bluuebunny/crossref_metadata_2025 huggingface dataset:
Potential coordinate mislocations in crosshole tomography: Results from the Grimsel test site, Switzerland
Authors: Maurer Hansruedi , Green Alan G.
Published: October 2002

Tomographic techniques based on borehole‐to‐borehole and tunnel‐to‐borehole traveltime data are now being employed in a wide range of studies associated with the exploration and exploitation of hydrocarbons and metallic minerals, the disposal of chemical and radioactive waste, diverse civil engineering projects, and archaeology. A fundamental assumption of currently employed tomographic inversion strategies is that the coordinates of the boreholes and tunnels containing the seismic sources and receivers are accurately known. By inverting both synthetic and observed traveltime data, we demonstrate that relatively minor coordinate errors (1–2%) in the deeper parts of long boreholes (>100 m) may produce artifacts in the tomographic images that are comparable in extent and amplitude to true velocity anomalies. To address this problem, we introduce the coupled inverse method, commonly used in earthquake studies, as a means to determine simultaneously borehole coordinate adjustments and an estimate of the tomographic image. This method has been applied to traveltime data generated and collected along a tunnel and in three boreholes within a granitic body situated in the central Swiss Alps (Grimsel test site operated by NAGRA, the Swiss National Cooperative for the Disposal of Radioactive Waste). Coupled inversions of two independent subsets of traveltime data that involve a common central borehole, together with a coupled inversion of the entire data set, yield consistent coordinate adjustments for all boreholes and tomographic images that are compatible with the known geology and a sonic log from the central borehole. Further tests with synthetic data demonstrate that certain types of weak anisotropy could influence the coupled inversions. Regardless of whether minor coordinate mislocations or weak anisotropy is the dominant effect at the Grimsel test site, distinct low‐velocity zones appear to delineate fractures zones that are conduits for groundwater flow.
Predictive processing of array acoustic waveform data
Authors: Tang Xiao Ming
Published: October 2002

Estimation of wave velocity (or slowness) from array waveform data is a basic and very important process in acoustic logging and seismic processing. A predictive method is developed to process array waveform data containing multiple wave modes. These wave modes may overlap in both time and frequency and are inseparable using conventional techniques. In this new technique, the waveform at a receiver is modeled by a combination of wave data at other receivers using a time‐domain prediction theory. It is assumed that the array data contain a number of propagating modes. A minimization procedure is formulated to optimize the match between the predicted and measured waveforms, yielding slowness estimates of the wave modes across the array. Most important, the optimization is performed directly in the time domain using the entire array wave data set, including all possible data combinations. This strategy effectively reduces the noise effects and enhances the robustness of the estimation. Furthermore, the estimated slowness values can be used in formulating a procedure to split the array data into individual wave modes, allowing their behavior to be analyzed. Examples are shown to demonstrate the ability of the technique to extract wave slowness from multiple wavemode data.
“Unexpected” shear‐wave behavior
Authors: Horne Steve , MacBeth Colin , Liu Enru
Published: October 2002

In a previous study, we inverted shear‐wave birefringence observations from an azimuthal vertical seismic profile (VSP) experiment conducted at the Conoco Borehole Test Facility, Oklahoma (Horne and MacBeth, 1994; Horne, 1995). Our results indicate that the observations can be interpreted in terms of two distinctly different transversely isotropic (TI) models (Figure 1). The first model predicts the symmetry axis to be at N165°E and dipping 10° to the northwest. This orientation coincides with geological information relating to the fracture system that strikes between N50°E and N75°E (Queen and Rizer, 1990). Thus, this first model is consistent with a priori information, so that a possible source of the anisotropy can be identified. However, the second model derived from the inversion results suggests the symmetry axis to be at N200°E and dipping 30° to the southwest. If we interpret this result in terms of an equivalent medium resulting from aligned cracks or fractures, then this inferred crack‐fracture strike would lie in a direction conflicting with the a priori measurements. The bimodal nature of this solution can be readily understood if we examine the shear‐wave behavior for the different models shown in Figure 2. In this plot, the symmetry axis is chosen to be the [Formula: see text]. If we consider the near‐vertical propagation directions that are typically measured in VSP experiments, it can be seen that the qS1 polarizations lie either perpendicular (model 1) or parallel (model 2) to the symmetry axis. Since these polarizations are usually interpreted in terms of aligned crack‐fracture systems, the inferred strike would lie in the [Formula: see text] plane for model 1 and the [Formula: see text] plane for model 2. This interpretation is completely incorrect for model 2, since this inferred alignment is actually orthogonal to the alignment implied by the symmetry of the TI system. This situation represents a worrying aspect to the interpretation of shear‐wave surveys used to characterize crack‐fracture systems. The question that we address is whether anisotropic materials that possess properties similar to those of model 2 can be constructed from equivalent media resulting from cracks or fractures. We also consider other sources of anisotropy that may lead to this behavior.
Wavelets, well ties, and the search for subtle stratigraphic traps
Authors: Ziolkowski Anton , Underhill John R. , Johnston Rodney G. K.
Published: October 2002

