandwidth of controllable seismic source excitation is wider than that of combined well excitation (Figure 1.4 and Figure 1.5), but its frequency components are less abundant.  Additionally, low frequency components below 8 Hz are missing, resulting in a single waveform of migration result, with which it is difficult to accurately reflect the spatial distribution characteristics of lithology. 

The processes in Figure 1.3 focus too much on high resolution and high SNR processing.  Therefore, both prestack and poststack deconvolutions have been applied.  In order to ensure the continuity of high‐resolution profiles processed by deconvolution, random noise attenuation (RNA) has also been employed, which gives out a good visual effect of migration profiles but greatly decreases the fidelity.  We will have to make further analysis to see whether the real seismic response of the Cretaceous Qingshuihe river sand formation is as shown in Figure 1.8. 

## 1.3 Discussion on the Cause of Notching

The scale of seismic data resolution is restricted by the signal to noise ratio of seismic signals.  During the resolution enhancement processing of seismic data, if the signal to noise ratio of seismic signals is small (SNR is less than 1), the credibility of processed high‐resolution data is very low. 

Among the effective frequency band of seismic record, the SNR of seismic signals is usually larger than 1; the SNR of high frequency components which are beyond such effective frequency band is generally less than 1.  Where the data in high‐frequency band (SNR is less than 1), the deconvolution method is adopted to boost its energy.  As a consequence, it amplifies noise energy significantly while boosting the effective signals.  When promoted SNR random noise attenuation modification (RNA) is applied to such seismic data with amplified high frequency noise, such high frequency noises are easy to change into some lateral extended high frequency events.  But this is only a false image and can mislead the interpretation. 

Figure 1.9 shows the results comparison of random noise data processed two times with RNA method repeatedly. 

**Figure 1.9** Results comparison of random noise data processed two times with RNA method repeatedly. 

Figure 1.9a1 shows the random noise profile with record length of 1 s (sampling at 1 ms) and channel interval of 25 m.

Figure 1.9a2 shows the spectrum of Figure 1.9a1, with a range of 0 ~ 500 Hz and a spectral value of almost 0.9, which belongs to typical white noise spectrum. 

Figure 1.9b1 shows the processing results of the random noise data of Figure 1.9a1 after two successive RNA (i.e. coherence enhancement, such a modifying module, is commonly used to boost S/N, and such a module is also adopted in the processing flow of Figure 1.3), and some laminar reflections are clearly discerned on the profile (as indicated by a red arrow). 

Figure 1.9b2 is the spectrum of Figure 1.9b1, and Figure 1.9b3 is the local zoom of Figure 1.9b2, which highlights the spectrum features of 0 ~ 100 Hz.  The spectrum features of 10 ~ 40 Hz share the same frequency band with the effective seismic signals, and its energy is nearly three times that of white noise spectrum.  Such laminar reflection caused by modification processing is only a false image, and it impacts seismic interpretation directly.  Such a false image can be interpreted as a thin layer in seismic interpretation, and its spectrum is hard to distinguish in the effective frequency band range.  Therefore, it is suggested that such a module is excluded in relative fidelity preservation processing, as the resulting profile visual effect is relatively poor. 

During the frequency spectrum analysis of seismic data processing, notch frequency is frequently observed in seismic record spectrum, which may be caused by the frequency response of the geological body itself (a section of frequency is absent).  Such phenomenon is quite normal in an effective frequency band (the seismic record in an effective frequency band has a relatively high SNR, and it can be used to analyze whether the notch frequency is the response of the geological body).  There is another kind of notch frequency existing on the high frequency band portion, which is no lower than the effective frequency band.  It may be caused by the high‐pass filtering of the deconvolution operator, which was the object of this study. 

The processing flow in Figure 1.3 overemphasizes high resolution and high SNR; therefore, two episodes of deconvolution (prestack and poststack) have been conducted.  In order to ensure the profile continuity after high resolution deconvolution, RNA has been performed to realize a better visual effect.  However, the fidelity obviously reduces, such as the seismic response distortion of sand body (Figure 1.1a) and thin layer at point D of Figures 1.8a1 and 1.8c1, which deserve to be studied further. 

  1.  The approximate expression of prestack and poststack deconvolution filters. 

To analyze whether the notch frequency phenomena (as indicated by blue arrows in Figures 1.8c2, b2 and e2) in the frequency spectrum of target layer (2000 ~ 2200 ms) in the final migration profile is the frequency response of the geological body itself, or the consequence of the deconvolution operator high‐pass filtering (as shown in the processing flowchart of Figure 1.3, prestack zero‐phase deconvolution is conducted to increase the resolution after surface consistent deconvolution; and after stack, another zero phase deconvolution is conducted to further increase the resolution), the prestack and poststack zero phase deconvolutions should be analyzed. 

If the seismic record is assumed to be:

(1.1)

Where, _S_ ( _t_ ) is the seismic signal; _r_ ( _t_ ) is the reflection factor; _g_ ( _t_ ) is the seismic wavelet. 

Equation 1.1 is written in frequency domain as:

(1.2)

If prestack deconvolution operator is expressed as F1 ( _ω_ ) in frequency domain, the seismic signal after prestack deconvolution will be:

(1.3)

Deconvolution is used to compress g(ω), so that the seismic signal is close to reflection factor to bring a higher resolution.  From equation 1.3, we get:

(1.4)

According to the processing flow in Figure 1.3, after prestack noise elimination in _f‐k_ and surface consistent deconvolution, another zero‐phase deconvolution is also conducted to increase the resolution, and F1(ω) in equation 1.4 is the embodiment of such composite filtering effect.  However, the main contribution of high frequency filtering is zero phase deconvolution filter.  Thus, to facilitate the discussion, F1(ω) is almost equivalent to the prestack zero phase deconvolution filter.  Poststack deconvolution is conducted on the basis of prestack deconvolution.  The operator of post‐pack deconvolution is F2(ω), and the signal spectrum after deconvolution is:

(1.5)

From equation 1.5, we get:

(1.6)

According to the processing flowchart in Figure 1.3, the velocity analysis, space variant removal, residual static correction, stack and migration are conducted after prepack deconvolution is completed.  Finally, another zero phase deconvolution is conducted to increase the resolution, and F2(ω) in equation 1.6 is the embodiment of such composite filtering effect.  However, the main contribution of high frequency filtering is also a zero phase deconvolution filter.  Thus, to facilitate the discussion, F2(ω) is almost equivalent to the prestack zero phase deconvolution filter. 

  2.  Description on notch frequency band. 

If the maximum frequency value of the low frequency end of notch frequency band (as indicated by green arrow in Figure 1.10) is XFLmax, with the minimum frequency value at XFmin, the average frequency of low frequency end will be:

(1.7)

If the maximum frequency value of the high frequency end of notch frequency band is XFHmax, with the minimum frequency value at XFmin, the average frequency of high frequency end will be:

(1.8)

  3.  The width of notch frequency band is defined as:

(1.9)

If the maximum frequency value of the low frequency end of notch frequency band (as indicated by green arrow in Figure 1.10) is XFLmax, with the maximum frequency value of its high frequency end at FHmax, the notch frequency band minimum value between the maximum values of low frequency and high frequency is Fmin. 

  4.  The relative amplitude of notch frequency band is defined as:

(1.10)

**Figure 1.10** The location of notch frequency band in seismic frequency spectrum. 

Figure 1.10 shows the location of the notch frequency band in the seismic frequency spectrum.  The blue dashed line illustrates the maximum value of the ultimate seismic frequency spectrum of the high frequency end (DFH) of original seismic spectrum effective band width (DF), with its left side notch frequency band within the effective bandwidth, and its right side as the extension of such frequency band.  The deconvolution method (green dashed line, the spectrum of the deconvolution operator) is adopted to increase the frequency band energy, especially for this type of high frequency band data (SNR is less than 1).  As a consequence, the effective signals are enhanced, while the noise energy is amplified significantly.  The lower the SNR, the higher noise energy is obtained, which hinders the processing of high‐resolution seismic data.  Therefore, the relative fidelity preservation processing should be analyzed and determined based on the notch frequency phenomena of high frequency band to ensure the reliability of seismic data processing. 

Figure 1.11 is the effect comparison between a prestack and poststack deconvolution filter in a single deep well during the study on high resolution and high SNR processing within frequency domain. 

**Figure 1.11** Filter frequency spectrum comparison between pre‐pack and post‐pack deconvolutions in single deep well. 

Figure 1.11a shows the frequency spectrum of a single deep well (for frequency spectrum in Figure 1.5a2, smoothing processing is applied to facilitate calculation), with frequency bandwidth of 4 ~ 50 Hz and dominant frequency of 22 Hz. 

Figure 1.11b is the prestack deconvolution filtering operator F1(ω), with frequency bandwidth of 30 ~ 60 Hz and dominant frequency of 48 Hz, which is a typical high frequency band‐pass filter.  Compared with F1(ω) spectrum, the red dotted line in Figure 1.11a shows different dominant frequency (22 Hz, 48 Hz), and the frequency difference is 26 Hz.  There is an obvious non‐overlapped area (as indicated by green arrow) in 30 ~ 45 Hz between the dominant frequencies; in 0 ~ 30 Hz, the low frequency value of operator is very small (as indicated by green arrow), which suppresses the low frequency information. 

Figure 1.11c shows the frequency spectrum after prepack deconvolution (for frequency spectrum in Figure 1.7a2, smoothing processing is applied to facilitate calculation), where there is a notch frequency in 0 ~ 12 Hz, a weak notch frequency in 20 ~ 30 Hz with XF of 5 Hz and PF of 31% and a severe notch frequency at 40 Hz with XF of 10 Hz and PF of 74%. 

Figure 1.11d is postpack deconvolution operator F2(ω), which is a wide band filter, with frequency bandwidth of 10 ~ 60 Hz and dominant frequency of 40 Hz.  Its spectrum is nearly identical to that of the red dashed line in frequency band of 10 ~ 50 Hz. 

Figure 1.11a and Figure 1.11c show the frequency spectrum of single shot recorded target layer (1800 ~ 2800 ms), and Figure 1.11e is the spectrum of migration profile target layer (2000 ~ 2200 ms); there is a certain amount of error between them (the error is within 5%, which makes no impact on analysis results), and the red dotted line is the envelope line of such spectrum; no obvious notch frequency is observed on such a line, its frequency bandwidth is 10 ~ 68 Hz, dominant frequency is 40 Hz, and the widened high frequency is 18 Hz. 

Figure 1.12 shows the effect comparison between prestack and poststack deconvolution filter in combined well during the study on high‐resolution and high‐SNR processing within frequency domain. 

**Figure 1.12** Filter frequency spectrum comparison between prepack and post‐pack deconvolutions in combined well. 

Figure 1.12a shows the frequency spectrum of combined well (for frequency spectrum in Figure 1.12a, smoothing processing is applied to facilitate calculation), with frequency bandwidth of 4 ~ 40 Hz and dominant frequency of 18 Hz. 

Figure 1.12b is the prestack deconvolution filtering operator F1(ω), with frequency bandwidth of 18 ~ 50 Hz and dominant frequency of 38 Hz, which is a typical high‐frequency filter.  Compared with F1(ω) spectrum, the red dotted line in Figure 1.12a shows different dominant frequency (18 Hz, 38 Hz), with the frequency difference at 20 Hz.  There is an obvious non‐overlapped area (as indicated by green arrow) in 18 ~ 38 Hz between the dominant frequencies; in 0 ~ 18 Hz, the low frequency value of operator is very small (as indicated by green arrow), which suppresses the low frequency information. 

Figure 1.12c shows the frequency spectrum after prepack deconvolution (for frequency spectrum in Figure 1.7b2, smoothing processing is applied to facilitate calculation), where there is a notch frequency in 0 ~ 12 Hz and a weak notch frequency in 20 ~ 30 Hz with XF of 5 Hz and PF of 31%. 

Figure 1.12d is the postpack deconvolution operator F2(ω), which is a high frequency filter, with frequency bandwidth of 35 ~ 60 Hz and dominant frequency of 47 Hz.  There is an obvious non‐overlapped area (as indicated by green arrow) between the spectrum of such filter and the red dashed line in 35 ~ 45 Hz (the dominant frequency in Figure 1.12c is about 30 Hz, and the dominant frequency difference is 17 Hz).  Therefore, an obvious notch frequency is formed (as indicated by green arrow at 40 Hz in Figure 1.12e).  Meanwhile, the notch frequencies in 0 ~ 12 Hz and 20 ~ 30 Hz (as indicated by blue arrow in Figure 1.8c) still remain. 

Figure 1.12e shows the final spectrum of target layer on the achieved profile.  Figure 1.12a and Figure 1.12c are the spectrum of single shot recorded target layer (1800 ~ 2800 ms), and Figure 1.12e is the target layer spectrum of migration profile (2000 ~ 2200 ms).  There is a certain amount of error between them (the error is within 5%, which makes no impact on analysis results), and the red dotted line is the envelope line of such spectrum.  Three obvious notch frequencies are observed on such a line, where in 0 ~ 12 Hz, two episodes of deconvolution suppress the low frequency below 10 Hz and result in severe notch frequency; in 20 ~ 30 Hz, the weak notch frequency XF is 5 Hz and PF is 31%; in 35 ~ 45 Hz, due to the relatively narrow frequency band of combined well excitation record, the high frequency components are rare, which results in severe notch frequency with XF of 10 Hz and PF of 56%.  As for the frequency bandwidth of 10 ~ 64 Hz, its dominant frequency is 36 Hz, and the widened high frequency is 24 Hz, which is 6 Hz higher than that of Figure 1.11e, resulting in severe notch frequencies, especially the false information in the thin layer (point D in Figures 1.8a1 and 1.8 c1). 

## 1.4 Discussion of Impact on Processing of Relative Fidelity Preservation Seismic Data for Seismic Acquisition and Observation Mode

In order to solve the actual seismic response problems of the Cretaceous Qingshuihe sand body (as shown in Figure 1.8), we put forward the relative fidelity preservation processing flow as illustrated in Figure 1.13.  Compared with high‐resolution and high‐SNR processing flow (Figure 1.3), the relative fidelity preservation processing eliminates processes of prestack zero phase deconvolution and RNA.  Additionally, 60 times of coverage are applied to facilitate the comparison. 

**Figure 1.13** The processing flow of relative fidelity preservation seismic data. 

During the relative fidelity preservation processing, eight controlling points (as shown in the dashed line box of Figure 1.13) were selected to conduct quality tracing and analysis.  Relative fidelity preservation processing flow (Figure 1.13) was adopted to reprocess the seismic data of the pilot survey line across Well Shidong‐2 and Well Shidong‐4 in the Shidong area. 

Figure 1.13 shows the single shot record of single deep well and the seismic spectrum of target layer at Well Shidong‐4 (SD4), which is different from the single shot location in Figure 1.4; however, it makes no impact on analysis results.  This figure also shows the single shot records and seismic spectrum of target layer at various stages as per the relative fidelity preservation processing flow in Figure 1.13. 

Figure 1.14a1 shows the original single shot record ①, and the quality of original single shot is good (the spectrum is 4 ~ 50 Hz, and the dominant frequency is 22 Hz). 

**Figure 1.14** Single shot record of single deep well and seismic spectrum of target layer (SD4). 

Figure 1.14b1 shows the single shot record ② after static correction of first arrival refraction, and the first arrival is continuous. 

Figure 1.14c1 shows the single shot record ② after spherical diffusion compensation, where the entire energy compensation effect is significant. 

Figure 1.14 d1 shows the single shot record ④ of regional abnormality processing, where the noise elimination effect is good. 

Figure 1.14e1 shows the noise after regional abnormality processing, where no effective signal is observed in this figure. 

Figure 1.14 f1 shows the single shot record ⑤ after seismic consistent amplitude compensation; compared with Figure 1.9c1, the entire energy is further compensated and the compensation effect is significant (as indicated by red arrows in Figures 1.14 f1 and 1.14 cl). 

Figure 1.14g1 shows the single shot record ⑥ after f‐k oblique disturbance removal, which suppresses oblique disturbance effectively. 

Figure 1.14h1 shows the single shot record ⑦ after surface consistent deconvolution, where the frequency increases slightly. 

Figures 1.14a2–1.14h2 show the target layer (2000 ~ 3000 ms) seismic spectrum corresponding to Figures 1.14a1–1.14h1. 

It is known from the spectrum that: (1) Low frequency (below 8 Hz) is well preserved in each step. ( 2) The frequency band of noise spectrum after regional abnormality processing is identical to the effective signal (Figures 1.14d2 and 1.14e2). ( 3) f‐k oblique disturbance removal can only suppress part of the oblique disturbance energy in 15 ~ 20 Hz (as indicated by blue arrow in Figure 1.14g2); the final surface consistent deconvolution promotes frequency band energy in 20 ~ 40 Hz (as indicated by blue arrow in Figure 1.14h2), but fails to widen the effective seismic frequency band (the effective frequency band maintains in 4 ~ 50 Hz with the dominant frequency at 22 Hz, and the widened frequency band is no more than 5 Hz), which only compensates the energy in low and high frequency bands (as indicated by blue arrow). 

Figure 1.15 shows the single shot record of combined well and the seismic spectrum of target layer at Well Shidong‐4 (SD4). 

**Figure 1.15** Single shot record of combined well and seismic spectrum of target layer (SD4). 

Figure 1.15a1 shows the original single shot record, where the quality of original single shot is good (the spectrum is 4 ~ 40 Hz with the dominant frequency at 18 Hz). 

Figure 1.15b1 shows the single shot record after first arrival refraction static correction, where the first arrival is continuous. 

Figure 1.15c1 shows the single shot record after spherical diffusion compensation, where the entire energy compensation effect is significant. 

Figure 1.15 d1 shows the single shot record of regional abnormality processing, where the noise elimination effect is good. 

Figure 1.15e1 shows the noise after regional abnormality processing, where no effective signal is observed. 

Figure 1.15f1 shows the single shot record after seismic consistent amplitude compensation; compared with Figure 1.15c1, the entire energy is further compensated and the compensation effect is significant (as indicated by red arrows in Figures 1.15f1 and 1.15c1). 

Figure 1.15g1 shows the single shot record after f‐k oblique disturbance removal, which suppresses oblique disturbance effectively. 

Figure 1.15h1 shows the single shot record after surface consistent deconvolution, where the frequency increases slightly. 

Figures 1.15a2–1.15h2 show the target layer (2000 ~ 3000 ms) seismic spectrum corresponding to Figures 1.15a1–1.15h1. 

It is known from the spectrum that: (1) Low frequency (below 8 Hz) is well preserved in each step. ( 2) The frequency band of noise spectrum after regional abnormality processing is identical to the effective signal (Figures 1.15d2 and 1.15e2). ( 3) f‐k oblique disturbance removal can only suppress part of the oblique disturbance energy in 15 ~ 20 Hz (as indicated by blue arrow in Figure 1.15g2); the final surface consistent deconvolution promotes frequency band energy in 20 ~ 40 Hz (as indicated by blue arrow in Figure 1.15h2), but fails to widen the effective seismic frequency band (the effective frequency band maintains in 4 ~ 45 Hz with dominant frequency at 20 Hz, and the widened frequency band is no more than 5 Hz), which only compensates the energy in low and high frequency bands (as indicated by blue arrow). 

Figure 1.16 shows the single shot record of controllable seismic source excitation and the seismic spectrum of target layer at Well Shidong‐4 (SD4). 

**Figure 1.16** Single shot record of controllable seismic source excitation and seismic spectrum of target layer (SD4). 

Figure 1.16a1 shows the original single shot record, where the quality of original single shot is good (the spectrum is 8 ~ 45 Hz with the dominant frequency is 20 Hz). 

Figure 1.16b1 shows the single shot record after first arrival refraction static correction, where the first arrival is continuous. 

Figure 1.16c1 shows the single shot record after spherical diffusion compensation, and the entire energy compensation effect is significant. 

Figure 1.16d1 shows the single shot record of regional abnormality processing, and the noise elimination effect is good. 

Figure 1.16e1 shows the noise after regional abnormality processing, and no effective signal is observed in this figure. 

Figure 1.16f1 shows the single shot record after seismic consistent amplitude compensation.  Compared with Figure 1.16c1, the entire energy is further compensated and the compensation effect is significant (as indicated by red arrows in figures 1.16f1 and 1.16c1). 

Figure 1.16g1 shows the single shot record after f‐k oblique disturbance removal, which suppresses oblique disturbance effectively. 

Figure 1.16h1 shows the single shot record after surface consistent deconvolution, where the frequency increases slightly. 

Figures 1.16a2–1.16h2 are the target layer (2000 ~ 3000 ms) seismic spectrum corresponding to these of Figures 1.16a1–1.16h1. 

It is known from the spectrum that: (1) The low frequency components below 8 Hz are absent. ( 2) The frequency band of noise spectrum after regional abnormality processing is identical to the effective signal (Figures 1.16d2 and 1.16e2). ( 3) f‐k oblique disturbance removal can only suppress part of the oblique disturbance energy in 10 ~ 20 Hz (as indicated by blue arrow in Figure 1.16g2); the final surface consistent deconvolution promotes frequency band energy in 20 ~ 40 Hz (as indicated by blue arrow in Figure 1.16h2), but fails to widen the effective seismic frequency band (the effective frequency band maintains in 4 ~ 50 Hz with the dominant frequency at 22 Hz, and the widened frequency band is no more than 5 Hz), which only compensates the energy in low and high frequency bands (as indicated by blue arrow). 

Figure 1.17a1 shows the single deep well shot (receiving with 1200 channels at the channel interval of 5 m), which adopts the migration profile processed by relative fidelity preservation processing flow in Figure 1.13.  The sand body reflection of target layer (2000 ~ 2200 ms) is relatively clear (as indicated by red arrow).  Its frequency bandwidth is 5 ~ 55 Hz (Figure 1.17a2), and the dominant frequency is 27 Hz.  The frequency band has not been widened, while only the dominant frequency (27 Hz or so) has been increased by 5 Hz. 

**Figure 1.17** Seismic profile and target layer spectrum processed by relative fidelity preservation. 

Figure 1.17b1 shows the single deep well excitation (receiving with 240 channels at channel interval of 25 m), which adopts the migration profile processed by relative fidelity preservation processing flow in Figure 1.13.  The sand body reflection of target layer (2000 ~ 2200 ms) is relatively clear (as indicated by red arrow), while compared with Figure 1.16a1, the detailed description is slightly inferior.  Its frequency bandwidth is 5 ~ 55 Hz (Figure 1.16b2), and dominant frequency is 27 Hz, where the frequency band has not been widened, and only the dominant frequency (27 Hz or so) has been increased by 5 Hz. 

Figure 1.17c1 shows the combined well excitation (receiving with 1200 channels at channel interval of 5 m), which adopts the migration profile processed by relative fidelity preservation processing flow in Figure 1.13.  The sand body reflection of target layer (2000 ~ 2200 ms) can be discerned clearly (as indicated by red arrow), and the continuity of target layer is also enhanced.  Its frequency bandwidth is 4 ~ 45 Hz (Figure 1.16c2), and dominant frequency is 25 Hz, where the frequency band has not been widened, and only the dominant frequency (25 Hz or so) has been increased by 7 Hz. 

Figure 1.17d1 shows the combined well excitation (receiving with 240 channels with channel interval of 25 m), which adopts the migration profile processed by relative fidelity preservation processing flow in Figure 1.13.  The sand body reflection of target layer (2000 ~ 2200 ms) is relatively clear (as indicated by red arrow), and the continuity of target layer is inferior to that in Figure 1.17c1.  Its frequency bandwidth is 4 ~ 45 Hz (Figure 1.16d2), and dominant frequency is 25Hz, where the frequency band has also not been widened, and only the dominant frequency (25 Hz or so) has been increased by 7 Hz. 

Figure 1.17e1 shows the controllable seismic source excitation (receiving with 300 channels at the channel interval of 25 m), which adopts the migration profile of relative fidelity preservation processing flow in Figure 1.13.  The sand body reflection of target layer (2000 ~ 2200 ms) is continuous (as indicated by red arrow).  Its frequency bandwidth is 8 ~ 50 Hz (Figure 1.17e2), and dominant frequency is 25 Hz.  Since the controllable seismic source excitation is absent at low frequency (below 8 Hz) and high frequency (the high scan frequency is 90 Hz), the continuity of target layer is relatively strong on the seismic profile, and the detailed description is relatively poor.  The frequency band has also not been widened, and only the dominant frequency (25 Hz or so) has been increased by 5 Hz. 

Figure 1.18 shows the effect comparison of both single deep well prestack and poststack deconvolution filters during the study on relative fidelity preservation processing within the frequency domain. 

**Figure 1.18** Spectrum comparison of single deep well prestack and poststack deconvolution filters. 

Figure 1.18a shows the spectrum of initial stacked profile of single deep well excitation, with frequency bandwidth of 4 ~ 50 Hz and dominant frequency of about 22 Hz. 

Figure 1.18b shows prestack deconvolution filtering factor F1(ω), with frequency bandwidth of 6 ~ 60 Hz and dominant frequency of 38 Hz.  It is a broad band filter (only the surface consistent deconvolution is used).  In spectrum map 1.18b, there is a large overlapped area (as indicated by green arrow in Figure 1.18b) between broad band filter and red dotted line spectrum (Figure 1.18a), where the dominant frequencies are 22 Hz and 34 Hz respectively, with the frequency difference at 12 Hz.  F1(ω) filter presents some values in 0 ~ 10 Hz, which preserves the low frequency (Figure 1.18b, as indicated by green arrow). 

Figure 1.18c shows the spectrum of stacked profile after prestack deconvolution, with frequency bandwidth of 4 ~ 55 Hz and dominant frequency of 25 Hz; there is no obvious notch frequency in this figure, except a weak notch frequency in 18 ~ 24 Hz with XF of 6 Hz and PF of 37%. 

In Figure 1.18d, F2(ω) is worked out based on equation 1.6, and from the final spectrum of target layer of the achieved profile in Figure 1.18e (spectrum in Figure 1.17a2, smoothing processing is applied to facilitate calculation) and f1(ω) in Figure 1.18c.  Since several methods like f‐k noise elimination, space variation removal and linear filtering are stacked during seismic processing, F2(ω) is the superimposition of multiprocessing results, but it basically reflects the effect of poststack zero phase deconvolution.  F2(ω) is designed to be broad band filter, and the low frequency below 10 Hz is boosted on purpose.  The filter operator nearly coincides with the red dotted line (Figure 1.18c).  The processed frequency bandwidth is not widened, and only the energy of high frequency components is enhanced (Figure 1.18e). 

As shown in Figure 1.18e, there is almost no notch frequency on the final spectrum of the achieved profile (Figures 1.18a, 1.18c and 1.18e show the spectrum of the target layer (2000 ~ 2200 ms) on the profile, to ensure the correctness of analysis results); the frequency band has not been obviously widened (frequency bandwidth of 4 ~ 55 Hz, widened by 5 Hz), and only the dominant frequency (about 30 Hz) has been increased by 8 Hz. 

Figure 1.19 shows the effect comparison of both combined well prestack and poststack deconvolution filters during the study on relative fidelity preservation processing within frequency domain. 

**Figure 1.19** Spectrum comparison of both combined well prestack and poststack deconvolution filters. 

Figure 1.19a shows the spectrum of stacked profile of combined well excitation, with frequency bandwidth of 4 ~ 45 Hz and dominant frequency of about 18 Hz. 

Figure 1.19b shows the prepack deconvolution filtering factor F1(ω), with frequency bandwidth of 6 ~ 60 Hz and dominant frequency of 34 Hz.  It is a broad band filter (only the surface consistent deconvolution is used).  In spectrum map 1.19b, there is a large overlapped area (as indicated by green arrow in Figure 1.19b) between broad band filter and red dotted line spectrum (Figure 1.19a), whose dominant frequencies are 18 Hz and 34 Hz respectively, with the frequency difference at 16 Hz.  F1(ω) filter presents some values in 0 ~ 10 Hz, which preserves the low frequency (Figure 1.19b, as indicated by green arrow). 

Figure 1.19c shows the spectrum of stacked profile after prestack deconvolution, with frequency bandwidth of 4 ~ 45 Hz and dominant frequency of 20 Hz; there is no obvious notch frequency in this figure, except a weak notch frequency in 18 ~ 24 Hz with XF of 6 Hz and PF of 37%. 

In Figure 1.19d, F2(ω) is worked out based on equation 1.6, and from the final spectrum of target layer of the achieved profile in Figure 1.17c (for spectrum in Figure 1.17c, smoothing processing is applied to facilitate calculation) and f1(ω) in Figure 1.19c.  Since several methods like f‐k noise elimination, space variation removal and linear filtering are stacked during seismic processing, F2(ω) is the superimposition of multi‐processing results, but it basically reflects the effect of poststack zero phase deconvolution.  F2(ω) is designed to be broad band filter, and the low frequency below 10 Hz is boosted on purpose.  The filter operator nearly coincides with the red dotted line (Figure 1.19c).  The processed frequency bandwidth is not widened, and only the energy of high frequency components is enhanced. 

As shown in Figure 1.19e, there is almost no obvious notch frequency on the final spectrum of the achieved profile (Figures 1.19a, 1.19c and 1.19e show the spectrum of the target layer (2000 ~ 2200 ms) on the profile, to ensure the correctness of analysis results); the only notch frequency is in 18 ~ 26 Hz, with XF of 6 Hz and PF of 37%, which is a weak notch frequency resulting from the original seismic spectrum (as indicated by green arrow in Figure 1.19a); the frequency band has not been obviously widened (frequency bandwidth 4 ~ 45 Hz, widened by 5 Hz), and only the dominant frequency (25 Hz or so) has been increased by 7 Hz. 

## 1.5 Comparison of Results of High‐resolution, High SNR Processing and Relative Fidelity Preservation Processing

Figure 1.8 shows the processing effect of high‐resolution and high SNR (a1–e1) and Figure 1.17 shows the processing result of relative fidelity preservation processing (a1–e1).  In the two figures, al represents single deep well excitation with channel interval of 5 m; b1 represents single deep well excitation with channel interval of 25 m; c1 represents combined well excitation with channel interval of 5 m; d1 represents combined well excitation with channel interval of 25 m; el represents controllable seismic source excitation with 300 receiving channels at channel interval of 25 m.

  1.  The frequency bandwidth and main frequency of target layer in Figures 1.8a2 and 1.8b2 or Figures 1.17a2 and 1.17b2 (single deep well excitation) are almost the same, the same as those in Figures 1.8c2 and 1.8d2 or Figures 1.17c2 and 1.17d2 (combined well excitation).  Thus, under the same frequency bandwidth and main frequency of target layer, the horizontal and vertical resolution of the target layer reflection event will be different if the interval of receiving channel is different.  It is obvious that the effects of single deep well excitation and combined well excitation with channel interval of 5 m are the best, with high horizontal and vertical resolution for target layer (especially the vertical resolution).  The resolution of single deep well excitation and combined well excitation with 25 m channel interval are a little bit poor. 
  2.  In frequency band analysis on original single shot records in Figures 1.5b2 and 1.5c2, it was believed that the data of controllable seismic source excitation was better than the data of combined well excitation at first, for the high frequency component is abundant.  However, the final processing result was obviously different from explosive source, either in terms of high resolution and high SNR processing profile (Figure 1.8e1) or the relative fidelity preservation processed profile (Figure 1.17e1), which shows almost continuous reflection in the target layer (only interrupted at the fault, indicated by arrows in figure) and poor description on sand body details.  The above defects are attributable to the controllable seismic source excitation itself.  The target sandstone's reflection wave is superimposed by harmonic from high‐frequency to low frequency, while the actual scanning frequency of controllable seismic source is 8 ~ 90 Hz (Figure 1.4b, the high frequency component of controllable seismic source scanning may be noise), so the low frequency component below 8 Hz and high frequency components above 90 Hz (Figures 1.8e2 and 1.17e2) are missing.  The band is narrow and the waveform reflection of target layer is stiff. 

From the point of processing profile of explosive source, the information of the target layer reflection waveform feature of single deep well or combined well is more abundant than that of controllable seismic source, especially the profile with small channel interval, which has high horizontal resolution and description accuracy.  It shows the importance of broadband seismic acquisition. 

  3.  From the point of high‐resolution processed profile and relative fidelity preservation processed profile, the former has obvious advantage in resolution and SNR, but its authentic response to seismic effects on subsurface sand reservoirs may not be high.  That is to say, distortion of the image is inevitable if we increase its resolution and further modify the coherence to ensure a good visual effect. 

Figure 1.20a1 shows a sand interpretation mode established on the basis of the reflection characteristics of target layer presented in Figure 1.8a1. 

**Figure 1.20** Sand interpretation based on results of high‐resolution (a1, b1) and relative fidelity (a2, b2) seismic data processing. ( a1,a2) single deep well, 1200 receiving channels, channel interval of 5 m; (b1,b2) combined well, 1200 receiving channels, channel interval of 5 m.

Figure 1.20b1 is a sand interpretation mode established on the basis of the reflection characteristics of target layer presented in Figure 1.8c1, in which the thin‐reservoir information is more abundant than that in Figure 1.8a1 (it may be false). 

Figure 1.20a2 is a sand interpretation mode established on the basis of the reflection characteristics of target layer presented in Figure 1.17a1. 

Figure 1.201b2 is a sand interpretation mode established on the basis of the reflection characteristics of target layer presented in Figure 1.17c1, which is almost the same as the characteristics in Figure 1.17a1. 

From comparison between high‐resolution and high‐SNR processing and relative fidelity preservation processing, the following points can be obtained: (1) The former fault and breakpoint marked by A and B are less clear than the latter ones. ( 2) The former thin reservoir marked by D (more distinct in Figure 1.8c1) does not exist in the latter, which may be a false image formed in the process of improving resolution. ( 3) Point E in the former image is a weaker reflection event, representing a continuous sand layer, while the latter is comprised of two to three sand bodies. ( 4) A section processed with high resolution and high SNR has higher longitudinal resolution and SNR, with better visual effect (particularly, the thin‐reservoir information in Figure 1.8c1, which is the most abundant; it may be false).  However, false image is unavoidable if we improve the resolution and intensify the coherent processing. ( 5) A profile processed with relative fidelity preservation has lower longitudinal resolution and higher lateral resolution as well as lower SNR.  But it can truly reflect the seismic response of subsurface sand reservoirs. 

## 1.6 Elastic Wave Forward Modeling

Figure 1.21 shows how to analyze the reliability of profiles processed with high resolution and high SNR.  Model 1 is designed as per the sand body model (to simplify the sand body model and for easy identification, Figure 1.20a1 was chosen instead of Figure 1.20b1, which contains more information on thin layers), interpreted from Figure 1.5.1a1, with the specific dimension of the model being shown by Model 1 in Figure 1.21.  Model 2 is designed as per the sand body model (Figure 1.20a2 was chosen to study the lateral resolution of the sand body), interpreted from Figure 1.20a2, with the specific dimension of the model being shown by Model 2 in Figure 1.21.  Refer to Figure 1.21 for the acquisition scheme, spatial location and model parameters of the elastic wave forward model.  The designed elastic wave forward model focuses mainly on the research of the relation between the forward model's wavelet frequency and longitudinal resolution of the reflection event.  It is necessary to show how high frequency profile is required to image the thin layer shown at point D of Figure 1.8 (a1, c1). 

**Figure 1.21** Forward model design. 

Provided the longitudinal resolution is λ/4 (λ is seismic wavelength), the radius of Fresnel band can be approximated to be:

(1.11)

Where, _v_ is seismic velocity; _f_ is seismic frequency. 

Parameters of the model in Figure 1.17 are as follows: range of model, 12,100 m (length), 4000 m (depth); unilateral shot; wavelet frequency, 100 Hz; recording time, 3.5 s; sampling interval, 0.5 ms; number of shots, 176;shot interval, 50 m; channel interval, 10 m; length of seisline, 3000 m; maximum shot‐geophone distance, 3000 m; speed for sandstone, 4100 m/s; density, 2400 kg/m3; speed for mudstone, 3000 m/s; density, 2200 kg/m3. 

Figure 1.22 shows the prestack time migration profile (depth domain) of the elastic wave forward model (the wavelet frequency of 100 Hz and channel interval of 10 m are chosen for elastic wave forward modeling, as per equation 1.11; the lateral and vertical resolution of model parameters is about 10 m).  From the profile, it can be seen that the seismic response of No.  1 sand body is clear (as shown by Model 1 in Figure 1.21); No.  1 sand body and No.  2 sand body in the figure show that the lateral resolution is higher than the lateral distance and is also higher than the channel interval (the channel interval design is also correct); the seismic trace energy between No.  1 sand body and No.  2 sand body becomes smaller; thus a sand body can be laterally identified.  At the intersection between No.  2 and No.  3 sand bodies, it is impossible to identify vertically, and the reflection energy at the vertical stacked section of the two sand bodies increases, while the energy of the non‐stacked section (thinner No.  2 sand body) is weak; the seismic response of No.  3 sand body is clear. 

**Figure 1.22** Forward model 1 (100 Hz, channel interval of 10 m) prestack time migration profile (depth domain). 

The results of the elastic wave forward model suggest that the vertical resolution of the forward model with 100 Hz wavelet is unable to identify the stacked No.  2 and No.  3 sand bodies of the forward model.  Actually, the frequency bandwidth and the dominant frequency of the target layer on seismic profile are only 4 ~ 55 Hz and 25 Hz respectively (while those for the target layer of the combined well are 4 ~ 45 Hz and 18 Hz respectively).  There is something wrong with the high frequency information on the seismic profile suggested by the high resolution and high SNR results, which means that thin layers shown at point D in Figures 1.8a1 and 1.8c1 may be false. 

Figure 1.23 is the prestack time migration profile of elastic wave forward model 2 (depth domain).  From the profile, it can be seen that the energy at the pinch‐out point of the sand body becomes low between sand body No.  1 to No.  2, No.  2 to No.  3, and No.  3 to No.  4, while the lateral distance among sand bodies (max.  15 m) is far greater than the lateral resolution (10 m), and the lateral resolution can identify the contact relationship among sand bodies. 

**Figure 1.23** Forward model 2 (100 Hz, channel interval of 10 m) prestack time migration profile (depth domain). 

The comparison of results from different elastic wave forward models clearly shows that the vertical resolution of the forward model with 100 Hz wavelet cannot identify the results interpreted by the seismic profile of stacked No.  2 and No.  3 sand bodies in forward Model 1.  There may be some false image caused by the high resolution and high SNR processing results (thin layers shown at point D in Figures 1.8a1 and 1.8c1 may be false). 

## 1.7 Conclusions

  1.  For the processed profile of explosive source, the reflection waveform feature information of target layers in either single deep well or combined well is more abundant than that of target layers in controllable seismic source profile.  This is decided by the controllable seismic source itself.  The reflected waves indicating target layer sandstone are formed by harmonic superimposition from high frequency to low frequency, but the actual scanning frequency of controllable seismic source is 8 ~ 90 Hz, lacking low frequency components below 8 Hz and high frequency components above 90 Hz.  Therefore, the frequency band is narrow and hence the reflected waveform feature on target layer is rigid, which shows the importance of seismic wideband acquisition. 
  2.  For the profile of single deep wells or combined wells, the receiving channels are different under almost the same frequency bandwidth of target layer reflection and dominant frequency, and the longitudinal and transverse resolutions vary from each other for target layer reflected waves.  It enjoys high longitudinal and transverse resolutions for target layer reflected waves received by small trace (5 m trace). 
  3.  During exploration of lithology reservoirs, it is recommended to use the explosive source as seismic source (seismic broadband acquisition), and the small receiving channel for observation, so as to effectively identify the lithology reservoirs. 
  4.  In view of seismic data processing for lithology reservoirs, we have come up with the relative fidelity preservation processing method, that is, four key principles for relative fidelity preservation processing of broad band: (1) Protection of effective frequency band, in principle.  The widening of effective band should rely on SNR of high frequency widening components; while the high frequency widening of low SNR seismic data should be controlled (to control the bandwidth and dominant frequency of the deconvolution operator, thus preventing the noise energy at high frequency end from being amplified, will cause different level of notch frequency; deconvolution will only increase the energy of the frequency band within effective frequency band).  The final spectrum of target layer of the achieved profile should not cause severe notch frequency at high frequency end (DFH) of effective bandwidth (XF < 6 Hz and PF < 40% as reference indexes for notch frequency control). ( 2) Protection of low frequency, especially that of 3–8 Hz. ( The scenarios that suppress low frequency data of 10 Hz and below in high‐resolution and high‐SNR processing, or significant loss of effective low frequency information with adoption of strong f‐k noise elimination should be avoided.) ( 3) Amplitude preservation.  Modification module like RNA should not be applied, to avoid damaging the lateral relationship of seismic channel amplitude. ( 4) Phase preservation.  The module should not be used as it may damage the phase position in processing, while the zero‐phase deconvolution will not damage the phase relation, and surface consistent deconvolution may adjust the phase position slightly, but will not damage the phase relation. 

## References

  1.  1 Wang X. The prediction and evaluation of lithological reservoir. _ Geophysical Prospecting for Petroleum_ , 2004, 43 (6): 511–517. 
  2.  2 Wang X, Liu Q, Lv H _et al_.  Application of reservoir prediction technique in the exploration and development of lithologic oil‐gas reservoirs. _ Petroleum Exploration and Development_ , 2006, 33 (2): 189–193. 
  3.  3 Wang X, Liu Q, Su M _et al_.  Precision predicting reservoirs on the stages of progressive of exploration and development. _ Petroleum Exploration and Development_ , 2002, 29 (6): 51–53. 
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  5.  5 Wang X, Zhao B, Lv H _et al_.  Relative amplitude preservation method for seismic data processing. _ Geophysical Prospecting for Petroleum_ , 2009, 48 (4): 319–331. 
  6.  6 Wang X, Liu Q, Lv H _et al_.  Relative amplitude method to merging processing of 3‐D seismic data from multi‐area. _ Geophysical Prospecting for Petroleum_ , 2006, 45 (2): 105–120. 
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#  2   
Method and Principle for Seismic Migration and Imaging

The seismic migration imaging technology plays an import role in the seismic exploration, and is becoming an integrated system, including the structure imaging, the velocity modeling and the seismic attribute prediction.  As per the realization theory of the algorithm, the seismic imaging technologies can be divided into two major categories: Kirchhoff integral migration method, based on ray theory, and wave equation migration method, based on wavefield extrapolation.  The wave equation migration method can be further divided into two methods: one‐way wave migration method and reverse time migration method. 

In China, lithology reservoirs have become an important area for enhancing oil and gas reserves and production in recent years.  The lithology analysis has higher requirements on the amplitude preservation of the seismic migration imaging results.  However, the previous prestack depth migration method mainly focuses on the structure imaging.  In view of this, the geophysics industry has implemented extensive research works on different preserved‐amplitude prestack depth migration methods.  This chapter introduces in detail the principles of the above stated prestack depth migration methods and the development of preserved‐amplitude migration algorithms. 

## 2.1 Kirchhoff Integral Prestack Depth Migration

### 2.1.1 History of Kirchhoff integral prestack depth migration

The ray theory‐based Kirchhoff integral prestack depth migration is developed on the basis of wave equation Kirchhoff integral solution [1], where the Green's function in the Kirchhoff integral is replaced by its high frequency asymptotic solution.  Its migration implementation process is realized in the following steps: conduct simultaneous ray tracing to underground target imaging points from both seismic sources and receiving point, and the ray tracing can present the travel time information and the ray direction.  The Kirchhoff migration, however, shifts energy on the seismic record, shifting the input energy at the unmigrated time position to the output migrated depth domain position. 

The Kirchhoff integral prestack depth migration has proved to be an efficient and practical prestack depth migration method.  It is characterized by great migration angle, no frequency dispersion, less resource occupancy and high implementation efficiency.  In addition, it adapts to various changes of the observation systems and the complicated ground surface relief.  Therefore, the Kirchhoff integral prestack depth migration is widely applied in the actual seismic data processing. 

Schneider (1978) set up the theoretical basis for the wave equation of the Kirchhoff integral migration [1], and Bleistein (1987) extended the application of the integral method to solving the reflection coefficient [2].  The following problems still exist in Kirchhoff migration method.  First, this method applies the zero‐order, high‐frequency asymptotic approximation of the wave equation, the ray equation.  In this case, the diffraction points within several wavelengths of the source point and the receiving point cannot be imaged correctly, while the caustic region exists.  Second, the long‐standing problem that is difficult to overcome in the Kirchhoff migration method is the multi‐path problem, which leads to the difficult calculation of the travel time.  Third, when the steep section of the diffraction surface is imaged by the Kirchhoff migration method, operator alias will be produced.  To solve this problem, Gray _et al_.  proposed reducing the wavelet frequency components scanned from the steep section of the diffraction surface [3,4], and achieved success.  Hill proposed the Gaussian beam migration method [5,6], which can both maintain the flexibility of Kirchhoff integral migration method and improve the precision of migration. 

Currently, the development of Kirchhoff integral migration mainly focuses on the improvement of the calculation method of the travel time, amplitude preservation and illumination intensity compensation.  For the calculation of the travel time, wave front reconstruction method is generally used for ray tracing in most countries, while in China, based on the Eikonal equation, research on the calculation method of fast marching travel time has been developed.  At the same time, some researchers calculate the maximum energy 3D focus operator within the effective band range of the seismic wave, and realize the Kirchhoff integral depth migration, based on this calculation. 

### 2.1.2 Implementation principle of Kirchhoff integral method prestack depth migration

The basic process of the Kirchhoff integral prestack depth migration includes underground imaging points that are traced by ray simultaneously from the seismic source and the receiving point.  Then, the seismic migration imaging results of the underground interface are obtained through extracting the wavelet from the seismic record as per the calculated travel time information and being stacked. 

The Kirchhoff integral prestack depth migration mainly relies on the integral solution of the wave equation [1], with the solution being expressed as the surface integral on the known seismic observation object.  As per the Kirchhoff integral solution of Green's functions WKBJ approximation acoustic wave equation, the surface integral can be expressed as the migration of one single shot, with the specific expression formula as below:

Where: Σ is the recording surface; τ _s_ is the travel time from the source point _x s_ to the underground imaging point _x_ ; _τ r_ is the travel time from underground imaging point _x_ to the receiving point _x r_; n is the exterior normal direction of the recording surface; _u_ is the recording wavefield; _u m_ is the derivative of the recording wavefield to the time; A is the geometrical spreading factor (amplitude weighing factor), which can be analyzed out as functions of the velocity, travel distance and recording surface incident angle.  Therefore, in the Kirchhoff integral method prestack depth migration, the calculation of the travel time is quite critical. 

There are three core issues in the Kirchhoff integral method prestack depth migration: the calculation method of the travel time, the anti‐alias and the migration aperture optimization. 

The key to the Kirchhoff integral method depth migration is the calculation of the diffractive travel time, which is generally realized by the ray tracing method and the finite difference method [7].  However, some disadvantages exist in conventional ray tracing methods.  First, the ray tracing can only be implemented by the analytical method when the velocity is not too complicated, thus limiting its application scope.  Second, the shooting method may sometimes lead to the blind zone, while the existence of the blind zone will lead to the failure of the shooting.  Third, with the perturbation method, though it will not lead to the blind zone, it is difficult to achieve better effect under complicated velocity structure and far distance.  Fourth, the complicated velocity structure often causes problems of multiple solutions.  Therefore, for the calculation methods for the finite difference travel time, much research work has been performed in geophysics.  Based on the Fermat principle, the calculation of the finite difference diffractive travel time can be implemented both in the Cartesian coordinate system and the spherical coordinate system.  For example, Vidale proposed the travel time calculation method with finite difference method being applied to solve the Eikanol equation under Cartesian coordinate system [8].  This method can be applied to the non‐smooth velocity model.  In recent years, outside China, the wavefront reconstruction method has mainly been applied for the calculation of the travel time, while China conducted research works on the Eikanol equation based Fast Matching Method (FMM) for travel time calculation, which has been continuously improving the precision and efficiency of the travel time calculation. 

Data alias, operator alias and imaging alias may exist in the process of Kirchhoff integral method depth migration, while they are independent of each other and different from each other.  Among them, the data alias and the imaging alias can be eliminated by reducing the sampling interval.  For the migration imaging of data by the diffractive surface, the frequency components of data are usually not in the considering scope, thus the operator alias will certainly appear.  For the Kirchhoff integral method prestack depth migration, the alias may be generated under the existence of steep dip operator trace, strong high‐frequency energy and sparse spatial sampling.  At present, triangular, rectangular and multi‐band‐pass filters are generally used to prevent alias, with the computation being speeded up successively in the above order.  However, the rectangular operator's suppression capability with high frequency components is not as strong as the triangular operator, while the multi‐band‐pass filter operator is equivalent to several fixed rectangular functions, which is determined by the chosen frequency band.  The experiment shows that the triangular anti‐alias operator has the best effect, while it is of the highest computational complexity. 

For the research on the Kirchhoff type preserved‐amplitude migration, three major theories have been developed.  The first theory is the extension of typical Kirchhoff migration theory, which is based on the concept of the wavefield.  It also proposed a measuring device for the common‐source points and common receiving points, with its weight function being given by the Green's function of WKBJ ray theory.  The second theory is presented by Bleistein, with its weight function being obtained based on the Beylkin determinant.  The third theory is proposed by Cerveny and Castro, where they linked the Beylkin determinant with the vector, with the kinetics ray tracing method being applied for the calculation.  Nowadays, there are many theoretical methods for the Kirchhoff‐type preserved‐amplitude migration, while all of them require that the algorithm itself is of better computation precision and higher computation efficiency.  In addition, the weight function should eliminate propagation loss of the seismic wave properly. 

## 2.2 Amplitude Preservation Fourier Finite Difference Prestack Depth Migration Method

Due to some inherent disadvantages existing in Kirchhoff integral method prestack depth migration, the one‐way wave prestack depth migration methods were developed.  Among them, Zhang Yu _et al_.  proposed the fidelity‐preserved amplitude one‐way wave prestack depth migration method [9–11].  Compared with Kirchhoff integral migration method, the one‐way wave prestack depth migration method can effectively solve the imaging problem of the complicated structural areas where severe lateral velocity variation exists, especially the Fourier finite difference method based on the one‐way wave equation [12] that is based on the idea of splitting the velocity field.  It regards the whole velocity field as the superposition of the constant velocity background and variable velocity disturbance.  Fourier finite difference prestack depth migration is a kind of dual‐domain continuation algorithm, The first step is the phase shifting processing to the background slowness in the frequency‐wavenumber domain; the second step is the time shifting processing to the variable velocity perturbation in the frequency‐wavenumber domain; the third step is the calculation of the finite difference compensation items to the velocity perturbation above the second order.  The method owns the advantages of both the phase‐shifting method and the finite difference method, and well adapts to the underground severe lateral velocity variation. 

The lithology analysis has higher requirements on the amplitude preservation of the seismic migration imaging result [13].  However, the conventional Fourier finite difference prestack depth migration method mainly focuses on the underground structure imaging, and it cannot provide accurate amplitude information.  Therefore, it doesn't satisfy the lithology analysis requirement [10,11].  Moreover, the conventional Fourier finite difference method does not comply with the spherical diffusion theory, and cannot effectively compensate the energy loss during the seismic wave propagation, which is also not good for the structure imaging in the complex areas.  The preserved‐amplitude migration should be implemented through adding the amplitude recovery item and varying the imaging condition on the basis of the conventional migration method.  The continuation factor and its imaging condition for the preserved‐amplitude Fourier finite difference prestack depth migration will be introduced here [14–16]. 

The specific implementation process of Fourier finite difference preserved amplitude continuation operator is as follows. 

The 2D scalar wave equation of the compression wave propagation in the constant density media is:

(2.1)

To satisfy the spherical diffusion theory, the following formula needs to be used to convert the one‐way wavefield into the acoustic pressure wavefield. 