We examine the conventional methodology for tying wells to processed seismic data and show why this methodology fails to allow for reliable interpretation of the seismic data for stratigraphy. We demonstrate an alternative methodology that makes the tie without the use of synthetic seismograms, but at the price of measuring the seismic source signature, the cost of such measurements being about 1% of data acquisition costs. The essence of the well tie is (1) to identify geological and seismic interfaces from the logs and core, (2) to measure the one‐way traveltime to these interfaces using downhole geophones, and (3) to use the polarity information from (1) and the timing information from (2) to identify the horizons on the zero‐phase processed seismic data. Conventional processing of seismic data usually causes the wavelet to vary from trace to trace, and conventional wavelet extraction at a well using the normal‐incidence reflection coefficients relies on a convolutional relationship between these coefficients and the processed data that has no basis in the physics of the problem. Each new well introduces a new wavelet and poses a new problem—how should the zero‐phasing filter be derived between wells? Our methodology consists of three steps: (1) determination of the wavelet consisting of all known convolutional effects before any processing using measurements of the source time function made during data acquisition, (2) compression of this wavelet to the shortest zero‐phase wavelet within the bandwidth available, and (3) elimination of uncontrolled distortions to the wavelet in subsequent processing. This method is illustrated with data from the prospective Jurassic succession in the Moray Firth rift arm of the North Sea in which we have identified, for the first time on seismic data, a major regional unconconformity that cuts out more than 20 Ma of geological time. This method offers two major benefits over the conventional approach. First, all lateral variations in the processed seismic data are caused by the geology. Second, events on the processed seismic data may be identified from well logs simply by their polarity and timing. It follows that events can then be followed on the seismic data from one well to another with confidence, the seismic data can be interpreted for stratigraphy, and subtle stratigraphic traps may be identified.
Smooth approximation of potential fields from noisy scattered data
Authors: Rauth Michael , Strohmer Thomas
Published: October 2002

Geophysical potential‐field data generally are observed at scattered sampling points and are contaminated by measurement and preprocessing errors. Analysis and further treatment require a representation of the underlying potential fields on a regular grid. In the presence of noise, an approximation of the data is more appropriate than an exact interpolation. Analysis of the smoothness of potential fields indicates an approximation by band‐limited functions. The resulting least‐squares problem can be formulated as a linear system of equations in which the system matrix is of block‐Toeplitz type. This special structure allows a computationally attractive and robust solution via the fast Fourier transform and the conjugate gradient algorithm. On this basis, we present a gridding method that incorporates additional knowledge about the physical properties of potential fields and the statistics of the data. Experimental results for synthetic and real‐world gravity data demonstrate good performance for highly scattered noisy data.
Reflection of rays in a constant gradient medium: CRP geometry
Authors: Levin Franklyn K.
Published: October 2002

In a medium having a velocity that increases linearly with depth (constant gradient), rays are arcs of circles (Slotnick, 1936). A constant gradient medium is not a good approximation to a real subsurface. Not only does velocity increase without limit with depth, but the rate of increase is constant. Nonetheless, over a finite range of depths, a constant gradient medium is closer to reality than a medium having constant velocity down to reflector of interest. For that reason, a number of investigators have considered the changes in processes applied to seismic data when a constant velocity gradient other than zero is assumed.
On Talwani’s “Errors in the total Bouguer reduction”
Authors: LaFehr T. R.
Published: October 2002

Talwani (1998) shows that the differences between the values for the Bullard B correction published in Swick (1942) and those I calculated (LaFehr, 1991b) owe their existence to the fact that we now use a different gravitational constant. I am grateful to Talwani for pointing this out and regret that this simple (and now obvious) explanation had not occurred to me. However, my effort to change the practice by those who directly use the values published by Swick is still valid: while the major contributions to these differences are not “errors,” they nonetheless exist, and those including the Bullard B correction in their reductions should use the updated values that I have published. The values in Swick’s table should not be used mainly because of the different value for the gravitational constant now in use but, in addition, because small Swick errors from computation or round off also may be avoided. Both components of the differences are shown in detail in Figure 3 of LaFehr (1991b).
Prestack Kirchhoff depth migration of shallow seismic data
Authors: Pasasa Linus , Wenzel Friedemann , Zhao Ping
Published: October 2002

Prestack Kirchhoff depth migration is applied successfully to shallow seismic data from a waste disposal site near Arnstadt in Thuringia, Germany. The motivation behind this study was to locate an underground building buried in a waste disposal. The processing sequence of the prestack migration is simplified significantly as compared to standard common (CMP) data processing. It includes only two parts: (1) velocity‐depth‐model estimation and (2) prestack depth migration. In contrast to conventional CMP stacking, prestack migration does not require a separation of reflections and refractions in the shot data. It still provides an appropriate image. Our data example shows that a superior image can be achieved that would contain not just subtle improvements but a qualitative step forward in resolution and signal‐to‐noise ratio.
Electromagnetic and geological transect across permafrost terrain, Mackenzie River delta, Canada
Authors: Todd Brian J. , Dallimore Scott R.
Published: October 2002

The time‐domain electromagnetic (TDEM) method provides a surface geophysical technique suitable for interpreting deep permafrost conditions. This paper describes profiles collected in early spring in a transitional area of the Mackenzie Delta, Arctic Canada, with differing permafrost conditions and surficial geology. These data augment previously published profiles and allow the construction of a 30-km-long TDEM transect from the Holocene‐age Mackenzie Delta in the southwest to the Pleistocene‐age Tuktoyaktuk Coastlands in the northeast. The geoelectric section produced from the TDEM data is interpreted in terms of permafrost distribution. This interpretation provided a basis for inferring lithologic changes. Unconsolidated, non‐ice‐bonded (unfrozen) sediment has resistivities less than 10 ohm-m. Partially ice‐bonded sediment ranges in resistivity from 10 to 40 ohm-m. Ice‐bonded (frozen) sediment has resistivities from 30 to 300 ohm-m. Bedrock has low resistivities (from 5 to 15 ohm-m). Interpretation of the geoelectric section derived from both the shallow (<200 m) and deep (>500 m) TDEM data suggests that the main body of permafrost increases in thickness from 50 to 500 m over a few kilometers. A horizontally persistent unfrozen zone (talik) is situated from 50 to 100 m in depth within the main body of permafrost. Ice‐bonding models derived from the TDEM surveys provide constraints on the geologic history of the Mackenzie Delta.
2.5-D modeling of seismic wave propagation: Boundary condition, stability criterion, and efficiency
Authors: Cao Shunhua , Greenhalgh Stewart
Published: October 2002

The modeling of 3-D wave propagation in media having only 2-D variation in the elastic properties—so‐called 2.5-D modeling—is achieved using the wavenumber transform, in which multiple 2-D problems are solved, each one associated with a different strike‐direction wavenumber [Formula: see text] We derived a 2.5-D transmitting boundary condition in the frequency domain, which has no simple representation in the time domain. It yields significantly improved results over existing boundary conditions. For time‐domain methods, attenuating boundary conditions must be applied. The 2.5-D stability criterion changes from the 2-D to the 3-D criterion as the wavenumber increases from zero to the maximum value for traveling waves, respectively. In the frequency‐wavenumber ([Formula: see text]) domain at a given spatial location, the wavefield for a fixed frequency (ω) oscillates at progressively higher rates as wavenumber ([Formula: see text]) increases from zero to the maximum value for traveling waves. A nonuniform sampling scheme in wavenumber space, to exploit the oscillatory nature of the wavefield, yields significant efficiency improvement over the normal uniform sampling scheme.
Seismic attributes for monitoring of a shallow heated heavy oil reservoir: A case study
Authors: Schmitt Douglas R.
Published: October 2002