(2.2)

Where,

(2.3)

Where, _x_ is the horizontal spatial axis; _z_ is the depth axis; _t_ is the time; _w_ is the circular frequency;   is the one‐way wavefield;   is the acoustic pressure wavefield; V is the underground media velocity.  After the one‐way wavefield is converted into the acoustic pressure wavefield, Fourier finite difference amplitude preserved continuation operator is completed in the following three steps (take   as an example):

  1.  The phase shift against the background velocity and the amplitude recovery item. 

The phase shift against the background velocity is:

(2.4)

Where, _k x_ and _k z_ are respectively wavenumbers in the horizontal direction and the vertical direction.  While, the amplitude recovery item is:

(2.5)

Where, _c_ is the underground background velocity, the true travel time data and amplitude data against the underground background velocity continuation is obtained via equation 2.4 and 2.5. 

  2.  The time‐shift item and the amplitude recovery item against the variable velocity perturbation. 

The time‐shifting item against the variable velocity perturbation is:

(2.6)

While, the amplitude recovery item against the variable velocity perturbation is:

(2.7)

  3.  Frequency‐spatial domain finite difference compensation item processing and amplitude recovery item. 

The conventional finite difference compensation item is:

(2.8)

Where, the operator,

and,

where,

While the implicit format of the amplitude recovery item of the finite difference compensation is:

(2.9)

The amplitude recovery can be realized by using the formula above for the finite difference discrete in the spatial direction. 

The above is the specific implementation process of the Fourier finite difference preserved‐amplitude continuation operator.  The continuation operator is only one part of the prestack migration.  The boundary conditions and imaging conditions are of the same importance. 

In the boundary conditions for the preserved‐amplitude migration imaging, the boundary conditions for the upward pressure components are the same as conventional methods, which is:

(2.10)

Where, _Q_ ( _x_ , _w_ ) is the common‐source data received on the ground, while the downward pressure components need to be modified into:

(2.11)

Where, _x s_ is the shot position. 

The preserved‐amplitude migration imaging conditions can be obtained through the modification to the conventional kinetic imaging conditions, which is:

(2.12)

Relatively true underground travel time data and amplitude data can be obtained by applying the above fidelity‐preserved amplitude Fourier finite difference continuation algorithm.  To verify the correctness and effectiveness of the given fidelity‐preserved amplitude Fourier finite difference continuation algorithm, we selected the widely used Marmousi model data for the numerical test.  Figure 2.1a and Figure 2.1b are respectively the single shot illumination results at the 280 position of the CDP obtained through conventional Fourier finite difference continuation algorithm and fidelity‐preserved amplitude Fourier finite difference continuation algorithm.  While Figure 2.2a and Figure 2.2b present comparison of accumulated results of all 240 single shot illumination.  The comparison of the two types of illumination shows good consistency among the propagation energy of the illumination results obtained through the fidelity‐preserved amplitude Fourier finite difference continuation algorithm along different directions, which reflects the structure to some extent, as well as more details of the wavefield varying along with the velocity model.  As shown from different stacking results of single shot migration by the application of conventional Fourier finite difference continuation algorithm and fidelity‐preserved amplitude Fourier in Figure 2.3, the overall imaging quality of the migration results obtained by the fidelity‐preserved amplitude Fourier finite difference continuation algorithm is somewhat improved and the imaging energy is strengthened to a certain extent.  Its imaging energy of the medium and deeper part is strengthened, with more obvious improvement on the imaging effect of the deep anticlinal structure and the embedded low velocity intrusive body target area.  The above illumination analysis and the comparison of migration results all prove the effectiveness of the fidelity‐preserved amplitude Fourier finite difference continuation algorithm. 

**Figure 2.1** Single shot illumination analysis results by Marmousi model. ( a) Based on conventional Fourier finite difference operator. ( b) Based on fidelity‐preserved amplitude Fourier finite difference operator. 

**Figure 2.2** Illumination comparison results of all shots by Marmousi model. ( a) Based on conventional Fourier finite difference method. ( b) Based on preserved‐amplitude Fourier finite difference method. 

**Figure 2.3** Migration comparison results of all shots records by Marmousi model. ( a) Based on conventional Fourier finite difference method. ( b) Based on fidelity‐preserved amplitude Fourier finite difference method. 

The application of the above fidelity‐preserved amplitude Fourier finite difference prestack depth migration method is favorable for the structure and lithology imaging of the complex overthrust structure.  The test results to the model data of the Turpan‐Hami foothills in Figure 2.4 show that through the comparison of the preserved‐amplitude Fourier finite difference prestack depth migration results with the conventional Kirchhoff integral results, it can be seen that the imaging of the overthrust underlying structure is obviously improved.  The comparison of actual seismic data processing results in Figure 2.5 also shows that the preserved‐amplitude Fourier difference prestack depth migration provides clearer breakpoint and the fracture of the overthrust underlying structure. 

**Figure 2.4** Test result of foothills model data migration method. ( a) Kirchhoff integral method. ( b) Preserved‐amplitude Fourier finite difference method. 

**Figure 2.5** Test result of foothills actual seismic data migration method. ( a) Kirchhoff integral method. ( b) Preserved‐amplitude Fourier finite difference method. 

## 2.3 Reverse Time Migration

### 2.3.1 Isotropic reverse time migration

#### 2.3.1.1 Imaging conditions of reverse time migration

The imaging condition plays a critical role for the imaging effect of the reverse time migration profile, being one of the research focuses of the reverse time migration.  Nowadays, the commonly used imaging conditions include two major categories: excitation‐time imaging condition and cross‐correlation imaging condition. 

The excitation‐time imaging condition is based on the time consistency principle, that is, the upward wave generation time is equal to the downward wave arrival time.  It can be implemented by calculating the first arrival travel time of the direct wave at various underground imaging points.  The calculation methods of the first arrival travel time of the seismic wave can be divided into two major categories: ray tracing method and finite difference method.  The ray tracing method has the advantages of simple calculation, convenience and high efficiency, while its disadvantages include the existence of multiple travel time figures, caustic areas and shadow areas.  It cannot usually achieve good effects in dealing with acute varying velocity.  When calculating the first arrival wave travel time to underground targets by the Eikonal equation through the finite difference method, two methods are applied most widely: the finite difference algorithm based on the rectangular mesh and the finite difference algorithm based on the spreading wave, which are used to solve the travel time of the first arrival wave.  However, when the model is complicated, the reflection wave received on the ground may not be the reflection of the downward first arrival wave, but the reflection of the later arrival wave which has the maximum downward energy.  In this case, it is obviously unreasonable to use the above two methods to implement the imaging condition of reverse time migration.  The application of downward wave maximum energy imaging method can overcome this shortcoming, with more accurate travel time information being obtained.  The downward maximum energy time of the underground imaging point can be obtained through the wave equation forwarding.  The finite difference method, finite element method and the pseudo‐spectral method can be applied by the forward algorithm. 

The cross‐correlation imaging condition is used most commonly now, which was first proposed by Claerbout [17], with its theory being summarized as:

(2.13)

Where, _x_ and _z_ are the spatial coordinates; _u_ is the reverse time continuation seismic wavefield of the receiver point; Image ( _x_ , _z_ ) is the reverse time migration imaging result; _t_ is time; _t_ max is the maximum recording length; ε is the seismic wavefield of the source positive continuation. 

Actually, the above formula is the cross‐correlation calculation of the positive continuation wavefield of the seismic source and the reverse time continuation wavefield of the receiver point.  To the deep formation, energy attenuation also exists during the receiver point wavefield reverse time continuation.  This kind of attenuation is not caused by the elastic parameter of the media, but by the reverse time continuation algorithm itself.  It is essentially a kind of error, which has more effect on the migration results when the depth becomes bigger.  To overcome the limitation, Kaelin and Guitton normalized this formula 2.13 by using the shot wavefield value, with the new imaging condition being developed [18], which is:

(2.14)

Formula 2.14 is regarded as the normalized correlation imaging condition.  The research by Chattopadhyay and McMechan [19] showed that when other conditions are maintained, the application of the normalized cross‐correlation imaging condition could obtain better migration results in fidelity. 

#### 2.3.1.2 Generation and suppression of reverse time migration low‐frequency noise

### _2.3.1.2.1 Analysis of reasons for the generation of reverse time low‐frequency noise_

From the point of imaging condition, the wavefield extrapolation by one‐way wave extrapolation operator can be regarded as a kind of filter to the observed wavefield, with just one upward wave being extrapolated downward, where the downward wave is filtered out.  The source wavefield extrapolation by the downward operator extrapolation just contains downward wave, with the upward wave being filtered out.  To relative flat reflection interface, such source downward wavefield correlates to the upward wavefield of the extrapolated receiver point, which is equivalent to correlating the incident wavefield to the reflection wavefield at the reflection point.  The one‐way wave imaging satisfies the imaging condition defined by formula 2.13, with no low‐frequency imaging noise being generated. 

When the two‐way wave is applied for the reverse time migration imaging, upward wave and downward wave are both available in the extrapolated source wavefield and the receiver point wavefield.  When the imaging condition defined by formula 2.13 is applied, the imaging can only be implemented after the incident wave and the exit wavefield are separated out, which means the imaging is realized by the wavefield defined by the wave vector symmetric to the normal direction at some imaging point on the reflection interface.  The way of finding the wavefield corresponding to such wave vector is actually a course of filter to the extrapolated wavefield.  It is difficult to find the wavefield corresponding to such a wave vector.  There is no efficient way of doing this now for reverse time migration imaging.  If imaging is performed for a wavefield extrapolated by reverse time under the imaging condition defined by formula 2.13 at the imaging point, the imaging result will contain severe low‐frequency noise. 

The explanation by Liu _et al_. [ 20] is that the generation of low‐frequency noise is attributed to the application of full acoustic wave equation to the wavefield continuation of both the source and the receiver point.  As per the exchange law, the two wavefields have the same propagation paths.  Therefore, they will have the cross‐correlation calculation along the whole seismic wave propagation path, with non‐zero correlation coefficient being generated along the whole path.  It is true for the process of the reverse time migration imaging.  The receiver point's wavefield can be reverse time extrapolated to zero time, with the source wavelet for the time being recovered.  Excite this source wavelet and the given source wavelet simultaneously and propagate forward, and image at any time with formula 2.13.  In this way, the reverse time migration imaging can be obtained.  This process is very similar to the seismic wave illumination process, and the generation of the low‐frequency noise is a foreseen consequence. 

### _2.3.1.2.2 Suppression method of reverse time migration low‐frequency noise_

At present, the suppression methods for the reverse time migration low‐frequency noise mainly include: no‐reflective wave equation, imaging condition modification, imaging upon denoising and wavefield decomposition cross‐correlation imaging. 

In the no‐reflective wave equation method, the underground wave impedance is assumed to be a constant.  The low‐frequency noise generated when the source wavefield and the receiver point wavefield are cross‐correlation imaged is suppressed through weakening the reflection of the seismic wave.  The theoretical basis for the method is the equation proposed by Baysal _et al_. [ 21], as shown below:

(2.15)

Where, _u_ = _u_ ( _x,y,z_ ) is the sound field; _v_ = _v_ ( _x,y,z_ ) is the acoustic velocity of the media; _t_ is the time;∇2 is the Laplace operator. 

Later, Etgen _et al_. [ 22] successfully applied the above equation in the reverse time migration processing, which can suppress the low‐frequency noise to a certain extent.  However, the equation only describes the seismic wave propagation law for the case when the underground medium wave impedance is constant.  When the incident wave is vertical to the incident interface and its reflection coefficient is zero, the incident angle increases and its reflection coefficient also increases.  Therefore, the equation 2.15 is just an approximate non‐reflection acoustic wave equation.  For this purpose, Fletcher _et al_. [ 23] introduced a direction attenuation item to the non‐reflection wave equation, with the modified wave equation being expressed as below:

(2.16)

Where,   is the liner differential operator; ε is the damping factor.  By numerical test, Fletcher _et al_. [ 23] proved that the non‐reflection wave equation added with direction attenuation factor can further eliminate the reflected energy of the seismic wave, thus improving the low‐frequency noise suppression effect. 

The imaging condition modification method eliminates the reflected wave energy and suppresses the low‐frequency noise through direct modification to the cross‐correlation imaging condition or selecting of a new imaging condition.  The normalized cross‐correlation imaging condition shown by formula 2.14 is a kind of modified imaging condition.  The method improves the imaging condition with the help of the receiver illumination, and is simple and feasible, with no calculation complexity being increased.  It can attenuate shallow noise, especially the noise from the receiver points, and can compensate deep energy and improve the imaging effect.  Poynting vector imaging condition was proposed by Yoon and Marfurt [24].  It adds an angle discriminating factor, with the weighted ratio being set, and then applies the normalized cross‐correlation imaging condition, which can further effectively suppress the low‐frequency noise.  Costa [25] raised a kind of new imaging condition with inclination correction, and the illumination compensation, back scattering attenuation and man‐made noise are added, based on Poynting imaging condition, which improves the uniformity of illumination and the reverse time migration imaging effect. 

The imaging upon denoising method is a method that denoises the reverse time migration result of each shot or reverse time migration stack imaging result after the reverse time migration.  The commonly used methods include the high‐pass filtering method and Laplacian filtering method.  The high‐pass filtering method makes use of the low spatial frequency property of the noise generated in the reverse time migration, which can effectively suppress the low‐frequency noise.  But not all noises can be completely separated from the effective wave in the space‐frequency domain.  Therefore, during denoising, effective signals in the migration profile are often damaged.  The high‐pass filter processing can only eliminate noise to a certain extent, which means it needs applicable prerequisite.  Laplacian filtering method is another rather effective denoising method, with its filtering principle equivalent to the angle attenuation.  It can both effectively suppress the low‐frequency noise and maintain the useful imaging result, and is thus more popular in actual processing. 

The wavefield decomposition cross‐correlation imaging method was first presented by Liu _et al_. [ 20].  The method first decomposes the full wavefield into a one‐way component; and then selectively performs the cross‐correlation calculation to the wavefield components; finally it realizes the imaging of all effective paths and eliminates the low‐frequency imaging noise.  Taking the upward and downward wavefield in _z_ direction as an example, the source wavefield and the receiver point wavefield can be expressed as:

(2.17)

(2.18)

Where, Sz+(t,X), Sz−(t,X) and Rz+(t,X), Rz−(t,X) respectively represent the downward components and upward components of the source wavefield and the receiver point wavefield (it is assumed that the downward direction is positive).  Then, the cross‐correlation imaging condition can be expressed as:

(2.19)

Where: _I_ z1 is the cross‐correlation of the downward source wavefield and the upward receiver point wavefield, equivalent to the one‐way wave migration; _I_ z2 is the cross‐correlation of the upward source wavefield and the downward receiver point wavefield; _I_ z3 is the cross‐correlation of the downward source wavefield and the downward receiver point wavefield; _I_ z4 is the cross‐correlation of the upward source wavefield and the upward receiver point wavefield, equivalent to the one‐way wave migration.  Among them, the first two cross‐correlation calculations are only at the reflection interface, and the other two are not only at the reflection interface, but also through the ray path.  That is why low‐frequency noise is generated on the migration profile.  To eliminate these noises, we just choose the first two for the cross‐correlation calculation, which can eliminate the low‐frequency noise from the origin.  As per the explanations of Suh and Cai [26], the wavefield can be decomposed into the upward wavefield and the downward wavefield in _z_ direction, with the wavefield in the vertical direction being applied.  It mainly images the horizontal and small inclination angles, named the vertical imaging condition.  The wavefield can be decomposed into the leftward wavefield and the rightward wavefield in _X_ direction, with the wavefield in the horizontal direction being applied.  It mainly images the steep dipping formation, named the traverse imaging condition.  Through the application of the vertical and traverse imaging conditions, the whole path can be imaged accurately and the low‐frequency noise can be effectively eliminated. 

#### 2.3.1.3 Boundary conditions

### _2.3.1.3.1 PML absorbing boundary conditions_

The reverse time migration requires the numerical simulation method for the extrapolation of the seismic wavefield and the receiver point wavefield.  During the numerical simulation, meaningless artificial boundary reflection will occur when the seismic wave is propagated to the artificial boundary, which will cause the normal wavefield within the selected area to be seriously disturbed.  This is caused by the infinity of the underground propagation of the seismic wave and the finitude of the numerical simulated area.  Therefore, the absorbing boundary condition needs to be introduced at the boundary of the selected area to attenuate and absorb the artificial boundary reflection to the maximum extent.  In this way, the disturbance to the normal wavefield is reduced.  Consequently, the stability and the accuracy of the simulation results are improved. 

To solve the problem of artificial boundary reflection, various methods have been proposed to weaken and suppress the boundary reflection.  In 1977, Clayton and Engquist proposed the paraxial approximation boundary [27], which can completely absorb the reflection wave under the vertical incidence.  Moreover, the Clayton–Engquist boundary condition above the second order can better absorb in a certain range the reflection wave of the incidence angle.  However, when the incidence angle of the wave is big, intense reflection will still occur at the given boundary.  Other boundary conditions also include the multiple‐transmitting formula (MTF) boundary [28] and Higdon artificial boundary [29].  None of these approaches can achieve better absorbing effect under any incidence angle and frequency range.  To the magnetic wave propagation, Berenger (1994) presented an efficient absorbing boundary condition, named Perfect Matched Layer (PML), and when further proved this method can completely absorb the wave under any incidence angle and frequency, without occurrence of any reflection [30].  Currently, PML absorbing boundary condition has been successfully applied in other fields, and is also starting to be applied in the numerical simulation of the acoustic and elastic wave equation. 

PML absorbing boundary condition can be applied in the first and second order partial differential equations.  Nowadays, it is more popularly applied in the first partial differential equation, that is, velocity‐stress equation.  Actually, PML boundary condition is used for the field variable separation to the variable field (velocity field, stress field) of the seismic wave equation, which decomposes the field variables into two components that are respectively perpendicular to the transmitting boundary and parallel to the transmitting boundary for absorbing and attenuation.  Taking the first‐order stress‐velocity equation of the 2D acoustic equation as an example, this paper presented the equation's absorbing boundary layer equation and the structure of the PML. 

The first‐order stress‐velocity equation of the 2D acoustic wave is:

(2.20)

Where, _P_ = _P_ ( _x_ , _z,t_ ) is the acoustic wavefield; _K_ = ρv2 is the elastic modulus; _v_ is the _P_ wave velocity; ρ is the medium density; _v x_, _v z_ are the particle velocity in _x_ , _Z_ direction respectively; _t_ is the time.  The absorbing boundary layer equation is:

(2.21)

Where, _P x_, _P z_ are components of P in _x_ direction and _z_ direction respectively; _d_ ( _x_ ), _d_ ( _z_ ) are damping factors in _x_ direction and _z_ direction respectively.  For the definition of damping factor, a function proposed by Collino _et al_. [ 31], which reflects the decaying exponential relation following the distance between the interior domain truncation boundary and PML boundary, is adopted is here:

Where, _R_ is the theoretical reflection coefficient; δ is the thickness of PML; _v_ is the propagation velocity of the seismic wave of the matched layer; _h_ is the depth of PML, that is, the distance between the location of the matched layer and interior domain truncation boundary. 

The PML structure can be expressed by Figure 2.6, with the area being that to be studied by ABCD.  PML is added around the area.  In area 1, it is assumed that _d_ ( _x_ ) ≠ 0, _d_ ( _z_ ) ≠ 0 and velocity _v_ is equal to the corner velocity.  In area 2, it is assumed that _d_ ( _x_ ) = 0, _d_ ( _z_ ) ≠ 0 and velocity _v_ is equal to the boundary velocity.  In area 3, it is assumed that _d_ ( _x_ ) ≠ 0, _d_ ( _z_ ) =0 and velocity _v_ is equal to the boundary velocity. 

**Figure 2.6** Diagram of PML absorbing boundary. 

### _2.3.1.3.2 Random boundary conditions_

The absorbing boundary condition is the inevitable choice for the extrapolation of the reverse time imaging wavefield.  However, a big difference exists between the differential calculation of the absorbing boundary condition and that of the internal wavefield equation, which is not conducive to the implementation of the 3D reverse time migration algorithm on the GPU/CPU heterogeneous high performance computing platform and to the high computation efficiency.  The random boundary conditions make random disturbance of the velocity field at the boundary, with the diffuse reflection generated when the seismic wave propagating to this area.  Thus diffuse reflection affects the quality of the seismic wave forward results, while it has less effect on the seismic wave migration imaging.  This method, which varies only the velocity distribution of the media at the boundary, makes it unnecessary to consider the absorbing boundary conditions for the wavefield extrapolation.  Accordingly, it maintains the better parallel feature owned by the internal wavefield computation, very suitable for the application on the GPU/CPU heterogeneous platform. 

Random boundary conditions can be constituted by setting random varied velocity field at the boundary area of the velocity model, with the forming method indicated as below:

(2.22)

Where, _α_ is velocity dependent and of the same dimension with velocity; _R_ is the thickness of the random boundary area;   is the distance between the point in the random boundary area and the boundary; Ran(Idum) is the random number Ran(Idum)∈(0, 1) produced by seed number Idum Idum;   is the points in the random boundary;   is the random velocity value of point   in the random boundary;   is the velocity value of a point outside the random boundary, based on which the random velocity values of points in the random boundary are produced.  Proper imaging results can be obtained through regulating _a_ and _R_. 

##### 2.3.1.4 Implementation flow of reverse time migration

The reverse time migration mainly includes three parts, that is, the forward continuation of the source wavefield, reverse time continuation of the receiver point wavefield, calculation and application of the imaging conditions.  The reverse time continuation is the inverse problem of the numerical simulation of the seismic wave, in which the wavefield waves of various receiver points on the ground are known.  The wavefield values of various underground points are solved through the reverse time continuation.  The reverse time continuation of the wavefield can be expressed by the boundary value issue indicated by formula 2.23:

(2.23)

Where, _U_ ( _x_ , _z_ ) is the wavefield vector of various spatial points; _f_ ( _x_ , _t_ ) is the wavefield value of various receiver points on the ground; _t L_ is the maximum recording time of various receiver points on the ground; _x_ , _z_ are the horizontal distance and the vertical depth respectively; _z_ = 0 is the ground surface.  What the reverse time continuation requires is the wavefield value _U_ ( _x_ , _z_ ) of various underground points when _t_ ≰ _t L_ ( _x_ , _z_ ); based on the _U_ ( _x_ , _z_ ) solution, locations of underground imaging points can be solved through proper imaging conditions, so as to obtain correct underground model.  The reverse time continuation of the wavefield can be implemented by the finite‐difference method, finite element method and the pseudo‐spectral method.  Today, the most popularly used method is the high‐order staggered grid finite‐difference method, by which the high precision seismic wavefield can be secured, forming a necessary condition for obtaining the accurate imaging results by the reverse time imaging. 

The imaging conditions for the reverse time migration can be divided into two major categories: excitation‐time imaging condition and cross‐correlation imaging condition.  There are two corresponding implementation flows for the prestack reverse time migration.  Flowcharts of excitation‐time imaging condition and cross‐correlation imaging condition are presented in Figure 2.7 and Figure 2.8 respectively. 

**Figure 2.7** Flowchart of excitation time imaging conditions. 

**Figure 2.8** Flowchart of cross‐correlation imaging condition. 

#### 2.3.1.5 Theoretical model examples

### _2.3.1.5.1 NWGI model_

Refer to Figure 2.9 for NWGI model.  The seismic record applied by the reverse time migration is obtained through the forward modeling of the following observation systems: longitudinal wave source excitation, with Ricker wavelet of 40 Hz basic frequency as the source wavelet, and 250 shots in total at interval of 40 m. The first shot is located at the place of 1000 m of the lateral position.  The receiver points are distributed in the lateral position within 0 ~ 10990 m, with a maximum migration of [–6000, 6000] m. The recording time is 2.5 s, the sampling interval is 4 ms and the grid spacing is dx = 5 m, dz = 10 m.

**Figure 2.9** NWGI velocity model. 

The 2D acoustic wave equation reverse time migration algorithm is applied to execute the reverse time migration computation to the prestack shot record that is obtained by the forward modeling, with migration results shown in Figure 2.10.  From the figure, it can be seen that the reverse time migration has better imaging capability to the steep dip strata and the vertical strata. 

**Figure 2.10** Reverse time migration results by NWGI model. 

### _2.3.1.5.2 Marmousi model_

The Marmousi model is a complex geological model designed by Institute of France Petroleum (IFP), as shown in Figure 2.11.  In the model, there are three big faults.  The anticline containing the limestone stratum is located at the bottom of the fault, and is separated by the high velocity salt dome body at two sides of the deep strata.  The lowest part is the anticline containing the oil/gas reservoir.  The Marmousi model contains both the complex structure in the middle and the nearly horizontally layered simple structure at both sides. 

**Figure 2.11** Marmousi velocity model. 

The seismic record applied by the reverse time migration is obtained through the forward modeling of the following observation systems: longitudinal wave source excitation, with the source wavelet being of Ricker wavelet of 40 Hz basic frequency.  The buried depth of the shot point is 4 m, with 800 group reception, group interval of 4 m, and shot interval of 40 m. Shooting starts from the model left.  When the shot point is located within left 1600 m of the model, 800 group reception is at the model left.  When the shot point is located within the middle 6000 m, 400 group reception is at both sides of the shot point.  When the shot point is located within right 1600 m of the model, 800 group reception is at the model right.  The recording time is 3.15 s. There are 231 synthetic shot records in total.  The 2D acoustic wave equation reverse time migration algorithm is applied to perform the migration imaging to these shot gather, with migration results shown in Figure 2.12.  The figure shows that the reverse time migration not only accurately images the simple structures at both sides of the model, but also accurately images the complex structures in the middle of the model, including faults, anticlines and deep high velocity bodies.  This indicates that the reverse time migration is capable of dealing with the migration imaging issues under severe lateral velocity variation and steep dip strata, and is of better imaging capability on the complex models. 

**Figure 2.12** Reverse time migration results by Marmousi model. 

### 2.3.2 Anisotropic reverse time migration of VTI media

The reverse time migration was first put forward in early 1980s.  After 30 years' development, the two‐way acoustic wave equation based on the isotropic theory is now more applied in the industrial production, and has gradually shown obvious advantages in the seismic imaging of complex structural areas.  The two‐way elastic wave equation reverse time migration based on the isotropic theory is also nearly mature for the reverse time continuation algorithm and the imaging condition calculation method.  What hinders its industrial application is the huge amount of computation and computer memory required by the method, and the level of computational efficiency is hard to satisfy the industrial demand. 

For the reverse time migration of isotropic media, the research of both China and the rest of the world mainly focuses on the migration noise suppression and the migration result accuracy.  However, due to the prevalence of anisotropy in the underground media, the migration method based on the isotropic theory cannot effectively solve the seismic wave migration homing problem of the anisotropic media.  Therefore, the imaging precision is difficult to guarantee.  It is necessary to develop the migration methods based on the anisotropy.  Compared with other migration methods, the reverse time migration has many advantages.  Geophysicists developed much research work on the reverse time migration based on anisotropic theory.  However, in the anisotropic media, P wave and S wave are propagated in coupling, and its elastic wave is also quite complicated, with no decoupling phenomenon.  It is not practical to separate accurate P wave and S wave equations from the elastic wave equation.  For the reverse time migration algorithm, the initial idea is that based on the theory of elastic wave equation for the anisotropic media, the seismic wavefield migration homing is realized through the reverse time continuation and imaging of the three‐component seismic wavefield recorded on the ground.  The main advantage of the idea lies in the rigorous theory, by which the multi‐component data are regarded as the vector wavefield, and the P wave and S wave data are also processed.  Its shortcomings include: (1) It has too strict a requirement on input data.  It requires that all input data must be three‐component data, which doesn't work for the working areas without multi‐wave acquisition. ( 2) It is difficult to obtain the velocity model required by the migration.  Taking 2D VTI media as an example, it requires at least four elastic constants and density information of the known underground points, while the elastic constant is currently hard to obtain during the actual production. ( 3) It is of low efficiency.  The elastic wave equation contains multiple components that need to take up computer memory.  In addition, the S wave velocity is smaller than the P wave velocity, while the time and space steps are mainly controlled by the seismic wave's minimum velocity.  To ensure a stable computation, the time and space steps must be reduced, which will increase the quantities of time sampling points and space grids; accordingly, the computation speed will be lowered. 

In 2000, Alkhalifah put forward the assumed condition of acoustic approximation, which assumes the S wave velocity is zero, and the two‐way quasi‐P wave equation [32] in VTI media was derived.  This derived equation provided the basis for the anisotropic reverse time migration with only the P wave data.  The main advantages of performing the reverse time migration with the equation include: (1) For the work area where only P wave data are available, the reverse time migration algorithm of the equation can be used to implement the migration homing of the pure P wave. ( 2) It is easy to obtain the velocity model required for the migration.  Taking the 2D VTI as an example, it requires only the known NMO velocity, anisotropic parameter ŋ and density information.  The NMO velocity information and ŋ model can be obtained by such methods as P wave non‐hyperbolic moveout velocity analysis technology and travel time inversion.  For the density model, when wells are available, the well data can be applied to build the preliminary model, with further correction being performed as per geological or other prior information.  When wells are unavailable, the density model can be assumed to be a constant.  Relevant research results and model tests [33] show that if the density model is set as a constant, it will affect the accuracy of the migration results, but will not affect the imaging effect of the structure. ( 3) Compared with the elastic wave equation, it is of higher computation efficiency.  There is no S wave velocity parameter in the equation, so the relatively big time and space steps can be used for the reverse time continuation, which will improve the computation efficiency. 

The derivation of the quasi‐P wave equation for VTI media by Alkhalifah immediately attracted many scholars' attention, and they started to research it from different angles.  But until now, relevant research work has mainly focused on the optimization of the equation [34], numerical simulation [35] and pseudo‐wave removal [36].  There are rarely reports on the research of the reverse time migration algorithms of the equation.  In this chapter, starting from the first‐order quasi‐P wave in the VTI media, the high‐order finite difference scheme of the equation's reverse time migration is derived from the staggered grid space, and the stability conditions for the different algorithm are given.  The theory of PML absorbing boundary conditions is applied to derive its absorbing boundary layer equation; additionally, it also introduced the downward wave maximum energy method and normalized cross‐correlation imaging conditions, which are commonly used for reverse time migration so as to implement the prestack reverse time depth migration of quasi‐P wave equation in VTI media.  The trial computation results of the anisotropic Marmousi model show that the algorithm is not restricted by the variation of the underground structure dip and lateral velocity, and has better imaging capability on complicated models.  Under the same conditions, the imaging results obtained through the anisotropic migration algorithm is better than that through isotropic migration algorithm. 

#### 2.3.2.1 Quasi‐P wave equation in VTI media

### _2.3.2.1.1 Fourth‐order Quasi‐P wave equation_

The Quasi‐P (qP) wave equation for 3D VTI media derived by Alkhalifah is:

(2.24)

Where, _F_ = _F_ ( _x,y,z,t_ ) is the wavefield function, which is displacement‐independent quantity; _t_ is the time; _x,y_ , _Z_ are the 3D spatial coordinates; _V_ , _V V_ are the qP wave's NMO velocity and vertical velocity respectively; _ŋ_ is the anisotropic parameter, representing the anisotropy of the medium; and

(2.25)

Where, _v h_ is converted to the horizontal velocity of qP wave; _ε_ , _δ_ are Thomsen parameters [37]. 

The quasi‐P wave equation in VTI media is derived from formula 2.24 below:

(2.26)

Where, two solutions for formula 2.26 are:

(2.27)

(2.28)

Where, _k x_, _k_ z are the wavenumber in _x_ and _z_ direction respectively,  ; and

(2.29)

(2.30)

Alkhalifah's research shows that [32] the solution corresponding to formula 2.29 is qP wave, with the plus/minus sign in the index respectively representing the outward wave and inward wave.  The solution corresponding to formula 2.30 is the error solution introduced during the calculation of formula 2.26, which is just a set of 'artificial' seismic waves and doesn't actually exist.  Its propagating velocity is slower than qP wave; however, when ŋ < 0, it grows exponentially, which will cause the problem of serious unstable numerical calculation.  For convenience, therefore, the wave corresponding to formula 2.27 will be referred to as P2 wave.  When ŋ = 0, υ = υv, formula 2.26 is changed into the P wave equation for isotropic media, and formula 2.28 is changed into a time‐independent function, showing that the wave will propagate in the isotropic media.  Therefore, during actual computation, the effect of the wave can be eliminated by just putting the seismic source into the isotropic media. 

### _2.3.2.1.2 First‐order Quasi‐P wave equation_

The direct solving of formula 2.26 will waste a lot of memory and computer time.  Alkhalifah [23] converted the formula 2.16 into:

(2.31)

Where, _P_ = _P_ ( _x,y,z_ ) is the stress; _f_ ( _x_ , _z,t_ ) is the source distribution function.  Bingshou [35] applied the high‐order finite difference method to solve formula 2.31 and implemented the forward modeling of quasi‐P wave equation in the 2D VTI media.  But formula 2.31 contains fourth‐order partial differential and second‐order partial differential; the differential discretion of it with conventional rectangular grid will normally cause serious numerical dispersion, and also the boundary reflection problem is hard to solve.  The research results on the seismic wave equation forward field show that: the staggered grid technology based on first‐order stress‐velocity equation can effectively solve the above problem.  Hesiholm [34] derived the quasi‐P wave equation in 2D VTI media based on formula 2.31, shown by formula 2.32 below:

(2.32a)

(2.32b)

(2.32c)

(2.32d)

(2.32e)

(2.32f)

Where, _ρ_ is density; _υ x_, _υ z_ are the particle velocities on _x_ and _z_ direction respectively; _k_ , _ψ_ , _ζ_ are the intermediate variables during the calculation. 

#### 2.3.2.2 High order difference scheme of reverse time continuation of first‐order Quasi‐P wave equation in VTI media

The differential discretion of the formula 2.32 is performed by the staggered grid in Figure 2.13.  Refer to Table 2.1 for spatial locations of corresponding quasi‐P wavefield components and elastic parameters. 

**Figure 2.13** Staggered grid diagram. 

**Table 2.1** Spatial location of quasi‐P wavefield components and elastic parameters. 

**Grid point** | **1** | **2** | **3**  
---|---|---|---  
Wavefield components and elastic parameters | P, κ, ŋ, υ, υv | υx, ρ | υz, ψ, ζ, ρ

After differential discretion, the high difference scheme of the reverse time continuation of the first‐order quasi‐P wave equation in the 2D VTI media is obtained, as shown by formula 2.33. 

(2.33a)

(2.33b)

(2.33c)

(2.33d)

(2.33e)

(2.33f)

Where, Δ _x_ , Δ _z_ are spatial discrete steps; Δt is the time discretion step; _i_ , _j_ are spatial discrete point numbers; _n_ is the time discrete point number; _P n_( _i_ , _j_ ) is _P_ ( _i_ , _j_ ) at time _n_ ; _n_ is half of the differential coefficient;   is the differential coefficient, indicating the differential coefficient when order _m_ = 1, 2,..., N. When writing program, _n_ replaces _n_ \+ ½, _n_ −1 replaces _n_ −½, _i_ replaces _I_ \+ ½, _i_ −1 replaces _i_ −½, _j_ replaces _j_ \+ ½, _j_ −1 replaces _j_ –½.

#### 2.3.2.3 Stability conditions

The derivation method of Virieux [38] can be used to derive the second‐order time differential accuracy of first‐order quasi‐P wave equation in 2D VTI media, and the stability conditions of second‐order spatial differential accuracy scheme can be obtained. 

(2.34)

Where, max[ _υ_ ( _x_ , _z_ ), _υ v_( _x_ , _z_ )] is the maximum value of _υ_ and _υ v_ in the model. 

#### 2.3.2.4 Absorbing boundary conditions

As per the basic PML theory, the absorbing boundary layer equation along _x_ and _z_ direction can be derived by formula 2.32.  The absorbing boundary layer equation is shown by formula 2.35 below:

(2.35a)

(2.35b)

(2.35c)

(2.35d)

(2.35e)

(2.35f)

(2.35g)

(2.35h)

(2.35i)

Where, formula 2.35e and 2.35f correspond to _x_ direction and _z_ direction, respectively.  All other formulas can all be used in _x_ direction and _z_ direction. _ P x_, _P z_ are components of _P_ in _x_ direction and _z_ direction, respectively. _ d_ ( _x_ ), _d_ ( _z_ ) are the damping factors in _x_ direction and _z_ direction, respectively.  The structure of the PML is the same with model for the forward modeling of isotropic media acoustic wave equation, as shown in Figure 2.6. 

The differential discretion of formula 2.35 can obtain the high order difference scheme, which applies to PML absorbing boundary layer equation, as shown by formula 2.36 below:

(2.36a)

(2.36b)

(2.36c)

(2.36d)

(2.36e)

(2.36f)

(2.36g)

(2.36h)

(2.36i)

#### 2.3.2.5 Numerical test on pulse response

The size of the uniform media model is set to be 2000 × 2000 m, and the model parameters η, υ, υv, ρ are 0.2, 3500 m/s, 3000 m/s, 2500 kg/m3, respectively.  The main pulse frequency is 40 Hz, the same with the pulse energy, as shown in Figure 2.14. 

**Figure 2.14** Pulse response test data. 

Figure 2.15 and Figure 2.17, respectively, apply the downward wave maximum energy method imaging conditions, cross‐correlation imaging conditions and the normalized cross‐correlation imaging conditions to obtain the pulse response of the reverse time migration of first‐order quasi‐P wave equation in VTI media.  The disturbance produced by P2 wave can be observed in these figures, because the seismic source is generated in the anisotropic media.  The figure shows that the energy of response of each pulse at different angles is basically the same, which means the reverse time migration is of good inclination adaptability.  Figure 2.16 shows that a main defect exists in the cross‐correlation imaging conditions: the seismic wave amplitude attenuation in the deep imaging results is serious.  This is because the energy attenuation will occur due to spherical diffusion effect when the seismic wave is under forward propagation.  However, when the two‐way wave equation is applied for the reverse time continuation, the energy of the seismic wave will attenuate again.  The direct cross‐correlation calculation of the shot forward propagation wavefield and the receiver point reverse time continuation wavefield will lead to serious energy attenuation of deep imaging results.  Figure 2.15 shows the pulse response obtained by downward wave maximum energy method imaging conditions.  This method doesn't require the calculation of the wavefield under shot forward propagation, and only energy attenuation will occur during reverse time continuation.  Therefore, its deep energy attenuation degree is weak compared with the cross‐correlation imaging conditions.  The normalized cross‐correlation imaging conditions can effectively compensate for the energy loss produced during the reverse time continuation of the seismic wave, as shown in Figure 2.17.  The application of the normalization makes the energy of each pulse consistent, and the energy of the deep imaging results is effectively compensated. 

**Figure 2.15** Pulse response based on downward wave maximum energy method imaging condition. 

**Figure 2.16** Pulse response based on cross‐correlation imaging condition. 

**Figure 2.17** Pulse response based on normalized cross‐correlation imaging condition. 

#### 2.3.2.6 Model example

### _2.3.2.6.1 Horizontally layered medium model_

Refer to Figure 2.18a for the horizontally layered medium model.  The following observation system is designed for the forward modeling: the split spread scheme, 201 group reception, the shot location of (1000 m, 0 m), shot interval of 10 m, sampling interval of 1 ms, Ricker wavelet with basic frequency of 30 Hz as the excitation source wavelet.  Figure 2.18b shows the synthetic record in every fourth group with the direct wave being removed.  Figure 2.19 shows the reverse time migration result derived from the application of different imaging conditions. 

**Figure 2.18** Horizontally layered medium model and synthetic record. ( a) Horizontally layered medium model. ( b) Figure a model's synthetic record in every four groups. 

**Figure 2.19** Migration results under two imaging conditions. ( a) Migration results by downward wave maximum energy method imaging condition. ( b) Migration results by the normalized cross‐correlation imaging conditions. 

The analysis on Figure 2.19 will lead to the following conclusions: under the simple model, the two imaging conditions can both achieve better imaging results.  Compared with the downward wave maximum energy method, the normalized cross‐correlation imaging conditions can compensate to a certain extent the deep reflection wave energy, and improve the imaging results of deep stratum. 

### _2.3.2.6.2 Anisotropic Marmousi model_

The 2D anisotropic Marmousi model is applied to check the imaging effect of the reverse time migration algorithm of quasi‐P wave equation in VTI media on complicated models.  See Figure 2.11 for the 2D anisotropic Marmousi P wave velocity model.  Figure 2.20 shows the ŋ model obtained by Alkhalifah method [39].  It can be seen that the anisotropy is the strongest at the upper left of the model, weak at the upper right, and there is no anisotropy at the bottom.  NMO velocity _υ_ is from Marmousi P wave velocity model data, vertical velocity _υ v_ = _υ_ , and density is a constant.  The shallow layer of the model is 24 m thick isotropic media.  When the seismic source is located in the layer, the effect of P2 wave can be eliminated. 

**Figure 2.20** η model. 

The seismic record used for the reverse time migration is obtained through the forward modeling as per the following observations systems: P wave source excitation, with the source wavelet being Ricker wavelet of 50 Hz basic frequency, shot buried depth of 4 m, 800 group reception, group interval of 4 m, shot interval of 40 m. The shooting is started from the left end of the model.  When shots are located within the left 1600 m of the model, the left 800 groups of the model will receive.  When shots are located within middle 6000 m, 400 groups each on both sides of shots will receive.  When shots are located within right 1600 m, the right 800 groups of the model will receive.  The recording time is 3.15 s and the synthetic record of totally 231 shots is obtained. 

Based on downward maximum energy method imaging conditions and normalized cross‐correlation imaging conditions, the reverse time calculation by first‐order quasi‐P wave equation in VTI media is applied for the migration imaging of all shot gathers in which the direct wave is removed, with profiles (Figure 2.21) under two types of imaging conditions being obtained.  Figure 2.22 shows the Kirchhoff prestack time migration results (from Alkhalifah) [40,41]; Figure 2.23 shows the result obtained by the interception of 3.0 ~ 9.0 km on the right of Figure 2.21b.  In the migration results by the reverse time migration, the model's horizon imaging is accurate.  The three faults, fault blocks, deep high velocity bodies, anticline structures, oil gas reservoir (arrow direction in Figure 2.23) and the details of the model are all better reflected on the migration profile, which means the method can deal with the migration imaging of the strata with intense lateral velocity variation and steep dip, and has better imaging capabilities on the imaging of complex models. 

**Figure 2.21** The reverse time migration profile of Quasi‐P wave equation in VTI media. ( a) Imaging condition migration profile by downward wave maximum energy method. ( b) Imaging condition migration profile by normalized cross‐correlation method. 

**Figure 2.22** Krichhoff prestack time migration profile (from Alkhalifah, 1998). 

**Figure 2.23** Prestack reverse time depth migration profile. 

The analysis on Figure 2.21 can also lead to the following observations: (1) The imaging conditions by the downward wave maximum energy method and by the normalized cross‐correlation can both obtain better migration effect.  The later can better compensate the deep energy, and improve the imaging effect of obviously deep strata. ( 2) The unclear imaging appearing in the shallow layer of the migration profile is caused by the low frequency noise occurring during the course of the reverse time migration, which is a defect that is difficult to overcome for the reverse time migration based on the two‐way wave equation.  Its suppression method needs to be further studied. 

To analyze the effect of anisotropy on the migration effect, the reverse time migration algorithm by the isotropic medium wave equation is applied for the migration imaging of the above seismic records.  The applied imaging conditions are imaging conditions by downward maximum energy method.  The derived migration profile is shown in Figure 2.24.  Comparing Figure 2.24 with Figure 2.21a, it can be observed that: the migration results obtained by the isotropic migration algorithm are obviously not as good as the migration results by the anisotropic migration algorithm, which is mainly due to the following: (1) Serious disturbance exists in the former (see the white arrow in Figure 2.24), and also partial horizon is unclear; the continuity becomes poor (see the black arrow in Figure 2.24), and the imaging precision is obviously lower than that of the later. ( 2) The complicated structural area in the middle part of the model becomes poor (red elliptical area in the figure), the continuity of the steep dip strata and the fault plane becomes bad, and the precision is lowered, even distortion appears (see the red arrow in Figure 2.24).  From the above, the effect of the media's anisotropy cannot be neglected for the migration processing of the seismic data.  The P wave data acquired in the anisotropic area can have better imaging effect by the application of the migration method based on the anisotropic theory. 

**Figure 2.24** Reverse time migration profile of isotropic medium acoustic wave equation. 

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#  3   
Study of Reverse Time Migration Method for Areas With Complicated Structures Based on the GPU/CPU System

## 3.1 Introduction

Currently, seismic imaging is transferring from structure imaging to lithostratigraphy imaging, and the imaging technique should solve imaging problems while considering the preservation of data amplitude and phase.  The amplitude preservation imaging technique is developing continuously from ray theory to wave theory.  The prestack depth migration technique of wave equation can realize amplitude preservation to some extent, especially the Fourier finite difference (FFD) that combines advantages of the Fourier method and finite difference method, and energy normalizing based two‐way wave equation that combines advantages of the two‐way wave method and imaging conditions.  They are very suitable for steep dip formation and medium with strong lateral velocity variation, and are the prestack depth migration with the best accuracy.  This chapter focuses on discussing the suitability and practice strategy of the GPU/CPU based two‐wave prestack depth migration technique. 

Now, there are two commonly used prestack depth migration methods: one‐way wave equation migration and Kirchhoff integral migration.  The one‐way wave equation migration is based on one‐way decomposition, which has accuracy that is acceptable under normal speed.  Solving one‐way wave equation by difference method should conduct paraxial approximation to the equation.  The paraxial approximation means that one‐way wave equation can only describe these downward waves approaching vertical direction.  It has some problems in description of dip angle transmission, in terms of either phase or amplitude, which will cause large imaging error.  This explains why the one‐way wave equation cannot image the steep dip angle reflection accurately.  Instead, Kirchhoff integral migration is usually used for steep dip angle reflection imaging.  However, it cannot process the imaging for single single‐point imaging with multiple arrival times.  It can only describe the transmission of wave in smooth medium, with the difficulty in caustics phenomenon processing.  Therefore, neither one‐way wave equation migration nor Kirchhoff integral migration can realize clear and accurate imaging to complex structure, so the industry focus has shifted to reverse time migration again. 

The reverse time migration was first proposed by Whitemore _et al._ [ 1], and was studied by many scholars around the world.  Recently, the emerging multi‐core CPU heterogeneous high‐performance computing platform has made 3D reverse time depth migration a practical technology, and it has also inspired people's research enthusiasm.  The main research work focuses on the following two aspects: (1) Reverse time extrapolation of wave equation. ( 2) Imaging conditions of reverse time migration and its calculation methods.  The study on reverse time continuation algorithm of wave equation includes such items [2,3] as wavefield continuation algorithm operator structure, numerical dispersion suppressing and boundary reflection suppressing.  The research on imaging conditions mainly focuses on the excitation time imaging conditions and mutual correlation imaging condition, where the former is the nature of imaging conditions and the latter is a realization method of the former. 

Reverse time extrapolation of wave equation is mainly the algorithm of solving wave equation based on finite difference approach.  The finite difference approach has no limits on models, and it is the main method for present seismic wave forward modeling and reverse time migration.  In order to obtain higher accuracy, minor grid and high‐order finite difference equation would be used in simulation.  Additionally, compact difference scheme and staggered grid with higher accuracy are also used for wavefield extrapolation of reverse time depth migration. 

In respect of reverse time migration imaging conditions, the upward and downward traveling wave imaging conditions proposed by Claerbout [4] are commonly used by researchers.  Reverse time migration imaging is the zero delay cross‐correlation at any point in the space between reverse time extrapolation wavefield of two‐way wave equation and extrapolation of seismic source wavefield along positive time direction.  In terms of transmission path, the whole path of the above two fields from shot point to reflection point and then to receiver point overlap with each other.  It means that they have a positive correlation relationship at any point in the space.  That explains why the reverse time migration can generate very strong low frequency noise.  The above imaging conditions proposed by Claerbout are not completely applicable to reverse time migration, for seismic source wavefield and receiver point field both have an upward traveling wave and a downward traveling wave.  In one‐way migration, only a downward traveling wave exists in seismic source wavefield, while only an upward traveling wave exists in receiver point field.  The overlapping of the whole paths of the two wavefields from shot to reflection point and then to receiver point will not occur. 

Therefore, these imaging conditions for upward and downward proposed by Claerbout will not produce low‐frequency noise in one‐way wave migration.  Hence, Mulder and Plessix believe that false image can be eliminated on imaging results through high‐pass filtering method [5].  Yoon _et al_.  proposed introducing the Poynting vector (of seismic source and wavefield of receiver point) related to angle into imaging condition, so as to give proper imaging results, and then to eliminate false image [6–8]; Fletcher _et al_.  introduced directional damper to some limited areas to suppress the false image [9,10]; Liu _et al_.  proposed the imaging condition of wavefield decomposition [11].  However, all imaging conditions as above failed to solve the imaging problem for extrapolation wavefield in reverse time migration.  Actually, the essential issue is simply to extract imaging value from extrapolation wavefield based on the concept of: "The starting time of reflection wave is the same with the arrival time of incident wave on reflection interface".  It requires using the wave vector symmetrically along both sides of normal direction on reflection point to define incident wavefield and outgoing wavefield, and to generate image on correlation between incident wave and outgoing wave.  However, in practice it is not easy to realize this concept effectively and it remains a core problem in the field of reverse time migration. 

In respect of implementation strategy of reverse time migration, Symes proposed recording wavefields of two time horizons [12] on some checking points, thus saving hard disk room for storing seismic source wavefield after extrapolation and reducing the I/O times for reading seismic source wavefield after extrapolation from hard disk.  The room space derived from the number of checking points multiplying wavefields of two time horizons is the required hard disk storage memory capacity for seismic source wavefield after extrapolation.  For reverse time extrapolation, extract the seismic source wavefield after extrapolation of two time horizons on the checking points from hard disk and conduct synchronous reverse time extrapolation with the observed wavefield, for imaging.  This method is a compromise between the wasted calculation work and saved storage room.  Otherwise, storing seismic source extrapolated wavefield of thousands of time steps into hard disk is low efficiency work. 

On GPU/CPU, better storage room and I/O times can be obtained by scarifying calculation work amount due to the high calculation capacity of the computer.  It is available to store only seismic source extrapolated wavefields of two time horizons on the maximum time spot, and to generate image by reverse time extrapolation synchronous with the observed wavefield. 

Additionally, the variation in difference scheme of boundary condition equation and equation for wavefield within boundary, breaks the good parallel calculation features of internal wavefield.  For this, Clabb proposed using randomly scattered boundary condition to solve this problem [13,14].  The random boundary makes the velocity field on boundary disturb randomly, and the seismic wave that is transmitted to this area will generate diffuse reflection.  The diffuse reflection generated under this situation will impose influence on the quality of seismic wave forward modeling results, but little on the seismic wave migration results.  This method only changes the media velocity distribution, so that it can avoid absorbing boundary condition in wavefield extrapolation and maintain the good parallel feature of internal wavefield calculation, which suits the execution on the GPU/CPU heterogeneous platform.  High speed‐up ratio was obtained on the GPU/CPU heterogeneous platform for the above execution method, making it the 3D reverse time migration to be used in practice.  The value calculation proves the correctness and validity of the above analysis and program. 