In production geophysics, detecting the zones of production or constraining the in‐situ conditions within a reservoir are often of greater importance than obtaining highly resolved seismic structural images. Standard seismic data processing distorts the signal and limits the potential for extracting additional information, especially for shallow targets. An alternative “shift‐stack” procedure is applied in the processing of a shallow 12-fold, 1-m common midpoint (CMP) spacing reflection profile acquired over a heated Athabasca heavy oil sand reservoir. The shift‐stack involves summing of CMP traces which have been flattened to an appropriate reference event. Simple modeling confirms that the prestack waveforms are better preserved by this process. Amplitude and frequency attributes are extracted from the reflection profile. Amplitudes of a continuous reservoir event vary by 600% over 35-m intervals along the profile. Bright spots correlate with heated regions. Apparent frequencies, as measured by the instantaneous frequency and by short time‐window power spectral estimates of the subreservoir event are 20–30 Hz lower in these same regions. These diminished apparent frequencies most probably result from interference of the subreservoir reflection with events related to structural changes within the reservoir. A complete interpretation of the results has not been attempted as knowledge of the in‐situ conditions is incomplete. However, changes in the seismic response at the well locations suggest that these attributes are useful in detection and mapping of heated zones. The shiftstack procedure may also be useful in environmental and geotechnical applications.
Variogram analysis of magnetic and gravity data
Authors: Maus Stefan
Published: October 2002

Model variograms describe the space domain statistics of magnetic and gravity data. Variogram analysis can be used to map intensity, depth, and scaling exponent (self‐correlation) of source. In previous statistical methods the measured data were gridded and transformed to the wavenumber domain; then their power spectrum was analyzed using a spectral model. To avoid the loss and distortion of information during gridding and wavenumber domain transform, I transform the spectral model to the space domain instead. Variograms are the appropriate space domain counterparts of magnetic and gravity power spectra. The variogram of the field above a self‐similar half‐space model is governed by three parameters: intensity, depth, and scaling exponent. These source parameters can be mapped with high resolution and accuracy by fitting model variograms directly to magnetic and gravity line data variograms.
Seismic waveform inversion in the frequency domain, Part 2: Fault delineation in sediments using crosshole data
Authors: Pratt R. Gerhard , Shipp Richard M.
Published: October 2002

A crosshole experiment was carried out in a layered sedimentary environment in which a normal fault is known to cut through the section. Initial traveltime inversions produced stable but low‐resolution images from which the fault could be only vaguely inferred. To image the fault, wavefield inversion was used to produce a velocity model consistent with the detailed phase and amplitude of the data at a number of frequencies. Our wavefield inversion scheme uses a classical, descent‐type algorithm for decreasing the data misfit by iteratively computing the gradient of this misfit by repeated forward and backward propagations. Our propagator is a full‐wave equation, frequency‐domain, acoustic, finite‐difference method. The use of the frequency‐space domain yields computational advantages for multisource data and allows an easy incorporation of viscous effects. By running wavefield inversion on the field data, a quantitative velocity image was produced that yielded a significantly improved image of the fault (when compared with the original traveltime inversions). Because the original field data were noisy and contained a high degree of multiple scattering (from the layering of the sediments), the transmitted arrivals were selectively windowed to enhance the image. The sediments at the site were strongly attenuating; we therefore used a viscoacoustic model during the modeling and the inversion that correctly simulated the observed decrease in amplitude with increasing frequency and source‐receiver offset. Furthermore, since the traveltime inversion indicated a high degree of anisotropy at the site, a fixed, homogeneous level of anisotropy was used during the inversion. Tests at varying levels of anisotropy confirmed the improvement in image quality and in data fit when anisotropy was incorporated. The final image was verified by examining the distribution of the residuals in the frequency domain, by comparing time‐domain modeled wavefields with the observed data, and by direct comparison with borehole logs.
True‐amplitude frequency‐wavenumber constant‐offset migration
Authors: Ekren B. O. , Ursin Bjørn
Published: October 2002