## 3.2 The GPU/CPU High‐performance Calculation and Its Application in Seismic Exploration

### 3.2.1 Introduction of the GPU/CPU system

GPU, a hardware specially designed by NVIDIA, is exclusively used to accelerate graphic processing conveniently.  In recent years, GPU has been developed to a special unit for Thread Level Parallel Computing.  Together with CPU (applied for operating control such as Thread Level Parallelism and I/O, etc.),  it constitutes a high‐performance and universal computing platform.  Under the CUDA operating system, GPU and CPU coordinate with each other to execute high performance computing with processes and threads running in parallel.  Data necessary for GPU computation is required to load into GPU memory (which is relatively small and generally 4G at present) from CPU memory (which is relatively big and may reach to 128G at present) through the bus.  The function of GPU is similar to a multiplying and summing unit, which is particularly suitable for arithmetic product and summation of vector quantity (matrix multiplication can also be turned into vector quantity multiplication).  The internal GPU contains many computing units (S1070 launched by NVIDA contains 240 cores in each GPU, and each core is a processing unit).  Factors influencing GPU efficiency include communication from CPU memory to GPU memory, match between each communication volume and number of processing units in GPU [15]. 

Communication efficiency between CPU memory and GPU memory plays a major factor on whether the computation can be processed quickly and whether the heterogeneous computing platform performance can be fully exploited.  The _matching_ of the segmentation size of one computing block with the number of GPU processor as well as the delay between storage at different levels in GPU are also key factors influencing the GPU operation efficiency.  Further development orientation of GPU/CPU platform will tend to integrate GPU and CPU, eliminate and simplify the communication between them, and properly improve the logic computing function of GPU.  This is a basic judgment derived from processing algorithm programming of exploration geophysical data. 

GPU is able to support graphic chip of T&L (Transform and Lighting) in hardware, because T&L is an important part of 3D rendering with the function of computing the 3D position of polygon and processing dynamic lighting, which is also named "geometric processing".  A good T&L unit can provide delicate 3D objects and high‐level special lighting.  However, in most PCs, a large part of T&L operations are processed by CPU, which has many tasks except for T&L, including memory management, input response and other non‐3D graphic processing.  Therefore, the performance of T&L operation is normally degraded in practice, and it happens frequently that the graphic card waits for CPU data.  Even if the operating frequency of CPU exceeds 1GHz or more, it does little to help T&L operation.  This problem is due to PC design itself and does not affect the CPU speed. 

GPU is different from the DSP (Digital Signal Processing) high‐speed microprocessor in several aspects, which overcomes the real‐time obstacle of digital control technology.  The full digital control simplifies hardware circuit, improves control precision and makes the advanced control mode possible.  All the calculations apply floating‐point algorithm and there are no bit or integer operational orders at present.  In addition, because GPU is exclusively used for image processing design, the storage system is actually a 2D fragmentation space including a sector number and a 2D address.  The output address is decided by raster processor rather than changed by program, which is an enormous challenge for algorithms that naturally spread in the memory.  Finally, it does not allow for communication in different fragment processors.  In practice, the fragment processor is an SIMD data parallel execution unit and it executes codes independently in all the fragments. 

Despite all of the above restrictions, GPU can still efficiently execute multiple operations from linear algebra and signal processing to numerical simulation.  Although GPU has a simple concept, users still feel puzzled when using it for computation, because GPU requires special graphic knowledge.  Here, some software tools may provide help.  High‐level language CG and HLSL enable users writing codes similar to C, which are then compiled to fragment program assembly language.  Brook is an exclusively designed high‐level language for GPU computation with no need of graphic knowledge.  Therefore, Brook may be regarded as a very good starting point for the first users of GPU.  As an extension of C language, Brook integrates simple data parallel multiple programming constructions, which can directly map on GPU.  Data stored in and operated by GPU is vividly compared to "stream", which is similar to arrays in standard C language.  Kernel is the function operated on the stream.  Calling a kernel function from a series of input streams means implementing an implicit cycle, namely calling a kernel for each stream element.  Brook also provides a reduction system, such as summation, maximum value or arithmetic product computation of all the elements in one stream.  In addition, Brook completely hides all the details of graphic API, and conducts a virtualization process of the analogous 2D memory system in GPU.  Application programs compiled by Brook include linear algebra subprogram, rapid Fourier Transform, ray tracing and image processing.  By applying X800XT of ATI and GeForce 6800 Ultra GPU of NVIDIA, many similar applications may be accelerated up to seven times under the execution condition of the same cache and SSE assembly optimization in Pentium 4[16,17]. 

**Figure 3.1** Floating‐point computation efficiency development comparison between GPU and CPU from 2003 to 2007. 

Figure 3.1 shows a comparison of floating‐point efficiency development of GPU and CPU from 2003 to 2007, which is based on comparison between single GPU and CPU processors without regarding how many cores are inside each computing unit or the clock frequency of CPU.  Qualitatively, the floating‐point operation times of dual‐core 3.0G Hz computing units are about 0.05 T while those of Tesla C870 are about 0.5 T, about ten times the former.  The clock frequency of CPU cannot be developed any further according to the Moore's Law, and the number of cores inside a single CPU cannot be increased any more.  Too much power consumption is a key factor limiting CPU from continuing development according to the current pattern.  Integration of GPU and CPU is a reasonable development path for current high‐performance computing platform. 

### 3.2.2 GPU/CPU high‐performance computing and the application in seismic exploration

Geophysical exploration technology progress benefits from the rapid development of computer technology.  At present, although the PC cluster‐based computing mode has already enabled the Kirchhoff integral theorem prestack imaging algorithm to be put into practice, the mode of multi‐core CPU platform is unable to satisfy the practical requirements of seismic data wave equation prestack migration (due to difficulty in improving computing power and too much power consumption), and it cannot put into practice the wave equation prestack migration algorithm.  Three‐D reverse time migration and high‐dimensional parametric inversion require putting the huge computing amount method into practice. 

The emergence of the GPU/CPU computer makes it possible to put the wave equation prestack migration imaging method into practice.  GPU/CUP applies more transistors for data processing, and it has excellent parallel computing power.  At present, GPU of Tesla 10 series owns 240 stream processors and its computing power has improved up to over ten times higher than the currently most advanced CPU.  All the main imaging modules of seismic imaging software system (such as integral method PSDM, wave equation, maximum energy travel time computation, shot domain wave equation PSDM, double‐square‐root equation prestack depth migration and reverse time depth migration, etc.)  require massive parallel computation.  The heterogeneous operation mode of GPU/CPU, namely controlling small computing amount which is not suitable for thread‐level parallelism, completing logic operations on CPU and completing large amount of floating‐point operations suitable for thread‐level parallelism on GPU, can greatly improve the computation efficiency, save investment and promote the research and application level of wave equation prestack depth migration method. 

The GPU/CPU heterogeneous high‐performance computing platform has already played a significant role in prestack seismic data processing.  Many petroleum companies have owned GPU/CPU computer clusters with GPU nodes.  In this computer cluster, the wave equation prestack time migration (Institute of Geology and Geophysics of Chinese Academy of Sciences), wave equation unidirectional wave prestack depth migration (Tongji University), wave equation full 3D seismic migration (Tongji University) and 3D reverse time migration (CGGVeritas) show very high speed‐up ratio.  Figure 3.2 and Figure 3.3 are some simple examples showing the GPU computing result and efficiency.  However, the GPU computing unit also has very obvious disadvantages, among which the first one is small global memory, which cannot satisfy the requirements of 3D prestack depth migration.  For example, it is unable to finish high‐dimensional FFT independently.  Thus, a GPU computing unit cannot be regarded as a mature high‐performance computing unit [18] at present. 

**Figure 3.2** Reverse time depth migration result of the Marmousi model on GT200 GPU (from Tongji University). 

The Marmousi model can complete the migration in 44.8 s for every shot.  The 3D salt dome model narrow azimuth data volume is: 138 shots, 80 cm shot interval, 6 lines in every shot, 65 tracks in every line and 40 m line distance.  It completes the migration in 149 s for every shot on GT200.  The huge computing amount of geophysics determines that GPU computation will play an increasingly important role in the future geophysics computation, which is pushed forward crucially by GPU software research and development.  GPU technology research and application have already made some progress in the seismic exploration field.  Some related companies have already applied the technology.  For example, GeoStar, together with Institute of Geology and Geophysics of Chinese Academy of Sciences, Tsunami and Sinopec Petroleum Geophysical Research Institute, utilized the CUDA development tool in the GPU computing environment to realize Kirchhoff 3D seismic prestack time migration, wave equation seismic prestack depth migration and reverse time migration technologies.  GSS has launched a seismic pixel method geology imaging software (SVI), which supports GPU computation.  All these technological applications are pushing the industrialized application process of GPU computation technology forward in the oil exploration field. 

**Figure 3.3** Reverse time migration imaging result of 3D salt dome model on GT200 GPU (from Tongji University). 

## 3.3 Study on the Two‐way Wave Extrapolation Operator and Its Boundary Conditions

Reverse time migration mainly includes two steps: reverse time wave extrapolation based on the two‐way wave equation and application of the imaging conditions.  For the single shot gather imaging, the first step is to forwardly extrapolate the focus wavefield by two‐way wave equation and save all the extrapolation wavefield of the time steps.  The second step is to make reverse time extrapolation to the received wavefield by the two‐way wave equation.  Apply the imaging conditions after every reverse time extrapolation on the time steps and get the imaging result of the moment.  All the moment imaging results accumulate to obtain the imaging result of the shot gather.  Reverse time migration results of all the shot gathers accumulate to obtain the final prestack depth migration imaging.  Moreover, angle imaging gather can be generated based on the shot gather imaging result for later speed analysis and AVA analysis. 

### 3.3.1 High‐order difference method

In 3D forward modeling and reverse time depth migration, it is necessary to get very small difference grid when applying the difference scheme with truncation error of O(Δx2, Δy2, Δz2 and Δt2), in order to guarantee small frequency dispersion and stable recursive process, which will result in significant increase of computer memory and operation time for the computation.  Dablain (1986) used a high‐order finite difference equation to conduct the above model building and migration process.  During the application of the high‐order difference equation, the grid value may be set at a high one while the computational accuracy will not be lowered [19].  Therefore, the difference equation with truncation error higher than four orders is called "high‐order difference equation".  The high‐order difference equation of 3D sound wave equation can be derived in this way. 

The 3D sound wave equation is as follows:

(3.1)

Where, _u_ ( _x,y,z,t_ ) is the pressure wavefield recorded on the surface; _υ_ ( _x,y,z_ ) is the variable medium speed. 

**Figure 3.4** Diagram of network subdivision. 

In order to deduce the discretion difference scheme of equation 3.1, it has to discretize the underground medium domain corresponding to observation or the model domain simulated by the seismic waves, that is to say, to subdivide them into small squares. 

Let

In order to deduce high‐order difference equation, conduct Taylor spread on the wavefield with the ( _i_ , _j_ , _k_ ) in Figure 3.4 as the center. 

First, we come to the discussion on the deduction of four‐order difference from time second derivative.  In the following deduction process, only the discussed independent variables are given, though the wavefield _u_ is the function of ( _x,y,z,t_ ). 

(3.2)

(3.3)

The following equation can be obtained by adding the formula 3.2 and 3.3:

(3.4)

In the process of forward modeling or migration imaging by formula 3.4, the more time horizon involved in the difference equation, the bigger memory it will need.  To solve this problem, it may turn the high‐order differentiation of the time into space differentiation by the sound wave equation 3.1, namely:

(3.5)

Substitute formula 3.4 and 3.5 into formula 3.1 to obtain:

(3.6)

(3.7)

Formula 3.6 and 3.7 are starting equations, respectively, for deducing high‐order difference equation of forward modeling and reverse time migration.  Its truncation error in time orientation is O(Δt4), while the determination of difference quotient truncation error in space derivation is subject to specific requirements (at least above four orders).  In addition, difference scheme of different orders may be obtained as required. 

The difference quotient deduction process of truncation error in different orders of the _x,y_ , _z_ space derivation is similar to the above.  Here we only discuss the _x_ space derivation, assuming that the truncation error of the difference quotient is O(ΔxM) and M is an even number more than four. 

(3.8)

(3.9)

(3.10)

Let:

The following equation set may be deduced from formulas 3.8, 3.9 and 3.10, together with the above specifications:

(3.11)

The matrix form of the above equation set can be expressed as:

(3.12)

Let:

(3.13)

Obtain _a_ 1, _a_ 2,......, _a_ _M_ /2 by evaluating the inverse matrix _A_ −1 of _A_ , and then use formulas 3.6 or 3.7 to get the difference equation of various truncation errors for 3D wavefield forward modeling and reverse time migration.  From formulas 3.6 or 3.7, it is clear that only with a1 namely  , can we therefore get:

(3.14)

(3.15)

(3.16)

Substitute formula 3.14 into formula 3.16 or substitute formula 3.6 into formula 3.7 to get a high‐order difference equation with arbitrary truncation error.  Moreover, different truncation errors in equations 3.14, 3.15 and 3.16 can combine with each other to satisfy various requirements. 

The unitive 3D forward modeling high‐order difference equation with truncation error of O(ΔxM, ΔyM, ΔzM, Δt4) is:

(3.17)

The 3D reverse time depth migration high‐order difference equation with the truncation error of O(ΔxM, ΔyM, ΔzM, Δt4) is:

(3.18)

Formulas 3.17 and 3.18 will be greatly simplified if the difference quotient in time orientation keeps a truncation error of O(Δt2).  This does not have a great impact on the forward modeling or migration result [20–22]. 

The 3D forward modeling high‐order difference equation with the truncation error of O(ΔxM, ΔyM, ΔzM, Δt2) is:

(3.19)

The 3D reverse time depth migration high‐order difference equation with the truncation error of O(ΔxM, ΔyM, ΔzM, Δt2) is:

(3.20)

We list some coefficients in the high‐order difference equation with several common truncation errors, as follows:

> When M = 4, _ω o_ = ‐5.0, _ω 1_ = 2.666667, _ω 2_ = ‐0.1666667. 
> 
> When M = 6, _ω o_ = ‐5.444444, _ω 1_ = 3.000000, _ω 2_ = ‐0.3000003 **and** _ω 3_ = 0.0222225, a high‐order difference equation with a specific truncation error can be directly written out according to the above coefficients. 

### 3.3.2 Boundary condition issue of reverse time migration

Absorbing boundary condition is an inevitable choice for reverse time migration imaging wavefield extrapolation.  However, the difference calculations between absorbing boundary condition and internal wavefield equation are totally different, which is unfavorable for the realization of 3D reverse time migration algorithm on GPU/CPU heterogeneous high‐performance computing platform, and is unable to obtain high computing efficiency.  Thus, we think that the random scattering boundary condition deserves much attention, but we need flexible parameters to control the boundary condition. 

Set random varied velocity field in the boundary domain to form the random boundary condition.  We put forward a random boundary method as follows:

(3.21)

Where, _a_ refers to a value related to velocity which has the same dimension with the velocity; _R_ represents the thickness of random boundary domain;   represents the distance from dots in the random boundary domain to the boundary; Ran(Idum) represents the random number generated by seed number Idum, Ran(Idum)Є (0,1);   represents the dots in the random boundary;   represents the random velocity value of the dot   in the random boundary;   represents the velocity value of a dot outside of the random boundary, which generates the random velocity value of each dot in the random boundary.  Adjustment of _a_ and _R_ may help to get suitable imaging result. 

## 3.4 Study on the Imaging Condition and Low‐frequency Noise Suppression Method

### 3.4.1 Study on imaging condition and low‐frequency noise generation mechanism

#### 3.4.1.1 Imaging condition

The imaging condition in reverse time migration mainly applies the following physical reality.  At reflection point, incident wavefield and reflection coefficient convolution create reflected (or emergent) wavefield.  The incident wavefield and emergent wavefield are imminent in terms of minimum Least Square, consequently the following formula is valid:

(3.22)

The following formula can be deduced accordingly:

(3.23)

Generally, we use the following relative imaging condition:

(3.24)

The physical meaning of this imaging condition is to use zero lag autocorrelation to extract the wavelet energy on reflection point.  Near the imaging point, by Pasaval relation, the above formula may be expressed in time domain as:

(3.25)

In the seismic exploration, the z‐axis is normally downward.  The seismic waves propagating downward along the z‐axis are called "downward travelling waves".  For the common relatively gentle reflecting interface, the downward travelling waves and incident waves are often not differentiated strictly, which is the same with upward travelling waves and emergent waves.  The imaging condition of formula 3.24 is also simplified by Claerbout (1977) as follows: the arrival time of upward travelling waves equals the departure time of downward travelling waves.  In one‐way wave migration imaging, the wavefield is extrapolated along the depth direction.  The so‐called one‐way waves mean the waves propagating downward along the z‐axis (marked with kz > 0) and upward along the z‐axis (marked with kz < 0).  kz is the wave number along the z direction, which is also called "vertical wave number". 

For two‐way wave reverse time migration, the imaging condition defined in formula 3.25 is quite convenient to use, since the seismic wavefield extrapolation is conducted in time and spatial domain.  However, the incident waves and emergent waves on the reflecting interface required in formula 3.25 are contained in the wavefield after extrapolation, and it's necessary to separate them from the wavefield.  Only with the imaging condition extracted according to formula 3.25 will an ideal imaging result be generated.  There is no simple or convenient way to realize extraction of incident waves and emergent waves on the reflecting interface from the extrapolation wavefield.  Thus, the present reverse time migration imaging result is always interfered by low‐frequency noise, and the existing low‐frequency interference suppressing method is still imperfect. 

#### 3.4.1.2 Low‐frequency noise generation mechanism

In terms of imaging condition, the wavefield extrapolation conducted by a one‐way wave extrapolation operator may be regarded as a kind of filtering for observation wavefield, which only extrapolates downward the upward travelling waves and filters the downward travelling waves.  Downward travelling wave operator extrapolation on focus wavefield just includes the downward travelling waves.  For more gentle reflection interface, the downward wavefield is associated with the receiver point upward wavefield after extrapolation, which is equivalent to the incident wavefield at the reflex.  The one‐way wave imaging satisfies the imaging condition defined in formula 3.24 without any low‐frequency imaging noise. 

However, in wavefield reverse time extrapolation imaging, the extrapolated focus wavefield and receiver point wavefield both have upward travelling and downward travelling waves.  Certainly, some wavefields correspond to kx ≥ 0, ky ≥ 0 and kx < 0, ky < 0.  If the imaging condition defined in formula 3.24 for imaging is used, it will be necessary to separate the incident wavefield and emergent wavefield on the reflection point before imaging.  That is to say, use the wavefield defined by wave vector symmetric to normal direction at a certain imaging point on the reflecting interface.  However, it is expensive to find a wavefield corresponding to the wave vector and there is no high‐efficient implement method yet.  This is a problem waiting for solution in reverse time migration imaging.  If the wavefield after reverse time extrapolation at the imaging point is just put into imaging according to the imaging condition defined by formula 3.25, there will be serious low‐frequency noise in the imaging result. 

### 3.4.2 Theory and application of Laplace filtering suppressing low‐frequency noise

#### 3.4.2.1 Theory of Laplace filtering suppressing noise

Research suggests using the Laplace operator to filter low‐frequency imaging noise.  It is known through analysis that the imaging noise is always low‐frequency, most of which belongs to DC component.  Therefore, the Laplace operator may be used to eliminate the noise component.  This method is quite simple and easy to keep the parallel structure of the reverse time migration. 

Laplace filtering operator in the time‐space domain is:

(3.26)

The second‐order differential of wavefield about _x_ may be approximately shown as follows:

The same with:

Thus coming to the following formula:

(3.27)

If h2 = Δx2 = Δy2 = Δz2, the above formula will be changed into:

(3.28)

From formula 3.28, it is known that the Laplace operator is a band‐pass filter, which is suitable to eliminate the noise component of low wave number as well as to suppress the imaging noise in reverse time migration.  It is practically realized in the time‐space domain.  In order to keep the signal phase unchangeable, it is necessary to add a minus sign before the Laplace operator in the time‐space domain. 

It is known through analysis that a filter may be designed to suppress low‐frequency noise in the (kx, ky, kz) domain, which brings problems and error in filter design, such as how to design the pass band and stop band.  However, direct use of formula 3.26 will result in out‐of‐control for differentiated elimination of low‐frequency component.  Under 2D conditions, Mulder and Plessix (2003) put forward the following filtering formula:

(3.29)

The above analysis lacks a geophysics concept.  In the following, we make a deep analysis on the Laplace operator filtering theory in terms of local plane wave propagation.  First, use the Laplace operator on both sides of the imaging condition, namely:

(3.30)

The above imaging condition is only imposed near the imaging point.  Assuming the incident waves and reflected waves at the imaging point P are local plane waves, their direction will be determined by ray parameters ps and pr respectively.  Formula 3.25 may be changed into:

(3.31)

The Laplace operator working on the imaging result is actually to filter the imaging result.  The filtering operator is:

#### 3.4.2.2 Numerical experimentation on Laplace filtering suppressing low‐frequency noise

In order to test the algorithm validity, we have designed a "NWGI" model to research several prestack imaging methods and the low‐frequency noise suppressing effect.  The observation parameters of the model: 250 shot, 120 traces per shot, shot interval of 40 m, trace pitch of 10 m, offset of ‐6000 **~** 6000 m, record length of 2.5 s, sampling point number of 1250, time sample rate of 2 ms, velocity field x direction range [500, 11475] m,dx = 5 m; dz = 400 m, dz = 10 m. The velocity model is shown in Figure 3.5. 

**Figure 3.5** NWGI velocity model. 

As the noise elimination effect is not ideal enough by directly testing Laplace filtering, we combining the noise elimination method   proposed by Mulder with the Laplace filtering together.  In the formula, n1, n2 and n3 refer to the noise elimination parameters.  In this model, the execution of Laplace filtering only once may obtain the best effect.  The more iterations S1 filter has, the narrower the data band will be (see Figure 3.6 and Figure 3.7). 

**Figure 3.6** Profile comparison before (a) and after (b) low‐frequency suppression of RTM imaging result (parameters [32, 0, 8], wavelet dominant frequency of 20 Hz). 

**Figure 3.7** Profile comparison before (a) and after (b) low‐frequency suppression for RTM imaging result of SEG/EAGE Sigsbee model (parameters [32, 0, 8]). 

Considering that the sigsbee model imaging is influenced by random boundary, which makes it unable to judge correctly whether the noise elimination method is good or not, we decided to use the Marmousi model as a test so as to get more obvious and visualized comparison (Figure 3.8). 

**Figure 3.8** The Marmousi model RTM migration result. 

The migration result of Figure 3.9 has high resolution ratio but poor artistic quality.  The result of Figure 3.10 is obtained by Muder noise elimination method with the parameters of n1, n2, n3 = (32,0,2).  It's clear that the filter method Muder proposed is actually to smoothen the result of Laplace filtering with operators.  Too many smoothening times will lead to too low dominant frequency on the profile. 

**Figure 3.9** The Marmousi model RTM migration result by applying Laplace filtering. 

**Figure 3.10** The Marmousi model RTM migration result by applying Muder noise elimination method, parameters [32, 0, 2]. 

## 3.5 Study and Application of RTM Prestack Imaging Algorithm based on the GPU/CPU System

### 3.5.1 Analysis of structural characteristics of the GPU/CPU platform

The CPU/GPU heterogeneous platform integrates the CPU process parallel with GPU threads parallel to realize the high‐performance computing.  In the CPU, there are 20% transistors used for the computation; however, there are 80% transistors in the GPU used for the computation.  The GPU multicore is divided into multiprocessors, and each multiprocessor contains eight processors.  From the point of actual computation, the computation density in the CPU is low, where a large number of transistors are used for control and logic operation, while the computation density in the GPU is high, where a large number of transistors are used for computation and only a few of them are used for control and logic judgment. 

Figure 3.11a shows the structural characteristics of the CPU and the GPU.  From the figure, we can see the basic framework difference between them: the CPU is characterized by a large memory, large cache, strong control function and less computing units; the GPU is characterized by a small memory, small cache, weak control function and multiple computing units. 

**Figure 3.11** Comparison of (a) the CPU structure features and (b) the GPU structure features. 

Figure 3.12 shows the details of the GPU structure, which is very important for the programming on the heterogeneous platform of GPU/CPU.  There will be no efficient and parallel programs unless the full consideration is given to the hardware.  For this reason, an understanding of the details of the GPU is the foundation for taking advantage of the performance of the GPU/CPU platform and the parallel computation.  Tesla architecture is centered on the scalable multithreaded flow multiprocessor array.  When the CUDA program in the CPU calls the kernel network, the network block will be concurrently connected to the multiprocessor with the available execution capacity.  The threads of a thread block are concurrently executed in a multiprocessor.  When the thread is ended, a new block will be started in the idle multiprocessor. 

The multiprocessor includes eight scalar processor cores, two special function units for transcendental function, one multi‐threaded instruction unit and the on‐chip shared memory.  The multiprocessor will create, manage and execute the concurrent threads in the hardware, with the scheduling overhead remaining zero.  It can realize the barrier syncthread via an internal instruction.  The combination of the rapid barrier syncthread with the light thread creation and thread scheduling of zero overhead effectively provides supports for the fine‐grained parallelism. 

In order to manage and operate the threads of different programs, the multiprocessor has used a kind of new architecture named SIMT (Single‐Instruction, Multiple‐thread).  The multiprocessor will map various threads to a scalar processor core that will make use of its own instruction address and register state to conduct an independent execution.  The SIMT unit of the multiprocessor creates, manages, schedules and executes the threads by taking 32 parallel threads as a group that is called the Warp Block.  Various threads composed of SIMT‐Warp Block are started simultaneously in the same program address, and they can also be branched at random and executed independently. 

**Figure 3.12** Architecture model of GPU hardware. 

SIMT architecture is similar to SIMD (single instruction and multiple data) vector organization mode.  They share the feature of controlling multiple processing elements by using the single instruction, while differing in that the SIMD vector organization mode will be opened to the software and the SIMT instructions appoint the execution and branching behavior of the single thread.  SIMT is different from the SIMD support vector machine in allowing the programmer to create the thread‐level parallel code for the independent and scalar threads and also create the data parallel code for the collaborative threads. 

In order to ensure accuracy, the programmer can ignore the SIMT behavior.  However, the performance can be significantly improved by minimizing the thread branches in a warp block.  Figure 3.12 shows the GPU hardware architecture.  The basic structure of each multiprocessor is a group of 32‐bit registers in every parallel processor.  It provides the shared memory space for parallel data cache, the shared memory, and the shared scalar processors.  The read only constant cache, shared by all scalar processors, can accelerate the reading operation from the constant memory, while the read only texture cache, shared by all scalar processors, can accelerate the reading operation from the texture memory.  Each multiprocessor can access the texture cache by realizing the different addressing models and data‐filtering texture units. 

### 3.5.2 Analysis of the application features of CUDA programming language in the GPU/CPU platform

The programming in the CPU can be in either series or parallel mode.  The parallel programming is based on the MPI language, which is a kind of information exchange control language of conducting the process programming in the CPU.  The programming in the GPU must be parallel in principle, a thread parallelism, which should be conducted in a information exchange control language.  The information exchange mode is quite different from the information exchange mode in the CPU.  CUDA is a special software of NVIDIA for GPU computation, providing a software development environment and tool.  CUDA core has three important abstractions: thread group hierarchy, shared memory and barrier syncthread.  These abstractions provide the fine‐grained data parallelism and thread parallel, nested within the coarse‐grained data parallel and task parallel.  While programming via the CUDA, the GPU is treated as the computation device that can execute many threads in parallel.  The GPU is operated as co‐processor of the CPU and the data parallel portion and computation‐intensive portion in the applications running in the host computer are loaded onto the GPU.  Specifically, the application program of executing the same operation to different data can be independently placed onto the GPU to serve as the function executed by different threads. 

The maximum number of threads to be contained in the thread block is limited.  However, the thread blocks executing the same kernel and with the same dimension and size can be combined into the grid of thread blocks to increase the number of threads initiated in the kernel calls.  This is realized at the expense of sacrificing the thread collaboration, because the threads in different thread blocks in the same grid can neither communicate with each other nor be synchronized.  The CUDA programming interfaces mainly include four categories:

  1.  Function Type Qualifier: used to specify the execution condition in either the host or the GPU, and the calling condition from either the host or the GPU. 
  2.  Variable Type Qualifier: used to specify the memory position of the variables in the GPU. 
  3.  New Instruction: used to specify how to execute the kernel from the GPU. 
  4.  Four Built‐in Variables: used to specify the dimension of the grid and thread blocks, as well as the index of thread blocks and threads. 

The GPU is treated as the computing device that can execute many threads via the CUDA programming in parallel.  There are many blocks in each kernel and each block contains many threads.  Thirty‐two threads are treated as a warp, which operates on a multiprocessor.  Each multiprocessor can operate multiple threads.  CUDA has provided the management mode of multi‐threaded coordination. 

### 3.5.3 Realization strategy of RTM prestack imaging based on the GPU/CPU

The realization process of reverse time migration can be expressed by Figure 3.13. 

**Figure 3.13** Reverse time migration flowchart. 

The principal computation amount of 3D two‐way wave equation single shot reverse time depth migration relies on the extensions of seismic source wavefield and geophone wavefield in time and direction, respectively.  In this migration algorithm, the seismic source wavefield belongs to the positive time propagation process, while the geophone wavefield belongs to reverse time propagation process, and they are imaged through the appropriate imaging condition in the same time.  Because of the difference of time and propagation directions of both seismic source wavefield and geophone wavefield, the common practice is to store the wavefield of one direction.  It is necessary to obtain a very large hard disk space to store the wavefield for the 3D migration.  In addition, the data I/O in the hard disk also has a big influence on the efficiency of reverse time migration.  Check‐point technique can reduce the I/O amount of the hard disk and improve the efficiency of reverse time migration, but it cannot solve the problem fundamentally.  Based on the analysis of the bottleneck existing in reverse time migration computation efficiency and memory, we realize that the wavefield reverse time extrapolation needs the maximum computation amount via the GPU upon the researches centered on the GPU/CPU.  Furthermore, we have solved the I/O problem of large‐scale memory under the concept of random velocity boundary, which helps to improve the parallelism of the wavefield extrapolation algorithm.  The correctness of algorithms and methods are verified via the theoretical model computation. 

#### 3.5.3.1 Efficiency issue in computation of reverse time migration (RTM)

It is crucial to compute whether the efficiency meets the requirements of actual 3D seismic data migration imaging.  We believe that special attention should be paid to the following four factors in computational efficiency of 3D reverse time migration: (1) The reverse time migration of synthesis plane shot gather should maintain at high efficiency, especially after considering the phase encoding technique. ( 2) The difference scheme should be an explicit scheme. ( 3) The difference scheme should be high‐precision, ensuring the application of the large grid will not decrease the computational accuracy. ( 4) The algorithm should be suitable for the parallel computation of the GPU/CPU heterogeneous platform. 

We believe that it is necessary to further optimize the commonly used high‐order difference scheme proposed by Dablain [19] on the basis of maintaining the explicit difference scheme.  The compact difference scheme is an option. 

The pseudo‐spectral method discussed above can be interpreted in details in the constant velocity medium.  After introducing the ideology of self‐adaptive lateral velocity variation, it can be used in the reverse time depth migration imaging.  This method can take the big time step size, which is very conducive to the reduction of I/O and memory space.  In 2007, Symes proposed recording the wavefields of two time horizons on the checking‐points to save the hard disk space of seismic source wavefield of the memory extrapolation.  In 2009, Liu Hong and Li Bo of the Chinese Academy of Sciences and Wang Huazhong of Tongji University carried out the reverse time migration researches based on GPU [23,24], and applied the random boundary idea [14], which enables the shot wavefield forward extrapolation process to avoid the big memory and magnetic disk I/O and obtain a high speed‐up ratio on the GPU/CPU platforms. 

#### 3.5.3.2 Memory problem and solution

Because the seismic source wavefield belongs to the forward extrapolation along the time, and the prestack shot recording wavefield belongs to the reverse time extrapolation, one of these wavefields must be saved for zero‐delay cross‐correlation between two wavefields.  This is the memory problem encountered by the reverse time migration.  Under the 3D case, the wavefield D( _t_ , _y_ , _x_ , _z_ ) to be saved is a huge data volume.  For the typical case of Nx = 2000; Ny = 1000; Nz = 1500; Lt = 3000, this wavefield belongs to a data volume of 3.6 T. It is not practical to memorize such a huge amount of intermediate data for reverse time migration of each shot. 

Symes [12] has proposed using check‐pointing technique to solve the storage problem, which divides the entire recording time Lt into tens of segments.  During the forward extrapolation along time in the shot wavefield, the absorbing boundary condition should be integrated.  This approach of sacrificing the computation amount to get the memory amount did not solve the storage problem fundamentally.  For this reason, Clayton and Engquist [13] have proposed using the approach of random boundary condition for the reverse time migration, which is quite suitable to the computing characteristics of the GPU/CPU, enabling the reverse time migration to reach the maximum speed‐up ratio in the GPU.  Relying on the GPU/CPU computing platform, the random velocity boundary model is used to propagate the trigger point wavefield to Tn moment, and then take the wavefield at Tn moment as the initial condition to back‐propagate the trigger point wavefield and receiving point wavefield; meanwhile, the imaging condition is used for the formation of images simultaneously.  This can avoid requiring additional memory space.  The wavefield extension by GPU, despite one more time of trigger point wavefield computing, is worthwhile in its time consumption compared with the large‐scale disk I/O reading and memory. 

#### 3.5.3.3 Realization strategy of RTM prestack imaging based on the GPU/CPU

The principal computation amount of 3D two‐way wave equation single shot reverse time depth migration relies on the extensions of seismic source wavefield and geophone wavefield in time and direction, respectively.  In this migration algorithm, the seismic source wavefield belongs to the positive time propagation process and the geophone wavefield belongs to reverse time propagation process, both of which are imaged through the appropriate imaging conditions (this project belongs to zero‐delay cross‐correlation) in the same time.  Because of the difference of time and propagation directions of both seismic source wavefield and geophone wavefield, the common practice is to store the wavefield of one direction.  For the 3D migration, it is necessary to obtain a very large hard disk space to store the wavefield, and the data I/O in the hard disk can also severely affect the efficiency of reverse time migration.  Check‐point technique can reduce the I/O amount of the hard disk and improve the efficiency of reverse time migration.  However, it cannot solve the problem fundamentally. 

The treatment of reverse time migration boundary conditions directly affects the imaging efficiency and effect.  PML boundary condition is regarded as the most effective technology for solving the artificial boundary problems.  The absorbing boundary condition causes the differential mode difference between the boundary and the central area, which generates no problem for CPU algorithm, but for GPU kernel function, the excessive branches will seriously affect its computing efficiency.  By introducing the random boundary conditions, the differential scheme of boundary area is identical to that of central area, which contributes greatly to the differential operation in the GPU/CPU heterogeneous platform.  Under random boundary conditions, the wavefield propagation process is reversible.  Hence, we can solve the reverse time migration I/O problem by sacrificing wavefield propagation.  That is to say, propagate the seismic source wavefield forward to the maximum time and then back‐propagate the seismic source wavefield and geophone wavefield simultaneously from the maximum time.  An imaging value should be taken for each step of propagation.  This method will avoid the memory on hard disk and improve the computing efficiency of reverse time migration accordingly.  The I/O problem of reverse time migration and the realization problem of GPU/CPU heterogeneous platform are solved by introducing random boundary condition.  Figure 3.14 shows the GPU realization flowchart of single shot reverse time depth migration of 3D two‐way wave equation. 

**Figure 3.14** GPU flowchart of reverse time depth migration. 

The cycle structure of single shot reverse time depth migration of 3D two‐way wave equation is shot cycle for the outermost layer and followed by time cycle in each shot; each time step is composed of 3D differential.  According to the characteristics of single shot reverse time depth migration algorithm of 3D two‐way wave equation, the GPU/CPU parallel algorithm is realized through the following strategies: the single shot cycle of the outermost layer is controlled by the MPI on the different nodes (CPU kernel) and realized via the process‐level coarse‐grained parallel.  Within each shot, the input/output of the data and other operations (stacking of imaging results for single shot, removal of low‐frequency noise, etc.),  apart from the wavefield extension and extraction of imaging value, are all completed in the CPU.  After completing the input of the data and the corresponding velocity field, the seismic data, wavelet and velocity field are copied to the GPU memory to complete in the GPU the single shot data time extrapolation cycle and the extraction of imaging value after each step of wavefield extrapolation.  The realization of the outermost layer single shot cycle in this realization strategy is identical to the conventional CPU single shot migration, while the unique difference lies in the wavefield extrapolation within each shot and the extraction of imaging value.  The differential computation can be completely transformed into the vector multiply issue, and its computation in the GPU can reach a high speed‐up ratio. 

**Figure 3.15a** Inline velocity model. 

#### 3.5.3.4 Numerical experiment of model data

In order to test the imaging accuracy of the algorithm, we use the 3D salt dome model to research several prestack imaging methods and applicability.  The observation parameters of the model data volume are: 4780 shots in all, 68 traces/shot, shot interval of 80 m, trace spacing of 40 m, time sampling rate of 8 ms and sampling number of 615.  The migration parameters of numerical experiments include: main frequency of 20 Hz, frequency range of 5 ~ 55 Hz; migration aperture: Aperture _x = 6000 m and Aperture _y = 3000 m; imaging output spacing: dx = dy = 20 m, dz = 10 m; migration aging comparison: total time consumption of 3510 min.  for 60 nodes CPU system; total time consumption of 298 min.  for 12 nodes GPU/CPU collaborative system (S1070).  Therefore, single node speed‐up ratio: GPU:CPU = 58.89:1.  Upon the trial, this algorithm has not only an efficient speed‐up ratio, but also the maximum imaging precision. 

Figure 3.15 to Figure 3.17 present the comparison of reverse time depth migration results of SEG/EAGE 3D salt dome model data in the CPU platform and the GPU platform. 

In the imaging results of these 3D salt dome model data, (a) is the corresponding velocity field slice, (b) is the imaging result of the CPU and (c) is the imaging result of the GPU.  It can be observed that the computation result of the GPU platform is correct.  In order to test the imaging accuracy of the algorithm, we have designed "NWGI" model to research several prestack imaging methods and their applicability.  The observation parameters of the model data volume include: 250 shots in all, 120 traces/shot, shot interval of 40 m, trace spacing of 10 m, migration domain of 6000 ~ 6000 m, recording length of 2.5 s, time sampling rate of 2 ms and sampling number of 1250, as shown in Figure 3.18. 

Migration parameters of numerical experiments include: main frequency: 18 Hz; migration aperture: Aperture _x = Aperture _y = 800 m; imaging output spacing: dx = dy = 10 m, dz = 10 m; total time consumption: 98 min./480CPU; GPU/CPU collaborative platform (S1070), 5.2 min./12 GPU for 250 shots; speed‐up ratio: GPU _ Time: CPU _ Time = 1:94.2.  This algorithm has not only an efficient speed‐up ratio on this trial, but also the maximum imaging precision, as shown in Figure 3.19.  From these figures, we can learn that the imaging of depth domain can restore the true structural form of the underlying stratum when the velocity model is accurate.  However, neither the reflection angle migration nor the one‐way wave equation migration realizes the accurate imaging for the special structure.  The reverse time migration can image the vertical stratum with an inclination angle of 90° through the accurate propagation of the wavefield with complicated velocity structure. 

**Figure 3.15b** The CPU migration result. 

**Figure 3.15c** The CPU migration result. 

**Figure 3.16a** The GPU migration result. 

**Figure 3.16b** The CPU migration result. 

**Figure 3.16c** The GPU migration result. 

**Figure 3.17a** Depth slice velocity model. 

**Figure 3.17b** The CPU migration result. 

**Figure 3.17c** The GPU migration result. 

**Figure 3.18** NWGI model (a) forward wavefield and (b) forwarded zero migration domain profile. 

**Figure 3.19** Comparison between (a) NWGI velocity model and (b) imaging results of different migration methods. 

#### 3.5.3.5 Actual data test

For the subsalt seismic exploration, the big difference between salt dome velocity and surrounding rock formation, and great lateral thickness change will lead to such problems as the complicated seismic wavefield, pseudomorph of time domain [25].  In view of the geological features of the complicated salt dome in onshore Block B, the multi‐well constrained seismic velocity modeling method [17] is used to establish the salt dome velocity‐depth model, as shown in Figure 3.20. 

The imaging technology of two‐way wave equation depth domain is used to solve the subsalt and salt dome flank imaging problems and realize the accurate positioning of salt dome boundary and salt dome flank.  It can eliminate the time‐domain structure distortion of the underlying stratum caused by salt dome velocity anomaly and image the subsalt stratum accurately in the depth domain.  The salt dome top interface, salt flank boundary and salt flank special subsalt structure over 90° can be imaged accurately, as shown in Figure 3.21. 

**Figure 3.20** Velocity‐depth model of multi‐well restrained inversion. 

**Figure 3.21** Imaging result comparison of (a) subsalt structure one‐way wave migration and (b) reverse time migration. 

Figure 3.21 shows the imaging result comparison between one‐way wave migration and reverse time migration.  In the imaging of one‐way wave, the back‐refracted ray energy of salt dome cannot be highlighted and the steep flank of the salt body cannot form the images (due to the limitation of algorithm dip) because of insufficient lighting.  The reverse time migration is used to treat the steep dip, back‐refracted ray energy and the energy from other two‐way ray paths, enabling the rotary structure and steep dip to accurately form the images. 

## 3.6 Conclusions

The seismic migration imaging has theoretically entered a new stage of accurate imaging that takes the reverse time depth migration as the imaging technology and takes the full waveform inversion as the velocity estimation technology and relies on the close integration of the two technologies.  The 3D reverse time depth migration technology has gradually entered the industrial application stage.  However, the 3D full waveform inversion estimation migration technology will still need some time to enter the industrial application stage. 

A high‐performance computer system is the material basis for achieving the above two technologies.  The ultra‐large‐scale multi‐core/many‐core CPU computer system and the GPU/CPU heterogeneous computer system have promoted the rapid development of modern seismic imaging technology.  In the CPU platform, the parallel computation is subject to the process‐level parallel, multi‐instruction flow and multi‐data flow (MIMD).  This belongs to the coarse‐grained parallel operation (compared to the thread‐level parallel).  Subjecting to the thread‐level parallel, the GPU/CPU heterogeneous platform multiplexes the single‐instruction flow and multi‐data flow on the basis of multi‐instruction flow and multi‐data flow.  On this heterogeneous hardware platform, the CPU executes the process‐level parallel and the GPU executes the thread‐level parallel.  The multi‐core/many‐core CPU computer system can achieve the multi‐core process‐level parallels in the Open MPI programming mode.  For this reason the current GPU/CPU heterogeneous platform can possibly be replaced by the many‐core CPU computing platform due to its unclear development trend.  In addition, another question in significantly raising the computing efficiency is whether the algorithm is suitable for the thread‐level parallel operation. 

We conclude that the aforesaid 3D reverse time depth migration computation plan we proposed, through investigating a large number of references or literatures and by constantly modifying the execution plan, is relatively more practical.  We proposed the feasible execution plan of 3D reverse time depth migration and applied it to the Pre‐Caspian Basin.  Through the treatment of prestack reverse time depth migration, the false image fs resulting from the salt dome pull‐up phenomena are effectively eliminated, thus the subsalt imaging accuracy is improved accordingly and the salt dome boundary imaging becomes clearer.  The true subsalt structural form can be implemented.  Through the mapping of limestone anomalous body in the east, the influence of pull‐up false image of anomalous body is eliminated and the accurate structural form is implemented.  Theoretically, the 3D reverse time depth migration is nowadays the most accurate imaging method.  This is the inevitable development trend of prestack depth migration imaging technology.  Its combination with FWI velocity estimation technology is the development direction of accurate imaging.  Currently, the GPU/CPU heterogeneous high‐performance computer platform and multi‐core/many‐core CPU high‐performance computer platform are the preferred tools of large‐scale numerical computation.  It is exactly their powerful computing capability that will enable RTM + FWI high‐accuracy imaging mode to enter the actual production field in the near future.  This technology has great application prospects. 

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#  4   
Study and Application of Velocity Model Building Method for the Areas with Complicated Structures

## 4.1 Introduction

Seismic velocity modeling is an inversion process.  In order to meet the needs of precise imaging and energy focusing on the reflection point, geophysicists proposed many migration velocity model‐establishing methods for depth‐velocity model.  The methods of velocity modeling could be categorized into ray‐based method, wave equation method and synthetic method in terms of theory basis, while they could also be categorized into common midpoint (CMP), common reflection point (CRP), common imaging point (CIP), common focus point (CFP) and common reflection surface (CRS) methods in terms of the utilized gather.  The migration artifacts may exist in CIP gathers that were built through conventional methods, thus influencing the quality and amplitude preservation of CIP gathers and precision of migration velocity analysis.  Therefore, we conducted study on wavefield continuation based gather building method in angle domain, on the foundation of generating gathers through conventional ray based method.  The angle domain gather, the relative dynamic characteristics and the underground reflection angle (an underground index property) are introduced in addition to previous ground property indexes.  It would solve the multipath problem in CIP gathers and preserve their characteristics effectively, thus enhancing the quality of CIP gathers, reducing migration artifacts, and increasing relative fidelity preservation of migration result to some extent. 

The velocity parameter is the key factor in each stage of seismic imaging.  Many factors would generate influence in the propagation velocities of seismic waves, including lithology, density, porosity and burial depth of underground medium.  The influence may be presented in the form of changes in seismic wave properties such as travel time, waveform, amplitude and phase.  More knowledge and understanding of the relation between velocity and influencing factors will help the precise description of the underground structure.  During the imaging in depth domain, the purpose of the velocity analysis is to build a layer velocity model that varies with depth‐spatial position.  This model is composed of main velocity layers, named "macro‐velocity model", which has direct influence on the quality of prestack depth migration imaging. 

In general, velocity modeling is established and updated during iterative computation of prestack depth migration, namely the velocity modeling is close to prestack depth migration computation, where the result will verify the correctness of velocity model at the same time.  Their relationship may be expressed as co‐existence and mutual verification.  The velocity is the core for migration imaging, while its correctness needs the verification in migration.  Compared with the prestack time migration and the poststack depth migration, the prestack depth migration is more sensitive to the change of velocity.  In complex structural zone, many problems that are difficult to solve may occur in velocity modeling, such as low SNR of seismic data, and complex field and uneven illumination of seismic wave.  The practice of velocity modeling is as important as its method.  Effective and rational constraint and quality control in all stages, from establishment of initial velocity model, to update of velocity model, would affect the timeliness of velocity modeling and quality of migration imaging. 

For the establishment of macro‐velocity model, we analyzed many conventional velocity modeling methods, including coherent inversion, depth domain focus analysis, residual migration velocity analysis and tomographic imaging.  Through the analysis of the velocity modeling from establishment of initial model to modification and optimization, we proposed a comprehensive velocity modeling method. 

## 4.2 Status Quo and the Development of the Velocity Model Building Method

Prestack depth migration is one approach to achieve precise imaging in complex structure.  The migration velocity is crucial to the realization of precise imaging [1] in addition to proper migration algorithm.  The precision of prestack depth migration imaging is directly subject to the precision of migration velocity.  Vcrstccg (1994) tested the sensitivity of prestack depth migration to velocity model by the Marmousi Precise Velocity Model.  From the test, he concluded, based on the migration image result after smoothing real velocity model, that obtaining precise depth migration results from precise data requires the minimum spatial wavefield for velocity model at 200 m [2].  Therefore, for establishing a precise velocity model based on complex seismic data, constraining the space of model to be tested will help to increase the convergence rate and probability of iteration speed algorithm.  As stated by Ticman (1995), conventional velocity analysis methods such as focusing analysis and weighted stacking will fail to work when there is horizontal velocity variation, and the effect of horizontal velocity variation should be considered while analyzing migration velocity [3].  The combination of conventional velocity methods and tomographic imaging will contribute to address the potential problem of horizontal velocity variation.  Therefore, a precise velocity model is of great importance to guarantee the precision of seismic imaging in complex structure. 

The establishment of a velocity model, originating from the initial velocity model, is a process of iteration and calibration to the initial velocity model based on a judgment method.  It is realized through gradual approximation and repeated iteration.  For the establishment of precise velocity model, the first step is to build a relatively precise initial velocity model, with such common methods as stacking velocity inversion, DIX transformation, VSP initial inversion, travel time tomography inversion and coherent inversion.  These are the main methods for prestack depth migration velocity modeling.  The precision of initial velocity model determines iteration times of further optimization and the rate of approximation toward real velocity model [4,5]. 

Initially, the stacking velocity was used to calculate the layer velocity based on DIX formula under the assumption that the formation belongs to horizontal layer or has a low dip.  The computation error may enlarge with the increasing of underground interface dip.  Gazdag and Sgvazzero (1984) proposed the layer velocity analysis method based on wavefield continuation to deal with sloping event [6].  Guo Shuquan (1987) increased the precision of layer velocity obtained from stacking velocity through offset calibration [7].  Mikenare (1988) realized the 3D layer velocity field based on iterative operation.  Zhong Muzu (1989) listed and made comparisons of four dip calibration methods in layer velocity computation, analyzed the causes of error, and proposed the template method for dip calibration, which can get the layer velocity approach to sounding velocity.  Ma Zhengming (1992) proposed the two‐stage ray tracing method [8] by improving the ray tracing test.  By this method, searching the minimum objective function is realized in two steps, which achieved the nonlinear tomography inversion layer velocity and accelerated the rate of iterative convergence.  However, this method requires more from users, hindering its wide application.  Wang Shanshan _et al_. ( 1994) proposed an inversion layer velocity [9,10] based on a hybrid method for wavefield computing and optimization method, by which, the velocity data of long wavelength was recovered and the convergence of velocity iterative inversion.  Kim _et al_. ( 1996) determined the velocity interface by ray migration and determined the precision of velocity by CMP trace gathers.  Higher efficiency can be obtained from establishing velocity model by combining the above two methods than by prestack depth migration.  In this way, the high migration rate can be realized. 

The precise velocity model is necessary for prestack depth migration.  In the migration process, the precision of the initial velocity model is as important as the initial velocity model itself.  Therefore, the study on the initial velocity model improving methods is also a crucial work.  Currently, the migration velocity analysis method based on CIP trace gathers is very widely applied for velocity optimization, such as Residual Moveout Analysis (RMA) and Depth Focusing Analysis (DFA).  The RMA method, taking the flattening principle of CMP trace gathers proposed by Al‐Yahya in 1989 [11] as the foundation, processed the data with prestack depth migration in the initial velocity model.  For one subsurface imaging point, the generated imaging trace gathers should be in the flattened shape if the migration velocity model is correct.  It means that the seismic traces with different offsets in trace gathers have the same depth.  Otherwise, it will be attributed to the existence of residual moveout.  If the seismic event bends up, the migration velocity is deemed to be over small, while if the seismic event bends down, the migration velocity is deemed to be too large.  The velocity field is updated based on the velocity error.  The DFA method is based on the rule that the zero‐time imaging depth is consistent with zero‐offset imaging depth proposed by Doherty and Claerbout (1974).  It is believed by this rule that it has an equal function during prestack depth migration to obtain the right depth value from migration under the wrong velocity model and to obtain the wrong depth value from migration under the correct velocity model.  Jeannot _et al_. ( 1986) extended the application of DFA method to prestack depth migration.  In 1989, Mackay and Abma confirmed that the DFA data could be used to obtain seismic profile with better focusing.  In 1992, they discussed the application DFA under the circumstance of intransformational horizontal velocity change existing in slope formation.  In 1993, they proposed a new DFA method that took the wavefront curvature as the focusing standard, which reduced the uncertainty in interpretation of focusing velocity analysis [12,13]. 

In order to improve the precision and accuracy of the velocity data, some new methods for establishing velocity model (like tomography (1991)) have been proposed in recent years, in addition to the previous two methods.  Li Luming and Luo Shengxian (1997, 1998, 1999, 2004) studied the wave equation prestack depth migration velocity analysis method and P‐SV transformation wave velocity modeling method, and they achieved excellent results in some 3D data depth migration.  Furthermore, Li Zhenchun _et al._ ( 2002, 2003) proposed the linear weighting method and the CIP gather migration velocity modeling method based on the perturbation method [14,15].  In recent years, with the computing capacity development of computer system, waveform inversion research began its application in time domain and depth domain.  It has made some good application effects. 

## 4.3 Impacting Factors for the Velocity Model Building

The velocity used in prestack depth migration is interval velocity field, and it is very difficult to obtain interval velocity from actual data directly.  Through years of study, the industry has found the solution.  Prior to prestack depth migration, an initial velocity model was constructed, and then a series of methods and means were used to optimize and iterate the initial model; finally, a velocity model approaching to the actual formation interval velocity was obtained [16,17].  The effect of prestack depth migration mainly depends on two aspects: the chosen migration algorithm and the velocity model used in migration.  Prestack depth migration is very sensitive to velocity parameters, and the incorrect interval velocities usually result in wrong results in prestack depth migration processing.  Thus, it is the key issue to establish a correct velocity model in prestack depth migration imaging.  Velocity modeling is the comprehensive analysis process of geological data.  The study on velocity modeling mainly focuses on two parameters: the interval velocity of formation and the geometries of the horizon bottom boundary.  Therefore, only when both the above parameters are determined would it be possible to obtain the required interval velocity‐depth model.  Many methods are available to obtain the interval velocity‐depth model, but besides the limitations on the algorithm itself, several other factors may play a role in this work.  For example, low SNR of seismic data will result in very high error of initial velocity model, and insufficient accuracy of model optimization method and static correction will impact the velocity modeling. 

### 4.3.1 The influences of initial velocity model accuracy on velocity modeling

Since it is very difficult to directly obtain the interval velocity used in depth migration from the actual data, iteration is commonly used in the optimization of a velocity model, that is, a predetermined initial velocity model is given prior to depth migration; under certain judging conditions, the velocity model is iterated repeatedly until the final velocity model, which satisfies the prestack depth migration accuracy, is obtained.  The accuracy of the initial velocity model determines the convergence speed of iteration optimization; the smaller the difference between the initial velocity model and the actual one, the fewer iteration times are required, and the faster convergence speed against the actual results is realized.  The larger the error is between the initial velocity model and the actual one, the more iteration times are required, and the slower convergence speed against the actual results is realized; sometimes, it even gives incorrect migration results.  Therefore, in order to improve the accuracy and efficiency of prestack depth migration imaging, the initial velocity model should approximate the actual subsurface conditions to the best extent to reduce the times of model optimization iteration. 

### 4.3.2 The influences of static correction on velocity modeling

In the most areas of Eastern China, the terrain is relatively smooth, and the thicknesses and velocities of low speed‐reducing areas are slightly changed laterally.  The conventional static correction methods are sufficient to correct the data of undulated surfaces against horizontal benchmarks, and the influences on velocity modeling and migration are slight.  However, in Western China, that is, the Tarim Basin, the Huoyanshan of Turpan‐Hami Basin, the Kulongshan of Yumen Jiuxi, and the eastern part of the Qaidam Basin, the surface undulation is significant and surface cutting is obvious, the near surface structure is complicated, the thicknesses and velocities of low speed‐reducing areas are obviously changed laterally, and the outcrops of high velocity old strata are observed in regional areas.  Therefore, static correction problem is the main feature of the data from western China.  Generally, static correction problem is solved through replacing the near surface velocity with base rock velocity. 

Actually, it is an approximate calculation.  When the lateral variation of subsurface media is moderate, such methods can solve static correction problems properly.  Whereas, once the lateral variation of subsurface media is significant, it can produce obvious error, and the accuracy of seismic data static correction is also impacted.  Due to the accuracy difference in subsurface structure inversion, various static correction methods will result in the difference in static correction calculations.  With undulated surface, seismic data processing is commonly conducted through correcting the seismic data to a relatively smooth floating benchmark, and finally the correcting from a floating benchmark to a fixed benchmark is realized.  Thus, the smoothness of floating benchmark also impacts the errors of gather velocity inversion.  During static correction processing, the quality of CMP gather used in velocity modeling is influenced by the extent of solution to static correction problem, and the accuracy of velocity modeling is also influenced. 

### 4.3.3 The influences of SNR on velocity modeling

Theoretically, prestack depth migration is the most ideal method for complicated structure imaging.  However, when the SNR of seismic data is low, the effectiveness of prestack depth migration imaging is usually not so good, and accuracy imaging of complicated structure is difficult to be realized, because: (1) During migration, the imaging method itself needs to use the seismic data with a certain SNR. ( 2) The velocity modeling method has limited capacity to overcome noise interference.  Whatever velocity modeling method is adopted, for example coherence inversion and DIX conversion methods, all of them construct a velocity‐depth model on the basis of input seismic data.  In 2007, Gou Liming _et al_.  studied the influences of noise on the accuracy of prestack depth migration interval velocity and summarized the influencing rules of noise.  There is a limit to the influence of SNR: when the SNR is beyond the limited value, noise has a small impact on interval velocity; when it is below the limited value, noise will obviously influence the accuracy of interval velocity estimation.  Furthermore, the interval velocity error increases rapidly with SNR decrease, and the declined value is approximately linear to SNR.  Therefore, the accurate velocity model is the key of successful prestack depth migration. 

### 4.3.4 The influence of prestack data irregularity on velocity modeling

Due to the irregularity of land seismic data acquisition, phenomena like uneven folds, uneven offset distribution and uneven bin distances, are frequently encountered in seismic data.  Figures 4.1 and 4.2 show the distributing map of bin folds and the distribution of a given offset of the same 3D acquisition data.  Not only are uneven distribution of folds observed on such figures, the uneven distribution of shot‐to‐geophone distance is also spotted.  In some areas, such offset is densely distributed, whereas it is absent in other areas.  Such irregularities will result in arc phenomenon on prestack migration gather or migration profile.  Such arc phenomenon is not caused by inaccurate migration velocity in migration processing.  During the residual delay analysis of the further updated velocity model, trying to flatten the "arc phenomenon" on gather as event upward‐bending, will result in incorrect residual delay analysis and further damage to velocity field data, and can even influence the final imaging results.  Therefore, once prestack data irregularity is observed, it is necessary to conduct prestack data regularization to ensure the even distributions of folds and gather energy, as well as the reasonable distribution of offset to avoid "arc phenomenon" in migration processing. 

**Figure 4.1** The coverage plat. 

**Figure 4.2** Distribution of pre‐regularization offset. 

**Figure 4.3** Distribution of post‐regularization offset. 

Figure 4.3 is the corresponding post‐regularization offset distribution map of Figure 4.2, and it shows that the offset distribution after regularization is more even, and the "cavity" phenomenon caused by offset absence in pre‐regularization data is eliminated, which is beneficial to further migration processing.  Figure 4.4 shows the pre/post‐regularizations prestack migration results conducted on gather.  Prior to regularization, serious arc phenomenon is observed on migration profile and the imaging is heavily influenced; while after regularization, the folds are evenly distributed and arc phenomenon on migration profile weakens obviously; the migration imaging becomes clear.  No doubt, such prestack depth migration gather will render more reliable velocity modeling results. 

**Figure 4.4** The migration effects comparison of pre/post‐regularizations. ( a) Pre‐regularization migration. ( b) Post‐regularization. 

### 4.3.5 The influences of geological body on velocity

From structural factors of geological body, the interval velocity is influenced by such factors as lithology, density, porosity, burial depth, pressure and geological ages.  Lithology is the main influencing factor on seismic velocity.  Based on huge amounts of statistical study, it is found that the high velocity bodies are usually carbonate, salt rock and anhydrite, while the low velocity bodies are generally sandstone and mudstone.  Porosity is another important influencing factor on seismic velocity.  Generally, as the burial depth (or overburden pressure) increases, porosity reduces and velocity increases. 

### 4.3.6 The influences of subsurface structural features on velocity

Formation occurrence, interface morphology and strata contact relationship play important roles on interval velocity.  As for horizontally layered homogeneous medium, the stacking velocity is nearly equal to the generalized root mean square velocity.  In this case, the error of interval velocity converted with DIX expression will be very small.  However, when the dip angle is relatively large, the stacking velocity must be multiplied by cosθ (θ is dip angle) to approximate the generalized root mean square velocity.  Therefore, as for the relative large dip angle, the calculated stacked velocity is quite big, and the inverted interval velocity is also quite big; at this time, the error of interval velocity converted with DIX expression will be very large.  The top of convex interface and the bottom of concave interface also play a role on velocity. 

As for successive geological structure, due to the downward bending of both wings of overburden structure, the moveout between CMP gathers is reduced, and the hyperbolic reflection events are relatively gentle.  Therefore, the calculated stacking velocity is quite big, and the inverted interval velocity is also quite big.  Conversely, when the seismic ray passes through the horizontal interface, the moveout between CMP gathers is larger than that when it passes through the bottom of concave interface.  In this case, the shape of hyperbolic reflection events is steep, the calculated stacking velocity is a little small, and the inverted interval velocity is also a little small, as shown in Figure 4.5. 

Additionally, geological phenomena like fault, thin layer and pinch‐out also play a role on velocity.  Since geological phenomena like fault, thin layer, thin interbed and pinch‐out can result in the tuning of interlayer reflected waves, this undermines the assumption that the reflection event moveout curve should be hyperbolic.  Both the calculated stacking velocity and inverted interval velocity are not able to represent the velocity of a single interval, and they are the comprehensive reflection of such tuning effect instead.  The size of velocity is related to interval thickness, as well as the amplitude, frequency and phase of the tuning. 

### 4.3.7 The influences of media lateral anisotropy on velocity

During conventional velocity analysis, the lateral changes of velocity in CMP gather are not considered.  Within large fault zones and the areas with abrupt change of sedimentary environments, the anisotropy of media undermines the hyperbolic pattern of reflect event, and the analyzed stacking velocity and inverted interval velocity may be obviously different from the actual velocity.  There is no perfect solution to such influence yet.  Numerous studies have focused on anisotropy velocity analysis and inversion, expecting some breakthrough to be achieved. 

**Figure 4.5** The schematic map of subsurface media. 

### 4.3.8 The influences of multiples on velocity

Due to the existence of multiples, especially with the development of interlayer multiple, the inverted velocity will present multi‐value and deception, which should be identified carefully.  Figure 4.6 shows that coherent inversion has produced two coherent peaks, and two sets of velocities will also appear along the interval residual delay spectra.  As shown in Figure 4.7, careful discrimination is required to discern the energy and velocity of primary reflection. 

**Figure 4.6** Inversion coherence capacity of interval velocity. 

**Figure 4.7** The inverted interval velocity spectrum. 

### 4.3.9 Analysis of the accuracy of various velocity calculating methods

Velocity information is mainly obtained through the following ways: (1) The stacking or migration velocity in seismic data processing. ( 2) The interval velocity and mean velocity obtained in VSP (vertical seismic profile) data. ( 3) Sonic velocity obtained in sonic logging and dipole shear wave logging. ( 4) Pseudo mean velocity obtained from calibrated seismic horizon and drilling geological stratification. ( 5) Interval velocity and mean velocity inverted by prestack gather (or stacking velocity).  Based on the measures of velocity acquisition, it is analyzed that pseudo mean velocity has the highest longitudinal accuracy, followed by the inverted CMP gather velocity and mean velocity obtained from VSP and sonic logging; the mean velocity or interval velocity obtained from stacking velocity using DIX expression has the lowest accuracy.  By analyzing the aforesaid seismic velocity influencing factors, it is known that many factors can play a role in velocity.  Only when such factors have been analyzed would it be possible to overcome or bypass disadvantageous factors and improve the accuracy of seismic velocity modeling.  Through study, it is found that seismic velocity is able to control the lateral changing rules of velocity, but its longitudinal accuracy is low.  VSP, sonic velocity and pseudo mean velocity have high longitudinal accuracy, but are weak in controlling the lateral changing rules of velocity, and their resolution is low.  Therefore, both of them should be combined in seismic velocity modeling.  The interval velocity inversion under multi‐well constraint shall be adopted to improve the longitudinal accuracy of velocity and control the lateral change of velocity. 

The velocity modeling is also influenced by factors such as processing experiences and understanding the geological conditions of the research area.  Thus, velocity modeling is a comprehensive analyzing, studying and treating process.  Velocity model is constructed on the basis of perfect prestack data and on the premise of correct initial velocity model.  Based on migration velocity modeling tools and geological/logging data, as well as fully considering various influencing factors on velocity modeling, an accurate velocity model is provided for prestack depth migration imaging. 

## 4.4 Study and Application of the Seismic Velocity Model Building Method

The migration algorithm is not the only key factor influencing prestack depth migration imaging, and the migration velocity model plays a more important role.  The correctness of the velocity model is directly related to the success of migration imaging.  The largest difference between time migration and depth migration is how to make use of velocity accurately.  Time migration adopts the imaging velocity field, that is, the velocity field that produces the optimal migration imaging at each output position.  Such velocity field will remain unchanged with positions.  When a wave equation is used to migrate the surface recorded reflection data to the subsurface position, the potential non‐uniformity processing of velocity field may sometimes result in disappointing time migration results.  In fact, assuming that the imaging velocities are root mean square velocities, when they are translated into interval velocities with DIX expression (Dix, 1995), it commonly renders a velocity value that is unrealistic in physics.  However, such inconsistency doesn't bring too large an impact because the purpose of time migration is to produce image rather than the geologically effective velocity field. 

Depth migration adopts velocity field, that is, subsurface geological model, which is the mean value of actual earth velocity.  It enables depth migration to simulate subsurface seismic characteristics more accurately than time migration.  We can treat depth migration (especially prestack depth migration) as a velocity estimation tool.  The commonly used modeling method aims at disturbed velocity field, until a "seemingly geologically logical" model is constructed and the ideal imaging is generated, which means the events of prestack migration common imaging gathers should be as level as possible.  Velocity modification can be performed by means of simple velocity spectrum scanning, relatively complicated tomographic imaging velocity analysis, manual compiling based on geological model, or the combination of all these methods.  It is a pity that some incorrect velocity models can still result in an ideal image with flattened gathers (Stork, 1992).  As for migration, if a multi‐path arises from a diverging ray of velocity field, even the correct velocity model is not capable of generating a consistent flattened gather (Nolan and Syrnes, 1996).  In fact, the velocity estimation is guided by geological data to ensure the ultimate results are "geologically logical".  Depth migration is a processing procedure, and also an interpretative processing at the same time. 

Velocity estimation by depth migration has become one of the largest challenges for geophysicists.  In the past, it was expected that prestack depth migration could improve the accuracy and reliability of velocity estimation, and maintain the interval velocity error within 5%.  Currently, it is impossible to realize such a target under general conditions.  Velocity anisotropy is also one of the problems (Bank, 1984), and the improvement on the estimation of velocity anisotropy is also helpful in increasing velocity accuracy.  Assuming that the simplified form of anisotropy is adopted, that is, weak lateral anisotropy (Thomsen, 1986), the difficulty in velocity estimation is still larger than that in the past, because we have to evaluate 3 "velocity" fields and possibly 1–2 angle fields that are used to determine the symmetry axis of anisotropy.  If the correct velocity is adopted, depth migration generates a precisely positioned structural imaging.  During the actual process, failing to predict the accurate position of target interval generally doesn't represent the inherent drawbacks of the method itself; on the contrary, it indicates our inability in velocity estimation.  Even the given velocity field is not accurate enough; the inherent physical fundament of depth migration still ensures its imaging is more accurate than that of time migration in structure.  Meanwhile, the quality inspection of interval velocity is still practical on the basis of depth migration.  Depth migration is a powerful interpretative processing tool, and its migration results are better than that of time migration in understanding geological structure and velocity field construction. 

Travel time tomographic imaging attempts to project the offset dependent residual time difference to the ray path connecting subsurface position, source and geophone.  Tomographic imaging has made great progress in velocity estimation methods, which is obviously better than these simple methods based on vertically modified velocity.  In order to construct an accurate velocity model, we adopt mutual calibration among several velocity inversion methods to determine the suitable velocity model.  In shallow/mid‐deep layers, the combination of CMP coherence inversion interval velocity and stacking/inversion interval velocities is adopted to construct the velocity model.  As for deep layers with energy diffusion, RMS velocity conversion and cycling methods are adopted to construct the velocity field.  Aiming at the velocity modeling of complicated structure, we put forward the technology of multi‐information restricted interval control velocity modeling.  The main velocity modeling methods will be introduced here. 

### 4.4.1 Modeling method based coherence inversion velocity

During interval velocity inversion, the generated time model and equalized CMP gather are used as the input values, and the interval velocity is estimated point by point along the time model.  In fact, the coherence inversion velocity calculation is a ray tracing process, under the principle of giving out the parameters describing the distributing scope of such interval velocity.  First, the minimum interval velocity and maximum interval velocity providing the scanning step of interval velocity at the same time, which means a series of interval velocity values are provided.  As for a given velocity value, the time interface corresponding to this gather is converted into depth interface and migrated to its original position by virtue of ray migration.  Thus, such velocity is used to form a series of velocity‐depth models.  Ray tracing is applied to these models, and a series of CPM gather time difference curves are calculated by forward modeling.  Each curve corresponds to an interval velocity.  The maximum value of coherence function is calculated along the non‐hyperbolic travel time curve that was obtained from the ray tracing calculation of CMP gather.  Equation 4.1 is the calculation formulation of coherent inversion, with its detailed mechanism shown in Figure 4.8. 

(4.1)

Where, W is the length of time window; N is the folds of CMP gather; _t_ ( _k_ , _**υ** r_) is the time difference curve corresponding to interval velocity _**υ i**_; _coh_ ( _ **υ** i_) means the coherence function value corresponding to interval velocity _**υ i**_. 

The realizing process is as follows: first, pick up the main time horizon on horizontal stacking profile; then choose the position of CMP point, calculate velocity spectrum and conduct velocity analysis within a certain time window along the picked‐up time horizon.  Such a process starts with ground level and proceeds layer by layer.  Assuming that the interval velocity model of the upper layer _n_ ‐1 is already determined, the interval velocity model of layer _n_ can be calculated as per the following steps: (1) Conduct ray migration at the time horizon of layer _n_ with a testing velocity to obtain the depth interval of layer _n_. ( 2) Choose a certain CMP point, conduct ray tracing at the depth interval of layer _n_ with the same testing velocity, and forward a travel time curve that corresponds to this interval and has actual CMP gather parameters. ( 3) Pick up a time window at CMP gather along the travel time curve obtained in step 2, and calculate the similar function between the forward travel time curve and the event travel time on the actual gather in this time window. 

**Figure 4.8** Schematic diagram of coherence inversion. 

Repeat the above steps with a series of testing velocities to obtain a series of approximate values.  Among them, the velocity corresponding to the maximum approximate value is the actual interval velocity of layer _n_ at that point.  The same method can be used to calculate the interval velocity of random CMP or at CMP points with a certain interval.  Conduct poststack depth migration on stacked profile with calculated interval velocity to obtain the final depth position of layer _n_ , as shown in Figure 4.9. 

**Figure 4.9** Obtaining interval velocity with coherence inversion method. 

The principles and method of calculating velocity with a combination of model forward and inversion are essentially different from the method of obtaining velocity from the maximum stacking energy of CMP gather through hyperbolic dynamic correction (velocity spectrum method, which is used in conventional seismic data processing).  The basis of velocity spectrum method is as follows: within one gather length, as for the homogeneous medium with horizontally layered or monotonously inclined subsurface occurrence, all the descriptive time‐distance curve equations rely on this basis.  Obviously, such time‐distance curve equations can't describe the subsurface conditions with relative large dip angle or heterogeneous single layer velocity within one gather length, so the velocity obtained with velocity spectrum method is only an approximate value.  However, the method of combining the model forward and inversion solves this problem radically. 

The detailed practice of coherence interval velocity inversion method is to choose a CMP position for each seismic line and each horizon, and define an interval velocity scope and the scope of offsets; calculating the coherence value and the interval velocity corresponding to the maximum coherence value is just the required interval velocity.  The interval velocity analysis is carried out from shallow layer to deep layer step by step.  The advantages of coherence inversion velocity modeling include: (1) Based on ray tracing theory and suitable for any occurrence. ( 2) Eliminates the application of DIX expression. ( 3) Eliminates the application of hyperbolic theory assumption.  It also has some disadvantages: heavily relying on the SNR of CMP gather data; if such SNR is high, the velocity tracing and interpreting are easy to conduct; if the SNR is low, the velocity is difficult to interpret due to coherence spectrum diffusion. 

The entire ray tracing inversion process is carried out in 3D space, and the inverted interval velocity is returned in 3D space.  Meanwhile, it solves the problem that velocity in a 2D working area can't be returned in 2D space.  Thus, compared with DIX conversion, this method is capable of obtaining a more accurate inverted interval velocity.  Additionally, it also has two shortcomings: (1) Assuming that the regional velocity within a prestack CMP gather (fan ray area) is constant, when the lateral variation of velocity is obvious, it is difficult to reflect such variation, and easy to produce unstable inversion result and error; by way of infilling velocity inversion points and reducing velocity steps, such inversion results can reflect the lateral variation of velocity to the most extent. ( 2) The accumulative error of inversion can be successively amplified interval by interval, which results in the diffusion of deep interval velocity and obvious error.  As for the first interval, the accumulative error is small, as shown in Figure 4.10.  However, due to the propagation of velocity error in the upper interval, rock bed thickness and anisotropy, the velocity undulation of the second interval is obvious (as shown in Figures 4.11a and 4.12a).  In order to solve this problem, we adopt the method of single layer interval velocity inversion.  Figures 4.11b and 4.12b show that the velocity longitudinal undulation caused by error propagation of single interval inversion and other reasons has been solved perfectly. 

**Figure 4.10** Interval velocity inversion of the first interval. ( a) Model data. ( b) Actual data (anisotropy assumption). 

**Figure 4.11a** Successive interval velocity inversion of the second interval. 

**Figure 4.11b** Interval velocity inversion of the second interval. 

### 4.4.2 Constructing velocity field with root mean square (RMS) velocity conversion and cycling method

The construction of prestack depth domain interval velocity model is based on the initial model of time domain migration velocity, with the initial interval velocity obtained through RMS interval velocity conversion.  Prestack depth migration of seismic data is conducted with the initial interval velocity model, so as to obtain the CRP gather at depth domain velocity control point.  However, due to the improper initial velocity, the seismic reflection event at depth domain velocity control point gather is not always flattened.  Convert initial velocity CRP gather into time domain through time‐depth transition.  Within the depth domain, residual velocity rectification is conducted on the RMS velocity corresponding to initial interval velocity, so as to obtain the modified RMS velocity.  Then convert the new RMS velocity into depth domain to obtain a new interval velocity model, on which a migration calculation is conducted to get a new cycle of velocity control point gather.  After several times of interval velocity iteration, the final CPR gather event is flattened and proper interval velocity model is obtained.  The velocity analysis flow is shown in Figure 4.13. 

**Figure 4.12a** Interval velocity inversion of the second interval. 

**Figure 4.12b** Successive interval velocity inversion of the second interval. 

**Figure 4.13** Flow chart of prestack depth migration velocity analysis. 

### 4.4.3 CIG gathers velocity modeling

In 1989, Al‐Yahya proposed the concept of Common Image Gather (CIG) residual curvature analysis [18–20], which determined the validity of velocity models based on the leveling degree of CIG.  This method connects the velocity analysis closely with migration imaging, and the effect of dip angle is eliminated in migrated gathers.  Moreover, both multiples and diffracted waves are suppressed, which results in high SNR of gathers and is helpful for velocity analysis.  The basic steps of CIG gather velocity analysis are as follows: first, fix a CIP; second, carry out migration imaging to shot and gathers around the point; third, select and arrange gathers from the migrated imaging of shot and gathers related with CIP to obtain the CIP gathers.  The imaging velocity will be considered valid if the event of imaging gathers is leveled. 

The migration velocity modeling of CIP gathers is based on prestack depth migration, seismic tomography (ST) and depth focusing analysis (DFA).  In DFA, the migration velocity is deemed to be reasonable when there is no error between migration depth and focus depth.  Otherwise, the migration velocity should be corrected based on the error. 

CIG velocity modeling is competitive in terms of: (1) The dispersion of inclined bed reflection point is eliminated after depth migration. ( 2) The velocity analysis can be operated with horizontal change of velocity when the migration velocity approaches the real velocity, as the method is not affected by structure. ( 3) The velocity analysis can be operated in each interval using wavefield extrapolation.  The disadvantage is that this method is hardly adapted to regions with complex structures, as the method is designed for horizontal layered medium; in complex structures, the obtained velocity is just an average velocity. 

### 4.4.4 Velocity modeling by seismic tomography (ST) method

The velocity calculation through ST velocity modeling was first proposed by Stork (1992).  This method, working based on tomography of prestack depth migration CRP gathers, can correct the velocity‐depth model if error exists in the velocity model for depth migration.  The leveling degree of gathers (i.e. residual moveout) can be used to test the error of velocity model.  The measured residual moveout is used as input in tomography to find out an appropriate model, so as to minimize the velocity model error [1–5,21]. 

Assuming a 2D subsurface interface model, the tomography believed that the model is composed of a number of strata separated by reflection interface.  Thus, for the ray path of reflection event from NL interface, the integration for travel time along the ray is as follows (Madriage and Farra, 1998). 

(4.2)

Where, SL(x,y) is the slowness of medium.  If there is minor slowness perturbation,   is used to represent the vertical slowness change of ray between points just above and below the interface, and the expression for change of travel time is:

(4.3)

Where, the section   is also presented in tomography based on conventional methods; the section   represents the change of travel time caused by the adjustment of interface in details, as shown in Figure 4.14.  It is assumed that δZ represents the vertical depth change at point A; ΔPz = (cos _θ 1_ \+ cos _θ 2_)/C, C represents the velocity above the interface; _θ 1_ represents the angle between incident ray and vertical direction, and _θ 2_ represents the angle between emergent ray and vertical direction, which are shown in Figure 4.15.  Therefore, the travel time change δt caused by depth change is calculated with equation 4.3.  Then:

**Figure 4.14** Transformation from depth error to time error. 

**Figure 4.15** Vertical slowness angle at reflection point. 

(4.4)

The expression for scaling depth change δZ to time change δt is as follows:

(4.5)

Then we can have:

(4.6)

The relation between δt and δτ is expressed in equation 4.6, which transfers the depth error of prestack depth migration gathers to the time error of a pair of CRP ray from reflecting layer. 

In the equation, a stretching factor representing the relation between δt and δτ is used to transform the depth error of prestack migration gathers to time error of a pair of CRP ray from reflecting layer.  This transformation can utilize the time tomography of depth migration gathers, and input it as δt of all CRP gathers and offset to replace δz. 

If the velocity model is incorrect, the event of CRP gathers will not be leveled and there will be residual curvature (Figure 4.16).  Through analyzing residual velocity along the interval, the velocity model is corrected and optimized by the tomography method until the CRP gathers of target layer are leveled and the residual delay approaches zero, which are shown in Figures 4.16 and 4.17. 

**Figure 4.16** CRP gathers (a) before model optimization and (b) after model optimization. 

Compared with the layer stripping method, the tomography method, as a global method, transfers the time error at one point to the error of velocity and depth at the other point.  Thus, the tomography method is an overall velocity model.  If there is error in shallow layers, the layer stripping method would make the error accumulate in deep layers on the profile, while the tomography method would simultaneously update both shallow and deep layer models.  The tomography method is composed of the tomography based on layers and the tomography based on grid, both of which share the methods of updating model parameters (depth and velocity) through solving a series of equations.  The differences between them lie in the spatial distribution and allocation of input data (residual moveout) and their updating types.  The tomography based on layers requires acquiring the residual moveout along subsurface interface depth‐velocity model and updating depth interface and velocity of each layer, and then the updated parameters, are calculated with the same spatial interval to interpolate. 

The tomography based on grids does not need the model data, but it can be displaced with tomography interval or added with the surfaces model.  A complete depth interface is not necessarily defined in the interval, but defined in partial reflection interface identified during depth migration imaging.  For grid tomography, the updated amount of velocity is calculated in grids with the same interval and the velocity will be updated accordingly.  However, for tomography along the layer, the velocity is only updated in the layer with delay.  The grid‐based tomography is very effective where the velocity defining method based on horizons is not applicable.  For example, in very complex structural zone, it is difficult to define the subsurface initial velocity model. 

Only after repeated iterations based on grid tomography and migration, will the velocity model become clear.  When it is easy to determine the velocity of shallow layer and difficult to determine the velocity of deep layer (subsalt imaging), it is also hard to establish a consistent velocity model because of low SNR.  At this point, it is necessary to establish the velocity profile without establishing the model.  In practical velocity modeling, it would be better to combine the two methods.  For example in subsalt structure, it needs to define salt model and keep constant velocity, where the grid tomography is applicable. 

**Figure 4.17** Comparison of horizontal delay before and after model optimization. 

### 4.4.5 Velocity modeling of CFP gathers

In 1994, Common Focus Point (CFP) was developed by Berkhout _et al_.  from Delft University of Technology (Berkhout and Rietveld 1994).  CFP is a data‐driven process and its initial purpose was to realize imaging by avoiding velocity model.  In 1996, Kabir _et al_.  applied the method in velocity analysis.  The CFP migration common focusing imaging is a double focused imaging method based on emission focus and detection focus, and its outcome is depth migration profile of one‐way travel time.  Moreover, the seismic imaging method, one method based on equal travel time principle, realized the structural imaging and lithologic imaging based on zero travel time imaging principle in temporal‐spatial domain and zero intercept travel time imaging principle in Radon domain (Li Zhenchun _et al_.  2003), respectively.  During CFP migration, the migration velocity analysis and modeling can go on simultaneously.  One method is to approximate velocity through parameter constraint iterative inversion based on equal travel time principle and DTS analysis; the other method is to obtain the real focus operator based on symmetry of phase error in Radon domain, and compute the migration velocity field through velocity scanning and global optimization [6–14]. 

The CFP gather migration velocity modeling is to realize velocity modeling on the basis of equal time principle, CFP migration and forward modeling, namely analyzing the differential time shift (DTS) between time‐inverse focus operator and CFP response.  If the differential time shift (DTS) is over zero, the travel time error can be transferred to updated velocity model parameters.  The new focus operator and CFP focusing gathers are generated through iteration.  Then, develop the cross‐correlation between CFP gathers and time‐reverse focusing operator to obtain new differential time shift (DFS) until the CFP gathers are leveled when t = 0.  CFP gather velocity modeling is realized through layer stripping.  From the first layer, the velocity model is computed in the following steps: (1) Calculate the synthetic focus operator and time‐reverse operator using ray tracing method and wave equation. ( 2) Obtain the CFP focus gather by convoluting the synthetic focus operator and real single shot record. ( 3) Calculate cross‐relation time difference of CFP gathers and time‐reverse focus operator, obtain differential time shift, and determine whether DTS is zero. ( 4) If differential time shift is not zero, update the velocity using iterative inversion, and repeat steps (1)–(3) using updated velocity model; (5) realize CFP focus migration; if the differential time shift (DTS) is zero, go to step (5). 

The migration velocity modeling (using the first velocity modeling method) and migration results of seismic data in the Pre‐Caspian Basin are shown in Figure 4.18.  Figure 4.18a shows the velocity field after CFP modeling, and Figure 4.18b shows the result of CFP prestack migration of velocity field.  It can be observed from these figures that the effectiveness of velocity modeling is excellent and its modeling result is consistent with migration results. 

The advantages of migration velocity modeling using CFP gather include better convergence and effectiveness, while the disadvantage is in the proper parameter velocity function selection; the wrong parameter velocity function would result in wrong velocity model. 

**Figure 4.18** Field example of CFP modeling and imaging, where (a) is the velocity field after CFP modeling, and (b) is the CFP prestack migration profile of the corresponding velocity field. 

### 4.4.6 Multi‐information restricted interval control velocity modeling method

Seismic velocity modeling is a comprehensive multi‐source information analysis process [22].  Most velocity field analysis is based on ray tracing theory.  The construction of velocity model is related with geological structure.  There are two difficulties in seismic velocity modeling for complex structures: (1) For near‐surface complex zone in Western China, it is difficult to obtain the velocity structure of shallow layer based on reflected wave inversion velocity model. ( 2) It is difficult to reflect the change of small‐scale structure around wells in complex structural zone only through building velocity field by reflected wave seismic velocity.  Thus, we build a precise velocity model constrained by multi‐source information by integrating the small‐scale refraction, micro‐logging information and well velocity [23]. 

#### 4.4.6.1 Integrated velocity modeling method combining first arrival wave inversion and reflected wave inversion

The minimum offset in field seismic record is not always small enough, and the folds of seismic data in shallow layers are extremely low.  Therefore, it is hard to gauge the potential of seismic data processing.  Because of the influence on shallow layer data from refraction waves, surface interference and high frequency noise, and the dynamic correction, stretching and removal to gather data during stacking, shallow layer information is missed in gather data and poststack data.  Thus, the velocity modeling using the data of reflection wave cannot precisely reflect the velocity structural model and formation information of shallow layer.  There is an error accumulation effect in the depth migration velocity model, so depth migration requires higher accuracy of velocity of the shallow layer.  Therefore, we are searching for the seismic velocity modeling method that can enhance the SNR of seismic data of shallow layer. 

### _4.4.6.1.1 Current study situation_

Qin Ning _et al_.  proposed the tomography velocity inversion method based on undulated ground surface, acquiring angle domain CIP gathers by using Gaussian beam migration.  It does not make the static correction to data as required by conventional processing.  Instead it directly updates the velocity field from undulated surface.  Some researchers carried out fine velocity modeling for shallow layer, based on waveform inversion of first arrival wave, and the tentative calculation showed that the detail of surface velocity model can be built well by this method.  Although researchers have presented their methods and have obtained some effectiveness, they cannot satisfactorily solve the problems of low SNR and low fold of shallow layer data.  Hence, enhancing the accuracy of a velocity model of the shallow layer is still a tough problem. 

There is low deceleration zone in the surface in seismic exploration, where an excellent refracting interface forms because of velocity and density differences.  When the geophone offset reaches a certain distance, it is easy to receive the refracted first arrival wave from refraction interface.  During seismic data processing, the refracted waves are cut off as interference wave.  However, the first break of refracted wave has the highest SNR.  In the area with complex surface and low SNR, the first break of refracted wave is the effective information for obtaining velocity of the shallow layer.  The first arrival time contains the geophysical information of formation.  Static correction of first break refraction method needs to acquire the top of high velocity interval, which represents the real subsurface velocity change interface.  The depth migration needs a precise subsurface velocity model, but the gathers for prestack migration lack the information because of removal of first break.  Thus, a combination of the calculation result of refraction static correction and prestack depth velocity modeling can make up the missing velocity information and display the real formation and velocity structure, enhancing the accuracy of prestack depth migration modeling and migration imaging. 

### _4.4.6.1.2 Technical route_

It is difficult to obtain a reliable velocity model for shallow layers through refracted wave.  However, the velocity accuracy can be improved in deep formation through repeated iterative optimization of velocity model.  The velocity and depth of the bottom of ground surface low deceleration zone can be determined based on the first arrival wave.  This chapter looks at a velocity modeling method integrating the first arrival wave inversion and refracted wave inversion, which is used to enhance modeling accuracy during prestack depth migration velocity modeling of seismic data in a complex area.  In this way, the velocity model can reflect the velocity change of subsurface medium, enhancing the accuracy and quality of prestack depth migration imaging. 

The method calculates the velocity value and spatial depth of the top of high velocity interval below low deceleration zone near ground surface through first arrival wave tomography inversion near‐surface modeling, which reflects the change of some velocity structures between near‐surface and high interval.  In addition, the interface of high velocity interval actually exists.  The method can make full use of depth and velocity of high velocity interval top interface that was obtained from near‐surface velocity modeling, and input the information of high velocity interval top into depth migration velocity modeling through the combination of program translation and reflected wave velocity modeling.  In this way, it can address the problem of missing velocity interface information in the gathers for prestack depth migration due to low SNR, low folds and refracted wave removal.  Therefore, accurate inversion of shallow layer velocity can be achieved.  In this way, a comprehensive velocity model can be built, which integrates first arrival wave modeling with depth migration modeling, as shown in Figure 4.19. 

**Figure 4.19** Flow chart of comprehensive modeling combining first arrival wave with reflection wave. 

### _4.4.6.1.3 Combination of high velocity interval top and velocity model_

Since the gathers used for prestack depth migration lack the velocity information of shallow layer, the velocity of first layer is used to fill the accuracy which affects the velocity model.  The velocity information of shallow layer is obtained through inversion of first arrival wave.  During prestack depth‐velocity modeling, the velocity model of first arrival wave inversion is added to depth‐velocity model as a control layer to obtain the whole subsurface velocity structure, as shown in Figure 4.20.  Therefore, the change of real velocity interface is recovered to obtain the complete and fine subsurface shallow layer velocity structure.  The formation of velocity needs establishment of the initial model and optimization of the velocity model.  The depth migration velocity modeling goes from shallow layer to deep layer, and the validity of shallow layer velocity will determine the accuracy of deep layer velocity.  Thus, the velocity model of medium and deep layers is built based on the high quality shallow layer model, establishing the initial interval velocity‐depth model in this way. 

**Figure 4.20** Inverted shallow layer velocity model Velocity unit:m/s.

However, in the complex structural zones with well‐developed faults, it is difficult to obtain the precise interval velocity for modeling by using the above method.  First, we verify the validity of the above method based on the data of theoretical model.  The true velocity model and depth migration result of undulating surface is presented in Figure 4.21.  It can be seen from the figure that the depth migration of undulating surface will reflect the real subsurface structural features when the velocity model is correct. 

**Figure 4.21** (a) True velocity model and (b) depth migration result. 

As shown in Figure 4.22, the shallow layer model near ground surface and the top of high velocity interval is determined through first arrival wave inversion, and then a new velocity model is generated by integrating it with the reflected wave inversion velocity model.  The imaging result in depth domain shows poor effect, mainly because of unstable high velocity interval top.  Thus, it needs human‐computer interaction to determine the location of top interface of high velocity interval and form the horizon of high velocity interval top interface, as shown in Figure 4.23. 

**Figure 4.22** (a) Velocity model of inversion shallow layer and (b) depth migration result. 

**Figure 4.23** (a) Shallow layer velocity inversion model and (b) depth migration result. 

Usually, we utilize the replacement velocity to find an equal velocity interface in velocity model and smooth the interface, and then obtain the top of high velocity interval, as shown in Figure 4.23.  The green line in the figure represents the position of velocity interface.  We interpret and compile the equal velocity interface to form a new velocity interface based on the trend of velocity change.  All low deceleration zones should be kept above the top of high velocity interval.  Smooth the velocity interface to make the velocity change rational in geophysical sense.  Generally, we determine the low‐frequency smoothing diameter based on the designed spread length of field acquisition and the size of subsurface structure.  Structure diameter should be equal to or less than low‐frequency smoothing diameter, and low‐frequency smoothing diameter should be equal to or less than half of designed array length.  The velocity modeling of undulating surface is completed in this way by using the above method.  This method is applicable to the zone with large elevation changes, and even the zone with exposed high velocity area.  It can enhance the imaging accuracy of shallow layer and appropriately describe the structural features of shallow layer, as shown in Figure 4.24 and Figure 4.25. 

Since shallow layer data is subject to the influence of dynamic correction stretching, the data of gathers lack shallow layer information, and thus the velocity structural model of shallow layer cannot be well reflected.  During velocity modeling, we introduced the top interface of high velocity reflection interval based on the information of first break to remedy the drawbacks of velocity information of gather data, which rationally reflects the change of shallow layer velocity structure, describes the ray path during depth migration and makes depth migration result accurately describe the geological structure and structural features of shallow layer. 

#### 4.4.6.2 Kriging multi‐well constrained seismic velocity modeling

In previous establishment of seismic velocity field, the logging data were not well integrated with seismic data (inversive seismic velocity): (1) If we build velocity field only using logging data, it is hard to calculate precisely the large areas outside of the wells. ( 2) It is hard to reflect the small‐scale structural change because of low vertical resolution of seismic velocity.  If there are logging and VSP data, we can make the best of the well data to build KT equation and use the well block data to restrict inversion velocity of seismic data, which can reflect the vertical and horizontal changes of seismic data. 

**Figure 4.24** (a) Conventional velocity model and (b) velocity modeling integrating first arrival wave inversion with reflection wave inversion. 

**Figure 4.25** (a) Velocity modeling migration integrating first arrival wave inversion with reflected wave inversion and (b) comparison of geological outcrop interpretation profile. 

The Kriging with an external drift variable is the expansion form of KT, and its trend model consists of two items: m (u) = _a_ 0 \+ _a_ 1f1(u), where f1(u) is equal to a secondary variable (external variable).  It is believed that the smoothness of secondary variable is related with the estimated main variable Z(u). 

Assuming that Y(u) is a secondary variable, the trend model is:

(4.7)

Y(u) reflects the spatial trend of Z variable (corresponding to variables _a_ 0 and _a_ 1).  The estimate value of _Z_ variable is the same with the estimated value of KT of corresponding linear equation group when k = l and f1(u) _= Y_ (u), that is:

(4.8)

Where, _λ β(KT)_ is Kriging (KT) weight.  As shown in Figure 4.26, the Kriging with an external drift can estimate the main variable by effectively utilizing the information of secondary variable.  The basic assumption equation 4.8 must have some physical significance.  For example, if the secondary variable Y(u) represents the seismic velocity model, the depth Z(u) of reflection interface should be in proportion to velocity (in average sense), and hence the equation 4.8 makes sense. 

The application of external drift algorithm should meet two requirements: (1) The external variable should change smoothly in the space, otherwise the KT linear equation 4.8 can be unstable. ( 2) The external variable should be known in all data point ua and estimation point u of main variables.  In KT liner system, the residual covariance function is utilized, instead of covariance function of initial variable Z(u), and thus in the place and direction where the trend m(u) can be neglected, m(u) is assumed to be zero.  Two covariance functions should be equal to each other.  It should also be noted that the cross covariance function between Z(u) and Y(u) does not work in liner system 4.8, which is not the same as co‐Kriging system.  The interpolation result of Kriging with external drift combined with multi‐model is shown in Figure 4.27, which presents the Kriging trend as the same as the external drift body.  The interpolation of interval velocity result is satisfactory and the Kriging error is small, with better effect and higher accuracy than other Kriging algorithm. 

**Figure 4.26** Diagram of external drift Kriging principle. 

**Figure 4.27** Multi‐model external drift Kriging interpolation. 

The interval velocity inversion under multi‐well constraint through 3D ray tracing coherent inversion method is not subject to constraint of DIX formula precondition.  It is applicable to any subsurface occurrence and the interval velocity so inverted has a higher accuracy.  Figure 4.28 is the interval velocity inverted by using coherent inversion under multi‐well constraint; from the figure, it can be found that a small error exists between interval velocity and well velocity. 

**Figure 4.28** (a) Well constrained interval velocity inversion plane and (b) well velocity error. 

It is very competitive in two aspects: (1) Utilization of the known logging data assures the validity of inverted velocity in vertical change. ( 2) Combination of logging and seismic assures both high vertical resolution of inverted velocity (consistent with well velocity) and reliable horizontal trend of velocity, as shown in Figure 4.29. 

**Figure 4.29** Inverted interval velocity model under multi‐well constraint. 

## 4.5 Quality Monitoring and Accuracy Discussion of the Seismic Velocity Model Building

The core issues challenging PSDM accurate imaging are not only the migration algorithm, but also the accuracy of velocity model that is more important.  The key to solving this problem is how to impose reasonable constraints on velocity modeling and how to demonstrate the accuracy and reasonability of velocity.  Based on the PSDM imaging and combined with the practical experience of complex structure imaging in western China, we put forward the combined multi‐methods constraint method to improve the velocity of modeling accuracy and imaging quality.  This combined multi‐methods constraint method is the quality monitoring technology in the process of modeling. 

### 4.5.1 Velocity model under logging data constraint

In this process, we try to fully collect data like drilling data, well logging data, and make effective use of well data and other prior information.  We can use sonic log or the velocity of VSP for reference to determine the velocity interface.  In blocks with multi‐well data, the sonic log can be used to calculate the interval velocity field, to understand and recognize the characteristics of velocity and special varying regulation in the work area.  Then we can use all these results as constraint while calculating the migration velocity.  But we can't use well velocity as migration velocity, because logging velocity is the velocity longitudinally measured, while seismic velocity has a horizontal component, and it is affected by anisotropic factors.  Therefore, migration velocity is not equivalent to well velocity.  However, the common well velocity can be used to constrain the size of near‐well migration velocity, so as to avoid causing large velocity error and to reduce the migration velocity iterative scan times. 

**Figure 4.30** Well data constraint and velocity interface. 

Figure 4.30 is the interval velocity model of H area.  In the process of velocity modeling, we loaded well data first, including well coordinates, sonic logging curves and geological stratification.  With sonic logging curves we can determine the change of interval velocity.  In the blocks with few or no wells, we mainly rely on the root mean square velocity based on PSTM to calculate more accurate initial velocity model, and then update the velocity model by iteration.  We have proposed the multi‐well data constraining velocity‐modeling method, which uses the pseudo well velocity or the average velocity of large sets of layer to ensure the reasonability of horizontal and longitudinal velocity variation.  If collation of the depth of the migration imaging by wells is needed, we still have to use well VSP velocity as a constraint to correct velocity model. 

### 4.5.2 Velocity modeling constrained by geological structure pattern

The initial velocity model is the basis of velocity modeling and migration imaging.  First of all, we should build the initial velocity model, including layer information, velocity estimation and determination of depth interfaces.  The initial velocity model must be consistent with the geological structure. 

**Figure 4.31** Velocity modeling under geological structure constraint. 

For the blocks with gentle strata and little change of lateral velocity, the interval velocity is often used as the initial velocity model, which is transformed from the root mean square velocity after (prestack time migration) PSTM by DIX formula, and then PSDM iteration is used to update the velocity model.  But for the complex blocks with great changes in lateral velocity, layer velocity transformation can only be used as a reference and cannot be used as the initial velocity model, because DIX formula is not applicable to large dip angle, and the PSDM imaging is very sensitive to interval velocity.  With lack of geological structure constraint, we are often unable to control the change in the initial velocity model, thus pseudo structure may easily occur on prestack depth profile, corresponding to unreasonable velocity changes.  With the wrong initial velocity model, convergence cannot be obtained, regardless of how many times iteration and updates are taken and how advanced a migration algorithm is used. 

For the seismic data of complex structure and low SNR, we can use the constraint method and strategy based on the structure model of imaging to build the initial velocity model.  This means that we pick up the velocity interface layer from poststack depth migration profile, estimate the layer velocity along the depth, and then use this result as the initial velocity model to ensure that the velocity model is consistent with the geological structure.  To determine the velocity interface layer from the depth profile, we should start from geological stratification and lay emphasis on wave impedance interfaces.  Meanwhile, more layers are helpful for us to control the velocity change.  This initial velocity model, which is built under the constraint of a structural model, not only reflects the stratigraphic sequence and the complex contact relationship of formation accurately, but can also update the velocity model in only 2–3 iterative processes.  Therefore, it can greatly reduce iteration times and increase the efficiency of high‐speed modeling and the quality of migration imaging.  When we pick up the velocity interface, we must use geological stratification for reference.  With calibration by geological stratification, we can determine the velocity of interface through comparing interval velocity from sonic logging with geological stratification.  The depth interface in the velocity model shown in Figure 4.31 describes the geological structure in relatively great detail, and helps in imaging. 

In velocity model updating, it is better to adjust and monitor the horizontal and longitudinal change trend of velocity both in stratification and real‐time dynamically.  The iterative update is better implemented layer by layer.  Only after the right velocity and depth interface for overlying layer are obtained should the iterative update be executed.  Otherwise the error will be passed on to deep section and affect the velocity acquisition of underlying layer.  During velocity modeling, more seismic interpretation is required than that in data processing.  The modeling process is actually a process to understand the geological structure gradually. 

### 4.5.3 Optimization of the velocity model under seismic imaging constraint

In general, interval velocity analysis is calculated and updated by prestack migration imaging, and is itself also an important part of seismic migration imaging.  The levelling extent of migrated imaging gathers and energy focusing of imaging event are taken as double standards for the error judgment of migration velocity, which are complementary to each other. 

If the velocity is accurate, then the velocity of one point imaging gathers that come from the same reflection point will be horizontal.  If imaging gathers go upwards, it means the migration velocity is small and needs to be increased; if imaging gathers bends downward, it means the migration velocity is large and needs to be reduced.  In this way, the quantification of velocity can be realized by imaging gather curvature.  For a certain layer, the velocity error that is calculated along the depth of interval is often represented by residual delay.  We scan and calculate PSDM with different interval velocity so as to calculate the residual delay that can be used to judge the size and change of velocity. 

It should be emphasized that if the gradient factor of interlayer velocity has not been considered, the velocity should be adjusted slightly smaller under the principle of maintaining the image quality during picking up residual delay along the interval and adjusting the velocity.  In this way, both the imaging velocity and image quality of this interval and the imaging effect between this interval and its upper interval are considered.  After a great deal of velocity modeling practice, it has been shown that the velocity analysis and judgment are very effective for improving the effect of inter‐interval imaging.  A high capability in geological analysis and comprehensive judgment is guaranteed, for it requires quantitative analysis and inspection of the straightness degree of longitudinal imaging gathers, estimation of the velocity changes of each interval, and consideration of the reasonability of the entire velocity change tendency. 

The standard for judging the velocity model is the consistency of different offset imaging of gathers after migration, which can be predicated and analyzed by calculating the horizontal and longitudinal delay.  If CRP gathers are selected from the profile, the CRP gathers will show an almost straight shape; then calculate the longitudinal delay, and its energy spectrum is near the zero delay line, indicating the velocity corresponding to this CRP will be accurate.  If we calculate the delayed spectrum along the interval and the horizontal delay spectrum is near zero delay line, the velocity change of the interval is basically right.  The velocity is more accurate if the delay is close to zero, which means the imaging will be much better.  Thus, we can constrain the interval velocity from the horizontal and longitudinal directions, and the imaging effectiveness as well.  But the delay is calculated through the offset gathers and the travel time.  Certain offset, non‐unique reflection points and different travel time paths may exist under the ground.  Therefore, the delay judgment method also has some disadvantages.  We proposed an imaging constraint method, which is to build accurate velocity‐depth model by determining velocity through imaging scans on the basis of velocity optimization.  Angle gathers are the real gathers without illusion and belong to reasonable CIP gathers, which can be used to determine the size of interval velocity.  In order to obtain the angle gathers, the wave equation of PSDM needs strong computing ability, which should be considered comprehensively. 

### 4.5.4 Constraint from migration algorithm

Different migration algorithms have different adaptability to the velocity model, and their modeling methods and requirements are also different.  Kirchhoff integral migration can obtain the migration of target line quickly and it has good adaptability to the velocity model, which makes it easy to build the velocity model.  Kirchhoff integral PSDM and velocity modeling software are mostly used in combination to build the velocity model at present.  The wave equation PSDM velocity model is very sensitive to error, so a more accurate velocity model is needed.  The same velocity model using a different migration algorithm will lead to different migration results.  Figure 4.32 shows one‐way wave PSDM and reverse time migration using the same velocity model.  By comparison, it can be observed that it is different from the SNR to resolution of the profile, and the reverse time migration is better. 