Low S/N ratios, interfering diffractions, and dip‐related problems (e.g., reflector point dispersal, dip‐dependent NMO, and reflection angle) make reliable amplitude versus offset (AVO) analysis a difficult task. Prestack time migration (PSTM) collapses diffractions, increases the S/N ratio, and reduces dip‐related problems. Therefore, PSTM is usually required before offset dependent information can be extracted from seismic data, and PSTM is mandatory before comparing real seismic data with 1-D earth model synthetic data. We present a 2-D frequency‐wavenumber common‐offset prestack time migration algorithm. To treat the amplitudes correctly, a 3-D to 2-D transform of the data is required before doing the migration. This is done by correcting the data for out‐of‐plane geometrical spreading. Migration artifacts are attenuated, exploiting the fact that the maximum dip to be migrated decreases with increasing traveltime and offset. The final processing steps before further processing are 2-D geometrical spreading correction and removal of the implicit NMO correction inherent in the migration. Two marine data examples show improved data quality after prestack time migration, making subsequent amplitude analysis more reliable.
Finite‐element ray tracing through structurally deformed transversely isotropic formations
Authors: Daley P. F. , Marfurt Kurt J. , McCarron Eileen B.
Published: October 2002

Accurate ray tracing forms the central building block for prestack Kirchhoff depth migration, reflection tomography, and amplitude versus offset (AVO) analysis. We present an accurate method of tracing rays through an inhomogeneous transversely isotropic medium where the crystallographic axes of symmetry are rotated arbitrarily. We achieve this high degree of modeling diversity by discretizing our model into a piecewise homogeneous finite‐element representation of a continuously variable earth. Within each element the anisotropic parameters, together with the angle of rotation between the crystallographic and model axes, may vary arbitrarily. We obtain efficiency by approximating the exact expression for the eikonal equation given by Gassmann, which, after some minor manipulation, bears a striking resemblance to an empirical parameterization developed by Lecomte. This new algorithm produces results that compare favorably to first arrivals generated by the numerical solution of the full elastic wave equations for transversely isotropic (TI) media. In the limit of weak anisotropy, our results reduce to the well‐established Thomsen parameterization.
A transparent boundary technique for numerical modeling of elastic waves
Authors: Zhu Jianlin
Published: October 2002

In numerical modeling of wave motions, strong reflections from artificial model boundaries may contaminate or mask true reflections from the interior model interfaces. Hence, developing a kind of exterior model boundary transparent to the outgoing waves is of critical importance. Among proposed solutions, e.g., Smith (1974), Kausel and Tassoulas (1981), and Higdon (1991), the most widely used may be the Clayton and Engquist (1977) method of absorbing boundary conditions, based on paraxial approximations for acoustic and elastic‐wave equations. However, absorbing boundary conditions make the reflection coefficients zero only for normal incidence, and suppression of reflected S-waves (Clayton and Engquist, 1977) becomes poorer as the ratio of P- to S-wave velocity ([Formula: see text]) becomes larger.
Multiazimuthal modeling and inversion ofqPreflection coefficients in fractured media
Authors: Simões‐Filho Ivan A. , Neves Fernando A. , Tinen Júlio S. , Protázio João S. , Costa Jessé C.
Published: October 2002

We present a method for the exact modeling and inversion of multiazimuthal qP-wave reflection coefficients at an interface separating two anisotropic media. This procedure can be used for media with at least one of its planes of symmetry parallel to the interface (i.e., monoclinic or higher symmetries). To illustrate the method, we compute qP-wave reflection coefficients at an interface separating an isotropic medium (representing a seal rock) from a transversely isotropic medium (representing a reservoir rock with vertical aligned fractures). Forward modeling shows that the difference in the offset of the critical angles for different azimuths is proportional to the fracture density: the higher the fracture density, the larger the difference. In the second part of the paper, we use a global optimization technique (genetic algorithm) to invert wide‐angle amplitude variation with offset (AVO) synthetic data. The model space consists of mass density and five elastic parameters of a transversely isotropic medium with a horizontal symmetry axis (HTI medium), which, to the first order, represents the fractured reservoir rock. For this model, we find that the configuration of three azimuths of data acquisition is the minimum number of acquisition planes needed to invert amplitude variation with offset/amplitude variation with azimuth (AVO/AVA) data. Further, there is a need for incidence angles up to 40°; a more narrow range of angles can lead to models that fit the data perfectly only up to the “maximum” incidence angle. We assume that the velocities and density of the isotropic rock are known, but use no prior information on the values of the model space parameters of the fractured rock except for reasonable velocity values in crustal rocks and constraints of elastic stability of solid media. After inversion for the model space parameters, we compute statistics of the 30 best models and likelihood functions, which provide information on the nonuniqueness and quality of the AVO/AVA inverse problem.
A simplified Lax‐Wendroff correction for staggered‐grid FDTD modeling of electromagnetic wave propagation in frequency‐dependent media
Authors: Bergmann Tim , Blanch Joakim O. , Robertsson Johan O. A. , Holliger Klaus
Published: October 2002