**Figure 4.32** (a) One‐way wave of PSDM profile and (b) reverse time migration. 

If computer conditions permit, the angle gathers output can be realized through wave equation PSDM so as to calculate the migration velocity more accurately.  Well data constraint, geological structure constraint, imaging and migration algorithm constraint should go through the entire velocity modeling process, and the modeling personnel will complete this process mainly by self‐inspection.  Quality control is the process of approaching the real model through iteration. 

### 4.5.5 Velocity model accuracy and imaging effect evaluation method

Because migration velocity is calculated by prestack imaging method based on the seismic data, generally the obtained PSDM profile depth is greater than the drilling depth.  If comparison is needed, we can correct migration imaging depth with reference to well data.  Well data can also be used to verify the change trend of velocity field and to judge whether the pattern of interface depth is correct.  Forward modeling may be conducted, if necessary, in order to verify the correctness of velocity model.  To judge the precision of the velocity model for the whole work area, we must verify the accuracy and size of the whole velocity model by using velocity percentage scanning to make migration imaging separately.  Moreover, it is necessary to check in detail the main lines, the contact lines and slices of velocity in different depth, analyze and judge the reasonability and accuracy of the velocity model in combination with geological structure.  It is recommended to obtain cooperation from professional modeling personnel. 

Methods of evaluating the migration imaging result objectively and fairly have attracted a lot of attention in the field of seismic migration imaging.  The verification of well depth data is necessary.  According to the imaging requirement, it is necessary to do interval sampling for migration profiles of different directions, check their returning level by confirming whether structural distribution is reasonable, whether the cross sections and breakpoints are clear and whether the size of noise is good enough for geologists to interpret.  We should not adopt the currently popular method of "multimedia project report", which declares the quality of imaging by comparing several imaging profile pictures, still less cutting out part of imaging to make comparison within boxes or loops as some software companies advertise.  Comprehensive and objective evaluation for migration is really part of the monitoring for migration imaging quality. 

The seismic exploration targets are becoming more complicated.  With the rapid development of computer technology, PSDM imaging technology is being applied more and more to solving the problem of accurate imaging for complex structures.  However, PSDM is not necessary for all the data, and the PSDM wave equation is not a necessary process to make the data effective.  As to seismic data itself, we can use convenient PSTM or poststack depth migration to solve the imaging problems as long as the change of velocity is not great.  For very low SNR data, the effective signal is very weak, so the size of velocity could not be judged by imaging gathers from migration.  However, the PSDM is more sensitive to velocity error, and the effective quality control of velocity modeling is almost impossible.  Practice has proved that prestack migration cannot result in ideal imaging for this kind of information, no matter how advanced modeling methods and migration algorithms are used.  Therefore, project managers or project decision makers need to consider comprehensively from manpower and financial resources the kind of imaging processing that should be used for the seismic data and what kind of result could be expected from that. 

At present, a lot of time and energy is usually spent on building a velocity model and completing the processing of PSDM, but the migration result has not been fully and effectively used.  On the one hand, it is because the traditional methods of seismic data interpretation and reservoir description are limited in time domain; on the other hand, the velocity modeling and prestack migration imaging technology need further development and modification to make them more accurate and to enable them to be applied more widely.  The key factors influencing the PSDM imaging are the migration algorithm and the migration velocity model, while the latter is more important.  Whether the velocity model is right or not is directly related to seismic migration imaging.  Application of effective quality control techniques in the modeling is the key factor that affects the modeling time efficiency.  Well data constraint, geological structure constraint, imaging constraint and migration algorithm constraint can effectively monitor the quality of velocity modeling and PSDM imaging for complex structural areas in every step.  Only the velocity model based on strict quality control in every step can guarantee the reasonability of velocity and the accuracy of migration imaging. 

## 4.6 Velocity Analysis Method for Reverse Time Migration in Angle Domain

Compared with other prestack depth migration methods, reverse time migration enjoys higher sensibility to the precision of the velocity model in the areas with dramatic velocity variation of the subsurface medium, such as salt dome flanks.  If there are errors in the velocity model, false reflection and mirror image can be created by reverse time migration, which has a negative impact on structural interpretation [24].  Therefore, studying velocity analysis methodology of reverse time migration is necessary.  Studies show that angle domain velocity analysis method based on reverse time migration enhances the precision of the velocity model effectively.  It includes two core technologies, namely generation of CIP gathers in angle domain from reverse time migration and prestack angle domain velocity analysis. 

### 4.6.1 Generation of CIP gathers in angle domain from reverse time migration

#### 4.6.1.1 Why choose gathers in angle domain from reverse time migration

Research results show that conventional common shot domain migration and common offset migration cannot offer certain imaging correlation since all the CIP gathers are indexed by property of the surface, and thus artifacts of migration which may occur in the CIP gathers will have a negative impact on the quality of CIP gathers and the precision of migration velocity analysis [25].  By contrast, the index of surface property is combined with the index of subsurface reflex angle for angle domain CIP gathers, which addresses the problem of multiple paths in generation of CIP gathers, thus improving the quality of CIP gathers and reducing artifacts in migration [25]. 

Three prestack depth migration methods, namely the Kirchhoff integral method, one‐way wave equation and reverse time migration, can generate CIP gathers.  The main reasons for selecting reverse time migration to generate CIP gathers in angle domain include: (1) Reverse time migration has no limitation on dip angle, adapts to any velocity variation, and presents accurate image for all forms of waves. ( 2) Reverse time migration can offer angle domain CIP gather data with higher quality. ( 3) No additional computation is required to generate angle domain CIP gathers besides calculation of incident angle and acquirement of gathers. ( 4) Using reverse time migration to directly generate angle domain CIP gathers for velocity analysis is helpful for its migration calculation.  Above all, the reverse time migration is chosen to generate angle domain CIP gathers. 

#### 4.6.1.2 Conventional generation method of angle domain CIP gathers

A series of researches have been conducted on the generation method of angle domain CIP gathers based on the Kirchhoff integral method, with promising achievements in the geophysical field since 2000 [25,26].  As for conventional angle domain CIP gather generation methods that include pre‐imaging method [27,28] and after‐imaging method, wave number direction is obtained through slant stack or Fourier transform under spatial mobile imaging condition, and angle domain CIP gathers are obtained through further computation [29,30].  The key to computation of angle domain CIP gathers is angle decomposition.  Two kinds of methods are available: one is based on Fourier transform or slant stack [31] and the other is based on polarization direction or Poynting vector [32,33].  The former enjoys good stability but low computation efficiency, while the latter has high resolution but generates more noise under complex wavefield and bad stability. 

Based on geometric characteristics of wave front, the conventional computation for propagation angle of seismic waves uses 2D or 3D Fourier transform in the computing process, which acquires a huge amount of computation.  In addition, the conventional method to generate angle domain gathers by using wave equation requires both source wavefield and receiver wavefield.  But receiver wavefield has higher complexity and low SNR compared with source wavefield.  Therefore, it is necessary to develop a stable and efficient approach to generate angle domain gathers. 

#### 4.6.1.3 Computation of incident angle based on wave front vector

Computation of seismic wave incident angle is the core in generation of CIP gathers in angle domain from reverse time migration [33].  Figure 4.33 shows the relationship of incident angle, propagation angle, and dip angle, among which α represents the propagation angle of incident P‐wave, that is, the angle between incident P‐wave and coordinate axis Z. β represents the dip angle, and θi and θr represent the incident angle and reflected angle respectively.  In the acoustic wave medium, since incident waves and reflected waves are longitudinal waves, θi = θr.  According to the geometrical relationship shown in the figure, we can have:

**Figure 4.33** The relationship of incident angle, propagation angle and dip angle. 

(4.9)

Equation 4.9 shows that computation of propagation angle and dip angle comes first in order to gain incident angle.  As for computation of dip angle, Hilbert transform is chosen among many existing computing methods.  First, the velocity model Marmousi II shown in Figure 4.34 is used for numerical experiment and the results of reverse time migration are shown in Figure 4.35.  Spatial high‐order finite difference operator and stable mutual correlated imaging condition are used in the computation during reverse time migration and the results after Hilbert transform can offer information about dip angle, as shown in Figure 4.36. 

Since the conventional computation method of propagation angle has some disadvantages, it is necessary to develop a stable and efficient counterpart.  Therefore, research is conducted on computation of propagation angle with direct use of wave front polarization direction [33]. 

**Figure 4.34** The Marmousi II velocity model. 

**Figure 4.35** Reverse time migration results of the model Marmousi II. 

**Figure 4.36** Computation results of dip angle of the model Marmousi II. 

The constant density 2D acoustic wave equation is as follows:

(4.10)

Where, _p_ represents acoustic wave seismic wavefield; _x_ and _z_ represent horizontal coordinate axis and depth axis, respectively; _t_ represents time; _U_ ( _x_ , _z_ ) represents subsurface medium velocity.  The formula of plane wave in acoustic wave medium is as follows:

(4.11)

Where, _k x_ and _k z_ represent wave numbers;  ; ω represents frequency. 

We also have the following equation for propagation angle α:

(4.12)

Deducting equation 4.11 combined with equation 4.12 gives the computation formula of propagation angle:

(4.13)

That is:

(4.14)

Using the above wave front vector method, we first adopt the simple interval model data to verify the correctness of the method, and its reverse time migration results are shown in Figure 4.37.  Figure 4.38 shows the incident angle computed by aforementioned method but the positive and negative direction of the incident angle is not defined.  Here we define the left of shot point as positive and the right of shot point as negative.  In addition, the model Marmousi II with complex subsurface structure is adopted for numerical experiment and its velocity modelis shown in Figure 4.34.  Figure 4.39 shows incident angle of shot point CDP at points 150, 350 and 650. 

**Figure 4.37** Reverse time migration results of the simple interval model. 

**Figure 4.38** Computation results of the incident angle of the simple interval model. 

**Figure 4.39** Computation results of the incident angle at CDP points of the model Marmousi II. ( a) CDP = 150. ( b) CDP = 350. ( c) CDP = 650. 

#### 4.6.1.4 Generation of angle domain CIP gathers from reverse time migration and numerical experiment

Computation of the incident angle is the key to generating angle domain gathers of from reverse time migration.  After gaining the incident angle with the wave front vector method, angle domain CIP gathers can be obtained through extraction and computation of single shot reverse time migration results.  The whole process is illustrated with the model Marmousi II.  Figure 4.40 shows comparison of single shot reverse time migration results before and after Laplace filtering.  Angle domain CIP gathers can be extracted from single shot reverse time migration results by using incident angle information.  Figure 4.41 shows two angle domain CIP gathers of shot point CDP at 150 and 650 of the model Marmousi II. 

**Figure 4.40** Single shot reverse time migration results of the model Marmousi II. ( a) Single shot reverse time migration before Laplace filtering. ( b) Single shot reverse time migration after Laplace filtering. 

**Figure 4.41** Angle domain CIP gathers at different locations of the model Marmousi II.(a) CDP = 150. ( b) CDP = 650. 

### 4.6.2 Angle domain velocity analysis method

We have analyzed the reasons why angle domain CIP gathers are used for migration velocity analysis and why reverse time migration is used to generate angle domain CIP gathers, and introduced generation of angle domain CIP gathers through direct use of wave front polarization direction.  The following section will illustrate migration velocity analysis with angle domain CIP gathers of reverse time migration. 

#### 4.6.2.1 Response of angle domain CIP gathers to velocity errors in reverse time migration

First, we should analyze the response of angle domain CIP gathers to migration velocity errors.  If migration velocity is correct, focusing and imaging will happen at the same time on the reflecting interface, while if there are errors in the migration velocity model, focusing and imaging will not happen at the same time.  In order to verify the response of angle domain CIP gather to various velocity errors, we selected a simple flat bed model for numerical experiment.  The velocity model is shown in Figure 4.42.  Reverse time migration is conducted on real velocity of the first interval, 3000 m/s, by velocity model of 2760 m/s, 3000 m/s and 3240 m/s, respectively, and corresponding angle domain CIP gathers are gained through computation.  Figure 4.43 shows angle domain gathers gained at various velocities.  It is shown that angle domain CIP gathers gained at accurate velocity are leveled, ones gained at lower velocity bend upwards, and ones gained at higher velocity bend downwards.  This is the qualitative finding about the response of angle domain CIP gathers to various velocity errors. 

**Figure 4.42** The flat bed velocity model. 

**Figure 4.43** Angle domain CIP gathers gained by flat bed velocity model at various velocities.(a) Accurate velocity. ( b) Lower velocity. ( c) Higher velocity. 

#### 4.6.2.2 Update method of angle domain velocity

For angle domain CIP gathers, the leveling degree of event is used to judge errors in the velocity model.  Meanwhile, the residual moveout (RMO) is used for iteration updating of the velocity model.  Thus, it is very important to obtain a correct and effective correlation between RMO and velocity update value.  At present, the most commonly used angle domain velocity updating equation is [29,34]:

(4.15)

Where, Δz is RMO acquired from angle domain CIP gathers; θ is incident angle of seismic wave; zo is migration depth; ρ is the ratio between updated velocity and migration velocity. 

However, the impact of dip angle is not taken into account in the equation, which is suited to the velocity updating in flat formation.  However, requirements of computational accuracy cannot be met for formation with large dip angle.  Thus, the following angle domain velocity equation is chosen [29]:

(4.16)

Update the equation with the above angle domain velocity and conduct numerical experiment with model data.  The real velocity model is shown in Figure 4.44, which includes flat bed formation, small‐dip formation and steep‐dip formation.  Single shot record was obtained by operating forward modeling with real velocity model.  The constant velocity model was chosen as the initial velocity model (the velocity in the whole area equals the velocity of the first interval), and the reverse time migration calculation was operated using the constant‐velocity initial model, which is shown in Figure 4.45.  As is shown in the figure, the large error of velocity model causes worse imaging of reserve time migration.  The migration velocity model obtained from six times of angle domain velocity updating is shown in Figure 4.46, and the reverse time migration results obtained from updated velocity model are shown in Figure 4.47.  It can be observed from these figures that the reverse time migration obtained from the updated velocity model can greatly improve the effect of subsurface structural imaging.  Furthermore, the updated velocity model is compared with the real velocity model to verify the effectiveness of angle domain velocity analysis method.  Figure 4.48 shows comparison of real velocity (blue curve) and updated velocity (pink curve) of five CDPs, showing the effectiveness of methods. 

**Figure 4.44** The real velocity model and parameters for numerical experiment of angle domain velocity analysis. 

**Figure 4.45** Reverse migration results from the constant velocity initial velocity model. 

**Figure 4.46** The velocity model updated through the angle domain velocity analysis method. 

**Figure 4.47** Reverse time migration results obtained from the updated velocity model. 

**Figure 4.48** Comparison of the updated velocity model and real velocity model. ( a) CDP = 200. ( b) CDP = 450. ( c) CDP = 600. ( d) CDP = 750. ( e) CDP = 1000. ( f) Locations of five CDPs in the velocity model. 

## 4.7 Study of the Full Waveform Inversion Method

The Full Wave Inversion (FWI), based on full wavefield forward stimulation technology, is a process to obtain the geophysical parameters from inversion of seismic data.  The FWI can fully utilize prestack kinematics and dynamic data of prestacked seismic wave‐field to establish subsurface velocity model, which is capable of revealing the detailed information of structure and lithology in complex geological background and has a higher resolution than conventional method.  The full waveform inversion could be realized in time domain, frequency domain or Laplace domain. 

The theoretical framework of full waveform inversion was proposed in the 1980s, but it was not realized practically because of a deficiency of seismic data size and computation capabilities.  In recent years, the application of full waveform inversion has been realized because of the development of high‐density wide azimuth acquisition and high performance computers; the application possibilities of FWI are also shown in some of the latest research findings from outside China. 

### 4.7.1 Study status of full waveform inversion

The full waveform inversion of the 2D time domain wave equation was realized by Tarantola in the 1980s.  He learned from reverse time migration and had further studied full waveform inversion theory based on time domain, frequency domain and Laplace domain.  Many important achievements had been made.  However, the full waveform inversion had not been applied in practical production for a long time because of the limitation of computation capabilities.  Tarantola proposed the time domain full waveform inversion based on generalized least squares inversion theory (1984, 1986) [35]; Kosloff proposed the method to increase precision of forward simulation of sonic wave and elastic wave with pseudo‐spectral method (1982, 1984); Virieux proposed the method to realize the high precision seismic wave forward simulation by using staggered mesh finite difference (1984, 1986); Gauthier (1986) and Mora (1987, 1988) operated the sonic wave and elastic wave full waveform inversion test of theoretical model, which uncovered application prospects of full waveform inversion and analyzed the defects of method.  Marfurt (1984) conducted further study and confirmed that frequency domain finite element and finite difference is the most effective method to realize wave equation forward simulation of mass shot points.  Pratt (1990, 1998) developed the frequency domain sonic wave and elastic wave full waveform inversion by merging the method of Marfurt's concept and Tarantol's full waveform inversion method [36,37].  Bunks (1995) proposed the time domain multiscale waveform inversion method [38].  Shin (2008) proposed the Laplace full waveform inversion method [39,40]. 

**Figure 4.49** (a) Tomography inversion velocity. ( b) Inversion results after five times iteration with 2–10 Hz.; ( c) Inversion results after five times iteration with 2–3 Hz, 2–4 Hz, 2–6 Hz, 2–8 Hz. 

In recent years, it has been possible to apply full waveform inversion as computer technology has been greatly improved, and this technology has become the focus of international geophysical study.  More papers on full waveform inversion have been presented at SEG annual meetings.  Since 2009, the subject of full waveform inversion has been established.  Sixteen pieces of dissertation were published in this area at the 2009 SEG annual meeting, and the number increased to 32 in 2010.  In addition, several papers related to full waveform inversion have been published in _Geophysics_ in recent years, and good application effects were shown in many examples.  The full waveform inversion result of real data presented by H. Li _et al._  at the 2011 SEG annual meeting is shown in Figure 4.49.  The tomography inversion velocity slices are shown in Figure 4.49(a), and five times iteration with 2–10 Hz is shown in Figure 4.49(b), and velocity slices after five times iteration with 2–3 Hz, 2–4 Hz, 2–6 Hz and 2–8Hz are shown in Figure 4.49(c).  The resolution and precision of the velocity model was greatly enhanced, showing good prospects for full waveform inversion. 

### 4.7.2 Gradient guidance full waveform inversion

The full waveform inversion method based on Newtonian inversion and gradient guidance inversion need searching iteration and updating direction by obtaining the derivative of objective function against model parameters.  First, the gradient of quadratic error functional is obtained from sonic wave equation based on adjoint state equations.  Then, the gradient guidance iteration algorithm is obtained by acquiring the iteration step. 

#### 4.7.2.1 Calculation method of time domain objective functional gradient

There are many advantages of frequency‐space domain full waveform inversion (mainly scale advantage), but it cannot be applied in practical seismic data processing.  Thus, the analysis is based on the time‐space domain.  In fact, the establishment of full waveform inversion in time domain and frequency domain are the same.  Therefore, the analysis results based on time domain are adapted in the frequency domain after Fourier transform. 

The most direct field observation is about shot gather, and inversion is also targeted at shot gather data.  Furthermore, the model scale of discussion is limited to 2D space.  Both forward modeling and inversion are operated in shot gather, so the built framework could be transformed into 3D space. 

In sonic wave equation, the model parameter is velocity field _v_ (it could also be defined as slowness or the square of slowness, and a similar equation could be derived).  Defining the observed shot gather wavefield as d _abs_ ( _t_ , _x_ r, _x_ s), the full wavefield is obtained through simulation.  Here the basic conditions, correct wavelet and noise in accordance with Gaussian distribution (the noise could be statically ignored) are considered.  The defined error functional is:

(4.17)

The gradient could be derived by using variation principle, and the variation of error functional could be written as:

(4.18)

If the equation is transformed for acquiring δu, δu could be written as:

(4.19)

In the above equation, both _u_ ( _v_ ) and _u_ ( _v_ \+ _ε_ ∆ _v_ ) meet conditions of wave equation.  Thus, the following formula could be obtained:

(4.20)

(4.21)

(4.22)

Equation 4.18 is an expression of the wave equation.  Therefore, it represents the wavefield δu spread from the source of right end. 

(4.23)

Thus, it could be derived from equation 4.18 that:

(4.24)

The adjoint state equations were applied twice during derivation of equation 4.24 and the gradient of functional toward velocity model is:

(4.25)

It is thus clear that the value of gradient is obtained by operating the inner product of the second derivative of positive propagating wavefield against time and depropagation wavefield of residual data with time.  Positive propagation and depropagation wavefield of each shot is computed individually, and the gradient that is obtained is the superposition of computation results of each shot.  Equation 4.25 refers to twice wavefield propagation per shot, which is realized according to Figure 4.50.  The procedures for each shot include:

  1.  Calculate and record the positive propagation wavefield _u_ at each moment. 
  2.  Calculate the residual error at each geophone station. 
  3.  The depropagation data is obtained by spreading the wavefield residual error to model space. 
  4.  Calculate the inner product of depropagation wavefield and second derivative of positive propagation wavefield against time, and then obtain the single shot gradient. 

The global gradient of model space is obtained by superimposing gradient value of all shots.  Then, gradient direction of both gradient guidance and Newtonian inversion is obtained.  In this chapter, positive propagation and depropagation wavefield are obtained based on full wavefield simulation, and the computed gradient is the gradient of full waveform inversion.  Moreover, the wavefield operator in the direction defined in equation 4.25 could be calculated from other operators.  For example, the wavefield could be obtained by using radial trace, and the gradient becomes the gradient direction of tomography. 

The frequency domain inversion method proposed by Pratt is essentially the same with the time domain inversion method proposed by Tarantola.  However, the frequency domain can offer certain physical meanings through analysis.  The second derivative of positive transmission wavefield against time in equation 4.25 is shown in the form of a high pass filter of single frequency in the frequency domain.  Therefore, FWI is more sensitive to velocity structure of high frequency and high wave number, which causes FWI to tend to approach local minimum.  If the defined model deviates from the real model, it is difficult to get a favorable convergence effect. 

The inversion direction is defined in the gradient defined in equation 4.25.  Therefore, the gradient could be flattened with generally right direction (avoid reversal symbol).  The gradient value could be rapidly obtained based on approximate wavefield operator (such as radial trace) and Beam method. 

The procedure of full waveform inversion of gradient method is shown in Figure 4.50.  During each iteration, the operation of acquiring gradient needs twice full wavefield modeling, and the paralleled computation of shots is easily realized based on the single shot method.  The method based on step parabolic optimization method needs one time wavefield forward modeling, and the paralleled computation of shots could be realized to search the optimized step.  Most computation time of iteration lies in three times wavefield modeling, where paralleled computation can be realized.  The paralleled computation based on a computer group of multiple joint and multiple core CPU can provide hardware support for practical application of full waveform inversion. 

#### 4.7.2.2 Numerical calculation example of full waveform inversion

The Marmousi II model has often been used for full waveform inversion at the annual meeting of SEG/EAGE in recent years.  Therefore, the model was tested to compare methods.  In order to ensure stability in the forward modeling, we resampled the original model and generated data.  Horizontal coordinate is between 0–2376 m. Figure 4.51 shows the velocity model with velocity between [3000, 7000] m/s. There are a total 40 surface shots, with the first one located at 56 m. The wave is excited with zero phase Ricker wavelet with 30 Hz dominant frequency and is received in surface full aperture, with a time sampling rate of 0.5 ms and 1500 sampling points. 

A constant gradient model was chosen at start of inversion, and the gradient increased from 3000 m/s on the surface to 6000 m/s at the deepest point.  Two hundred times of iteration was operated in the model, and the results of 100th and 200th iteration are shown in Figure 4.52.  The inversion shows a good result with clear boundary, and convergence velocity approximates to real value.  The updated velocity of 100 times and 200 times iteration of 120th channel is shown in Figure 4.53.  It can be found that the velocity gradually approaches real value. 

**Figure 4.50** Flow chart of gradient full waveform inversion. 

**Figure 4.51** The Marmousi real velocity model. 

**Figure 4.52** Inversion results of the model Marmousi. ( a) The 100th iteration; (b) The 200th iteration. 

**Figure 4.53** Velocity value of the 120th channel with various iterations. ( a) The 100th iteration. ( b) The 200th iteration.  The green line represents real value while the red line represents inversion results. 

A conclusion could be drawn from the analysis that although the Marmousi II has complex velocity structure, the variation is small.  The travel time of wavefield could be well described as a constant gradient medium.  With correct low frequency information, the full waveform inversion shows the description capability in high frequency domain.  Therefore, if the initial velocity is relatively matched with travel time, an ideal inversion result could be obtained from FWI. 

### 4.7.3 FWI discussion and further development trend

Although full waveform inversion (FWI) has been making progress over recent years, many problems are still to be addressed.  Full functionalization of FWI has not been achieved, especially for land data, which is mainly caused by a huge difference between field data and synthetic data.  We hold that problems lie in two aspects: (1) Transmission laws of seismic waves cannot be described simply by constant density acoustic wave formula.  Real data have surface wave interference, conversion of waveforms (P‐S, S‐P, etc.),  noises of all sources, and possible absorption and attenuation of medium, etc. ( 2) Source wavelets are unknown.  For deep‐sea data, we could obtain relatively real source wavelets easily.  But for land data and shallow water data, even extraction of wavelets is a tough job. 

In order to conduct researches on FWI, we need to estimate source wavelets with field data (just relative value; amplitude of wavelet does not have reference value).  After that, we use estimated source wavelets and known initial velocity model for forward synthetic shot record, and then compare synthetic record with field shot record and analyze their differences.  In addition, computation efficiency is still a bottleneck for large‐scale application of FWI.  Anisotropy and elastic wave FWI will be the main work in the future. 

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#  5   
Case Study

In previous seismic survey practices, in order to meet the demand of structural interpretation, the seismic data imaging often sought high SNR at the expense of data fidelity and amplitude preservation.  Nowadays, with the advance of fine oil/gas exploration, the fidelity in seismic data image processing is more necessary.  In recent years, the author has done a large amount of research work in this field and has gradually formed the research approach and method flow for fidelity preservation imaging.  The previous chapters give an introduction to the overall concept and some key technical methods.  This chapter will present several pertinent fidelity preservation image processing approaches and application effectiveness. 

## 5.1 Application of 3D Prestack Reverse Time Migration in Subsalt Imaging

### 5.1.1 Main problems challenging subsalt seismic survey

There are a number of problems challenging subsalt seismic survey, and the major problems are velocity and imaging method.  The problems existing in subsalt imaging velocity include: (1) The floating paleo‐sediments are over the top of salt and sediments, flooding the top of salt, which results in the base of salt being hard to image. ( 2) It is extremely difficult to properly mark the boundary of salt, predictively. ( 3) Multiple salt invasion and impact generate the complex salt structure separated by deposited finger, so repeated iteration of salt coverage and sediment coverage should be conducted in order to obtain proper definition of salt boundary. ( 4) Boundary description that is true to the image is hard to generate on computer with definite imaging of salt boundary. ( 5) For locations with deep grooves on salt top, the imaged salt bottom may seem to be over the imaged salt top. ( 6) The salt body velocity is in spatial variation.  As for imaging method, the conventional integral method of seismic imaging technique can hardly depict subsalt imaging, while two‐way wave equation migration (WEM) method (reverse time migration) can produce quality images on synthetic complex deep salt structure.  The reverse time migration imaging method may be used to address the problem of subsalt imaging.  It can improve the remarkable imaging quality of structures with large dip, like vertical fault, flank on salt dome, salt dome.  In the reverse time migration, the distortion of underlayer caused by anomalous salt dome velocity can be eliminated, thus generating accurate images of subsalt formation at depth domain. 

### 5.1.2 Features of the Pre‐Caspian Basin and its seismic geological conditions

The Pre‐Caspian Basin is one of the largest hydrocarbon‐bearing basins in the world.  Now a number of large fields have been discovered, such as Astrakhan, Tengiz, Zhanazhol and North Troyes, indicating that this basin contains extremely abundant oil/gas resources.  This research block is in the center of an uplift zone at the eastern edge of the Pre‐Caspian Basin and is also the structural belt with richest hydrocarbon accumulations, with an area of about 2930 km2.  This basin has a developed salt bed in the Lower Permian Kungurian and generated a number of very thick salt domes, which are 200–3000 m thick.  The major target zone is the subsalt Carboniferous carbonatite.  Due to the great difference in velocity between the salt dome and surrounding rock and drastic variation in lateral velocity, the time domain is unable to accurately image the salt dome boundary, giving poor subsalt seismic data quality and severe upward pull of subsalt formation on the conventional time profile (Figure 5.1). 

There are apparent wave impedance differences between the formations of different epochs, thus generating a number of seismic reflection wave groups, including T, P1, KT‐1, MKT and Visean.  Their reflection strength (amplitude) ranges from moderate to strong, with favorable continuance and reflection characters that are distinct, which facilitates correlation and interpretation (Figure 5.2). 

**Figure 5.1** Seismic time profile through salt dome. 

**Figure 5.2** Reflection wave characters of main geologic horizons on seismic profile. 

The J‐bottom wave is a Jurassic‐Cenozoic structure, in distinct angle unconformable contact with the underlayer, a set of parallel moderate‐strong amplitudes on seismic profile with continuity in character.  The P1 bottom wave is an interface between the Kungurian halite bottom boundary and underlayer, with relatively strong amplitude and relatively good continuity.  KT‐1 wave shows reflection waves of the Upper Carboniferous Mid‐Gzhelian Group to the Mid‐Carboniferous Border Formation on top of the Upper Moscow Group, being a set of neritic light gray limestone and dolostone, with moderate to strong amplitude and favorable continuity.  MKT wave is a reflection wave from the Border interface top of the Mid‐Carboniferous Moscow Group, whose lithologies are mudstone interbedded with siltstone and thin sandstone interbeds, with unstable amplitude intensity and relatively good continuity.  The Visean wave is a reflection wave of the Devonian‐ Lower Carboniferous Visean Group interface, being a set of littoral interbeds of gray and dark gray mudstone and sandstone‐siltstone, interbedded with conglomerate; it has large variation in amplitude and relatively good continuity. 

Although two hydrocarbon‐bearing structures (No.  2 Structure and North Troyes) have been found in previous seismic surveys, the offset exploratory wells have not generated good results due to uncertainty of subsalt structure and complexity of trap types and reservoir lithology.  Identifying subsalt structure and restoring the true shape of subsalt structure have become important technical challenges to be solved in the exploration of this region.  For this purpose, the subsalt structure characteristics and influence factors are analyzed through seismic forward modeling, and the method for quantitatively identifying subsalt structure is proposed.  Meanwhile, the 3D velocity field is built based on seismic stacking velocity spectrum; hence realizing the time‐depth conversion of seismic interpreted time horizons and variable velocity mapping.  Through reverse time PSDM method and iteration of the velocity model, the subsalt structure is accurately imaged, thus restoring the true shape of subsalt structure in depth domain. 

### 5.1.3 Geologic structure of the Pre‐Caspian Basin

In geotectonic classification, the Pre‐Caspian Basin is the southeast corner of Eastern Europe Platform.  The northern and western parts of the basin are adjacent to some uplifted structural units in the south of Eastern Europe Platform, while the eastern and southern parts are adjacent to Hercynian Fold Belt (including the South Ural, South Embar and Karakul, etc.).  The Pre‐Caspian Basin is a superimposed basin from the late Proterozoic era.  The basement shows the characteristics of fault block structure, gradually declining from the edge to the center of the basin in a fault terrace (west and north) or a gentle slope (east and southeast).  It is overlaid by the Upper Proterozoic (Rife system) Quaternary ultra thick sedimentary caprock (6–15 km, maximum thickness in the basin center being 22 km).  The basin is divided into suprasalt and subsalt structural layers by upper Permian Kungurian halite, which has quite different structural features.  The subsalt hydrocarbon reservoir is mainly Devonian‐Lower Triassic carbonatite, and the types of hydrocarbon reservoirs are mainly bioherms and anticline.  The suprasalt hydrocarbon reservoir is mainly Jurassic‐Cretaceous sandstone, and the types of oil reservoirs are mainly structural hydrocarbon reservoirs of fault block and faulted anticline, related to salt dome.  The subsalt from the Paleozoic era is 3–4 km thick on the edge of the basin and increases to 10–13 km in the center of the basin, as shown in Figure 5.3. 

**Figure 5.3** Geologic structural map of Pre‐Caspian Basin Region. 

### 5.1.4 Sedimentary evolution and stratigraphic characteristics of the basin

As shown in Figure 5.4, the evolutionary history of Pre‐Caspian Basin has undergone the following stages: (1) Early Paleozoic era (S‐C1V2); the sag zone (IA) is the continental shelf detrital sedimentation stage of platform sag (Visean). ( 2) Early Carboniferous Epoch (C1V3‐C2b1); the sag zone (IA) is relatively lifted and combined with Cayan uplifted zone, being the sedimentary stage of neritic carbonatite platform of platform uplift (mid‐lower part of KT‐II). ( 3) Late Kashkirian Age (C1b2); the sedimentation suspension stage being exposed and becoming continent. ( 4) Early Moscow Epoch (C2m1); the sedimentary stage of neritic carbonatite platform of platform uplift (upper part of KT‐II). ( 5) Podolsk Age of Late Moscow era (C2m2po); the sedimentary stage of neritic carbonatite platform of platform uplift (MKT). ( 6) Late Carboniferous Era (upper C2m2po‐C2); the sedimentary stage of neritic carbonatite platform of platform uplift (KT‐I). ( 7) Denudation stage when the geosynclines on the east side at the end of the Carboniferous period returned and caused the sediments to be exposed and become continent. 

The Carboniferous system of middle block is divided from above and below into KT‐I oil layer group (including Gzhelian, Kasimovian and Upper Moscow series), carbonatite and gypsum salt bed, MKT (mid Moscow series), clasolite, KT‐II oil layer group (lower Moscow, Bashkirian, Serpukhovian and upper Visean series), carbonatite and small amount of mudstone, as well as Delmentian sand‐shale layer at mid‐lower Visean series and below. 

**Figure 5.4** Regional structure division map of the Middle Block. 

### 5.1.5 Analysis of subsalt seismic data features

The unified processed 3D seismic data (acquired in 2005, 2006, 2007, 2008 and 2009) from this region are all 3D seismic data gathered by controllable seismic source.  From the original records, we can see that the reflection wave groups of shallow, middle and deep layers in seismic data are full and complete, with moderate energy and high SNR, and multiple reflection wave groups are distinct and continuous.  Noise is intense in the survey area, mainly including linear interference, surface wave, acoustic wave and impulse interferences.  Figure 5.5 shows the field single shot acquired in 2005 and 2007.  These field single shots indicate that the presence of regular noise and surface waves impaired the quality of the data. 

**Figure 5.5** Quality of original single shots. ( a) Acquired in 2005. ( b) Acquired in 2007. 

Due to the fact that the 3D survey areas in the work zone were acquired in different years, differential analysis must be conducted to original single shots from different work zones during unified 3D seismic data processing.  For the single shots in 2005 and 2007 from the same location (Figure 5.6), we can see that there is certain time differential between them.  Figure 5.7 is stacked profile, which clearly shows certain systematic time difference between the profiles acquired in 2005 and 2007. 

**Figure 5.6** Correlation of single shot at the same location acquired in different years. 

**Figure 5.7** Profile correlation on the same CDP location in different years. 

Due to large lateral variation of surface lithologies in this work zone and the influence from acquisition methods, the quality of original data and SNR vary greatly with the location of seismic survey.  According to the analysis of seismic data, there are 21 salt domes of various sizes scattered in the work zone.  These salt domes are roughly divided into dome‐like and strip‐like, mainly found in the middle of the work zone.  The salt domes become smaller and thinner to the north and the south, gradually disappear to the west and become larger and thicker to the east.  These salt domes have no fixed strike, but are mostly in northeast‐southwest.  The variation of the dome thickness is 400–2600 m; the plane spread range of individual dome is usually small, and the flanks of most salt domes are steep.  It is difficult to image the salt dome boundary and subsalt structure accurately. 

### 5.1.6 Difficulties in seismic imaging of subsalt structure and analysis of the problems

Salt domes with thickness of over 1000 m have developed in the Lower Permian Pre‐Caspian Basin, with the greatest thickness up to 2600 m in the west, but generally 400–500 m in the east of the work zone.  Drilling data show that the interval velocity in the salt beds of this region is 4500 m/s, and the average velocity in the Upper Permian surrounding rock is 3800 m/s (data from only a few wells).  The velocity of surrounding rocks varies greatly.  For the marine sedimentary strata, the variation in velocity of subsalt sedimentary layers is steady.  In time domain, the subsalt formation velocity field is anomalous due to the influence from overlying salt domes, that is, the stacked velocity corresponding to high‐velocity salt dome anomalies and RMS velocity all show that the velocity on both flanks of salt dome is on the high side but low in the middle, where the velocity just beneath the dome top is the slowest, as shown in Figure 5.8.  The main reason for this anomaly is that, if there is great difference between the overlying salt dome velocity and surrounding rock velocity, the velocity of far and near offset rays penetrating the formations is different, and accordingly the variation in far and near offset moveout causes the change in stacked velocity.  Since the salt dome velocity is higher than that of the surrounding rocks, when the shot point moves to the dome top and gradually to the flanks, the moveout of the far and near offset begins to increase and the stacked velocity begins to decrease.  Therefore, in time domain, the underlayer velocity anomaly of the salt dome high‐velocity anomalous body is the normal geophysical phenomenon.  But for depth‐velocity modeling, if time domain velocity is used as the initial velocity model, the time domain velocity anomaly must be corrected. 

**Figure 5.8** Time domain‐velocity profile (anomalous subsalt velocity). 

The variation tendency and scope of velocity anomaly can hardly be estimated in time domain, and there is also uncertainty in velocity.  The sequential Gaussian Simulation method is used to simulate the maximum possible velocity structure and the inversion method of tendency constraining velocity is used to address the velocity anomaly in time domain and build the time‐domain interval velocity model.  Furthermore, the velocity difference exists between salt‐gypsum layer and surrounding rock, which causes upward pull on seismic event below the salt dome on seismic profile.  This phenomenon has a big effect on subsalt traps.  Meanwhile, due to the shielding effect of salt dome on seismic signals, the subsalt energy is lower than the surrounding formations, causing great difficulty in identifying the subsalt structures.  The velocity obtained by velocity spectrum is only the imaging velocity, but it remains difficult to conduct time‐depth conversion to the velocity data and accurately confirm the traps. 

### 5.1.7 Quantitative identification to subsalt pseudo‐structure by forward modeling

Based on statistics of VSP logging velocity for 48 wells in the middle block and the previous exploration experiences in salt‐bearing basins, it is believed that the interval velocity in halite is relatively steady, something between 4400–4600 m/s. The main factor influencing the subsalt structure is the velocity difference between halite and surrounding rock, the morphological distribution and thickness of salt domes.  In order to solve the subsalt structure problem, attention must be paid to the fine characterization of salt dome boundaries and analysis of lateral variation of velocity.  Assuming the average velocity of surrounding rock to be 3600 m/s, and the thicknesses of salt at 400 m, 800 m, 1200 m and 1600 m, and its velocity at 4500 m/s, a geologic model is built according to the development of formations in the work zone, which contains a number of salt domes.  Based on this, relevant time seismic profile is obtained through seismic forward modeling (Figure 5.9). 

**Figure 5.9** Forward geological model. 

The forward modeling result shows that the upward pull extent of subsalt formation has some linear relation with the thickness of halite.  The greater the halite thickness, the greater the upward pull extent.  On time‐domain seismic profile, this linear relation can be used to preliminarily identify the subsalt pseudo‐structure (Figure 5.10).  Therefore, we can draw the following conclusion: if the subsalt structure amplitude measured on the profile is greater than the calculated amplitude, it is real structure; otherwise it is pseudo‐structure. 

### 5.1.8 Research on subsalt seismic velocity modeling and imaging method

#### 5.1.8.1 Research on and application of subsalt seismic velocity modeling method

Velocity is one of the most important parameters of PSDM.  The building of the velocity model should also take into account the geophysical principles and the geological law of the work zone.  Meanwhile, the available prior information such as logging, layering by drilling and mud logging, should be used to eliminate multiple solutions and increase the velocity to find accuracy. 

**Figure 5.10** Relation between salt dome time thickness and upward pull height. 

For the anomalous body of salt dome in this work zone, the major problem hindering subsalt velocity modeling is still spatial characterization of salt dome and acquisition of seismic velocity.  The main modeling plan is to build the depth interval velocity model under multi‐well constraint using interval control method by considering seismic geologic characteristics of onshore salt dome area, based on an understanding of sedimentary systems and geologic information.  First, models are built for suprasalt sedimentary formation and inter‐salt clastic sedimentary formation; second, the spatial distribution of salt dome is characterized, and finally the model is built for subsalt sedimentary formation, as shown in Figure 5.11 and Figure 5.12. 

**Figure 5.11** Building time‐domain model with interval control method. 

**Figure 5.12** Space carving of salt dome. 

There are two main difficulties in seismic velocity modeling, due to the complex structure of salt domes: (1) Only logging data (well velocity) is used to build the model; the inter‐salt velocity structure of large extent cannot be accurately estimated. ( 2) If only the seismic velocity based on model inversion is used for modeling, it will be difficult to reflect the small‐scale structural changes near the well.  Therefore, using the spatial correlation between well velocity and seismic velocity variable to carry out an inversion estimate of spatial constraint for some variables; solve the optimum restraint coefficient of spatial variables by building the Kriging equation, and the inter‐well data (well velocity) can be used to constrain the inversion seismic velocity.  In this way, the vertical and horizontal changes in velocity are more reasonable (Figure 5.13). 

#### 5.1.8.2 Application of subsalt Kirchhoff imaging method

Just like NMO and PSTM, the purpose of PSDM is to eliminate the effect of seismic wave travel time.  With steep dips and lateral variation of velocity (as caused by salt domes), the travel time curve of seismic waves is generally a non‐hyperbolic type.  At this time, NMO may produce a common center point divergence, and PSTM can also generate amplitude error and location error of imaging in vertical and lateral directions.  Only PSDM can accurately locate the reflection of a common reflection point in depth domain and also achieve the same‐phase stacking.  In order to achieve this goal, PSDM will need correct migration algorithm and an accurate velocity model. 

**Figure 5.13** Velocity‐depth model built on multiple‐well constraint. 

The Kirchhoff integral method is used to optimize seismic imaging and velocity model.  This method is based on the non‐zero offset equation of point refection and sums the amplitude along refraction curve travel time track of non‐zero offset.  Its principle is as below:

As per the wave principle, the 3D seismic wavefield E can meet the wave equation in even isotropic medium:

(5.1)

Where, _k_ is propagation constant; when the seismic wave absorbing by media is not considered, _k_ 2 = 1/υ2 (υ is seismic wave velocity); take a closed surface around the observation point _P_ ( _x P_, _y P_, _z P_); take the surface observation surface S1 on the upper half of this closed surface, and the lower half is the hemisphere surface with infinite radius; then seismic wavefield intensity E (x _P_ , _y P_, _z P_, _t_ ) at point _P_ can be expressed by the seismic wavefield intensity on the surface observation surface, which is:

(5.2)

where:  ; _n_ is the surface normal direction;   ( _z_ is vertical to the surface and downwards); _r_ is the distance from input point ( _x,y,_ 0, _t_ ) to output point ( _x,y,z, t = 0_ ).  We took into consideration the divergence effect of wavefield and the effect of amplitude with changes of incident angle in Kirchhoff integral method.  Therefore, the result of depth migration can preserve the amplitude while accurately restoring the true structural shape of subsalt structure, as shown in Figure 5.14. 

**Figure 5.14** Correlation of (a) time migration and (b) depth migration crossing Well AL‐1 line (east‐west). 

**Figure 5.15** Comparison of low frequency noises from RTM of Marmousi Model (a) before suppression and (b) after suppression. 

Compared with conventional PSTM, this PSDM is more reliable in its structure location and more distinct in its imaging effect for salt dome boundary with steep dip and subsalt formation interface.  Due to lateral variation in velocity caused by salt domes, the time domain migration causes difference in imaging effect and arching up in terms of reflection interface imaging of highly steep subsalt formation.  Only PSDM can address these problems. 

#### 5.1.8.3 Research on and application of subsalt reverse time migration imaging method

At present, there are two main migration ways to achieve industrialized production: Kirchhoff integral method and one‐way wave equation method.  The Kirchhoff integral method is very efficient in migration calculation and is the most extensively used migration algorithm; this method can adapt to steep dip imaging but cannot solve the problem of multiple‐value travel time of single imaging point.  In addition, the Kirchhoff integral method can only describe the wave propagation in smooth media.  Therefore, it is somewhat limited in imaging of complex structures.  After one‐way wave equation migration is decomposed by wavefield, the wavefield can only propagate downward or upward and its propagation direction is restricted by 90o dip.  It cannot image the special wavefield like bow‐tie [1].  Additionally, when large‐angle propagation is described by one‐way wave equation, there are errors in both phase and amplitude.  Therefore, migration by one‐way wave equation and Kirchhoff integral method cannot image the reverse structure.  Geophysicists again turn to reverse time migration. 

In 1978, Hemon presented the idea of achieving reverse time migration by solving the wave equation using finite difference method [1].  In 1982, Whitemore [2] actually put forward the method for achieving reverse time migration.  Afterwards, Baysal _et al._  and McMechan [3,4] used it in poststack migration.  However, due to the difficulties in numerical calculation efficiency and storage, the reverse time migration method has not been applied on an industrial scale. 

In recent years, GPU/CPU coordinated high‐performance computation has greatly improved computational efficiency, making possible the industrial application of 3D reverse time depth migration.  Research work on reverse time migration mainly focuses on two aspects: (1) The reverse time extrapolation algorithm for wave equation. ( 2) Reverse time migration imaging conditions and computing method.  The research on reverse time extrapolation algorithm for wave equation mainly includes operator construction for wavefield extrapolation, numerical dispersion suppression and construction of boundary conditions.  The reverse time extrapolation algorithm for wave equation is mainly based on the algorithm of solving wave equation by finite difference approach.  The bottleneck in reverse time migration is the large amount of computation.  In the implementation strategy for reverse time migration, scholars from around the world have conducted much research.  In 2007, Symes [5] proposed recording the wavefield of two time horizons on checking‐points, which saved the hard‐disk space for storing the extrapolated source wavefield. 

In 2009, the Chinese Academy of Sciences conducted research on reverse time migration [6,7]; they used the concept of random boundary so that extrapolation of wavefield would not have to consider absorption of boundary conditions.  It had a very high acceleration ratio on the GPU/CPU coordination platform.  The northwest branch of the Research Institute of PetroChina Petroleum Exploration and Development started from high‐order finite difference approximation of acoustic wave equation and proposed an accurate and efficient reverse time wavefield extrapolation algorithm of difference scheme based on previous research findings; it realized reverse time migration based on the GPU/CPU heterogeneous platform and analyzed the relation between stability and dispersion of high‐order finite difference scheme.  Taking CPU/GPU as the computation core, the reverse time extrapolation of wavefield, which accounts for the largest computation amount, is realized by GPU, and the concept of random velocity boundary is used to improve the parallelism of wavefield extrapolation algorithm, which solves the I/O problem of large‐scale storage.  Its effectiveness is verified by numerical model and actual data.  By comparing with the one‐way wave migration method, the result shows that prestack reverse time migration has broken through the restriction of imaging dip angle and greatly improves the imaging of special structures like vertical faults and salt domes. 

### _5.1.8.3.1 Principle of reverse time migration method_

The reverse time migration method realizes migration by forward propagating the artificial source wavelet in time domain and back‐propagating the received seismic data for two‐way wave equation, while combining with imaging conditions (Claerbout, 1971) [8].  Relative to one‐way wavefield extrapolation, the reverse time migration uses two‐way wave for wavefield extrapolation, which avoids separate processing of upward wave and downward wave.  Therefore, it has become the most accurate imaging algorithm; it is not limited by dip angles and can realize imaging of bow‐tie and multiples. 

The two‐way acoustic wave equation for 3D medium is as below:

(5.3)

Where, _P_ = _P_ ( _x_ , _y_ , _z_ , _t_ ), the pressure field in the medium; _ρ_ = _ρ_ ( _x_ , _y_ , _z_ ), the medium density; υ = υ( _x_ , _y_ , _z_ ), the velocity field; S( _x_ , _y_ , _z_ , _t_ ), the source item.  Dablain (1986) elaborated the high‐order finite difference solution [9] for 3D two‐way wave equation.  This chapter only lists the basic calculation equations for forward and reverse time extrapolation.  By using temporal second‐order centered finite difference approximation   and using spatial high‐order centered finite difference approximation  , we can obtain a 3D high‐order difference wavefield extrapolation equation whose truncation error is O(Δ _x_ M, Δ _y_ M, Δ _z_ M, Δt2) as below:

(5.4)

From the above equation and coefficients, we can directly write out the high‐order difference equation of some truncation errors.  If we use Δ _x_ and Δ _y_ , Δ _z_ for interval of difference grid, Fmax for the maximum value of wavelet frequency and Vmin for minimum value of velocity model, the dispersion conditions of difference scheme can be expressed as:

(5.5)

### _5.1.8.3.2 Reverse time migration imaging conditions and low‐frequency noise suppression_

The reverse time imaging conditions are the key to reverse time migration, including the imaging conditions related to upward wave and downward wave presented by Claerbout (1971).  But reverse time migration imaging is a cross‐correlation of zero delay at any point on the space between reverse time extrapolation wavefield by two‐way wave equation and seismic source wavefield along the forward time direction extrapolation.  Considering the realizability of complex wavefield, this chapter adopts the cross‐correlation imaging principle proposed by Claerbout.  The imaging equation for cross‐correlation imaging conditions is expressed as:

(5.6)

Where, _U_ ( _x_ , _z_ , _t_ ) is upward wavefield; _D_ ( _x_ , _z_ , _t_ ) is downward wavefield; dt is continuation step length.  In two‐way wave migration, the extrapolated observation wavefield _U R_( _x_ , _z_ , _t_ ) replaces the upward wave, and the source extrapolated wavefield _U_ S( _x_ , _z_ , _t_ ) replaces the downward wave, so equation 5.4 becomes:

(5.7)

The integrand in the equation is expressed by _U R_( _x_ , _z_ , _t_ ) _U S_( _x_ , _z_ , _t_ ), indicating that an imaging operation is to be performed for the whole wavefield at _t_ time.  The integral shows that the image in space like _I_ ( _x_ , _z_ ) is the stacking of the image composed by time step.  Therefore, the cross‐correlation imaging conditions make full use of imaging information, which intensifies the imaging signal while effectively suppressing the imaging noise. 

From the propagation path, these two wavefields are correlated on the entire path from shot point to reflection point and to geophone point.  Therefore, reverse time migration produces strong low frequency noise.  In 2003, Mulder [10] proposed applying high‐pass filtering in imaging results to remove false image; Yoon _et al_.  proposed that introduction of angle‐related shot source and geophone wavefield information to the imaging conditions could be used to pick out the proper imaging results and then remove the false image [11]; Fletcher _et al_.  proposed the idea of introducing directional damper to a specific region to suppress false image [12]; Liu _et al_.  proposed the imaging conditions of wavefield decomposition [13]. 

From the practical point of view, the low frequency filtering may be used to filter the frequency noise (Figures 5.15).  Noise imaging is low frequency, mostly DC composition.  Therefore, these noises can be removed using the Laplace operator.  The Laplace operator is easy for filtering and for maintaining the parallel computing structure for reverse time migration.  The Laplace operator for temporal‐spatial domain is:

(5.8)

Through differential approximation of wavefield‐related _x_ , the equation 5.8 can be expressed as:

(5.9)

From the equation 5.9, we can see that the Laplace operator is a band‐pass filter, which is suitable for removing low‐wave‐number noise and can be used to suppress the imaging noise in reverse time migration, and realize filtering in time‐space domain.  The equation 5.9 alone cannot control which low frequency noise is to be suppressed.  Therefore, it is improved according to the concept proposed by Mulder [10], that the Laplace operator filtering is used from the angle of plane wave propagation.  First, use the Laplace operator on both sides of the imaging condition; suppose assume the incident wave and reflected wave at imaging point P are local plane waves, and its direction is determined by ray parameters Ps and pr, then we can obtain:

(5.10)

Where, γ is the incident angle; υ is the velocity at imaging point.  We can see that the effect of the Laplace operator on the imaging result filters the imaging results; the filtering operator is:  . 

### _5.1.8.3.3 Implementation strategy of reverse time algorithm_

The imaging condition for reverse time is to correlate the shot source wavefield of the same time with the reverse time anti‐propagation recorded wavefield.  The source wavefield is forward wavefield, while the reverse time back‐propagation recorded wavefield is back‐propagation wavefield.  If you want to obtain two wavefields of the same moment, you must store the travel process of one wavefield.  The simplest method is to store the To‐Tn wavefield, then back‐propagate the recorded wavefield; then read the coherent imaging of shot point wavefield at some moment of propagation.  However, the memory size of this method is huge, and can hardly be realized in real computation.  We came up with the following method through research work: with the help of the GPU/CPU computer platform, use the random velocity boundary model to transfer the shot point wavefield to Tn; then, using the Tn wavefield as the initial condition, back‐propagate the shot point wavefield and geophone wavefield and use the imaging condition to image at the same time.  In this way, the extra storage space is avoided; although the shot point wavefield needs to be re‐calculated, the GPU is used to calculate the wavefield extrapolation; compared with large‐scale I/O reading and storage, its time consumption is acceptable [14,15]. 

This chapter presents an implementation method for reverse time migration favorable for GPU computation based on the random velocity boundary model proposed by Robert [16,17] in 2009.  The random boundary function of structure in this chapter is:

(5.11)

Where, α is a coefficient related to velocity; _R_ is the thickness of random boundary region;   is the distance from the point in the random boundary region to the boundary; I( _x_ ) is the random number generated by seed number _x_ , and I( _x_ )∈(0, 1);   is the random velocity value;   is the velocity value of some point outside the random boundary.  Proper imaging results can be obtained through adjusting α and _R_. 

In a theoretical model trial a 3D salt dome model was used to study the accuracy and suitability of various prestack imaging method algorithms.  The following observation system parameters were designed for this model to perform forward modeling: altogether 4780 shots; 68 traces each shot; shot interval: 80 m; trace interval: 40 m; time sampling rate: 8 ms; number of samples: 615.  The migration parameters for numerical test are: main frequency: 20 Hz; frequency scope: 5–55 Hz; migration aperture: Aperture _ x = 6000 m, Aperture _ y = 3000 m; imaging output interval: dx = dy = 20 m, dz = 10 m; comparison of migration time: 3510 min.  of total time consumption for using a 60‐node CPU system, and 298 min.  of total time consumption for using a 12‐node GPU/CPU coordinating system (S1070).  Therefore, the single node speed‐up ratio is GPU: CPU = 58.89:1.  Through trial, we can see that this algorithm not only has efficient speed‐up ratio, but has the greatest imaging accuracy, as shown in Figure 5.16. 

From the above figure, we can see that, when the velocity model is accurate, the depth‐domain imaging can restore the true structural shape of underlayer; but for special structures, neither integral migration or one‐way wave equation can generate accurate image.  By wavefield accurate propagation to complex velocity structure, the reverse time migration can realize the imaging to steep‐dip formations and complex structures.  From the depth slices of 2100 m (Figure 5.17), we can see that reverse time migration is very accurate for salt dome boundary characterization and geologic interface imaging. 

**Figure 5.16** Comparison between (a) one‐way wave migration and (b) reverse time migration results of salt dome model. 

**Figure 5.17** Comparison between (a) velocity slice and (b) reverse time migration velocity slice of salt dome model. 

### 5.1.9 Comparison and research on reverse time migration imaging effect

The combination of velocity modeling and migration algorithm is the key to accurate seismic imaging.  Reverse time migration is now the depth‐domain imaging method with the highest accuracy, which can realize accurate imaging of various waves and can accurately image the high‐angle reflecting interface (the interface being even more than 90o).  From the result of reverse time migration imaging, the two‐way wave equation depth‐domain imaging technique is obviously better than the one‐way wave equation in imaging subsalt and salt dome flanks.  It accurately locates the salt dome boundary and dome flanks, as shown in Figure 5.18 and Figure 5.19, and also removes the time‐domain structure distortion caused by salt dome velocity anomaly to underlayers.  The subsalt formations can be accurately imaged in depth domain [18].  The top interface of salt dome, dome flank boundary and special subsalt structure with salt flank of over 90o can be accurately imaged [19].  Complex geologic bodies like salt dome are lit by many channels, and the steep halite flank arrival is lit by prism wave, showing that these salt bodies cannot be imaged by a conventional one‐way propagation operator.  The application of a two‐way wave equation method improves the imaging of salt dome flanks and subsalt formations [20,21]. 

**Figure 5.18** Comparison of imaging results of subsalt structure by (a) one‐way wave migration and (b) reverse time migration. 

**Figure 5.19** Comparison of imaging slices of subsalt structure by (a) one‐way wave migration and (b) reverse time migration. 

### 5.1.10 Study on subsalt structure features and description of major traps

Figure 5.20 shows P1 top structural form (salt base) with east‐high and west‐low monocline as a whole; on iso‐t0 graph.  A series of local traps have developed in the middle of work zone, while on the structural map generated by reverse time migration, the traps have not developed (Figure 5.20).  Through analysis of seismic profile features, it is found that the east part of the work zone has developed seismic anomalous bodies, which have been verified by drilling (YKT‐1). 

KT‐I structural form: on iso‐to graph of KT‐I top surface, KT‐I is in southeast‐high and northwest‐low monocline, and is missing along NIK‐3 in the west and to the west of NIK‐3.  This formation has developed six structural traps, mainly in NE strike and few in NW strike.  Except for the North Troyes Structure and No.  2 Trap, the areas of other traps are small, as shown in Figure 5.21. 

KT‐II top surface structural form is due to the fact that two horizons of KT‐I and KT‐II are two near‐parallel reflectors on seismic profile; the iso‐to graphs and structural forms of them have more or less the same features.  The difference is that the KT‐II formation is found in the whole bock, and the number of its traps and area are more than KT‐I top surface (Figure 5.22).  The MKT top and Visean top formations are also near‐parallel reflectors just like KT‐I and KT‐II top formations, so their iso‐to graphs and structural forms have the same features of KT‐I and KT‐II tops (Figs.  5.23 and 5.24). 

**Figure 5.20** (a) Iso‐to graph and (b) structural map of the Lower Permian top in mid block. 

**Figure 5.21** (a) Iso‐to graph and (b) structural map of KT‐I top in mid block. 

**Figure 5.22** (a) Iso‐to graph and (b) structural map of the Carboniferous KT‐II top in mid block. 

As a whole, the iso‐to graph and structural map patterns of subsalt structural horizons are quite different: (1) The North Troyes structure is shown as a number of trap highs on to graph and as a complete fault nose on the structural map. ( 2) Wells W‐1 and AL‐1, are affected by overlying salt domes, and the amplitude is great on iso‐to graph, but relatively gentle on structural map. ( 3) The anomalous body (Well YKT‐1) in the east is like a strip belt on iso‐to graph, and its location is obviously higher than the surrounding structure; but on the structural map after the effect of anomalous body velocity is removed, the high point location migrates to its right side, indicating that some subsalt structures are pseudo‐structures caused by velocity anomaly of salt domes.  Through structural interpretation and imaging, altogether 11 local traps have been discovered in subsalt target zone (KT‐I and KT‐II), which are mainly anticline or faulted anticline, mainly in NE strike; the areas of North Troyes, No.  6 structure and No.  2 Trap are relatively large (Figure 5.25). 

**Figure 5.23** (a) Iso‐to graph and (b) structural map of the Carboniferous MKT top in mid block. 

**Figure 5.24** (a) Iso‐to graph and (b) structural map of the Carboniferous Visean top in mid block. 

**Figure 5.25** Distribution map of traps on KT‐I and KT‐II tops in mid block. 

## 5.2 Application of High‐density All‐round Seismic Data Processing in the Carbonatite Region

### 5.2.1 General

With the PSTM data of a conventional bin of carbonatite, low SNR inside reservoirs [22,23] and spatial resolution are not able to meet the demand for identifying solution caves of below 25 m, and the carved cave volume is larger than the actual volume.  There is a difference in spatial distribution.  In addition, the azimuth of existing 3D seismic data is narrowly distributed, which affects the imaging accuracy of anisotrophy processing and cannot meet the requirement of fracture identification and reservoir characterization.  In order to improve the quality of original seismic data of carbonatite and accuracy of the "beads" and fractures, and to finely characterize the development features of fractures and caves, we selected a wellblock in Tabei as the pilot field for research on high‐density, full azimuth seismic data imaging technique [24]. 

#### 5.2.1.1 Overview of the research

The key of the research work was to improve the original seismic data quality of carbonatite and imaging accuracy for fault and fracture‐cavity and to carry out research on data imaging for azimuth fractures forecast and prestack reservoir forecast, with the Ordovician carbonatite reservoir of strong heterogeneity as the target. 

The specific research work includes: (1) To carry out data comparison, processing analysis and demonstration for several observation portfolios based on bin dimension of prestack migration, folds, distance between shot and geophone line and S‐P ratio, in order to provide an optimized design basis for promotion and application of field optimal observation system, high‐density full azimuth seismic exploration technology. ( 2) To carry out research on normalized processing technique and anisotropic prestack time and PSDM processing technique based on full azimuth data and azimuth data of prestack and poststack joint fracture forecast. ( 3) To carry out research on processing of azimuth seismic data and their fracture detection data volume so as to provide high‐quality data and gathering data for identification of carbonatite fractures and to lay a technical foundation for further promotion of high‐density full azimuth seismic survey technique. ( 4) To carry out research on processing of anisotropic amplitude‐preserved PSDM so as to provide high‐quality basic data with high fidelity, good amplitude and abundance of geologic information for identification of carbonatite fracture reservoirs. 

#### 5.2.1.2 Overview of the work zone

The high‐density 3D seismic work zone (Figure 5.26) belongs to the Kuqa Country of Xinjiang Uygur Autonomous Region, located on the north edge of hinterland of the Takla Makan Desert, about 50 km to the north of Kuqa Town and 20 km to the south of Tarim River.  The land types of the work zone can be categorized into three types: Euphrates poplar and rose willow, loose saline‐alkali soil and farmland villages (Figure 5.27). 

**Figure 5.26** Deployment diagram for high‐density 3D seismic survey. 

**Figure 5.27** Distribution map of high‐density 3D surface types. 

The topography of the work zone is generally high in the northwest and low in southeast, with the surface relief being generally gentle.  The elevation is 975–955 m, with a relative height difference of 20 m (Figure 5.28).  The surface layer is simple in structure, being a two‐layer structure of low and high velocity, of which the low‐velocity layer is 1–11 m thick, with parts up to 20 m in thickness (Figure 5.29).  The velocity of low‐velocity layer is 360–550 m/s. The top interface of high‐velocity layer is a gentle water table, high in the west and low in the east; its velocity is 1600–1700 m/s. All the shot‐points are below the water table, with the favorable shot conditions. 

**Figure 5.28** Plane variation diagram of high‐density 3D surface elevation. 

**Figure 5.29** Thickness variation diagram of high‐density 3D low‐velocity belt. 

#### 5.2.1.3 Existing problems and analysis of difficulties

### _5.2.1.3.1 Geologic issues_

Due to the strong anisotrophy of the carbonatite reservoir itself and interpretation limitation of low‐frequency and low SNR seismic data, many petroleum geologic conditions are not understood and more basic research and development of methods are required.  The geologic problems are summarized as below:

  1.  Too many reservoir types.  The major accumulation space of Ordovician carbonatite reservoir is solution cavity first, then the structural fractures and network micro‐fissure system, and the stylotite and stylotite‐associated solution void as the third.  The inter‐crystalline pore and inter‐crystalline solution void, inter‐granular solution void, intragranular solution void and micro‐fissures contribute little to the reservoirs. 
  2.  Too many bed series and types of effective reservoirs and large lateral variation, making it difficult to identify effective reservoirs. 
  3.  Multi‐stage activity of the structure, generating complex fault systems and enhancing the complexity of the reservoir space. 
  4.  Too large lateral variation of the reservoir. 
  5.  Too difficult in fluid identification and oil/gas bearing prediction. 

The large lateral variation of reservoir is mainly in two aspects: difficulties in identification and forecast of effective reservoirs and of oil/gas possibilities, which decreases the drilling success rate in exploration and production. 

### _5.2.1.3.2 Analysis of original data_

The original data quality is analyzed in two ways.  The first is to analyze the SNR, energy and frequency of the data and the characteristics of previous data processing, so as to find out the existing problems in original data, seize the key points to be solved during data processing and find out the solution to the problems.  The other way is to make detailed analysis and judgment of each processing step according to technical characteristics of prestack migration and the requirement on high SNR and resolution of the data, thus selecting proper processing method and parameters accordingly. 

  1.  Analysis of interference waves. Subject to the influence from surface and near‐surface conditions, the surface wave in the work zone is developed.  The main interference wave is the surface wave interference with the highest velocity at 1200 m/s. From the spectrum analysis, we can see clearly that, at low‐frequency end, the frequency energy of surface wave is far greater than the effective wave energy in this frequency, while the wave frequency is between 2 Hz and 12 Hz.  Moreover, the original single shot records also show some frequency noise, high‐energy anomalous amplitude, linear interference wave and random noise (Figure 5.30). 
  2.  Analysis of frequency. Relative to the shallow layer clastics, the original dominant frequency of target zone in the work zone is low and the high frequency signal is weak.  Through spectral analysis of original single shot, the original dominant frequency of shallow reflection wave is about 24 Hz, and that of the target zone is about 22 Hz (Figure 5.31).  The range of frequency is from 6 Hz to 60 Hz and the dominant frequency of surface wave is about 8 Hz. 
  3.  Correlation of original data from high‐density full azimuth acquisition and conventional acquisition. Figure 5.32 shows two arrays of 3D data from high‐density full azimuth acquisition and conventional acquisition where the shot points and geophone points are exactly the same.  It can be seen that the original data from single shot is close in overall features like energy and spectrum; but from single shot data, the surface wave from high‐density full azimuth gathering is strong in both low‐velocity noise and effective signal; from the spectrum, the data from high‐density full azimuth gathering has wider bandwidth and richer low frequency and high frequency components than conventional data.  In addition, due to their small trace pitch and rich high frequency components, the high‐density full azimuth data is stronger in resisting aliasing frequency. 
  4.  Analysis of single‐noise ratio (SNR).This SNR shows certain spreading law in space.  From the attribute of SNR in Figure 5.33, we can see that SNR generally shows the tendency of low in the west and high in the east, low in the south and high the north.  From seismic profile, the SNR is from shallow to deep.  The reflectors above the Carboniferous system are good in continuity and have high SNR; the main target zone of the Ordovician system has great burial depth and it is hard to generate a wave impedance interface in carbonatite due to its special complexity.  Therefore, the reflection is weak and imaging is poor, and the inside data resolution and SNR are relatively low. 
  5.  Analysis of anisotrophy. The seismic data from high‐density and wide azimuth acquisition contains rich fractures and reservoir information, providing favorable basic data for prestack azimuth processing.  The high‐density full azimuth seismic data from the work zone is divided into six equal azimuths as per 30°, and the number of folds of each azimuth trace gathering is between 30–40 times, which can satisfy the demand of prestack forecast.  From the analysis of azimuth stacking velocity (Figure 5.34), it can be seen that the velocity changes with azimuth and the problem of anisotrophy would occur accordingly. 
  6.  Analysis of evenness of data sampling. In recent years, the prestack migration imaging technique has been gradually normalized, and the prestack imaging technique is more demanding of the acquisition observation system.  Insufficient sampling of common central point and offset during migration can cause severe spatial aliasing.  The data evenness should be analyzed from multiple aspects.  The evenness of CMP trace folds alone does not mean the evenness of spatial sampling, so it is more important to conduct analysis in terms of common offset and common azimuth.  The folds of high‐density full azimuth data in the work zone are even and the azimuth is also even.  When displacement distance is up to about 5000 m, the azimuth can be as high as 360°, but there is obvious unevenness in offset distance, especially at near‐offset end and far‐offset end.  The sampling of common offset gather is sparse (Figure 5.35), requiring normalized processing of data. 

**Figure 5.30** Analysis of interference wave. 

**Figure 5.31** Analysis of spectrum. 

**Figure 5.32** Comparison chart of (a) single shot and (b) spectrum of acquired data by conventional method and high‐density full azimuth method. 

**Figure 5.33** (a) SNR attribute and (b) original stacked profile. 

**Figure 5.34** Comparison of velocity spectrum and gather of high‐density full azimuth data at different azimuths. 

**Figure 5.35** Attribute graph of folds, azimuth and offset in work zone. 

### _5.2.1.3.3 Geophysical issues and processing difficulties_

The structural complexity in this area and the high imaging requirement caused by the difficulty in forecasting carbonatite reservoir lead to the following problems and difficulties in seismic imaging in two aspects:

  1.  The carbonatite oil reservoir types are complex, the S and P heterogeneity of the reservoir is strong, the difference in filling of solution cavities is great and the oil/water relation is complex.  The first challenge is how to improve the fidelity preservation of data amplitude and resolving ability of seismic signals. 
  2.  This area has developed faults with "beads", pinchout and unconformity, and the imaging accuracy requirement is high and migration velocity is sensitive.  The second challenge is how to improve the imaging accuracy effectively. 

Therefore, for forecasting the distribution of effective reservoirs and fluid identification using prestack seismic technique, the key is to improve the processing of dominant frequency and SNR based on fidelity preservation processing, and meanwhile to improve the imaging quality using the PSTM processing concept.  Reverse time migration technique is used to improve the accuracy of bead restoration [4,5]. 

### 5.2.2 Research concept and technical strategy

#### 5.2.2.1 Research concept

The oil/gas bearing reservoir distribution is extremely complex in this work zone.  The seismic data inside the carbonatite has low SNR and spatial distribution and cannot meet the demand for identifying solution cavity of below 25 m. In addition, the azimuth of conventional 3D seismic data is narrow, which affects the imaging accuracy of anisotrophy processing and can hardly satisfy the fine characterization of fracture reservoirs.  As a result, in view of the above problems, it needs to adequately and fully tap the potential and advantage of the high‐density full azimuth seismic data in terms of imaging and interpretation, adopt the research concept of integrating processing and interpretation with the geology and geophysical, and carry out the research work as per the amplitude preservation idea as discussed in Chapter 1 during the entire processing to ensure the fidelity and amplitude preservation of the processing results. 

According to the characteristics of high‐density full azimuth data and considering the geological conditions of the work zone, we first carried out data comparison and analysis to a number of observation schemes with the fine processing of seismic data.  We then carried out research work on normalized processing of full azimuth data and azimuth data based on forecast of prestack and poststack joint fractures, and research on anisotropic PSTM and PSDM processing technique.  In subsequent interpretation work, we performed the interpretation to azimuth data in terms of structure, fault and forecasting of prestack and poststack fractures, compared the advantages of high‐density data and conventional data in reservoir forecast and fluid identification, and analyzed the reflection features of "non‐bead" reservoir and "bead" reservoirs [26,27]. 

#### 5.2.2.2 Technical strategy

In view of the complex geological characteristics of carbonatite reservoir in this work zone, we mainly took the following technical strategies in prestack processing:

  1.  Seismic data processing technique with relative fidelity preservation [28,29].During the entire processing, the selection of processing modules and parameters should take into full consideration the fidelity preservation of the processing technique.  The wide‐band processing procedure was used to protect the low‐frequency component to the greatest extent possible so that the amplitude of the resultant profile was good, the resolution was obviously improved and the breakpoints were clear.  The "bead" reflection features of the target zone was more apparent and the SNR of CMP gather was moderate, but good amplitude preservation and azimuth information enabled proper forecasting of fracture distribution law. 
  2.  Anisotropic PSDM imaging technique. The anisotropic PSDM can well address the problem of lateral variation of velocity.  Compared with time migration, the "bead" restoration is more accurate, and the various fluid response of the profile matches well with the hole, which maintains the true signals of the data. 
  3.  Fractional azimuth PSDM imaging technique. The fractional azimuth gather prestack migration technique can improve the accuracy of fracture forecast.  By observing the layer slices, there are evident differences of fracture system on different azimuth spatial spread. 

### 5.2.3 Key processing techniques

#### 5.2.3.1 High fidelity preservation full azimuth noise suppression technique

This research has developed a set of linear noise suppression technique series for full azimuth seismic data [30,31], which properly suppresses the noise and ensures the SNR and amplitude information of internal carbonatite reservoirs.  During the entire noise suppression, the noise is suppressed in multiple steps in different processing stages according to the development characters of the noise. 

  1.  Processing of anomalous amplitude in frequency division domain. 

The processing of regional anomalous amplitude is to perform four‐domain decomposition of seismic recorded energy at common shot gather, common geophone gather, common offset gather and CDP gather, according to conformity of seismic record energy to surface consistency assumption, to calculate the anomalous amplitude, which can be used to attenuate the anomalous amplitude of strong energy. 

Just like the effective signals, the frequency of noise is different in different time periods.  The processing of frequency‐division region anomalous amplitude is to perform proper frequency band division to the seismic data, understand the spread regularity of signals and noise in different frequency band and perform pertinent processing, which can further enhance the fidelity preservation of the denoising result and hence improve the data processing accuracy.  Compared with the conventional regional anomalous processing, the frequency‐division regional anomalous processing is advantageous in using the superior frequency band of interference wave to extract its features and using the available features in non‐superior frequency band as a restriction, so as to identify the interference waves. 

During processing of the frequency division region anomaly, three time windows are divided, according to noise frequency features, for statistics.  The dominant frequency of anomalous amplitude in the windows is determined by scanning as 14 Hz, 8 Hz and 6 Hz; the low‐frequency surface wave is calculated out as strong energy.  From the stacking profile, the refraction wave and surface wave are well suppressed, as shown in Figures 5.36 and 5.37. 

  2.  Full azimuth linear noise suppression technique. The observation system of full azimuth data has a large S/P ratio.  For the same shot gather, the spatial sampling of a single shot subset on a different receiving line has different evenness; the sampling of the single shot subset nearest to the shot location is the most uniform, while the farther the array is from the shot location, the less uniform its sampling, which causes changes to linear interference pattern on far‐shot array.  Linear noise suppression like f‐k conversion needs relatively even data sampling, but due to the fact that the full azimuth data sampling cannot meet the requirement of algorithm, the linear noise is difficult to suppress.  Two techniques are used to suppress the linear interference wave: cross‐array based 3D f‐k and linear moveout correction combining 2D f‐k.  These two methods can adjust the spatial sampling of seismic data from different angles and make it become even, satisfying the requirement of f‐k conversion.  They can both suppress the linear interference wave of full azimuth data well.  
    1. _ f‐k x ‐ky_ on cross‐array. 

Just like shot gather and CMP gather, the cross gather is a means of data gathering of seismic data received by one seisline with the shot line crossing it, or it can be simply construed as a small piece of local single fold profile in 3D data volume.  For the poststack data, the spatial sampling is even, and it is specified that the inline is in x direction and xline is in y direction.  In this way, the prestack offset can be broken into two vertical components: x and y. The actual spatial sampling rate is accordingly broken into two components: geophone interval and seisline interval, so that both directions of inline and xline have even sampling.  Compared with conventional acquisition, high‐density acquisition has smaller geophone interval and seisline interval (Figure 5.38), which indicates that spatial aliasing can be more readily suppressed under smaller spatial sampling rate.  Therefore, the 3D _f‐k_ on cross‐array can well estimate the velocity distribution range of linear noise. 

On cross‐array gather, the surface wave is in a cone‐shaped distribution on 3D space.  The linear noise can be well forecast and fitted in this direction, and the spatial sampling is also regular, hence the 3D f‐kx‐hy cone filtering can well suppress linear noise, like surface wave on cross‐array data volume, and realize the real prestack 3D filtering.  Its denoising effect is better than 2D f‐k, as shown in Figure 5.39.  From the profile, the low‐frequency linear interference is well suppressed.  Additionally, from the point of the single shot noise, the noise filtered by 3D f‐kx‐ky is more reasonable, and the fidelity preservation is also greatly improved as compared with 2D denoising method. 

    2.  Joint technique of linear moveout correction and 2D _f‐k._  This technique starts from the seismic propagation path and eliminates the effect of lateral offset on group interval, so that the group interval of each array is all constant, satisfying the requirement of _f‐k_ variation and achieving the goal of suppressing the far‐array linear noise [32,33].  As shown in Figure 5.40, the underground refraction velocity is _V_ 2, and R1 and R2 are the receiving traces on the same location on two parallel geophone lines, respectively.  If the shot point falls on R1 geophone line, then the travel times of refraction wave received by R1 and R2 lines respectively are:

(5.12)

(5.13)

They are the same refractor, the intercept time T0 in the above two equations is equal to refractor velocity _V_ 2, so the time curve pattern of refracted wave in different array is only related to offset.  Assume the interval between lines R1 and R2 (seisline interval) is M, then M1 and M2 have the following relation between them:  . 

Similar to the realization process of calculating the reflected wave normal moveout, this chapter conducts linear moveout correction through calculating the refracted wave moveout, eliminates the effect of lateral offset and restores the group intervals of each array to the interval designed by the observation system. 

The equation (5.14) is the formula to calculate the linear moveout, that is:

(5.14)

Implementation steps for linear moveout correction:

> Calculate the lateral offset of each array M.
> 
> Calculate the offset M1 of each seismic trace in each array when lateral offset is 0. 
> 
> Find linear moveout ΔT and use it on each array to eliminate the effect of lateral offset. 
> 
> Use linear noise suppression technique like f‐k to attenuate the linear noise. 
> 
> Carry out reverse correction of linear moveout to restore the normal offset. 
> 
> After application of moveout correction, the effect of lateral offset on trace interval is eliminated, as shown in Figure 5.41.  The group interval of all the arrays are normalized to 30 m, so that the spatial sampling of the data is even. 
> 
> Figure 5.42 is a chart showing the effect of joint denoising by linear moveout correction and f‐k.  After linear moveout correction, the effect of lateral offset can be eliminated, and all the arrays are corrected to the receiving state when lateral offset is zero, that is, 2D data.  The linear interference wave restores the linear pattern, and the 2D f‐k filtering is very effective.  After reverse correction, the single shot restores to normal offset and the linear noise is effectively suppressed. 

  3.  Attenuation of 3D prestack random noise. Apart from surface wave interference and regular linear interference, the noise on original data from the work zone also includes some random noise with poor coherence.  In particular, the SNR of the target interval is low, the effective waves on CMP gather cannot be continuously tracked and the presence of random noise severely affects the SNR of seismic data, all of which directly affects the result of prestack forecast.  In view of this kind of interference wave, and after many tests, it has been determined that the method of 3D prestack random noise attenuation on cross array can be used to suppress these random noises, which works effectively.  The SNR of CMP gather after suppression of prestack random noise is improved, especially the target interval.  What is more important is that the improvement of CMP gather quality provides very good basic gather data for subsequent prestack time migration and prestack characterization of oil/gas reservoir.  Figure 5.43 shows the CMP gather before and after 3D prestack random noise attenuation. 

**Figure 5.36** Single shot before and after frequency division anomalous amplitude processing. 

**Figure 5.37** The profile before and after frequency division anomalous amplitude processing and noise profile. 

**Figure 5.38** Cross‐array observation system chart. 

**Figure 5.39** 3D f‐kx‐ky before and after single shot prior to denoising on cross‐array gather. 

**Figure 5.40** The figure of refracted wave about different arrays of lateral offset. 

**Figure 5.41** Distribution of group interval before and after linear moveout correction. 

**Figure 5.42** Implementation process schematic of linear moveout correction with 2D f‐k. 

**Figure 5.43** Comparison of CMP gathers (a, b) before and after 3D prestack random noise attenuation. 

**Figure 5.44** Comparison of profiles before and after serial deconvolution. 

#### 5.2.3.2 Technique for improving prestack vertical resolution

In carbonatite regions, the effective signals of fractures and solution cavities included in seismic records are weak and difficult to separate from other signals.  This involves the two basic problems of SNR and resolution of seismic signals.  In view of this problem, the processing of resolution and SNR should be enhanced in seismic data processing.  The processing technique for deconvolution wavelet is the key technique to improve the resolution.  In carbonatite areas, both fidelity and resolution of seismic data should be improved, so the selection of the deconvolution method is critical. 

The target zones in the work zone are mainly limestone with low frequency, the main frequency is about 22 Hz, and its SNR is low.  The selection of deconvolution and parameters should be very prudent.  The following tasks should be performed during processing: (1) Using multi‐time‐window deconvolution technique to eliminate the effect of the time‐dependence character of seismic wavelet on stacked profile. ( 2) Resolution improving must take into account the SNR.  If resolution prior to prestacking is raised too high, it will reduce the SNR of seismic records, which will be unfavorable for the subsequent velocity analysis and residual static correction, and is especially unfavorable for reservoir forecast by prestack seismic data and detection of oil/gas; therefore, the resolution should be increased gradually. ( 3) Eliminating the non‐surface consistence factors.  Theoretically, the seismic waves from the same source received by different geophones have the same seismic wavelet features, but in practice, due to changes in surface conditions, the different shooting conditions cause the single shot to produce different seismic wavelet.  The application of surface consistent deconvolution can eliminate these factors, which affects the inconsistency of the seismic wavelet spatial phase. 

Fractures and cavities have fully developed inside carbonatite in the work zone, especially in the northern part, where the density of solution cavities is very large.  The identification of fractures and cavities is closely related to seismic resolution.  In practice, the seismic identification capability is limited and small size fractures are difficult to identify.  As a result, the resolution of seismic data needs to be improved as much as possible within the effective frequency band of seismic data. 

Depending on the characteristics of solution cavities in the work zone, the resolution of seismic data may not be improved to the optimal result in one attempt.  Accordingly, we used a serial deconvolution method and integrated the advantages of various deconvolution methods.  First, the surface consistency deconvolution was used, with the main purpose of eliminating the effect of surface factors and making the results after deconvolution more truly reflect the change in formation lithology.  It is a processing module with relative amplitude preservation.  Then based on the above, we conducted serial tuning of deconvolution to preserve SNR and also improve the resolution.  In addition, the lateral resolution of seismic data after PSTM was greatly improved, but the longitudinal resolution was somewhat reduced compared to that before migration.  Therefore, serial tuning of deconvolution on PSTM CRP gather and poststack data gives the best ultimate resolution of gather and migrated data volume. 

The relation between SNR and resolution is well dealt with during processing.  The resolution of target zone is improved while maintaining SNR, which is more favorable for "bead" imaging and will not immerse the weak "bead" reflection in low‐frequency background.  It will make the faults and reflected top interface of "beads" clearer, as shown in Figure 5.44. 

#### 5.2.3.3 Data regularization technique

From the fold attribute chart, we can see that the folds in this area are very even, but geophone offset is not evenly distributed.  During prestack imaging, this kind of unevenness will lead to occurrence of empty CMP on common offset, causing the presence of spatial aliasing and migrated arcing, hence reducing the SNR of the data.  For this reason, the data regularization technique is used to eliminate the empty CMP on common offset and make folds relatively even, thus improving the imaging effectiveness. 

At present, there are a number of techniques to realize data regularization [34,35], including interpolation method, trace‐borrowing method, DMO, DMO−1.  In view of the characteristics of development of small fractures and cavities inside carbonatite in this region, the method of borrowing traces from the same bin on common offset gather is adopted to realize the goals of non‐mixing waves and high fidelity. 

In common offset gather where the two ends of offset is are less than 1500 m and greater than 5000 m (Figure 5.45), due to sparse spatial sampling, the data regularization technique cannot compensate all the empty CMP, but after being regularized, the fold attribute is remarkably improved.  However, at advantageous offset of between 2000 m and 5000 m (Figure 5.46), the regularization technique plays a very good role due to dense spatial sampling. 

**Figure 5.45** Comparison of common offset folds before and after data regularization. 

**Figure 5.46** Comparison of common offset folds before and after data regularization. 

Similarly, from the prestack imaging profile (Figure 5.47), the amplitude feature of the profile after data regularization is well maintained, and the amplitude features of near offset and far offset of CRP gather (Figure 5.48) are apparently improved; this is more favorable for extraction of prestack AVO attribute. 

**Figure 5.47** Comparison of profiles (a) before and (b) after data regularization. 

**Figure 5.48** Comparison of profiles (a) before and (b) after data regularization. 

#### 5.2.3.4 Technique for high accuracy migration velocity modeling

### _5.2.3.4.1 Technique for PSTM root mean square velocity modeling_

The fractures and cavities in the work zone are adequately developed (Figure 5.49); in particular, solution cavities are very dense in the northern part of the work zone.  Each solution cavity can be deemed as a small subsurface anomaly.  The velocity of these cavities is very sensitive, and very small velocity difference during migration will cause large difference in imaging.  In view of this character, we adopted the technical concept of high precision velocity analysis (Figure 5.50).  First, we used large migration velocity grid to control the velocity variation in the whole work zone, then gradually intensified the velocity grid and continuously improved the imaging accuracy of the cavities; the velocity grid density of the entire work zone was controlled at 150 × 150 m. Intensification of velocity spectrum can better characterize the "bead" reflection imaging and "bead" boundary, and greatly improves the lateral resolution, which provides more reliable basic data for accurate positioning of well location. 

Migration velocity is the major factor affecting PSTM.  The accuracy of migration velocity directly affects the migration imaging.  PSTM is a process of continuous iteration to migration velocity and migration processing.  The building of the initial velocity model is not only a process of data processing, but also of analysis and understanding of the subsurface geologic structural configuration, various geologic phenomenon and division of various geologic sequences [36].  The building of the initial velocity model is the key link in PSTM imaging technique.  The initial velocity model of this work zone is from the stacking velocity obtained from previous processing.  The subsurface bed series of this work zone is close to the horizontal layered medium, so its stacking velocity can be regarded as root mean square velocity. 

Velocity model optimization and processing iteration are the main means of obtaining accurate imaging.  In order to obtain accurate velocity, the vertical migration velocity iteration analysis method and migration velocity scanning method are combined to modify and optimize the migration velocity.  When the prestack CRP imaging gather event is flattened it is used as a major means to judge the correctness of migration velocity.  In the event of CRP imaging gather being flat and straight, the migration profile imaging effectiveness is good, indicating that the migration velocity is correct.  However, if the CRP gather is not flat and straight, but bends up or down, it indicates that the migration velocity is over small or over high.  The migration velocity will have to be adjusted and optimized accordingly until CRP gather is flat and straight and the migration profile is correctly imaged (Figure 5.51). 

**Figure 5.49** Distribution map of fractures and cavities. 

**Figure 5.50** Processing flow for PSTM. 

**Figure 5.51** Criterion for velocity rationality in velocity analysis. ( a) Analysis of root mean square velocity on CRP gather. ( b) Residual delay analysis to perform fine tuning of velocity. 

Through multiple iteration to PSTM of target line and migration velocity migration, we can make a better time migration velocity model and hence obtain accurately imaged 3D PSTM imaging velocity body.  The faster speed of computers greatly facilitates the rapid realization of enormous amounts of migration computation.  In order to verify the accuracy of the obtained final migration velocity, we scan the velocity by 100% and then select the velocities of different percentages of the final migration velocity to compute the PSTM of target lines in order to obtain the relevant CRP gather and PSTM profile.  Comparison shows that optimizing and fine‐tuning have finalized the optimized PSTM velocity (Figure 5.52). 

### _5.2.3.4.2 PSDM depth – interval velocity modeling technique_

Compared with PSTM, the PSDM should take into consideration the underground travel time of seismic waves and the refraction phenomenon on velocity interface.  Therefore, a model, which reflects subsurface velocity variation and velocity interface depth, must be provided.  The building of velocity model is a key to PSDM.  PSDM needs an accurate depth domain interval velocity model.  The prestack depth imaging is more sensitive to velocity error than time migration, which may cause problems in two aspects: one is that the imaging error caused by incorrectness of velocity field can easily offset or even surpass the improvement on migration method; the other is that the incorrectness of PSDM velocity field will generate pseudo‐structures. 

**Figure 5.52** Root mean square velocity model for final PSTM. 

It is very difficult to build an accurate velocity model for this area to influence igneous rock and carbonatite velocities, with sensitivity of the "beads" to velocity and the existence of a number of small faults.  In line with the characters of the data from the work zone, we put forward the S‐P united velocity modeling technique.  First, pick up the geologic horizon, then find the macro‐velocity by using the structure constrained velocity modeling technique and control the overall velocity pattern.  After that, for small size velocity anomalies like fracture reservoirs, we use longitudinal velocity analysis to accurately obtain the "bead" imaging velocity and make it more convergent.  In this way, the boundary is also characterized more clearly, hence addressing the problem of local anomaly and sensitivity of "bead" velocity in target zone. 

  1.  Building of time interval model. The structures in the work zone are not complex.  First, interpret the structural horizons on time migration domain, and combine closely with geologic horizons during interpretation to control the variation law of velocity interface, as is shown in Figure 5.53.  Then, use the ray migration and proportion to project the time interval onto depth domain; through initial velocity migration, use the interval and imaging gather to obtain horizontal delay spectrum.  By picking up the delay spectrum, we use the method of tomographic inversion for travel time to optimize and iterate the velocity; subsequently, pick up vertical delay and use the method of restrained interval velocity inversion to optimize and iterate "bead" imaging velocity. 
  2.  Optimizing interval velocity by reflected wave tomography. 

The depth migration based tomography method is a velocity model optimizing method based on tomography of depth migration gather.  This method converts the depth error on migrated CRP gather into relevant time error along the CRP ray path; hence we can use the conventional travel time tomography.  Through tomography, we iterated and optimized the PSDM interval velocity, causing the residual delay spectrum along the interval focusing and tending to zero, as shown in Figure 5.54.  Through a number of iterations, the macro‐velocity was virtually correct. 

After the accurate macro‐velocity was obtained, the "bead" imaging velocity of target zone was finely adjusted and optimized with the remaining vertical delay so that a satisfactory imaging effectiveness could be achieved (Figures 5.55 and 5.56).  Form Fig.  5.57 we can conclude that the vertical‐horizontal model building method overmatches the conventional ones clearly. 

**Figure 5.53** Building the time interval model. 

**Figure 5.54** Lateral delay spectrum of target zone. 

**Figure 5.55** S/P velocity analysis and quality control. 

#### 5.2.3.5 Azimuth PSDM and effectiveness

The seismic data from the work zone is high‐density and full azimuth information, including rich information on fractures and reservoirs.  The Kirchhoff PSDM technique was used for azimuth division processing to the data.  The result of PSDM shows that the full azimuth data has remarkable fracture identifying capability.  By correct application of the direction‐velocity difference, direction‐amplitude difference, direction waveform and phase difference, we can get more information on fracture reservoirs, which will help the design of horizontal drilling and production and also lay a good foundation for non‐bead reservoir forecast. 

**Figure 5.56** Velocity profiles of P‐velocity modeling and S‐velocity modeling. 

**Figure 5.57** Comparison of P‐modeling and P‐joint modeling imaging profiles. ( a) Along‐interval lateral velocity adjustment result. ( b) Fine adjustment result of longitudinal velocity. 

**Figure 5.58** Six azimuth folds and azimuth attribute chart. 

In this research, the data is equally divided into six azimuths according to analysis of fracture orientation and distribution law (Figure 5.58): 158° ~ 8°, 8° ~ 38°, 38° ~ 68°, 68° ~ 98°, 98° ~ 128° and 128° ~ 158°.  The folds of six azimuths are about 30 ~ 40 in average, which are virtually sufficient. 

Analysis was conducted to on the variation of fractures and cavities with azimuths through profiles and CRP gathers.  Figure 5.59 shows three fractures, of which Fracture 1 is more remarkable in directions 158° ~ 8°, 8° ~ 38° and 98° ~ 128° than in other three, while Fracture 3 is more remarkable in two directions: 38° ~ 68° and 98° ~ 128°.  From CRP gather (Figure 5.60), there is significant difference in amplitude and phase position of different azimuths.  Figure 5.61 shows the difference of amplitude and patterns at different azimuths, which clearly demonstrates that various geologic features like amplitude, phase positions, and velocities of fractures and "beads" in this area differ at different azimuths with apparent anisotropy. 

**Figure 5.59** Comparison of fractures on different azimuth profiles. 

**Figure 5.60** Remarkable amplitude difference of fractures on different azimuth gather. 

**Figure 5.61** Velocity difference of "beads" at different azimuths. 

As a result, the processing of azimuth division provides rich and varied information for prestack and poststack fracture forecast and lays a solid foundation for further understanding subsurface rock features and various parameter responses. 

#### 5.2.3.6 Anisotropic PSDM

While calculating the travel time, the anisotropic Kirchhoff PSDM introduced anisotropic parameters.  The key to anisotropic PSDM lies in the finding of anisotropic parameters.  In the work zone, the overlying formation lithologies are sandstone, shale and igneous rock with development of fractures, thus causing anisotropy of seismic wave propagation directions.  The anisotropy correction plays a crucial role, favorable for AVO analysis.  In the areas with severe anisotropy, the imaging quality may be improved greatly [37,38]. 

The anistropic parameters ε and δ can be obtained by three approaches.  The direct approach is to measure the acquired rock samples.  This method is direct and reliable, but in practice, we cannot find such rock samples for measuring.  The second approach is to use Walk‐away VSP data for computation.  In the work zone, only one well has such Walk‐away VSP data, which is used to obtain an anisotropic parameter body and conduct anisotropic depth migration, but the result was unsatisfactory.  One well alone cannot control the anisotropy of the entire area, so the indirect computation of seismic and logging data (the third method) was used to find the anisotropic parameter body.  In this process, the logging data from thirteen wells, and Walk‐away VSP data from one well were used to find the Thomsen parameters. 

Processing flow for anistropic PSDM is as below:

  1.  Data loading
  2.  Obtain isotropic velocity – depth model
  3.  δ value calculation, η function scanning, and ε value calculation to generate initial anisotropic interval velocity field
  4.  Reverse geometric spreading compensation, anisotropic PSDM of target lines
  5.  Residual delay analysis, ε correction, and optimization of anisotropic interval velocity field
  6.  Anisotropic prestack depth body migration

Due to insufficient log layered data, only the anisotropic parameters of two intervals (Figures 5.62 and 5.63) are obtained through iteration of anisotropic parameter ε; but by obtaining the anisotropic parameters of three intervals, the effect of overlying igneous rock on the underlying structure imaging is well eliminated (Figure 5.64), and the location error at about 6600 m in known well is greatly reduced from original 190 m to 50 m.

**Figure 5.62** Plane graph of the obtained anisotropic parameter δ. 

**Figure 5.63** Anisotropic parameters δ body and ε body. 

**Figure 5.64** Comparison of (a) isotropic depth migration and (b) anisotropic depth migration. 

#### 5.2.3.7 Reverse time migration

Reverse time migration mainly includes two steps of wavefield extrapolation and applied imaging conditions based on the two‐way wave equation [39,40].  The reverse time migration flow is as shown in Figure 5.65.  For imaging of single shot gather, first use two‐way wave equation for forward extrapolation for seismic source field and keep the extrapolation field of all time steps.  Then use two‐way wave equation for reverse extrapolation for received wavefield, and apply the imaging conditions after each step of reverse time extrapolation to obtain the image of that instant.  Add up the images of all instants to obtain the image of this shot gather.  Stack the reverse time migration of all shot gathers to obtain the final PSDM image. 

**Figure 5.65** Reverse time flow chart. 

We proactively explored the reverse time PSDM technique in the research zone.  The elevation change of this area is not great and the SNR of the data as a whole is high, so the velocity model built through conventional integral PSDM has high accuracy.  Therefore, the reverse time PSDM can be very effective in this area.  Figure 5.66 is a comparison of effective profiles by integral PSDM and reverse time PSDM.  We can see from the figure that the accuracy of reverse time migration profile imaging is higher, and the restoration of fractured reservoirs like "bead" fractures is more accurate. 

**Figure 5.66** Comparison of (a) integral PSDM and (b) reverse time PSDM. 

### 5.2.4 Analysis of difficulty tackling effect

Through processing, research and exploration of the high‐density and full azimuth seismic data from this work area, we have a better understanding of accurate imaging of carbonatite fractures in this area.  The high‐density and full azimuth seismic data shows favorable research value and practicability, which are described below:

  1.  The processing result of seismic data acquired by two different ways – high‐density full azimuth and conventional narrow azimuth, shows that the internal SNR of target carbonatite zone on high‐density full azimuth data is greatly improved, spatial resolution is also improved significantly and the number of identified "beads" is obviously increased (Figure 5.67). 
  2.  In respect of imaging, the depth migration has obvious advantage over PSTM in terms of spatial resolution, quantity and spatial location of fracture systems.  About four small size "beads" are clearly characterized (Figure 5.68).  This is mainly because PSDM can address the lateral velocity variation in overlying formation.  From the plane graph of PSDM (Figure 5.69), the quantity of "beads" is apparently increased compared with PSTM plane graph; the bead location of PSTM and PSDM in the north is almost the same; the bead location of PSTM profile in the middle is deviated to the north for about 30 ~ 45 m; and the bead location of PSTM profile in the south is deviated to the north for about 60 ~ 105 m. Drilling proved that PSDM profile is more consistent. 
  3.  High‐density full azimuth acquisition provides a guarantee for processing of divided azimuth PSDM.  In general, the folds of conventional acquisition are low and it is difficult to guarantee enough folds for divided azimuth gather.  When performing prestack migration, too sparse spatial sampling often leads to a large amount of spatial aliasing and very low SNR of profile and gathers, which does not satisfy the requirement of prestack and poststack forecast.  However, the high‐density azimuth gather has enough folds and the fracture system shows obvious inconsistency in features at different azimuths, which meets the requirement of expected processing. 
  4.  The reverse time migration technique for high‐density full azimuth data was explored and studied.  Due to its advantages, the reverse time migration technique has better amplitude and higher imaging accuracy than ray migration technique under the accurate velocity.  From Figures 5.70 and 5.71, which show the comparison of the effectiveness of Kirchhoff depth migration and reverse time migration, we can see that reverse time depth migration makes the spatial position restoration of fracture reservoirs more accurate.  Figure 5.72 shows that these two techniques have similar imaging quantity on beads, but reverse time migration gives a better characterization of river channels and faults; in particular, it is better for focusing of long vertical beads developed at steep faults and has finer characterization of bead boundary. 

**Figure 5.67** Comparison of PSTM of (a) conventional data and (b) PSTM of high‐density full azimuth data. 

**Figure 5.68** Comparison of (a) PSTM and (b) PSDM of high‐density full azimuth data. 

**Figure 5.69** Bead profile superimposition map for PSTM and PSDM of high‐density full azimuth data. 

**Figure 5.70** Comparison of (a) Kirchhoff depth migration and (b) reverse time migration. 

**Figure 5.71** Comparison of (a) Kirchhoff depth migration and (b) reverse time migration. 

### 5.2.5 Conclusions and understandings

The high‐density full azimuth seismic survey is the development direction of future research work.  This section describes research on high‐density full azimuth imaging technique for carbonatite geologic data, and the development of prestack imaging technical flow for high‐density full azimuth seismic data.  The key techniques include high fidelity preservation full azimuth noise suppression technique, the technique for improving prestack longitudinal resolution, full azimuth data regularization technique, full azimuth high accuracy migration velocity modeling technique, divided azimuth PSDM technique, anisotropic PSDM and reverse time migration technique. 

**Figure 5.72** Comparison of (a) Kirchhoff depth migration and (b) reverse time migration. 

The full azimuth data acquired by the above seismic imaging techniques has clear reflection on target zone beads and solution caves, correct restoration of spatial position and clear characterization of faults.  The Ordovician internal reflection quality is significantly improved compared with 3D processing results.  Its fracture forecast effect is obviously better than normal data and matches well with the log data interpretations, so it can fully satisfy the requirement of fine interpretation and prestack reservoir forecast. 

The research on seismic prestack imaging for carbonatite is a long‐term process.  Although some progress has been made in recent years, especially in the implementation of high‐density full azimuth seismic survey and the development of the new reverse time PSDM technique, there are still some constraints which are difficult to solve completely, such as quantitative characterization to "beads", solution caves and fractures.  It needs further research work to address the seismic imaging difficulty for carbonatite formations. 

## 5.3 Application of Seismic Imaging Method for Complicated Structures in the Tuha and Jiuquan Basins

### 5.3.1 Overview

The basins in western China mostly have complex surface and subsurface structures [41,42], especially in the main part of the structure.  The seismic data has low SNR, severe static correction problem, steep formation dip and development of fractures, making it hard to image seismic data accurately and to locate structures accurately, which materially restricts the progress of oil/gas exploration in this area [43,44].  In order to ensure further development of the Yumen and Tuha Oilfields, in pushing forward the exploration of succeeding blocks and improving the oil/gas exploration value of the Turpan‐Hami and Jiuquan Basins, there is an urgent need to carry out research on systematic geophysical technologies and formulate the key techniques and flows for oil/gas seismic imaging for the Turpan‐Hami and Jiuquan regions, to accurately locate the subsurface structures in this area and finely characterize the development of fractures and faults in this area, thus looking for favorable traps and expanding reserves.  It will provide a basis for well‐site planning and hence promote the development of oil/gas exploration in Turpan‐Hami and Jiuquan in an orderly, effective and rapid manner. 

For this purpose, PetroChina has deployed some geophysical technology projects in the northern Turpan‐Hami foothills, Qingxi of Jiuquan and Yumen, successively for several years.  In view of technical difficulties like seismic imaging and structural interpretation, in this field, PetroChina has carried out profound research into the integration of seismic prestack imaging and interpretation, and has developed a technology series for seismic prestack imaging in this area.  The key techniques among them mainly include integrated static correction technology for undulating surface model constrained fitting reconstruction, fidelity preservation processing technique for reservoirs shielded by coal bed, the "six‐division method" prestack noise suppression technique for complex regions and reverse time PSDM technique for floating surface.  During the work, the research team combined their research closely with production and applied the pertinent technique series developed in the research to oilfield exploration practices.  By using the new findings, the team confirmed the overall structural pattern and local structural features of the Baka and Wenjisang regions in the Turpan‐Hami Basin and the Qingxi region in the Jiuquan Basin, and virtually identified the size, strike and plane distribution law of the faults as well as fault activity stages, times and fault evolution law, verified and discovered a number of structural traps and optimized the favorable drilling targets. 

#### 5.3.1.1 Overview of the research area

  1.  The southern slope area of the Taibei Depression in the north foothill of Turpan‐Hami Basin. 

The research area, in Shanshan County, Xinjiang Uygur Autonomous Region, is located on a large alluvial fan of Bogda Mountain, which extends to the south in stagger and superimposition, with the 3D plan shown in Figure 5.73.  The general terrain is high in the north and low in the south, with various surface types and sharp topographical relief changes.  The surface in the research area is divided into three main types: gobi gravel area, hilly area and ultra‐thick gobi gravel area.  This surface is covered mainly by Quaternary gravel, with the surface type division as shown in Figure 5.74.  From the overall trend, the mountain front alluvial fans overlap and the mountain area has sharp relief and large relative elevation difference, with no clear regularity in alluvial fan distribution, causing large vertical and horizontal variation in surface structures.  The thickness difference of low deceleration zone is over dozens of meters.  In the Baka region, the structures are complex, and the velocity in steep dip structures changes violently; the SNR of both structure flanks is high, but the resolution of target zone is low, which cannot meet the requirement of reservoir forecast.  However, in the major part of the structure, the seismic data has low SNR, severe static correction problem and development of interference waves, so the seismic data cannot be accurately imaged.  As a result, the boundary of major structure is not clearly characterized and the structures are difficult to verify, which significantly restricts the steps of oil/gas exploration in the Baka area, and delays the exploration progress in these areas to some extent.  In the Wenjisang Block, the distribution of oil/gas/water is complex, the reservoirs have strong heterogeneity, and the subsurface geologic conditions are complex.  The S‐P resolution of seismic data is low, the mid‐deep target zones that are affected by coal bed shielding have especially weak energy and low frequency.  It is difficult to satisfy the requirement of fine reservoir forecast and fluid test, challenging the reserves confirming steady production of matured oilfields. 