The Lax‐Wendroff correction is an elegant method for increasing the accuracy and computational efficiency of finite‐difference time‐domain (FDTD) solutions of hyperbolic problems. However, the conventional approach leads to implicit solutions for staggered‐grid FDTD approximations of Maxwell’s equations with frequency‐dependent constitutive parameters. To overcome this problem, we propose an approximation that only retains the purely acoustic, i.e., lossless, terms of the Lax‐Wendroff correction. This modified Lax‐Wendroff correction is applied to an O(2, 4) accurate staggered‐grid FDTD approximation of Maxwell’s equations in the radar frequency range (≈10 MHz–10 GHz). The resulting pseudo-O(4, 4) scheme is explicit and computationally efficient and exhibits all the major numerical characteristics of an O(4, 4) accurate FDTD scheme, even for strongly attenuating and dispersive media. The numerical properties of our approach are constrained by classical numerical dispersion and von Neumann‐Routh stability analyses, verified by comparisons with pertinent 1-D analytical solutions and illustrated through 2-D simulations in a variety of surficial materials. Compared to the O(2, 4) scheme, the pseudo-O(4, 4) scheme requires 64% fewer grid points in two dimensions and 78% in three dimensions to achieve the same level of numerical accuracy, which results in large savings in core memory.
Seismic trace interpolation using half‐step prediction filters
Authors: Porsani Milton J.
Published: October 2002

A method to perform seismic trace interpolation known as the Spitz method handles spatially aliased events. The Spitz method uses the unit‐step prediction filter to estimate data spaced at Δx/2. The missing data are obtained by solving a complex linear system of equations whose unknowns are the coefficients at the interpolated location. We attack this problem by introducing a half‐step prediction filter that makes trace interpolation significantly more efficient and easier for implementation. A complex half‐step prediction filter at frequency f/2 is computed in the least‐squares sense to predict odd data components from even ones. At the frequency f, the prediction operator is shrunk and convolved with the input data spaced at Δx to predict data at Δx/2 directly. Instead of solving two systems of linear equations, as proposed by Spitz, only a system for the half‐step prediction filter has to be solved. Numerical examples using a marine seismic common‐midpoint (CMP) gather and a poststack seismic section were used to illustrate the new interpolation method.
Ultrasonic velocity and shear‐wave splitting behavior of a Colton sandstone under a changing triaxial stress
Authors: Dillen Menno W. P. , Cruts Helma M. A. , Groenenboom Jeroen , Fokkema Jacob T. , Duijndam Adri J. W.
Published: October 2002

Ultrasonic experiments on a dry Colton sandstone placed in a triaxial pressure machine show that effective stress changes lead to distinct anisotropic velocity changes in compressional waves and shear waves. The stress imprint can be recognized from the associated velocity pattern by relating the velocities to the three normal stress directions. The ultrasonic velocities indicate that the sensitivity of the different waves to stress predominantly depends on stresses applied in the polarization and propagation directions of the particular wave mode. Also, stress‐induced changes in shear‐wave splitting are observed.
Incorporating geological dip information into geophysical inversions
Authors: Li Yaoguo , Oldenburg Douglas W.
Published: October 2002

Geological bodies are often linear structures that have well‐defined strike direction and dip angle. We develop a new model objective function that allows this important information to be incorporated into geophysical inversions. A rotation matrix is applied to the horizontal and vertical derivatives of the model so that the derivative in an arbitrary direction is obtained. A model objective function that measures the flatness with respect to the rotated derivatives favors models that have elongated features with the specified strike and dip angle. Formulations for both 2-D and 3-D cases are presented, and they are illustrated using examples from dc resistivity and induced polarization (IP) problems. Synthetic and field examples show that an inversion carried out using known dip information produces a model that has higher resolution and provides a better representation of the true structure.
Green’s function for migration: Continuous recording geometry
Authors: Schuster Gerard T. , Hu Jianxing
Published: October 2002