The Turpan‐Hami Basin has formed a structural framework of foreland basin since the Yanshanian period, and has developed two favorable survey fields of thrust belts and slope belt on the southern edge of the depression.  Two types of tight sandstone gas pools have developed in the basin: lithologic gas reservoir of thrust belt structure, with the "sweet point" being controlled by structural setting; lithologic gas reservoir of slope belt on the depression, whose boundary is controlled by the intensity of hydrocarbon generation and depositional system, with the "sweet point" being controlled by favorable phase belt.  The area of mountain front of the northern Taibei depression belt (Qalkan) Dabu thrust belt, is 3500 km2, where the tight sandstone gas reservoir of late reformation has developed.  The structural high is the preferred "sweet point" of exploration; the slope area of structural transition is the extended favorable field for exploration. 

  2.  The Qingxi Depression in Jiuquan Basin. 

The Yumen Oilfield has an exploration and development history of 70 years.  With the increase of the degree of exploration in each depression of Jiuquan Basin and an in‐depth understanding of geology, the difficulty in exploration increases year by year, and the exploration field evolves from structure to lithologic formations.  The oilfields in the western Basin like Laojunmiao and Yaerxia, are now in their later stage of development; the production of fracture reservoirs in Qinxi declines quickly.  Due to strong heterogeneity of the Changshaling oil reservoirs in the eastern basin, the production of single well is not stable.  In order to ensure the sustainable development of the oilfield and lay a solid foundation for stable production in Jiuxi depression, the research work will focus on fine exploration to the structural lithology of the Qinxi Depression main body, strengthen exploration and evaluation on the Cretaceous system of Yaxi, and enhance understanding in oil reservoir geology.  Meanwhile, it will work on engineering technological difficulties and also develop new reserve blocks, which are of great significance to the oil/gas exploration of the Yumen Oilfield. 

The Qinxi Depression of the Jiuquan Basin is a Cretaceous depositional depression with the best oil geologic conditions and the largest exploration potential in Yumen Oilfield.  This depression, as an oil source, has developed a number of oil/gas reservoirs such as Kulongshan, Liugouzhuang, Yaerxia and Laojunmiao inside the Qinxi Depression and in surrounding areas, which is the major oil producing area of the Yumen Oilfield.  It is also one of the regions for rolling extension of the oilfield and increasing reserves and production.  Figure 5.75 presents an exploration plan map of the research zone. 

The research zone is located on the foothills thrust belt at north edge of Qilianshan.  The mountainous area is 275 km2, accounting for 85% of the total work area.  The mid‐west part of the work zone has some Quaternary gobi area, about 48 km2, only accounting for 15% of the work area.  Most of the work zone belongs to the Quaternary mountainous area, and a small part of the southern area is steep mountain, which is the outcrop of old formations.  The terrain of the work zone is high in the south and low in the north, high in the east and low in the west, with large relief.  The average elevation is about 2600 m, while the lowest is 1680 m and the highest is 3500 m. The mountain foothills have developed with crisscrossing ditches and valleys.  Five north‐south large gullies like East Ditch, West Ditch, Daxiaoliu Ditch and Large and Small wind ditches have developed from east to west, as shown in Figure 5.76. 

**Figure 5.73** 3D seismic survey deployment map for the north foothill of Turpan‐Hami Basin. 

**Figure 5.74** Division of surface types in the research area. 

**Figure 5.75** 3D seismic survey deployment map for the Qingxi Depression of the Jiuquan Basin. 

**Figure 5.76** Surface types division of the research area. 

#### 5.3.1.2 Current problems and analysis of difficulties

The research area is located on the large alluvial fan of Bogda mountain front and thrust belt of mountain foothills at north edge of Qilianshan.  The surface is complex, with various types of sharp reliefs, and the subsurface structures are also very complicated.  There are many problems like low SNR and severe static correction.  Additionally, the highly steep formations and development of fractures exist in this region.  All of the above features cause difficulties in accurate imaging of seismic data structure verification.  It is impossible to perform fine structural interpretation and division of fracture system.  The mid‐deep target zone has weak energy, low frequency and poor SNR, making it difficult to satisfy the requirement of fine reservoir forecast and fluid detection, which causes difficulty in stable production of mature oilfields and verifying the reserves.  Therefore, it is necessary to enhance fundamental research and techniques, striving to improve the quality of seismic data from this field and imaging accuracy.  This task faces many geophysical unsolved difficulties. 

  1.  Static correction. The research area is located on the foothills thrust belt and large alluvial fan, as shown in Figure 5.77.  There are a number of surface types, including mountains, hills and extremely thick gobi gravel zone.  The mountains have sharp reliefs, with poor shooting and receiving conditions.  Furthermore, from Figure 5.78, we can see the violent variation of surface velocity and thickness, and great vibration in first arrival of original single shot, indicating the existence of severe static correction problem. 
  2.  Seismic imaging. Figure 5.79 shows the single shots in the western, middle and eastern parts of the Baka work zone in Turpan‐Hami from left to right.  From the figure, we can see that the effective signal is difficult to identify and the SNR is low due to the development of various interference waves.  For this kind of original data, the basis for further key processing procedures, like velocity modeling and prestack migration, is to effectively suppress various noises and improve SNR of the data. 
  3.  Structure identification. The subsurface conditions in the research area are complex, where fractures have developed and formations are highly steep.  The boundaries of the main body structure have not been characterized clearly, and it's difficult to identify the structure accurately.  Additionally, the burial depth of target zone varies greatly, and its seismic data quality is relatively poor, which results in a challenge in building an accurate and appropriate migration velocity model.  Due to the great changes of longitudinal and transverse velocities, the conventional integral migration method cannot achieve ideal imaging effect.  During drilling development wells in each work zone, the drilled depth had large differences with the migration profile interpretation as a whole, and some wells encountered formations with conditions greatly deviating from those presented on the existing profiles.  Therefore, the selection of proper PSDM method is the key for building an accurate velocity model in these areas. 

**Figure 5.77** Geomorphologic map of the research zone. 

**Figure 5.78** Near‐surface inversion profile of the research area and original single shot record. 

**Figure 5.79** Original single shots in different locations of Baka region (a) single shot in western work zone (b) single shot in middle work zone (c) single shot in eastern work zone. 

### 5.3.2 Key techniques

The Turpan‐Hami and Jiuquan areas share many common characteristics in the seismic data, such as complex surface and subsurface structures.  The factors limiting the seismic imaging mainly include static correction, improvement of SNR, migration velocity modeling and migration method.  Some key techniques will be introduced in the following sections. 

#### 5.3.2.1 Integrated static correction technique for undulating surface model constraining fitting reconstruction

This technique, addressing the surface type variation and the complexity and diversity of surface low deceleration zone, carries out multiple information constraint and fitting reconstruction of multiple static correction methods.  It processes the basic static correction [45] and residual static correction separately, and can satisfactorily address the problem of static correction caused by complex near surface. 

In the western China foothills, one single method cannot address the problem of static correction [46] thoroughly, as shown in Figure 5.80.  The static correction effect is different on different surface locations on the same survey line.  The tomographic static correction is good for mountain areas, and the refraction static correction is satisfactory for slope and gobi areas.  It is necessary to analyze the application conditions of each static correction method, and take specific static correction methods for different surface conditions by considering the tests and analysis results.  Then a proper near‐surface model suitable for this surface condition can be built.  After that, a large amount of micrologging and short‐refraction data can be used to control the accuracy of surface model, and obtain a proper surface structure model through fitting and reconstructing based on the model, thus realizing the model‐restrained static correction technique.  Compared with conventional static correction technique, this model‐constrained static correction technique can more accurately invert the extremely shallow near‐surface model (Figure 5.81), hence helping improve the imaging quality, especially the imaging effect for highly steep structures, as shown in Figure 5.82. 

**Figure 5.80** Profile comparison of static correction effect at different locations. ( a) Tomographic static correction profile. ( b) Refraction static correction profile. 

**Figure 5.81** Comparison of near‐surface model for tomographic inversion. ( a) Constraint inversion model. ( b) Inversion model by conventional method. 

**Figure 5.82** Comparison of tomographic inversion stacking profile effect. ( a) Model‐constrained stacking profile. ( b) Non‐model‐constrained stacking profile. 

After obtaining an accurate near‐surface model, select different filling velocity, replacement velocity and datum to finally obtain datum statics with higher accuracy that can address the basic static correction to relief area on the mountain front.  Figure 5.83 shows the application analysis for integrated static correction to the northern Turpan‐Hami foothills seismic data.  The database static correction method alone will not generate ideal imaging effect (Figure 5.83a).  Based on database static correction, the integrated chromatographic static correction technique for fitting reconstruction is used and has improved the seismic imaging quality of this area (Figure 5.83b).  Figure 5.84 shows the application analysis of integrated static correction to seismic data from the Qingxi region in the Jiuquan Basin of the Yuanmen Oilfield.  Using only field model static correction method or tomographical static correction cannot generate ideal imaging effect.  Instead, good imaging effect can be achieved through model constraint and algorithm integration.  Compared with original profiles, the integrated chromatographic static correction technique for constrained fitting reconstruction has greatly improved the seismic imaging quality of this area. 

**Figure 5.83** Stacking results correlation of various static correction methods for northern Turpan‐Hami foothills. ( a) Stacking results of database static correction. ( b) Stacking result of integrated chromatographic static correction by fitted reconstruction. 

For residual static correction, three major processing methods are proposed based on a large amount of research, while considering the actual seismic data characters of complex structures in Turpan‐Hami and Jiuquan:

  1.  Multilayer residual static correction. Multilayer residual static correction is used to find the residual statics along multiple reflecting interfaces.  When calculating the residual statics, pick up the models for shallow, medium and deep horizons, then perform iteration computation, and then the resultant statics are an integrated effect of shallow, medium and deep horizons.  In practice, apart from the time difference caused by static correction, the residual statics of complex areas also include residual normal moveout, the time difference caused by lateral variation of velocity and the time difference caused by anisotropy.  Calculate the residual statics for shallow, medium and deep horizons respectively to find the same part and different part of the residual statics.  The same part indicates the variation of true statics, while the different part indicates the effect of other factors.  Using the true statics to find the static correction can avoid the effect of other factors. 
  2.  Integrated global optimization static correction technique. Based on the above conventional static correction for multilayer reflected wave, the integrated global optimization static correction method is adopted [47].  This method is actually an improvement for simulated annealing and genetic algorithm in some points or aspects, which makes full use of respective advantages of maximum energy method, simulated annealing method and genetic algorithm.  It has the characteristics of rapid convergence and effective energy stacking.  This method can address large statics with long mid‐wave, which the conventional residual static correction cannot handle.  Figure 5.85 shows an iterative combination of conventional reflected wave method with integrated global optimization method that was used to address the residual static correction in complex regions.  After using residual static correction of reflected waves, the quality of profile imaging is somewhat improved, but when global optimization method is used, the seismic imaging quality is further improved.  Therefore, the integrated global optimization method is a very effective static correction technique for complex topographic conditions. 
  3.  Single‐layer residual static correction method. 

The residual static correction method described above still takes the surface consistency as a principle.  For most survey lines, this method can work effectively.  In some cases, however, the delay caused by surface factors may change with the incident angle of seismic waves, that is, the residual statics are not surface‐consistent.  Additionally, factors like the normal moveout error caused by velocity error will cause the statics of deep and shallow layers at the same location to change with time, so it is not a constant.  It presents as follows: (1) After residual static correction, the improvement in deep and shallow layers varies greatly. ( 2) Within the static correction time window, the continuity and stacking energy of reflector are enhanced, while outside the time window, they do not change much, or the overlay effect becomes even worse.  In this case, the conventional residual static correction cannot take different horizons into consideration.  The layered residual static correction is an effective way to tackle this problem.  The actual method is to divide different time windows longitudinally and to calculate statics in each time window respectively, and then correct them.  In this way, the normal moveout caused by non‐surface factors can be solved. 

For areas with severe static correction problems in the Turpan‐Hami and Jiuquan areas, there are three key points for static correction: (1) To build accurate near‐surface model constraint database. ( 2) Integrated basic static correction under model constraint. ( 3) Integrated residual static correction.  Only when these three points are dealt with effectively can the static correction problem be satisfactorily handled.  Figure 5.86 shows an effect comparison after two‐step integration.  It can be seen from the figure that each step of integrated application can produce an effective result, and that the final profiles after integrated static correction have been greatly improved in SNR compared with original profiles. 

**Figure 5.84** Stacking results comparison of various static correction methods for the Qingxi Region of Jiuquan. ( a) Profile prior to static correction. ( b) Static correction profile by field model. ( c) Tomographic static correction profile. ( d) Constrained integrated static correction profile. 

**Figure 5.85** Application effects analysis of residual static correction in the Baka Region. ( a) Profile prior to residual static correction. ( b) Profile after residual static correction to reflected waves. ( c) Profile after global optimization static correction. 

**Figure 5.86** Application effects analysis of constraint integrated static correction in the Qingxi Region of Jiuquan Basin. ( a) Original profile prior to static correction. ( b) Profile after constraint integrated basic static correction. ( c) Profile after integrated residual static correction. 

#### 5.3.2.2 The "six‐division" prestack noise suppression technique for complex regions

Improving the SNR of seismic data is a key link in the processing of land seismic data at present.  In complex mountain areas, the landform is of up‐and‐down relief.  Due to the influence from strong surface absorption, as well as the shooting and receiving conditions on loose surface, various types of noises have developed, including surface waves, linear interference wave and various irregular interference waves.  In recent years, high fidelity preservation processing has been a constraining condition for the entire processing flow, and development of the noise suppression process has also been implemented to suppress the noise and preserve the fidelity.  Now there are a number of noise suppression techniques, but a single denoising technique always addresses a specific type of noise.  In fact, they all have some applicability.  However, the blind application may cause negative effects like aliasing and damage to signals. 

The "six‐division" prestack noise suppression technique [30,31] takes into full consideration various types of noise features and technical strength.  The contents of this technique mainly include: (1) Classification to eliminate the noise in terms of noise types of surface wave, acoustic wave, refraction, industry electricity, random noise. ( 2) Implementing by steps to gradually attenuate the noise with energy going from strong to weak in different processing stages. ( 3) Frequency division to suppress the noise of different frequency in different frequency bands. ( 4) Domain division to suppress the noise at different visual angles in different domains like common shot point, common geophone point, common offset, common midpoint and cross arrays. ( 5) Zone division to suppress the noise by selecting suitable denoising methods for mountain area, mountain front, loess, gobi and oil well sites. ( 6) Time division to use different denoising parameters in line with differences in frequencies and velocities at different reflection times. 

  1.  Noise suppression by classification method. 

The noise in seismic data can be classified in several different ways.  There are three conventional classifications: (1) The noise is divided into regular noise (often equivalent to coherent noise) and irregular noise (often equivalent to random noise) according to the features of noise on seismic profile. ( 2) According to noise propagation mechanism, the noise is classified into surface wave (ground roll), refracted wave, acoustic wave, lateral wave, multiples and tube wave. ( 3) According to spectrum characteristics, the noise is classified into low frequency noise, high frequency noise and 5 Hz industrial interference. 

The noise features are different, and the denoising methods are also different accordingly.  For regular noise, if there is simple spatial feature, such as surface wave, the noise can be removed by f‐k filtering; lateral wave can be removed by f‐k filtering or K‐L filtering; multiples can be removed by Radon transform or beam filtering.  Irregular noise is difficult to remove in time domain, but if its spectrum has obvious features, such as low frequency noise or high frequency noise of 50 Hz industrial interference, it can be easily removed by frequency domain filtering.  With random noise, we change our denoising idea: we do not process the noise, but instead remove the noise by multi‐trace fitting according to the coherence of effective signals.  In practice, the seismic data include both effective wave and noise, which cannot be distinguished very clearly.  The above methods can roughly remove the principal energy of the noise.  As a result, the denoising method should be improved continuously according to noise features and the best method to actually improve the SNR of seismic data should be looked for.  Figure 5.87 shows the noise suppression effect with suitable methods for anomalous amplitude and surface waves. 

  2.  Noise suppression by steps. The data from complex mountains often intertwines with effective reflections, and the range of velocity varies greatly, with low velocity and high velocity occurring at the same time and in multiple‐group distribution.  The principle for prestack denoising is that, for different types of noise, different methods should be used to remove the noise step by step.  The denoising process should be conducted with care.  While cutting and attenuating the noise, try not to damage the effective reflected signals and avoid generating too many side effects.  The principle of step‐by‐step denoising should be followed, thus gradually improving the SNR.  First, suppress the mid‐low velocity noise in seismic data according to the characteristics of f‐x domain denoising; then remove the high‐velocity linear interference once again by using ω‐x domain operator extrapolation denoising method, hence achieving satisfactory noise suppression effect.  Figures 5.88 and 5.89 show denoising effect comparisons by step method for seismic data from the northern Turpan‐Hami foothills and the Qingxi region in Jiuquan, both of which have very good denoising effects. 
  3.  Frequency‐division noise suppression. In addition to the regular interferences identifiable in the seismic data, there are often random abrupt large value interferences, including acoustic wave, burst impulse and cluster noise.  Their amplitude energy is usually several times higher than that of reflected wave of the same time, which poses certain effects on deconvolution, velocity analysis and stack imaging.  Seismic trace editing and amplitude processing will lose the effective information in the original data, so it is not desirable in amplitude processing.  This type of interference can be removed by using frequency division self‐adaptive high‐energy noise attenuation.  The field record is from subsurface interface reflection, and the amplitude, frequency and phase features of its waveform are determined by reflection coefficient sequence or wavelet.  Within the length range of seismic wavelet, the amplitude strength of seismic wavelet follows some regularity; the strength of reflected signals from top down on a trace record follows a proportional relationship, and the frequency is also in a certain range.  This technique adopts the time‐frequency analysis method.  Through analysis to the spatial distribution features, the frequency distribution feature and the energy distribution features of seismic wave and high‐energy noise on seismic records, and taking the wavelet amplitude obtained by tree median on time direction and trace direction as the standard amplitude, the amplitude and frequency values close to wavelet can be calculated in order to determine the noise and effective signals.  Use the statistic analysis method to formulate a self‐adaptive rule for detection and suppression of high‐energy noise, multi‐trace identification and single trace suppression.  Figure 5.90 shows that for 50 Hz anomalous strong industrial energy, it should not be simply cut off but should be suppressed according to its frequency features, so that the effective waves can be preserved.  The single shot, spectrum and f‐k spectrum proved that its suppression effective is very good. 
  4.  Zone‐division noise suppression. In Turpan‐Hami and Yumen basins, the surface conditions change sharply.  The same seismic work zone covers very steep valleys, gobi and plains, so there are great differences in noise features.  In mountainous areas, the linear interference has great velocity and extensive scattering; while in plains, the linear interference velocity is small, only half of that in mountain areas; in the transit zone from plain to mountains, the linear noise in seismic data has both low‐velocity linear interference on plain area and high‐velocity linear interference in mountains.  If the same denoising method is used, over high velocity will damage the effective waves in plain data, but if the selected velocity is only suitable for plain noise, the linear interference from mountainous areas cannot be effectively cut off.  The zone‐division method can handle this problem.  In actual processing, first divide the data on the zone and perform noise deduction to the data as per positive and negative offsets in order to avoid the effect of alias.  In this way, the noise can be effectively suppressed with no alias being produced, hence generating good noise suppression effect. 
  5.  Domain‐division noise suppression. The multiple coverage seismic data can be combined into different seismic gathers according their domains.  Different types of seismic noise show different features on different gathers and should be suppressed on gathers of different domains; for example surface waves are suppressed on shot gather and linear interference is suppressed on common receiving point gather, while random noise can be better suppressed on common offset gather.  The 3D prestack seismic data contains rich information of seismic wavefield, and can be used to perform flexible gather combination.  
    1.  Noise suppression in shot point and geophone point domain. After linear noise suppression on shot domain, the linear noise on shot gather becomes weaker, but a large amount of linear noise with high energy would remain on stacking profile, because linear noise not only develops in shot domain, but also in geophone points.  Secondary suppression in geophone domain can remove the noise more completely (Figure 5.91).  Therefore, more tests should be carried out on multi‐domain analysis and multi‐domain prestack noise suppression for complex foothill structures. 
    2.  Noise suppression for cross array domain. 

For complex mountain noises, the multi‐domain denoising method described above works effectively, but still some unidentifiable and unremovable noises will remain, which severely affect the SNR of seismic data.  For this reason, the cross array domain is introduced, which mainly uses 3D f‐kx‐ky filtering and RNA technique to suppress residual low frequency linear noise, 2D source noise and random noise.  The definition of cross array and the spread features of noise on cross array have been discussed in the previous section. 

The f‐k filtering belongs to multi‐trace processing, which makes the mixing effect inevitable.  By combining the effect of alias, an intolerable modification will be generated to record features and effective wave features.  The 3D f‐kx‐ky cone filtering method is used to find and retain the noise part, and then the self‐adaptive method is used to cut off the noise.  In this way, we maintain the wave group features of the records and also overcome the mixing and alias producing by f‐ _k_ filtering.  Therefore, the 3D f‐kx‐ky cone filtering can well suppress the residual refracted wave and surface waves. 

The seismic data from the mid to western part of the areas usually have low SNR stack profile.  Where there is low SNR seismic profile with strong random noise, if no poststack denoising is performed, the continuity of reflected wave event will be poor, hence affecting the interpretation accuracy of seismic data.  At present, the denoising techniques used in seismic data processing are almost all multi‐trace denoising methods, but each of them achieves the goal of improving SNR at the cost of lateral resolution.  If the poststack denoising method is not properly used, the small faults may be smeared and may cause the faults with large fault throw to be continuous at places where there should be a breakage.  It will result in difficulties for the interpreters and fault interpretation. 

The suppression of random noise assumes the record is composed of two parts, namely effective signals and random noise.  The effective signals can be forecasted, while the random noise cannot be forecasted.  First, perform Fourier transform to time‐domain signals, scan and fit the event within the inclination range given by f‐x domain, and then cut off the remaining part – the random noise – from the records. 

At present, the prestack noise suppression for 3D seismic data is realized on 3D single shot by using the 2D random noise attenuation technique.  In practice, the data is only forecasted and suppressed along the geophone line, but the geologic body is three dimensional; if a single 2D seismic profile is used as a processing unit, it is certain that some useful information will be neglected, hence affecting the processing results.  The 3D poststack random noise attenuation technique is used to perform Fourier transform on 3D poststack data volume, scan the events within the inclination range given by _f‐x‐y_ domain and carry out fitting.  Then cut off the remaining part, that is, the random noise, from the records.  This technique, taking the information from all directions in 3D space into account, is the processing to 3D spatial data volume.  Through the application of poststack 3D random noise attenuation technique to prestack data of cross array domain, the true attenuation of 3D prestack random noises can be realized, and it avoids the effect of poststack random noise attenuation on lateral resolution and improves the SNR.  The imaging effect is also improved. 

Figure 5.92 shows a comparison of denoising effects on cross array gathers.  It is observed that the energy of single shot surface wave, refracted wave and linear noise is very strong, which results in the effective reflection being totally immersed in noise background.  By using cross array gather noise suppression method, all the noise is suppressed completely, and the effective signals are well highlighted, thus the SNR is obviously increased.  In addition, through analysis of the noise suppression by prestack step‐by‐step method and domain‐division method as shown in Figure 5.93, it can be observed that noise suppression should be broken into several domains and steps.  In this way, various types of noises can be well identified, with pertinent denoising methods and parameters being adopted.  The obtained overall noise suppression effect is more satisfactory, which protects the effective signals well and improves the SNR remarkably. 

  6.  Time‐division noise suppression. In the research area, the noises in seismic data vary greatly in different longitudinal time sections.  The multiple refracted wave of shallow layers are mixed with effective waves, and the velocities of deep layer linear noise and multiples are often very close to the velocity of shallow effective signals.  In order not to damage the effective signals, it is necessary to suppress the noise in time sections.  Choosing proper methods and parameters in different time windows can avoid damage to effective signals, obtain good noise suppression and improve the SNR of seismic data to the maximum extent. 

**Figure 5.87** Single shot comparison before and after anomalous amplitude and surface wave suppression. ( a) Original single shot. ( b) Single shot after noise suppression. ( c) Suppressed noise. 

**Figure 5.88** Single shot linear interference wave step suppression in the northern Turpan‐Hami foothills. ( a) Original single shot. ( b) Single shot after mid‐low velocity interference suppression. ( c) Single shot after high velocity suppression. 

**Figure 5.89** Step suppression of 3D single shot linear interference in the Qingxi Region of Jiuquan. ( a) Original single shot. ( b) Single shot after mid‐low velocity interference suppression. ( c) Single shot after high velocity suppression. 

**Figure 5.90** Step suppression of 3D single shot linear interference in the Qingxi Region of Jiuquan. ( a) Original single shot. ( b) Original single shot spectrum. ( c) Original single shot f‐k spectrum. ( d) Single shot after suppression. ( e) Single shot spectrum after suppression. ( f) Single shot f‐k spectrum after suppression. 

**Figure 5.91** Suppressing of prestack domain noise. ( a) Original shot gather. ( b) Result after shot gather noise suppression. ( c) Gather of common geophone points. ( d) Results after geophone domain noise suppression. 

**Figure 5.92** Noise suppression comparison of prestack multi‐domain and cross array domain. ( a) Original shot gather. ( b) Result after noise suppression. 

**Figure 5.93** Comparison of prestack step‐by‐step and multi‐domain noise suppression. ( a) Original single shot. ( b) Result of shot‐domain noise suppression. ( c) Result of geophone‐domain noise suppression. ( d) Result of cross‐array surface wave suppression. ( e) Result of cross‐array domain anomalous energy suppression. ( f) Result of linear noise cross‐array domain suppression. 

#### 5.3.2.3 Integrated velocity modeling for optimal imaging

Due to the influence of complex surface and subsurface structures, the seismic data of Turpan‐Hami and Jiuquan areas has low SNR.  A single modeling method alone cannot give an accurate and proper velocity model, which severely affects the migration imaging.  Improving migration imaging is needed to improve the SNR of seismic data, but more importantly, it is necessary to adopt the highly accurate velocity modeling method.  The migration velocity modeling methods used now mostly adopt the correlation method and moveout analysis to discriminate and pick up the velocity.  These two velocity analysis methods cannot discriminate proper velocity values when processing low SNR data, and are far from satisfying migration imaging in areas with low SNR and complex structures.  For low SNR data, the conventional stacking processing usually uses the constant velocity scan method to improve the analysis precision and imaging quality.  Historically, constant velocity scan modeling cannot be achieved during migration due to limitation of computers, but now with the rapid development of computer clusters, this migration scan modeling method is now a reality.  A new modeling method has been developed from the concept of integrating processing and interpretation [48,49].  It is competitive in that it is applicable to migration velocity modeling for seismic data with low SNR in western China, it can intuitively and accurately pick up the velocity on velocity scan migration profile and the velocity model picked up by horizons has more characteristics in regional structures. 

The core of high precision velocity modeling method is the migration velocity scan technique.  Its principle is to discriminate and analyze the migration profile imaging effects of different percentage velocity to obtain the most suitable velocity.  If velocity is too high or too low this will cause insufficient or excessive migration of the inclined event model.  The greater the inclination angle, the more obvious the migration error.  The uncertainty of migration velocity will lead to the uncertainty of migration profile and interpretation, so the accuracy of velocity model determines the effect of imaging.  For complex structures, when migration velocity is close to medium velocity, the effect of structures tends to vanish; when an event is in parallel arrangement in a migrated common imaging gather (CRP), the imaging is correct.  In order to check the flattening extent of this array, we stack CRP gather and observe which velocity gives the optimal stack effect to each travel time.  Extending this concept from velocity point to velocity line, that is, continuously analyzing the CRP gather scan coefficient, perform prestack migration percentage velocity scanning for the whole line of each velocity line in the work zone.  Similarly, each velocity line can generate a migration profile of different percentage velocity, and each migration profile corresponds to a scan factor and velocity model.  We combine all the migration profiles scanned for percentage velocity into 4D data volume, and then analyze the features like imaging and event continuity of migration profile in 4D data volume to pick up the corresponding velocity and time.  The specific modeling process is as below:

  1.  Building of initial velocity model. For prestack migration, it is of ultimate importance to build the initial velocity model accurately.  An incorrect initial velocity model will lead to non‐convergence of velocity iteration, so we will not obtain the final correct model.  First, the stacked velocity is properly edited and smoothed to use as initial RMS velocity model; then gradually optimize RMS velocity based on the analysis on maximum relevant energy spectrum of inverse dynamic correction to CRP gather and residual delayed iteration, and finally characterize the model through 4D modeling technique finely for low SNR data to obtain the accurate root mean square velocity field, which conforms to geologic law.  This obtained velocity can be taken as the initial model for layer velocity, laying a foundation for building accurate layer velocity field.  Figure 5.94 presents a comparison of PSTM effect after root mean square velocity modeling.  It is seen that the layer imaging of target interval is obviously improved in positioning of faults and break points, proving that accurate velocity field is an important basis for time domain migration imaging. 
  2.  Depth domain interval velocity modeling.  
    1.  Building of time domain structural model: Interpretation of time interval on PSTM profile is mainly used to define the velocity interface, and then finally move it to depth domain by reverse bias to obtain the depth domain interval model.  In general, logging the velocity inflection point is used to discriminate the velocity interface and then check and correct it through PSDM velocity spectrum. 
    2.  Building initial interval velocity depth model: At present, the methods to find the interval velocity mainly include coherent inversion method, stacked velocity inversion method and root mean square velocity conversion.  These methods all adopt CMP gather, stacked velocity and root mean square velocity with the help of time interface.  In horizontal layered or gentle formations, the root mean square velocity is often used to convert interval velocity.  When the SNR of the work zone is low, the stacked velocity inversion is a preferred option.  Meanwhile, the coherent inversion method is not restricted by formation dip and is of relatively high accuracy.  Therefore, these three methods are often combined together to find the interval velocity for seismic data with low SNR.  The principle and methods of finding velocity by combining forward and inversion are intrinsically different from the conventional velocity method (velocity spectrum method) that obtains the maximum stacked energy of CMP gather through dual‐curve normal moveout.  The basis of velocity spectrum method is that the subsurface is a horizontal layered or monoclinal uniform medium in the length of a gather, which provides foundation for the time‐distance curve equation used for characterization.  Apparently, these time‐distance equations cannot actually describe the subsurface formations that have large dip variation and inhomogeneous single layer velocity within a gather length, so the velocity found by this velocity spectrum method is only a rough approximate value.  However, the velocity estimate by combination of model forward and inversion can radically address this problem.  The inversion method for coherent interval velocity is to select a CMP position for each interval of each survey line, define a range of interval velocity and then set the range of offset to calculate the coherent value.  The interval velocity corresponding to the maximum coherent value is the interval velocity to be calculated.  Interval velocity analysis is performed interval by interval from shallow to deep. 
    3.  Iterative optimization of velocity model: The above methods are used to build the initial interval velocity‐depth model.  The building of such a model is a step‐by‐step iteration and convergence process, but the building of the initial velocity model poses significant effects on iterative optimization of subsequent velocity models.  If the initial velocity model deviates greatly from the correct velocity model, the velocity model cannot converge even through multiple iterations.  The model optimization mainly includes time model and velocity model optimization; for optimization of time model, the criterion is to make the time model roughly conform to the subsurface geologic conditions through repeated iterations; for optimization of the velocity model, the principle is to modify and optimize the interval velocity‐depth model by along‐interval residual velocity analysis and 3D tomographic imaging technique. 
    4.  Fine characterization by velocity‐depth model: For areas with low SNR, the above interval velocity‐depth model is not fine enough and needs to be improved in some areas.  The above‐mentioned velocity analysis of 4D data volume is to pick up the most reasonable interval velocity through 4D velocity scanning and build the optimized interval velocity‐depth model, as shown in Figure 5.95.  We can obtain a satisfactory imaging effect by PSDM with this interval velocity‐depth model (Figure 5.96). 

**Figure 5.94** Comparison of PSTM profiles for high precision root mean square velocity modeling. ( a) PSTM profile for conventional velocity modeling method. ( b) PSTM profile for high precision velocity modeling method. 

**Figure 5.95** Final interval velocity‐depth model. ( a) Final interval velocity profile. ( b) Final interval velocity body. 

**Figure 5.96** Final interval velocity‐depth model. ( a) PSTM profile. ( b) PSDM profile. 

#### 5.3.2.4 PSDM technique for floating surface

  1.  Selection of floating datum. 

There are two main techniques for migration datum in PSDM for complex structures. 

One technique is to perform low frequency correction to seismic data, that is, vertical time shifting correction; then perform prestack migration computation while starting from common fixed datum.  A basis for this simple time shifting method is surface consistency hypothesis, which means that static time shift only relates to the surface positions of shot source and geophone points, regardless of ray paths of wave propagation.  This hypothesis is effective for all rays (excluding geophone offset), which are vertical near the surface.  In areas where surface relief is not great and lateral velocity variation in low velocity zones is slow, the reflection on subsurface shallow, medium and deep layers almost follows the same nearly vertical path to the surface while passing the low velocity zone.  At this time, their statics are almost the same, and can be corrected with simple vertical time shift.  Their processing accuracy is adequate.  In areas with great surface reliefs and large lateral velocity variations, such as mountain areas, the surface consistency hypothesis will not be satisfactory, and the rays when the seismic wave passes the subsurface layers and reflects back to the surface will not be vertical to the surface any more.  Therefore, this simple time shift cannot eliminate the terrain effect and properly adjust the position of the event.  Thus, it cannot accurately reflect the subsurface structures during migration imaging.  In inclined intervals and steep dip reflectors, it will cause over‐migration or under‐migration.  Figure 5.97a shows one PSDM result of some survey line fixed datum on mountain foothills whose imaging quality is poor. 

The other technique is to perform migration directly from the float datum.  As we know, setting the level datum in the work zone cannot satisfy the requirement for seismic imaging of complex structure with the increase of surface condition complexity in the survey area.  Therefore, the concept of float datum is introduced to address it. 

Using the float datum PSDM method can effectively remove the negative effect of the common fixed datum migration vertical time shift on migration result, described above.  But how should the float datum be selected?  The float datum we use here is not the true ground surface.  The geophysicists have researched the PSDM of true surface, but they mainly focus on theory research and model experiments.  In actual data processing, there are many insurmountable influence factors (such as the building of true surface velocity model), so there are few examples of good application effects.  Here, we use the near‐surface float datum, that is, the CMP often mentioned in seismic data processing nowadays, to perform the migration operation.  Figure 5.97b shows the result of float datum PSDM of some survey line on mountain foothills, which is relatively satisfactory compared with the previous ones in terms of imaging and break points.  The specific selection method for near‐surface float datum is introduced briefly here. 

In order to reduce the effect of static correction on time‐distance curve distortion of reflected waves and on velocity analysis and migration, we adopted this high and low frequency separation technique based on CMP static correction.  The fixed datum are used during computing statics, then average the statics of each trace involved in stacking within each CMP gather and take the average value as CMP correcting value (low frequency), so as to obtain the CMP datum.  This will not change the t0 of reflected waves and the properties of dual curves.  After stacking, correct to the fixed datum with CMP correcting value, where the stacked zero line is static correction datum, and the zero line of velocity spectrum is CMP datum.  In this way, the reflection time t0 and velocity v on the velocity spectrum will not change with changes in low frequency components of static correction.  It is the true reflection of the actual subsurface velocity model.  The velocity obtained on CMP datum is the true velocity of seismic wave propagation, which is free from the influence of filling speed of static correction.  However, attention should be paid to the following aspect: due to the application of high and low frequency separation of static correcting value, only the relevant high frequency components are used in velocity analysis.  On the other hand, the CMP datum is a time domain surface, which needs depth domain conversion with displacement velocity in order to be similar to near‐surface smoothing surface.  In practice, it is different to some extent from the near‐surface smooth face obtained by surface elevation smoothing. 

  2.  Integral PSDM method. PSDM is a powerful tool to confirm the complex structures on mountain foothills.  During the research work, we further improved the Kirchhoff integral PSDM method for float datum and obtained satisfactory application effect.  Figure 5.98 shows a result comparison between new and previous Kirchhoff integral PSDM.  It can be found that the new migration result works effectively for imaging of highly steep structures and fractures. 
  3.  One‐way wave PSDM method. In line with the characteristics and technical demand for seismic data from the research zone, we have developed this one‐way wave PSDM method for float datum of complex areas in mountain foothills [50–53].  Figure 5.99 presents a result comparison between shot‐domain one‐way wave PSDM and integral PSDM.  We can see that the float datum one‐way wave PSDM is clearer in the characterization of small faults. 
  4.  Two‐way wave reverse time PSDM method. In the research work, we explored this reverse time PSDM method.  Reverse time migration, as a wave equation migration technique with no operator approximation, is now the migration method with the highest imaging accuracy.  This reverse time migration is different from conventional migration, with the following advantages: (1) It is based on two‐way wave equation, and generates no decomposition, with high accuracy of computation. ( 2) It is suitable for sharp velocity change and high angle imaging of complex structures. ( 3) It can accurately image the different types of waves like bow‐tie, prism wave and multiples. ( 4) It can easily address the problem of anisotropy. ( 5) It has no amplitude or phase position approximation, so can well solve the problem of amplitude.  Reverse time migration realizes extrapolation on the time axis, which can be seen as forward modeling opposite to time direction.  The traditional along‐depth‐direction migration method is based on one‐way wave equation, while the reverse time migration is based on full‐wave equation, allowing the seismic waves to propagate in all directions.  Therefore, there is no dip restriction.  In the present conditions, the reverse time migration as a PSDM method with the highest imaging accuracy has become a hot spot and focus of geophysical research.  Figures 5.100 and 5.101 present result comparison between reverse time PSDM and Kirchhoff integral migration for different blocks in complex areas of Turpan‐Hami and Jiuquan.  We can see that reverse time PSDM is advantageous in characterization of subsurface fractures and small faults, and has more distinct imaging in steep formations and medium to deep target zones. 

**Figure 5.97** PSDM effects comparison between floating datum and fixed datum of some survey line. ( a) PSDM of fixed surface. ( b) PSDM of float datum. 

**Figure 5.98** Comparison of new and previous migration imaging results for highly steep structures. ( a) Previous migration result. ( b) New migration result. 

**Figure 5.99** PSDM results comparison of different methods. ( a) Kirchhoff integral migration. ( b) One‐way wave migration. 

**Figure 5.100** PSDM result comparison of different methods for the Qingxi area. ( a) Kirchhoff integral PSDM. ( b) Reverse time PSDM. 

**Figure 5.101** PSDM result comparison of different methods for the Qingxi area. ( a) Kirchhoff integral PSDM. ( b) Reverse time PSDM. 

### 5.3.3 Application effect and actual survey effectiveness

The seismic imaging techniques (described above), used in the complex areas of Turpan‐Hami and Jiuquan, have shown good application effect, and subsequent interpretation and integral research also resulted in new geologic understanding and favorable survey effectiveness.  See Figure 5.102. 

**Figure 5.102** PSDM result comparison of different methods for the northern Turpan‐Hami mountain foothills. ( a) Kirchhoff integral PSDM. ( b) Reverse time PSDM. 

#### 5.3.3.1 Baka region on the northern Turpan‐Hami mountain foothills

  1.  Analysis of seismic imaging effect. Compared with previous research findings, prestack migration results from the research work have produced improved imaging quality.  The new research findings can more accurately characterize the subsurface structure shapes and fracture locations in the Baka region.  Figure 5.103 presents a comparison between previous PSTM results and the new research findings.  The new migration result shows that the target interval is a fault‐block structure instead of a complete anticline structure as previously recognized.  Figure 5.104 presents a comparison between new and previous PSDM results of INLINE644 survey line, which crosses Well Ke21‐P1.  We can see that the fault moves about 80 m to the south in the new migration results, and fault dip becomes greater and the south wing formation becomes steep, matching with the drilling data.  From Figure 5.105, the comparison proves the new migration result has a better characterization to the target interval fractures. 
  2.  Integrated research achievements. 

For the structural interpretation based on the new research findings, the Baka region is divided into three structural patterns: monocline, fault block and faulted anticline from west to east.  Figure 5.106 presents a representative profile of various structural patterns.  Compared with the time migration, PSDM can handle the problem of drastic lateral velocity variation caused by complex structures.  Meanwhile, during research on the PSDM velocity model building, the geologic understanding, structural pattern and drilling rate, was fully used to guide the building of velocity field.  Therefore, PSDM result can better reflect the true geologic structures.  In particular, it is finer than PSTM in imaging fault blocks at anticlinal belly and small throw faults.  Through structural interpretation with depth domain seismic data and structural mapping, we confirmed the structural particulars of this block and further understood the fracture features and strata spread regularity of this area.  As a result, we re‐identified a number of traps inside the work zone, including seven fault block traps. 

In the research work, we combined the regional structural setting, identification extent of trap elements and drilling and test results, and integrated reservoir forecast results.  Figures 5.107 and 5.108 present a sandstone forecast spread map of the Badaowan Interval in the Baka Work Zone and its multi‐attribute fusion plane spread map, respectively.  We optimized some favorable drilling targets, and forecasted favorable gas bearing area of 73.6 km2 among them.  Meanwhile, ten well locations were planned, in which four wells have been drilled, and the other six wells are the key preparatory well sites to be drilled on mountain foothills in the northern Turpan‐Hami Basin. 

**Figure 5.103** Comparison between new and previous PSTM results. ( a) Previous migration results. ( b) New migration results. 

**Figure 5.104** Comparison between new and previous PSDM results (inline 644). ( a) Previous migration results. ( b) New migration results. 

**Figure 5.105** Comparison between new and previous PSDM results. ( a) Previous migration results. ( b) New migration results. 

**Figure 5.106** Representative profile of various structural patterns in the Baka region. ( a) Monoclinal structure. ( b) Fault structure. ( c) Fault anticline structure. 

**Figure 5.107** Sand body forecast spread map of J1b interval. 

**Figure 5.108** Multi‐attribute fusion plane spread map of J1b interval. 

#### 5.3.3.2 The Wenjisang Region in the northern Turpan‐Hami Mountain foothills

  1.  Analysis of seismic imaging effect. 

For the Wenjisang region on the southern Taibei Depression slope in the Turpan‐Hami Basin, the PSTM and PSDM results are reasonable in the structural pattern, and show the distinct fracture system and the accurate break point locations.  The reverse time migration result is apparently better than the integral PSDM in the imaging of steep dip fault.  Figures 5.109 and 5.110 show the comparison between previous PSTM results and the new research achievements.  As shown in the comparison, the new PSTM result improved the imaging to target zones remarkably, where the small fault blocks and the inner particulars of fault block are presented more clearly, the SNR is significantly increased and the structural pattern is more distinct and reasonable. 

Figure 5.111 is a comparison between new integral PSDM (depth domain) and previous PSTM results.  As indicated in the figure, the new PSDM remarkably improved the imaging quality of target zones.  The fractures and break points are more distinct and the new PSDM can more accurately characterize the location of break points and structural pattern.  On depth migration profile, the imaging of the target zones above and beneath the coal bed is more distinct, and the inner particulars of the complex fault block area are clearer, which provides accurate and reliable basic data for identification of subsurface structures.  Figure 5.112 shows a comparison of reverse time PSDM result and Kirchhoff integral migration result.  Compared with integral PSDM profile, the reverse time PSDM profile shows clearer fractures in complex fault block areas and higher quality of imaging, with richer inner reflected particulars, because of remarkable previous gather processing effects during the research process.  In addition, the velocity model so built is more accurate, and the algorithm for the new reverse time PSDM technique is more suitable for drastic lateral velocity variation in complex fault block areas.  Therefore, the supporting techniques with this new reverse time PSDM technique as the core is an effective way to handle the imaging of complex fault block in this area. 

  2.  Findings from integrated research. 

Based on time domain seismic data interpretation, we performed fine structural interpretation to the new PSDM seismic data.  During PSDM, we used such information as our knowledge about geology, structural patterns and drilling rate to guide the building of velocity field, so that the PSDM seismic data can better reflect the actual geologic structures; in particular, it is finer than PSTM in imaging fault blocks at anticlinal belly and small throw faults.  Through structural interpretation with depth domain seismic data and structural mapping, we confirmed the structural particulars of this block once more and further understood the fracture features and strata spread regularity of this area, and hence re‐identified the structural traps inside the work zone (Figure 5.113). 

On this basis, we analyzed the tight sand gas accumulation conditions in the Xigou formation of the Wenjisang region in the Turpan‐Hami Basin, and understood the characteristics and regularity of tight sand gas accumulations.  Through integrated research, we believe that "sufficient gas source, tight reservoir, fracture connectivity and near‐source accumulation" is the key to tight sand gas accumulation in the Turpan‐Hami Basin.  We confirmed the structure features by combining the new and previous seismic data, and found or re‐identified six favorable drilling targets and forecasted favorable area of 103.54 km2 through petrophysical analysis, petrophysical amount combined with seismic attribute, hydrocarbon detection, gas possibility detection, inversion of characteristic wave impedance, prestack AVO analysis and prestack sync inversion (Figure 5.114).  The drilled Well Ji‐3 had industrial oil flow; breakthrough was made in exploration of tight sand gas in the north area of the slope; Well Ji‐3 had a daily gas production of over 4000 m3 and oil of over 20 m3.  All these achievements show a good potential for tight sand gas exploration in the north of the Wenjisang area, providing conditions for further expanding the size of tight sand gas pools. 

**Figure 5.109** Comparison between new and previous PSTM results (inline 740). ( a) Previous migration results. ( b) New migration results. 

**Figure 5.110** Comparison between new and previous PSTM results (inline 420). ( a) Previous migration results. ( b) New migration results. 

**Figure 5.111** Comparison between new and previous migration results (inline 410). ( a) Previous PSTM profile. ( b) New integral PSDM profile (depth domain). 

**Figure 5.112** Comparison between new and previous PSDM results (inline 420). ( a) Previous integral PSDM profile. ( b) New reverse time PSDM profile. 

**Figure 5.113** Structural map of coal bed top boundary in Badaowan Formation. 

**Figure 5.114** Favorable reservoir distribution map forecasted by multi‐information fusion. 

#### 5.3.3.3 The Qingxi region in the Jiuquan Basin of Yumen

  1.  Analysis of seismic imaging effect. We performed geophysical difficulty researches to seismic data from the Qingxi Region of the Jiuquan Basin by using the key imaging technique and supporting technologies for seismic data from the complex Turpan‐Hami and Jiuquan areas mentioned above.  The imaging accuracy of the PSTM ad PSDM results is significantly improved, which can more accurately characterize the break point location and structure patterns.  The effects are mainly reflected in the following four terms: 
    1.  In terms of imaging: Compared with the previous processed profiles, the SNR and imaging accuracy are greatly improved; the denuded plane is clearly reflected, the Cretaceous top and bottom interfaces are easy to identify, and the faults and breakpoints are distinct (Figure 5.115); the frequency band of the target zone is broadened by 14 Hz (Figure 5.116). 
    2.  In terms of fracture: Compared with continuous seismic data, we can more accurately characterize the breakpoint location and have better understanding of structural patterns (Figure 5.117); compared with recent data, the breakpoint locations and structural patterns are more distinctly characterized (Figure 5.118). 
    3.  In terms of structure: Figure 5.119 shows a comparison of PSTM and PSDM results.  The PSDM result shows a clear imaging of Cretaceous target zones, a clear characterization of fractures and fault surfaces, and it can accurately characterize the breakpoint locations and structural patterns; the imaging of top surface of buried hills is clear and apparent; furthermore, there are some changes in structural pattern and structure highs on PSDM profile, as shown in Figure 5.120.  The structure high in Well Liu‐108 is shifted to northeast and the area of trap is enlarged. 
    4.  In terms of amplitude: The new results show clear seismic reflection horizon and interval wave group features, where the reflection features of structure and sediments are easy to identify.  The results reflect the lateral change features of the reservoirs; the oil‐bearing sand body and dolostone are remarkably reflected on the profile.  As shown in Figure 5.121, drilling of Well Liu‐12 encountered development of sandstone and thick oil layer, indicating oil/gas accumulating in local structures in favorable phase belts. 
  2.  Integrated research findings. 

Based on PSTM and PSDM seismic data and combining the sequence and sedimentation study, structural interpretation, reservoir forecast, oil/gas detection and accumulation conditions analysis, we performed systematic analysis and study on the oil/gas accumulation conditions of the whole block, and proposed exploration suggestions in line with the status quo of the present exploration and development.  As shown in Figure 5.122, we found thirteen favorable exploration targets in three fields (Liubei coastal subsea apron, Yaxi Fan delta front and Liugouzhuang dolostone), and suggested ten well sites (one for Liubei coastal subsea apron, four for Yaxi Fan delta front and five for Liugouzhuang dolostone), which effectively guides the exploration planning. 

Figures 5.123 and 5.124 show typical profiles of prestack migration crossing the designed Well 5, which is located in the favorable predicted dolomite fracture development zone on the east side of Liugouzhuang major block with significant reserves.  In the design basis through fine calibration of well‐shot like Wells Liu‐4 and Liu‐108, it is found that most oil reservoirs in Liugouzhuang dolostone fractures clearly show strong seismic response features on 3D seismic data, and the target zone K1g2+3 also shows a group of strong reflection features of "a valley between two peaks".  It is predicted to be a development zone of dolostone fracture oil reservoirs.  A number of Y‐shaped faults have developed in the target zone, indicating that this area has strong stress effect, which is favorable for development of fractures.  On the other hand, the development of faults helps communicate the lower oil/gas, which is very favorable for oil/gas migration and accumulation in this block. 

**Figure 5.115** Comparison between new and previous PSTM results. ( a) Previous PSTM profile. ( b) New PSTM profile. 

**Figure 5.116** Comparison between new and previous PSTM results before and after the research (I). ( a) Previous PSTM profile. ( b) New PSTM profile. 

**Figure 5.117** Comparison between new and previous PSTM results before and after the research (II). ( a) Previous PSTM profile. ( b) New PSTM profile. 

**Figure 5.118** Comparison between new and previous PSTM results before and after the research (III). ( a) Previous PSTM profile. ( b) New PSTM profile. 

**Figure 5.119** Comparison between PSTM and PSDM results after the research (I). ( a) PSTM profile. ( b) PSDM profile. 

**Figure 5.120** Comparison between PSTM and PSDM well‐tie profiles after the research (II). ( a) PSTM profile. ( b) PSDM profile. 

**Figure 5.121** Comparison of amplitude on prestack migration well‐time profile. 

**Figure 5.122** Proposed well site map on sub‐depression in the Qingnan region. 

**Figure 5.123** Seismic profile I of sub‐depression of the Qingnan Area. 

**Figure 5.124** Seismic profile II of sub‐depression of the Qingnan Area. 

### 5.3.4 Conclusions and understanding

The research on seismic imaging of mountain foothills complex structures is a long and complex process, and the core problems in processing are still static correction, SNR and imaging.  Through long‐term research, we have developed relevant seismic imaging technique series.  The key techniques among them mainly include integrated static correction technology for undulating surface model constrained fitting reconstruction, the "six‐division method" prestack noise suppression technique for complex regions, integrated velocity modeling based on optimal imaging and reverse time PSDM technique for floating surface.  After application of these techniques, the seismic imaging quality is greatly improved, and the new results can more accurately characterize the subsurface structural patterns and fracture locations in complex block.  In particular, the PSDM results dominated by reverse time migration can more distinctly characterize anticlinal belly fault block and faults with small throw, hence providing reliable data for structural interpretation.  Through such integrated researches as fine structural interpretation and reservoir forecast based on new PSDM results, we re‐identified the structural particulars of the work zone and further understood the fracture features and strata spread law of this block. 

## 5.4 Application of the Seismic Prestack Imaging Method in the Buried Hill Structural Zone in the Nanpu of Jidong Oilfield

### 5.4.1 Overview of the project

#### 5.4.1.1 Overview of the work zone

The Nanpu Depression of the Jidong Oilfield, located in the north of the Bohai Bay Basin, is a superimposed oil/gas sag of mid‐Cenozoic Group.  The Nanpu buried hill structural belt is located on the southwest slope of the Nanpu Depression (Figure 5.125); the Neogene and Paleogene systems of mid‐shallow intervals in this block are faulted anticlinal structures developed on buried hill; the subsurface faults have developed with broken faulted block; the structure is dominated by tensile normal fault.  The bottom of the Neogene Guantao Group is scattered with a large area of igneous rock, which is also developed inside the Dongying Group.  The main body of the buried hill is composed of Ordovician limestone.  From the surface, the main part of the work zone is in shallow sea below the low tide line with seawater depth of 0–10 m. There are three surface conditions and geomorphic features within the work zone: land area, intertidal zone and shallow water zone.  No.  1 Nanpu Structure is of mid‐shallow layer with large scale and favorable setting.  There are two major oil reservoirs: the Guansi Interval and Dongyi Interval on the main part of the structure, which are already in production.  The main task in this block is looking for mid‐shallow layer rolling evaluation targets and identifying exploration potential [54–56]. 

**Figure 5.125** Schematic of work zone location. 

#### 5.4.1.2 Existing problems and technical difficulties

The previous exploration proved that the work zone has subsurface faults and broken blocks, and the structure is dominated by tensile normal fault [57].  There is great lateral variation of formation lithology and the propagation path for seismic wave is complex, which caused obscurity on the local seismic imaging on the profile.  The bottom of the Neogene Guantao Group is scattered with a large area of igneous rock, which is also developed inside Dongying Group.  In this region, the seismic wave shielding is a severe problem and the SNR of the seismic data is low.  Various interferences within the work zone are very severe, especially the wide distribution of strong igneous reflecting interface, which has caused extreme development of multiples. 

From the aspect of geologic horizons in this block (Figure 5.126), the seismic reflector wave impedance features are significant above the Neogene system, with high SNR.  Some areas of Dongyi Interval have developed igneous rock, which is characterized by random development.  The contact relation between basalt and surrounding rock is complex and varied; the stratification ability is poor and it is difficult to identify and characterize the range of igneous rock effectively.  Furthermore, from the quality of seismic data, we can see that the dominant frequency is low and frequency band is narrow, with little recoverable high frequency data. 

**Figure 5.126** Stacked profile. 

The main difficulties in processing the seismic data from this area include: (1) Effectively improving SNR, resolution and high accuracy velocity modeling for igneous rock to obtain high accuracy imaging, then to carry out fine structural interpretation and characterization of igneous rock. ( 2) Performing fidelity preservation processing during data processing in order to ensure research on lithology spread characteristics and forecast of favorable reservoirs. 

### 5.4.2 Research route and technical measures

Improving imaging accuracy of igneous rock is one of the main jobs in seismic data processing for this work zone.  The routes of seismic data imaging research for this area are: (1) To ensure the amplitude preservation and fidelity during the entire processing.  For prestack processing, stick to the principle of wideband high fidelity processing, which protects low frequency in the following two areas.  One is the suppression of high frequency ocean noise, trying to separate the signals from noise and to suppress the noise so as to protect the effective signals.  The other is to handle the problem of migrated noise and alias caused by uneven spatial sampling during processing. ( 2) Trying to finely characterize the igneous rock velocity and spatial spread for velocity modeling, so as to ensure high imaging accuracy. ( 3) The selection of migration method is also a very important step.  This area has extreme development of fractures and rapid changes in lateral velocity, so an effective migration algorithm with high imaging accuracy should be selected to obtain high‐accuracy images. 

For amplitude processing, the key task is to carry out further research into suppression of high frequency ocean noise, amplitude recovery, wavelet processing and data normalization.  For structure identification and imaging, the key task is to carry out research into velocity modeling and imaging methods.  The two‐way wave reverse time migration algorithm is used for this block and research is being conducted on PSDM processing for mid‐shallow formations seismic data in order to improve the imaging accuracy and resolution.  Work is based on carrying out fine structure confirmation, igneous rock characterization and favorable reservoir forecasting. 

### 5.4.3 Key processing techniques

#### 5.4.3.1 Technique for high frequency ocean noise suppression

The acquisition modes in the work zone include onshore acquisition and offshore acquisition, so the land and offshore noises within the work zone are extremely developed.  These noises can be roughly divided into three types: (1) Low frequency strong energy surface waves with continental features. ( 2) High frequency strong energy interference with offshore data features, such as fishing net noise, large boat noise, surge noise and high frequency secondary interferences. ( 3) Low frequency or high frequency anomalous amplitude.  According to the difference in noise features of originally acquired data, we determined two processes for suppressing offshore and onshore data noise, respectively.  The idea of separately processing signal and noise was adopted, by which the low frequency surface wave and high frequency interference were suppressed by steps in different processing stages.  In this way, the noise was properly suppressed, the SNR of seismic data was improved and the fidelity was high during denoising [57,58].  The onshore data interference suppression method has been discussed in other chapters, so we will not go into details here.  Our focus is on the offshore high frequency coherent noise attenuation. 

  1.  Analysis of offshore coherent noise characteristics. 

From the pattern, we can see that the time‐distance curve features of offshore coherent noise change with the differences in interference sources and the distance to such sources.  The time‐distance curve features are mainly in the following patterns: (a) Linear. ( b) Dual‐curve pattern with interference source as the apex. ( c) Dual curves parallel to first arrivals caused by secondary interference of shot source. ( d) Single‐trace high frequency noise.  All these noises have developed all the way from shallow to deep formations. 

Compared with land noises, the offshore noise is characterized by high frequency and wide frequency band.  From the aspect of single shot (Figure 5.127), the noise covers the whole single shot from shallow to deep.  The effective waves from mid‐deep layers are hard to identify.  The analysis of frequency spectrum (Figure 5.128) shows that the high frequency strong energy noises have mainly developed within 60–220 Hz, with energy higher than that of effective waves.  They are superimposed with 60–80 Hz frequency head of effective waves.  The f‐k spectrum (Figure 5.129) clearly shows the noise background of high frequency and strong energy.  When seismic waves propagate to igneous rock formation, the energy level of high frequency components of effective waves is less than that of high frequency interference due to the effect of attenuation by absorption.  In general, the energy of offshore high frequency coherent noise is 208 times that of normal subsurface reflected waves.  This high frequency noise with strong energy covers the effective signals and decreases the SNR of seismic data.  Therefore, effective prestack suppression to these interferences is a key link in data processing for this area. 

  2.  Suppression of frequency‐division anomalous amplitude. 

Like the effective signals, the frequencies of noises vary in different times.  The processing of frequency‐division regional anomalous amplitude properly segregates the frequency band of seismic data according to the frequency distribution law of noise in different time periods.  It helps in understanding the spread law of signals and noises in different frequency bands, thus performing pertinent processing, which can further improve the fidelity preservation of denoising and the processing accuracy of seismic data.  Compared with conventional processing of region anomalies, the advantage of frequency‐division processing of regional anomalies is that the superiority frequency of interference wave can be used to extract its features and the available features can be used in the non‐superiority frequency as constraint, which help identify the interference waves. 

From the previous analysis, we understand the two features of noise with high frequency and high energy: (1) High frequency, mainly concentrates at 60–220 Hz, while the effective frequency band of effective wave is 8–50 Hz. ( 2) High energy, the energy level of high frequency noise is greater than that of effective wave due to effect of absorption attenuation.  Based on the difference of effective waves and high frequency noise in frequency and energy, we can take the high frequency noise with high energy as anomalous amplitude and suppress it within the effective frequency band of high frequency noise. 

From the 60–250 Hz single shot (Figure 5.130), the high frequency noise has strong coherence, and is in continuous spread in deep layers.  It is very difficult to identify it with anomalous amplitude suppression.  In order to ensure fidelity and amplitude preservation during noise suppression, while not damaging the effective signals, and achieve satisfactory suppression effect, we rearranged the single shots as per offset (Figure 5.131), disturbing the noise coherence.  A satisfactory suppression effect (Figure 5.132) was achieved in this way. 

  3.  High frequency coherent noise suppression technique. High frequency noise shows strong coherence on shot gather of offshore seismic data, but shows very poor coherence on common geophone line.  We designed a rectangular time window on moveout shot gather with three quadrants – time, shot point and geophone point, with a series of frequency band range being designed.  It is believed that the high frequency noise has features of single frequency, high energy and large dip in each band range, while the effective signal is an event with weak energy and gentle dip after normal moveout correction.  Performing f‐x filtering in cross‐line direction can well eliminate the effect of high frequency coherent noises.  Figures 5.133 and 5.134 show suppression of high frequency coherent noise.  We can see that the linear noise with large dip, high frequency and secondary source noise caused by air bubbles are all well suppressed. 

**Figure 5.127** Record of original single shot (development of high frequency noise). 

**Figure 5.128** Spectrum of original single shot record (development of high frequency noise). 

**Figure 5.129** f‐k spectrum of original single shot record (high frequency setting developed in tidal flat). 

**Figure 5.130** Separation of high frequency noise and signal. 

**Figure 5.131** Comparison between (a) shot gather sequencing as per trace number and (b) sequencing as per offset. 

**Figure 5.132** Comparison of (a) high frequency noise before suppression, (b) after suppression and (c) after denoising. 

**Figure 5.133** Effect graph of high frequency coherent noise suppression. 

**Figure 5.134** Effect graph of air‐bubbled secondary source suppression. 

#### 5.4.3.2 Normalization processing technique for merging data

The design of a 3D field acquisition and observation system, whether in fasciculation or block, generally has the characteristic of even folds unless affected by surface factors.  However, with the development of imaging technology and computer technology, the prestack imaging technology is now very mature, and single CMP gather folds cannot completely judge the evenness of spatial sampling.  For Kirchhoff integral prestack migration, the evenness of common‐offset gather folds is even more important.  In this work zone, the offset is not evenly distributed, which will cause the presence of empty CMP point on common‐offset profile, leading to occurrence of spatial alias during prestack migration and migration arcing and hence reducing the SNR of seismic data.  In addition, during merging processing, the intersect part of the work zone shows a sharp increase in folds, and over high folds may occur locally on common‐offset profile, resulting in energy unevenness and migration arcing. 

Therefore, the application of merging data normalization processing technique mainly focuses on two aspects: (1) Offset‐division normalization to improve spatial sampling, weakening the effect of alias and improving imaging effect. ( 2) Locally adjusting the over high and over low folds at intersection areas with over high folds to decrease migration arcing. 

At present, there are a number of techniques for bin homogenization, including interpolation method, trace‐borrowing method, DMO, DMO−1.  In line with the development of fractures in this block, we used the method of borrowing traces from similar bins on common‐offset gather. 

From the actual effect, we can see that, after bin homogenization, the folds on common‐offset profile are even.  Taking an offset of 3100 m (Figure 5.135), for example, the effective bin after homogenization is greatly increased and the empty CMP points are greatly reduced, hence reducing the spatial alias and migration arcing caused by lack of traces.  From the point of migration profiles, the profile SNR is also well improved (Figure 5.136), with the increase of spatial sampling points after data normalization.  After data normalization at intersection within the work zone and with the evenness of folds, the profile arcing is remarkably weakened (Figures 5.137 and 5.138). 

**Figure 5.135** Folds comparison of (a) common‐offset profile bin and (b) after homogenization. 

**Figure 5.136** PSDM profile comparison (a) before and (b) after bin homogenization. 

**Figure 5.137** Folds comparison (a) before and (b) after bin homogenization. 

**Figure 5.138** PSDM profile comparison (a) before and (b) after bin homogenization. 

#### 5.4.3.3 Velocity modeling technique for complex structures

The building of a velocity model is key to PSDM [59] that needs an accurate depth domain velocity model.  The prestack velocity imaging is more sensitive to velocity error than time migration, so two problems are introduced: (1) If the velocity field is not correct, the imaging error so caused may easily offset or even surpass the improvement in migration methods. ( 2) The sensitivity of PSDM to velocity provides a better tool for velocity analysis than PSTM. 

The seismic data from this work zone has the following characteristics: the shallow sedimentation setting is steady and the velocity is relatively stable; the igneous rock target zone shows obvious high velocity and great lateral variation of the velocity due to the influence from the structure and igneous rock distribution.  Subject to the large‐dip structure and lithology, the velocity of deep layers is relatively high and varies greatly longitudinally and laterally.  Meanwhile, the fractures in this block were greatly developed, so there are a number of broken zones.  It is very difficult to identify the horizons, which can easily lead to such problems as zone channeling, un‐closure.  In order to build the velocity model efficiently and accurately, the method of P‐S joint velocity analysis is mainly used to build the velocity‐depth model. 

Step 1: The building of an initial velocity model is by longitudinal velocity analysis; the longitudinal velocity modeling method is efficient, but its sensitivity is also high, which may readily cause distortion.  Therefore, it is necessary to remove velocity distortion points by smoothing after pickup.  Figure 5.139 shows the initial velocity model in depth domain obtained from the longitudinal velocity model.  From every direction, we can see that the initial velocity is smooth and locally changes in the structure location of the target zone. 

Step 2: Determine the velocity model by lateral zone velocity modeling method.  First, we interpret the structural horizon on the time migration domain, then use ray migration and proportion to project the time zone onto depth domain, and obtain the horizontal delay spectrum by using the horizon and imaging gathers through migration of initial velocity.  Then perform optimized iteration to velocity by using tomographic inversion of travel time through pickup of the delayed spectrum.  Second, pick up vertical delay and utilize the method of inversion of constraint zone velocity to carry out optimized iteration to imaging velocity. 

  1.  Building of time horizon model. The structures in this block are complex, with igneous rocks that are greatly developed.  Additionally, there is great variation in longitudinal velocity.  First, we used well data to determine the velocity interface of formations, and then performed fine structural interpretation.  During interpretation, we combined closely with geologic horizons so as to control the varying law of velocity interface, as shown in Figures 5.140 and 5.141. 
  2.  Optimizing interval velocity by reflected wave tomography. The depth migration based tomography method is a velocity model optimizing method based on tomography of depth migration gather.  This method is to convert the depth error on migrated CRP gather into relevant time error along the CRP ray path, hence we can use the conventional travel time tomography.  Through tomography, we iterated and optimized the PSDM interval velocity, causing the residual delay spectrum along the interval focusing and tending to zero.  Figure 5.142 shows a comparison of Ed2 zone velocity before and after optimization.  Figure 5.143 is a quality control diagram for velocity analysis.  The final velocity ensures that horizontal delay and vertical delay almost come to zero and CRP gather is flat.  Through repeated iteration, the macro‐velocity model conforms to subsurface structural features (Figure 5.144). 

Step 3: To improve spatial imaging quality through grid tomography velocity modeling.  This technique performs fine processing of reflected grid tomography to its interval velocity through structural constraint during PSDM, after determining the macro‐velocity imaging.  It can improve the interval imaging quality.  The grid tomographic imaging technique realizes gridding by picking up residual moveout at different spatial points, and then conducting tomographic inversion to each point, based on the known residual moveout, so as to get the velocity at different grid points finally.  The velocity optimization and calculation can be realized in this way.  Figure 5.145 shows the flow chart of grid tomographic imaging.  Better effects can be achieved by the application of the grid tomographic imaging. 

In actual operations, in order to obtain the spatial grid control points, we irst need to extract the structural attribute body of the seismic data.  In general, the geologic structure features of this data can be characterized by extracting the attributes like dips, azimuths and continuity of the seismic data (Figure 5.146).  By constraining these structural attribute bodies, we can automatically pick up the geologic horizons and describe the seismic data accurately.  Meanwhile, we pick up the residual delay of seismic data to obtain the residual delay body of the spatial distribution, and then perform gridding processing of the picked up geologic horizons.  In this way, we get a large grid matrix in the space.  By using a tomographic algorithm, we get an optimized velocity‐depth model.  Figure 5.147 shows a comparison of velocity profile before and after optimization.  It can be seen that the optimized interval velocity accuracy is higher.  From the effect chart of migration profile (Figure 5.148), the interval imaging accuracy is effectively improved after velocity optimization to grid tomographic imaging. 

**Figure 5.139** Initial velocity model in depth domain obtained from longitudinal velocity modeling. 

**Figure 5.140** Determining velocity interface as per log data. 

**Figure 5.141** Building time horizon model. 

**Figure 5.142** Comparison of Ed2 zone velocity before and after optimization. ( a) Velocity prior to correction. ( b) Depth domain residual moveout. ( c) The velocity after reflected wave tomography. 

**Figure 5.143** P‐S velocity analysis and quality control. 

**Figure 5.144** Final velocity model. ( a) Horizon depth. ( b) Layer velocity (c) Final velocity‐depth model. 

**Figure 5.145** Flow chart for grid tomographic imaging. 

**Figure 5.146** Various attribute chart for seismic data. 

**Figure 5.147** Comparison of velocity profiles before and after grid tomographic imaging. 

**Figure 5.148** Comparison of depth migration profiles (a) before and (b) after grid tomographic imaging. 

#### 5.4.3.4 Assymetric travel time PSTM technique

It is well known that an important step in realizing PSTM is to compute the seismic travel time [60].  The computing methods can be roughly divided into three types: straight ray, curved ray and asymmetric travel time.  The model of a straight ray travel time algorithm is homogeneous medium.  The seismic waves travel in a straight line, and migration gives the medium above the imaging points as equivalent homogeneous medium.  It uses the equivalent velocity at the imaging points to indicate the constant velocity of the medium above this point.  The equation for computing the straight ray travel time is simple to operate with efficient migration computation, but its imaging quality is not satisfactory. 

The common computation of curved ray travel time gives the medium above the imaging point as horizontal layered medium, so it can be described as a group of interval velocity.  The seismic waves travel like curved refracted ray.  Therefore, the assumption of horizontal layered medium is also referred to as the assumption of curved refracted ray.  However, this kind of travel time cannot be expressed by simple explicit function, and it is not easy to apply in imaging computation.  But if the numerical method of ray tracing is used to calculate the travel time, there may be such problems as cumulative error, low stability and low computing efficiency.  Based on the time‐distance relation in uniform medium and the theory of function approximation, Taner & Koehler [61] proposed the relation expression algorithm for time‐distance in horizontal layered medium, which has been widely used in actual field operations.  A kind of Lie algebra integral algorithm was developed for asymmetric travel time, moving away from the restriction of horizontal layered medium model. 

When there is strong lateral velocity variation, it may cause wave front assymmetry, which is the form of assymmetry of time‐distance curve on stacked profile, and the form of assymmetry of ray tracing path on PSTM.  In areas of No.  1 and No.  2 buried hills, the multi‐stage tectonic movements caused the development of fractures, and there are also missing formations, resulting in great lateral velocity variation.  Therefore, the Kirchhoff integral method PSTM for curved rays, based on layered uniform medium, cannot meet the requirement of imaging accuracy.  The asymmetric travel time PSTM breaks through the assumptions of "constant velocity media or slightly varying velocity media", and takes into account the lateral velocity variation, and introduces the lateral derivative method in the equation.  After polynomial expansion, the equation contains both even terms and odd terms, then infers the travel time equation for lateral velocity variation, and this equation applies to PSTM of uneven medium.  The main advantages of this equation include:

  1.  Introducing lateral velocity derivative in travel time equation to improve the travel time computing accuracy. 
  2.  Improving the focusing quality of seismic wave under complex conditions. 
  3.  Computing more accurate weighted coefficient which maintains relative amplitude,
  4.  The travel time equation has a higher accuracy than the currently used one that was proposed by Water Lynn (1988).  The equation of Water Lynn is suitable for cases with 10% lateral velocity variation, while this one is for 50% variation of lateral velocity. 

**Figure 5.149** Comparison between (a) curved ray PSTM and (b) asymmetric travel time PSTM. 

This method can be simply outlined as improving the quality of seismic imaging under complex structure conditions and computing more accurate weighted coefficient, which maintains relative amplitude by increasing the travel time computing accuracy.  This research has achieved this asymmetric travel time algorithm on GPU and has worked effectively in actual data processing.  Figure 5.149 shows a comparison of asymmetric travel time PSTM and curved ray PSTM.  It can be seen that the asymmetric PSTM has rich low frequency components, and maintains the phase position and amplitude features well.  Additionally, it is advantageous in characterizing the fracture system, and the boundaries of igneous rock are clearly defined. 

#### 5.4.3.5 Inverse time PSDM technique

The reverse time migration technique [62] was effectively used in the research work in this work zone.  The imaging accuracy of small fractures is higher and more focused, and the SNR and resolution of the target zones is significantly improved (Figures 5.150 and 5.151).  Compared with Kirchhoff prestack depth, the reverse time migration has the following characteristics:

  1.  The dominant frequency of igneous rock increased by 5 Hz. 
  2.  The small fracture system of the target zone is more distinct and the SNR is somewhat improved. 
  3.  The imaging quality in the eastern part of the work zone is improved greatly. 

**Figure 5.150** Profile comparison between (a) Kirchhoff PSDM and (b) reverse time migration (I). 

### 5.4.4 Analysis on research and processing effects

Through detailed analysis on seismic data from the buried hill structural belt in Nanpu, the resultant profiles are greatly improved in terms of imaging quality and geologic understanding.  The prestack imaging technique flow was also improved for seismic data from the buried hill structural belts in Nanpu of the Jidong Oilfield.  In mid‐shallow layers, the SNR and the resolution are high, and the faulted block and fractures of the target zones are more distinct (Figures 5.152 and 5.153).  The asymmetric travel time PSTM and reverse time migration have good amplitude preservation, and the varying relation of spatial amplitude is well maintained.  From time slices, it is found that the integral migration result shows development of north‐east fractures in the work zone, while the reverse time migration result shows that this work zone has also developed some north‐west small fractures, which can rarely be seen on integral migration result (Figure 5.154). 

**Figure 5.151** Profiles comparison between (a) Kirchhoff PSDM and (b) reverse time migration (II). 

**Figure 5.152** Profile comparison between (a) previous migration result and (b) new migration results (I). 

**Figure 5.153** Profile comparison between (a) previous migration result and (b) new migration results (II). 

**Figure 5.154** Time slices comparison between (a) previous PSDM result and (b) new reverse time migration result. 

### 5.4.5 Conclusions and understanding

In view of the complexity of seismic data from the buried hill structural belt in Nanpu, and through in‐depth analysis to geologic problems and characteristics of seismic data, we conducted profound research into imaging processing techniques and have developed practical technical measures.  In particular, we have introduced the new technique: asymmetric travel time PSTM and reverse time PSDM to the work zone, which has satisfactorily addressed the effect of lateral velocity variation on imaging.  The imaging quality in complex structures with large dips is remarkably superior to the previous research findings, and the final processing results well reflect the various geologic features.  Finally, we have improved and developed the technology series and flow, which are suitable for accurate imaging of seismic data from the buried hill structural belt in Nanpu.  These technologies have great potential for application in similar areas. 

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#  Index

  * _a_
  * absolute seismic fidelity preservation processing, difficulties
  * absorbing boundary conditions, reverse time migration method (RTM)
  * acoustic approximation
  * acoustic pressure wavefield
  * air‐bubbled secondary source suppression
  * alias factors
  * Alkhalifah's VTI media research
  * alluvial fan
  * ALU, GPU/CPU heterogeneous computing system
  * amplitude compensation
  * amplitude preservation
    * background
  * amplitude preservation Fourier finite difference prestack depth migration method
    * background
    * implementation
    * results
  * amplitude preservation item of consideration, relative fidelity preservation of seismic data
  * amplitude recovery item
  * analysis of subsalt data features, Pre‐Caspian Basin
  * angle discriminating factor
  * angle domain velocity analysis method
  * anhydrite bodies
  * anisotropic PSDM _see also_ PSDM
  * anisotropic reverse time migration of VTI media
  * anisotropy of media
  * anticlines
  * apertures
  * arbitrary truncation errors
  * arc phenomenon
  * artificial boundary reflection problems
  * asymmetric travel time PSTM
  * ATI
  * AVA analysis
  * azimuth PSDM effectiveness _see also_ high‐density wide azimuth seismic data imaging technique; PSDM

  * _b_
  * Badaowan Interval in the Baka Work Zone
  * Baka region
  * band‐pass filters, _see also_ Laplacian filtering method
  * basalt
  * 'beads'
  * Beam method
  * Berkhout et al CFP development
  * Beylkin determinant
  * bin folds
  * blind zones
  * Bogda Mountains
  * Bohai Bay Basin
  * boundary conditions _see also_ perfect matched layer absorbing; random
    * GPU/CPU heterogeneous computing system
    * reverse time migration method (RTM)
    * study on the two‐way wave extrapolation operator and its boundary conditions
  * Brook programming language _see also_ GPU/CPU heterogeneous computing system
  * buried hill structural zone in the Nanpu Depression of Jidong Oilfield

  * _c_
  * cache, GPU/CPU heterogeneous computing system
  * carbonate bodies
  * carbonatite region _see also_ high‐density wide azimuth seismic data imaging technique
    * analysis of difficulty tackling effect
    * case study
  * Cartesian coordinate system
  * case study
    * buried hill structural zone in the Nanpu Depression of Jidong Oilfield
    * carbonatite region
    * Kuqa Country of Xinjiang Uygur Autonomous Region
    * offshore high frequency coherent noise attenuation
    * Pre‐Caspian Basin
    * reverse time migration method (RTM)
    * subsalt imaging case study
    * Tabei
    * Tuha and Jiuquan Basins
  * Caspian Basin
  * caves
  * 'cavity' phenomenon
  * CDPs
  * CGGVeritas
  * CG programming language
  * check‐pointing techniques, storage problems
  * China
    * Junggar Basin
    * static correction
    * Tuha and Jiuquan Basins
  * Chinese Academy of Sciences
  * CIG _see_ Common Image Gather
  * Claerbout imaging conditions
  * classification method, noise suppression technique
  * Clayton–Engquist boundary condition
  * coal beds
  * coherence enhancements
  * coherence inversion _see also_ velocity modeling
    * advantages
    * background
    * critique
    * definition
    * multi‐well constraint
    * schematic diagram
  * combined well excitation factor, seismic acquisition and observation
  * common focus point (CFP)
    * definition
  * Common Image Gather residual curvature analysis (CIG)
  * common imaging point (CIP)
  * common midpoint (CMP)
  * common reflection point (CRP)
  * common reflection surface (CRS)
  * complicated structures
    * reverse time migration method (RTM)
    * velocity modeling
  * computing systems _see also_ CPU; GPU/CPU heterogeneous computing system
  * concave interface roles, velocity modeling
  * control, GPU/CPU heterogeneous computing system
  * controllable seismic source excitation factor, seismic acquisition and observation
  * control points
  * conventional narrow azimuth results
  * conventional seismic profiles
  * convex interface roles, velocity modeling
  * covariance functions, KT
  * C programming language
  * CPU _see also_ GPU/CPU heterogeneous computing system
    * multi‐core CPU platform model
  * Cretaceous Qingshuihe Formation, Shidong area of Junggar Basin
  * cross‐array domain noise suppression
  * cross‐correlation imaging condition
    * background
    * definition
    * normalized cross‐correlation imaging method
  * CUDA operating system _see also_ GPU/CPU heterogeneous computing system
  * cycling method, velocity modeling

  * _d_
  * Dablain's high‐order difference method proposal
  * damping factor, definition
  * data alias
  * Daxiaoliu Ditch
  * deconvolution method _see also_ poststack; prestack
    * background
  * deep wells _see also_ Well
  * Delft University of Technology
  * denoising noise suppression method
  * depropagation wavefields
  * depth domain focus analysis
  * depth domain interval velocity modeling
  * depth focusing analysis (DFA)
  * difference equations
  * differential time shift (DTS)
  * diffractive travel time
  * diffusion theory
  * dipole shear wave logging
  * distance between channels, seismic acquisition and observation
  * distances, seismic acquisition and observation
  * DIX transformation _see also_ root mean square velocities; velocity modeling
  * DMO
  * dolostone
  * domain‐division noise suppression
  * dominant frequencies
  * Dongyi Interval oil reservoir
  * downward pressure components
  * downward travelling waves, _see also_ z‐axis
    * definition
  * DRAM, GPU/CPU heterogeneous computing system
  * drilling effectiveness
  * dual‐core 3.0G Hz computing units
  * dual time‐distance curves

  * _e_
  * East Ditch
  * Eastern China, static correction
  * efficiency issues, GPU/CPU heterogeneous computing system
  * Eikonal equation _see also_ finite difference method
  * elastic wave forward modelling
    * background
    * definition
  * emergent waves
  * excitation‐time imaging condition, definition
  * explosives
    * dosage
  * external drift algorithm, Kriging multi‐well constrained velocity modeling

  * _f_
  * Fast Matching Method (FMM)
  * faults
  * Fermat principle
  * fidelity preservation of seismic data
  * filtering methods _see also_ high‐pass; Laplacian; linear; Muder; noise; rectangular; triangular
    * background
  * finite difference methods _see also_ amplitude preservation Fourier; Fourier; high‐order staggered
  * finite element method
  * first arrival refraction
  * first‐order quasi‐P wave equation, reverse time migration method (RTM)
  * first‐order stress‐velocity equation
  * fishing net noise
  * fixed benchmark, static correction
  * f‐k noise elimination
  * flat bed velocity model
  * flattening principle CMP trace gathers
  * floating benchmark, static correction
  * floating datum, PSDM technique
  * floating‐point efficiency comparisons, GPU/CPU heterogeneous computing system
  * focusing analysis
  * folds
  * forward modelling, background
  * 4D modeling
  * Fourier finite difference method (FFD), _see also_ amplitude preservation; finite difference methods; Laplacian filtering method
    * critique
    * definition
    * results
  * fourth‐order Quasi‐P wave equation
  * fractures
  * frequency band of seismic data
  * frequency‐division noise suppression
  * frequency domain full waveform inversion theory
  * frequency‐spatial domain finite difference compensation item processing
  * Fresnel band
  * full waveform inversion (FWI)
    * background
    * critique
    * definition
    * discussion
    * flowchart
    * future prospects
    * gradient guidance
    * historical background
    * numerical calculation example
    * study status
  * fusion plane
  * FWI _see_ full waveform inversion

  * _g_
  * gas reserves, _see also_ oil
  * Gaussian beam migration method
  * GeForce 6800 Ultra GPU of NVIDIA
  * geological body influences, velocity modeling
  * geologic structure, Pre‐Caspian Basin
  * geometrical spreading factor
  * geometries of the horizon bottom boundary
  * geophone wavefields
  * GeoStar
  * gobi gravel zone
  * GPU/CPU heterogeneous computing system _see also_ reverse time migration method
    * actual data tests
    * advantages
    * applications
    * background
    * boundary conditions
    * conclusions
    * CUDA operating system
    * definition
    * efficiency issues
    * floating‐point efficiency comparisons
    * flowcharts
    * hard disks
    * high‐performance computing applications
    * I/O
    * memory
    * numerical experimentation
    * realization strategy of RTM prestack imaging based on the GPU/CPU
    * research background
    * restrictions
    * results
    * schematic of the structure features
    * structure features
    * study and application of RTM prestack imaging algorithm based on the GPU/CPU system
    * study on the imaging condition and low‐frequency noise suppression method
    * study on the two‐way wave extrapolation operator and its boundary conditions
    * warp block group
  * gradient guidance, full waveform inversion (FWI)
  * Green's function
  * GSS
  * GT200 GPU
  * Guansi Interval oil reservoir

  * _h_
  * halite
  * hard disks
    * GPU/CPU heterogeneous computing system
    * utilization
  * Higdon artificial boundary
  * high‐density wide azimuth seismic data imaging technique _see also_ carbonatite region
    * analysis of difficulty tackling effect
    * azimuth PSDM effectiveness
    * case study
    * conclusions and understanding
    * future prospects
  * high frequency coherent noise suppression technique
  * high frequency deconvolution method
  * high‐order difference method
  * high‐order staggered grid finite‐difference method
  * high‐pass filtering method
  * high‐performance computing applications
  * high‐resolution and high SNR
    * background
    * conclusions
    * definition
    * over‐emphasizing issues
    * processing flow
    * relative fidelity preservation of seismic data comparisons
  * high‐resolution seismic processes
    * background
  * high velocity interval top combination, velocity modeling
  * Hilbert transform
  * HLSL programming language
  * horizontally layered medium model
  * horizontal resolution
  * horizontal velocity variations
  * Huoyanshan of Turpan‐Hami Basin
  * hyperbolic reflection events
  * H2 zone
  * H5 zone

  * _i_
  * igneous rock
  * imaging alias
  * imaging conditions
    * definition
    * modification noise suppression method
    * reverse time migration method (RTM)
    * study on the imaging condition and low‐frequency noise suppression method
  * imaging upon denoising noise suppression method
  * incident waves
  * initial velocity model _see also_ velocity modeling
  * INLINE420 survey line
  * INLINE644 survey line
  * Institute of France Petroleum (IFP)
  * Institute of Geology and Geophysics of Chinese Academy of Sciences
  * integral PSDM method
  * integrated velocity modeling method
  * interpolation method
  * interval velocity
    * errors
    * field
    * of formation
  * inverse‐time PSDM
  * inversion layer velocity
  * I/O, GPU/CPU heterogeneous computing system
  * irregularity of prestack data, velocity modeling
  * isotropic reverse time migration _see also_ reverse time migration method

  * _j_
  * J‐bottom wave
  * Jidong Oilfield
  * Jiuquan Basin
  * J2t0 reservoir of SN31 wellblock, seismic profiles
  * Junggar Basin

  * _k_
  * Kaelin and Guitton normalized cross‐correlation imaging method
  * kernel functions
  * kinetic imaging conditions
  * Kirchhoff integral prestack depth migration method _see also_ PSDM; ray theory; seismic migration imaging
    * background
    * critique
    * definition
    * GPU/CPU heterogeneous computing system
    * historical background
    * implementation principle
    * problems
    * research
    * results
  * K‐L filtering
  * Kriging multi‐well constrained velocity modeling
  * KT, 151–6, _see also_ Kriging
  * KT‐1 wave
  * Kulongshan of Yumen Jiuxi
  * Kuqa Country of Xinjiang Uygur Autonomous Region

  * _l_
  * Laojunmiao
  * Laplacian filtering method, _see also_ band‐pass filters; Fourier finite difference method
    * background
    * definition
    * numerical experimentation
  * large boat noise
  * lateral resolutions
  * lateral velocity variation
  * layer velocity analysis
  * Li Bo
  * limestone
  * linear filtering
  * linear time‐distance curves
  * linear weighting method
  * lithology reservoirs, _see also_ reservoirs of lithology formation
    * background
  * Liu et al
  * Liugouzhuang
  * Liu Hong
  * local plane wave propagation, Laplacian filtering method
  * location of notch frequency band
  * logging data constraints, velocity modeling
  * longitudinal resolutions
  * longitudinal wave source excitation
  * low‐frequency noise generation and suppression
    * reverse time migration method (RTM)
    * study on the imaging condition and low‐frequency noise suppression method
  * Luxi area of Junggar Basin

  * _m_
  * macro‐velocity model
  * magnetic wave propagation
  * Marmousi II model
  * Marmousi model
    * definition
  * matrix forms of equations
  * maximum energy
    * 3D focus operator
  * mean velocity
  * memory, GPU/CPU heterogeneous computing system
  * methods, relative fidelity preservation of seismic data
  * migration profiles _see also_ seismic migration imaging
  * MIMD _see_ multi‐instruction flow and multi‐data flow
  * minimum least squares
  * MKT wave
  * monoclinal structures
  * Moore's Law
  * Muder noise elimination method
  * mudstone
  * Mulder and Plessix filtering formula
  * multi‐attribute fusion plane
  * multi‐band‐pass filters
  * multi‐core CPU platform model _see also_ GPU/CPU heterogeneous computing system
  * multi‐information restricted interval control velocity modeling
  * multi‐instruction flow and multi‐data flow (MIMD)
  * multimedia project reports
  * multi‐model external drift Kriging interpolation
  * multiples
  * multiple‐transmitting formula boundary (MTF)
  * multiprocessors, GPU/CPU heterogeneous computing system
  * multi‐well constraint, coherence inversion

  * _n_
  * Nanpu Depression of Jidong Oilfield
  * narrow frequency bandwidth
  * Newtonian inversion _see also_ full waveform inversion
  * NIK‐3
  * NMO velocity
  * noise elimination _see also_ filtering methods; low‐frequency; Muder; random noise; signal‐to‐noise ratios
    * f‐k noise elimination
    * high‐resolution and high SNR
    * Laplacian filtering method
    * offshore high frequency coherent noise attenuation
    * 'six division' prestack noise suppression technique
    * study on the imaging condition and low‐frequency noise suppression method
  * no‐reflective wave equation noise suppression method
  * normalization processing technique for merging data
  * normalized cross‐correlation imaging method
  * North Troyes structure
  * notching
    * background
    * causes
    * definitions
    * location of notch frequency band
  * number of receiving channels, seismic acquisition and observation
  * number of wells, seismic acquisition and observation
  * numerical dispersion suppressing
  * numerical experimentation
    * GPU/CPU heterogeneous computing system
    * Laplacian filtering method
    * reverse time migration method (RTM)
  * numerical tests on pulse response, reverse time migration method (RTM)
  * NVIDIA _see also_ GPU/CPU heterogeneous computing system
  * NWGI model, reverse time migration method (RTM)

  * _o_
  * oblique disturbance
  * offset distances, seismic acquisition and observation
  * offshore high frequency coherent noise attenuation
  * oil _see also_ gas reserves
    * seismic profiles
  * one‐way wavefield
  * one‐way wave migration method, _see also_ wave equation migration method
    * critique
  * one‐way wave prestack depth migration methods
  * one‐way waves, z‐axis
  * operator alias
  * Ordovician carbonatite reservoir
  * Ordovician limestone
  * original single shot record control point
  * over‐emphasizing issues, high‐resolution and high SNR

  * _p_
  * parallel computing, _see also_ GPU/CPU heterogeneous computing system
  * paraxial approximation boundary
  * PC cluster‐based computing mode, 80–82 _see also_ GPU/CPU heterogeneous computing system
  * Pentium
  * perfect matched layer absorbing boundary condition (PML)
    * definition
    * reverse time migration method (RTM)
  * PetroChina
  * phase preservation item of consideration, relative fidelity preservation of seismic data
  * phase‐shifting method
  * pinch‐out point of lithologic reservoir
  * PML _see_ perfect matched layer absorbing boundary condition
  * porosity influences, velocity modeling
  * positive propagation wavefields
  * poststack
    * deconvolution method
    * deep well comparisons
  * poststack depth migration
  * Poynting vector imaging condition
  * Pre‐Caspian Basin
    * analysis of subsalt data features
    * case study
    * difficulties and problems with seismic imaging
    * features and conditions
    * geologic structure
    * sedimentary evolution and stratigraphic characteristics
  * precise velocity model _see also_ velocity modeling
    * establishment
  * preserved‐amplitude migration algorithms _see also_ amplitude preservation Fourier finite difference prestack depth migration method
    * definition
    * implementation
    * results
  * prestack _see also_ Kirchhoff integral prestack depth migration method
    * deconvolution method
    * deep well comparisons
  * prestack depth migration methods _see also_ PSDM; velocity modeling
    * definition
  * propagation wavefields
  * protection of effective frequency band item of consideration, relative fidelity preservation of seismic data
  * protection of low frequency band item of consideration, relative fidelity preservation of seismic data
  * PSDM _see also_ Kirchhoff integral prestack depth migration method; prestack depth migration methods
    * anisotropic PSDM
    * azimuth PSDM effectiveness
    * floating datum
    * powerful aspects
    * reverse‐time PSDM
  * pseudo mean velocity
  * pseudo‐spectral method
  * P‐S ratio
  * PSTM
    * asymmetric travel time PSTM
  * pull‐up false image of anomalous body
  * pulse response tests, reverse time migration method (RTM)
  * P wave
    * anisotropic reverse time migration of VTI media
  * P1 wave

  * _q_
  * Qaidam Basin
  * Qilanshan
  * Qingnan region
  * Qingxi of Jiuquan and Yumen
  * Qin Ning et al tomography velocity inversion method
  * Qinxi Depression
  * qP wave
  * Quadro FX5600
  * quality monitoring and accuracy discussion, velocity modeling
  * quasi‐P wave equation for VTI media
  * Quaternary mountainous area

  * _r_
  * Radon domain
  * random boundary conditions, reverse time migration method (RTM)
  * random noise attenuation (RNA)
    * background
    * repeated application comparisons
    * uses
  * random noise data
  * random numbers
  * ray theory _see also_ Kirchhoff integral prestack depth migration method; velocity modeling
    * critique
  * realization strategy of RTM prestack imaging based on the GPU/CPU
  * rectangular filters
  * reflection factors
  * regional anomaly processing
  * registers, GPU/CPU heterogeneous computing system
  * regularization of data, velocity modeling
  * relative amplitude of notch frequency, definition
  * relative fidelity preservation of seismic data _see also_ seismic broadband acquisition
    * amplitude preservation item of consideration
    * background
    * conclusions
    * definition
    * high‐resolution and high SNR comparisons
    * items of consideration
    * phase preservation item of consideration
    * processing flow
    * protection of effective frequency band item of consideration
    * protection of low frequency band item of consideration
    * seismic acquisition and observation mode
    * study on method
  * relative fidelity seismic profiles
  * relative imaging conditions
  * reservoirs of lithology formation, _see also_ lithology
    * background
  * residual migration velocity analysis
  * residual moveout analysis (RMA)
  * residual static correction
  * resolution of seismic data
    * background
  * reverse time continuation, definition
  * reverse time migration method (RTM), –115, 1–209, 2–303, 326–9 _see also_ GPU/CPU heterogeneous computing system; time migration; wave equation migration method
    * absorbing boundary conditions
    * advantages
    * angle domain velocity analysis method
    * anisotropic reverse time migration of VTI media
    * background
    * boundary conditions
    * case study
    * complicated structures
    * components
    * critique
    * definition
    * first‐order quasi‐P wave equation
    * flowchart
    * historical background
    * imaging conditions
    * implementation flow
    * isotropic reverse time migration
    * low‐frequency noise generation and suppression
    * Marmousi model
    * model example
    * numerical experimentation
    * numerical tests on pulse response
    * NWGI model
    * PML absorbing boundary conditions
    * quasi‐P wave equation for VTI media
    * random boundary conditions
    * realization strategy of RTM prestack imaging based on the GPU/CPU
    * research background
    * results
    * stability conditions
    * study and application of RTM prestack imaging algorithm based on the GPU/CPU system
    * study on the imaging condition and low‐frequency noise suppression method
    * study on the two‐way wave extrapolation operator and its boundary conditions
    * subsalt imaging case study
    * theoretical model examples
    * two‐way wave application
    * velocity modeling
  * reverse‐time PSDM
  * Ricker wavelet
  * RNA modification module _see also_ random noise attenuation
  * root mean square velocities (RMS) _see also_ DIX transformation; velocity modeling
    * background
    * velocity field construction

  * _s_
  * salt domes
  * salt rocks
  * sand
  * sandstone
  * scanning 
    * high‐resolution and high SNR
  * sea
  * second‐order spatial differential accuracy scheme
  * sedimentary evolution and stratigraphic characteristics, Pre‐Caspian Basin, 186–7 _see also_ velocity modeling; VSP initial inversion
  * SEG/EAGE
  * seismic acquisition manner
    * background
  * seismic attribute prediction, seismic migration imaging
  * seismic broadband acquisition _see also_ relative fidelity preservation of seismic data
    * background
  * seismic data processing, background
  * seismic imaging constraint optimization, velocity modeling
  * seismic migration imaging _see also_ Kirchhoff integral prestack depth migration method; migration profiles; preserved‐amplitude migration algorithms; reverse time; velocity modeling; wave equation migration method
    * background
    * method and principle
  * seismic observation means
    * background
  * seismic pilot survey lines
  * seismic profiles
  * seismic tomography (ST)
    * background
    * definition
  * seismic wavelets
  * self‐adaptive lateral velocity variation
  * shale
  * shallow layer data
  * Shanshan County
  * Shidong area of Junggar Basin
  * shots
  * Sigbee model
  * signal‐to‐noise ratios (SNRs), 1–18, –28, 131–3, 136–7, 1–62, 187–8, –29 _see also_ high‐resolution and high SNR
    * offshore high frequency coherent noise attenuation
    * velocity modeling
  * SIMD data parallel execution unit, GPU/CPU heterogeneous computing system
  * SIMT unit, GPU/CPU heterogeneous computing system
  * single shot record control point
  * single‐trace high frequency noise time‐distance curves
  * single well excitation factor, seismic acquisition and observation
  * 'six division' prestack noise suppression technique
  * slant stack methods
  * slowness, sonic wave equation model parameter velocity field
  * smoothing processing
  * SNRs _see_ signal‐to‐noise ratios (SNRs)
  * SN31 wellblock, Luxi area of Junggar Basin
  * sonic logging
  * sonic velocity _see also_ velocity modeling
  * space variation removal
  * spectrum analysis results _see also_ notching
  * spherical coordinate system
  * spherical diffusion theory
  * spherical spreading compensation
  * S‐P ratio
  * square of slowness, sonic wave equation model parameter velocity field
  * SSE optimization, Pentium
  * stability conditions, reverse time migration method (RTM)
  * stacking velocity inversion
  * static correction
    * China
    * velocity modeling
  * step noise suppression
  * Stork's ST proposal
  * structure imaging, seismic migration imaging
  * ST _see_ seismic tomography
  * study and application of RTM prestack imaging algorithm based on the GPU/CPU system
  * study and application of the velocity modeling building method
  * study and application of velocity model building for the areas with complicated structures
  * study on method, relative fidelity preservation of seismic data
  * study on the two‐way wave extrapolation operator and its boundary conditions, GPU/CPU heterogeneous computing system
  * study status, full waveform inversion (FWI)
  * subsalt imaging case study _see also_ Pre‐Caspian Basin
    * problems
  * subsurface structural features
  * superposition
  * surface consistent amplitude compensation
  * surface consistent deconvolution
  * surge noise
  * SVI
  * S wave
    * anisotropic reverse time migration of VTI media
  * 'sweet point'
  * Symes implementation proposals

  * _t_
  * Tabei
  * Taibei Depression
  * Takla Makan Desert
  * Tarantola's full waveform inversion
  * Tarim Basin
  * Taylor spread
  * tensile normal fault
  * Tesla C870
  * theoretical model examples, reverse time migration method (RTM)
  * thin layers
  * thin sand layers
  * Thomsen parameters
  * thread level parallel computing
  * 3D reverse time depth migration _see also_ GPU/CPU; reverse time
  * 3D reverse time depth migration high‐order difference equation with truncation errors
  * 3D space, velocity modeling
  * time‐distance curves
  * time‐division noise suppression
  * time domain full waveform inversion
  * time interval models
  * time migration _see also_ reverse
    * depth migration contrasts
  * time‐shifting item
  * time‐space domains, Laplacian filtering method
  * T&L _see also_ GPU/CPU heterogeneous computing system
  * tomographic imaging
    * background
    * flowchart
  * Tongji University
  * trace‐borrowing method
  * travel time _see also_ velocity modeling
    * asymmetric travel time PSTM
  * triangular filters
  * truncation errors
  * Tsunami and Sinopec Petroleum Geophysical Research Institute
  * Tuha Basin
  * Turpan‐Hami Basin
  * Turpan‐Hami foothills
  * 2D addresses _see also_ GPU/CPU heterogeneous computing system
  * 2D high‐resolution pilot lines
  * 2D scalar wave equation
  * 2D working areas, velocity modeling
  * two‐way wave application _see also_ reverse time
    * case study
    * reverse time migration method (RTM)
    * study on the two‐way wave extrapolation operator and its boundary conditions
    * subsalt imaging case study

  * _u_
  * undulated surfaces
  * unitive
    * 3D forward modeling high‐order difference equation with truncation errors
  * upward pressure components

  * _v_
  * Vcrstccg's research
  * velocity analysis
    * flowchart
  * velocity errors
  * velocity modeling _see also_ coherence inversion; DIX transformation; root mean square
    * anisotropy of media
    * application of the building method
    * background
    * calculation‐accuracy analysis
    * case study
    * common focus point (CFP)
    * Common Image Gather residual curvature analysis (CIG)
    * common imaging point (CIP)
    * complicated structures
    * constraints
    * definition
    * development
    * difficulties
    * errors
    * flat bed velocity model
    * full waveform inversion (FWI)
    * geological body influences
    * high velocity interval top combination
    * impacting factors
    * integrated method
    * irregularity of prestack data
    * Kriging multi‐well constrained velocity modeling
    * lithology influences
    * logging data constraints
    * Marmousi model
    * migration algorithm constraints
    * multi‐information restricted interval control velocity modeling
    * multiples
    * NWGI
    * porosity influences
    * quality monitoring and accuracy discussion
    * regularization of data
    * research background
    * residual moveout analysis (RMA)
    * results
    * reverse time migration method (RTM)
    * seismic imaging constraint optimization
    * seismic migration imaging
    * seismic tomography (ST)
    * shallow layer data
    * signal‐to‐noise ratios (SNRs)
    * static correction
    * study and application for the areas with complicated structures
    * study and application of the building method
    * subsurface structural features
  * velocity spectrum method
  * vertical resolution
  * Visean wave
  * VSP initial inversion
  * VTI media, anisotropic reverse time migration of VTI media

  * _w_
  * Walk‐away VSP data
  * Wang Huazhong
  * warp block group
  * Water Lynn equation
  * wave equation migration method (WEM) _see also_ one‐way; reverse time; seismic migration imaging; wavefield extrapolation
    * definition
  * wavefield continuation algorithm operator structure
  * wavefield decomposition noise suppression method
  * wavefield extrapolation _see also_ wave equation migration method
  * wave front vector, velocity modeling
  * weighted stacking
  * Well Ke21‐P1
  * Well Liu‐4
  * Well Liu‐108
  * Well Shidong‐2 (SD2)
  * Well Shidong‐4 (SD4)
  * Well S302 of SN31 wellblock, seismic profiles
  * Well S303 of SN31 wellblock, seismic profiles
  * Wenjisang region
  * West Ditch
  * Western China
  * Whitmore et al studies
  * wide frequency bandwidth
  * width of notch frequency band, definition
  * WKBJ approximation acoustic wave equation

  * _x_
  * Xigou formation of the Wenjisang region in the Turpan‐Hami Basin
  * Xinjiang Uygur Autonomous Region
  * X800XT of ATI

  * _y_
  * Yaerxia
  * Yanshanian period
  * Yaxi Fan delta front
  * Yumen

  * _z_
  * z‐axis _see also_ downward travelling waves
    * seismic exploration
  * zero‐phase deconvolution method
  * zone‐division noise suppression

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