Analytical formulas are derived to give the point scatterer responses for the zero‐offset and nonzero‐offset migration operators. These formulas are derived under the far‐field approximation for a continuous distribution of sources and receivers, and are denoted as migration Green’s functions. By specifying a homogeneous velocity model with irregular layers, these Green’s functions can be used to quickly compute the synthetic migrated sections without having to compute the modeled data. Thus, these formulas provide a fundamental understanding of migration artifacts and their relationship to the image point location and source‐receiver configuration. This understanding lays the foundation for the next step, elimination of these artifacts by migration deconvolution.
3-D broad‐band estimates of reflector dip and amplitude
Authors: Marfurt Kurt J. , Kirlin R. Lynn
Published: October 2002

Estimates of seismic coherence of 3-D data sets have provided a radically new way of delineating detailed structural and stratigraphic features. Covariance matrices provide the natural formalism to extend the original three‐trace crosscorrelation algorithm to larger analysis windows containing multiple traces, thus providing greater fidelity in low signal‐to‐noise environments. By use of 3-D phase compensation using Radon transforms, we exploit advances made in the high‐resolution multiple signal classification (MUSIC) algorithms, originally developed for the defense industry. All three families of multitrace attributes (coherence, amplitude, and phase) are coupled through the underlying geology, such that we obtain three families of complimentary images of geologic features that result in lateral changes in wave form. The phase attributes of dip/azimuth and curvature allow us to image areas that have undergone folding or draping that can not be seen on coherence or amplitude images. The amplitude attributes allow us to image oil/water contacts or other areas of amplitude variation that may not be seen on coherence or dip/azimuth images. Coupled with coherence and the conventional seismic data, these new multitrace dip and amplitude data cubes can greatly accelerate the interpretation of the major features of large 3-D data volumes. At the reservoir scale, they will be of significant help in delineation of subtle internal variations of lithology, porosity, and diagenesis. In computer‐assisted interpretation, we strongly feel these new attributes will become the building blocks for the application of modern texture analysis and segmentation algorithms to the delineation of geologic features.
Electrical impedance variation with water saturation in rock
Authors: Su Qingxin , Feng Qining , Shang Zuoyuan
Published: October 2002

We measured the electrical impedances of 22 sandstone samples during oil‐driving‐water tests using the two‐electrode method. Experiments show that the imaginary part X of the impedance (R + iX) of rock may respond well to water saturation in the frequency range 100 Hz–15 MHz. We found that the maximum −X values and their corresponding interfacial polarization frequencies are linear with water saturation. The lower critical frequency is found to vary with water saturation, in an unclear relationship with the characteristic length of rock. The dissipation factor at the interfacial polarization frequency remains quite stable and may be an indicator of the pore structure of rock. We used an equivalent circuit to explain the dispersive behavior of rock. More than one interfacial polarization frequency in the impedance Argand plot is predicted and can be observed if the measurement frequency range is wide enough.
Reconstruction of 1-D conductivity from dual‐loop EM data
Authors: Zhang Zhiyi , Routh Partha S. , Oldenburg Douglas W. , Alumbaugh David L. , Newman Gregory A.
Published: October 2002

Inversions of electromagnetic data from different coil configurations provide independent information about geological structures. We develop a 1-D inversion algorithm that can invert data from the horizontal coplanar (HC), vertical coplanar, coaxial (CA), and perpendicular coil configurations separately or jointly. The inverse problem is solved by minimizing a model objective function subject to data constraints. Tests using synthetic data from 1-D models indicate that if data are collected at a sufficient number of frequencies, then the recovered models from individual inversions of different coil systems can be quite similar. However, if only a limited number of frequencies are available, then joint inversion of data from different coils produces a better model than the individual inversions. Tests on 3-D synthetic data sets indicate that 1-D inversions can be used as a fast and approximate tool to locate anomalies in the subsurface. Also for the test example presented here, the joint inversion of HC and CA data over a 3-D conductivity provided a better model than that produced by the individual inversion of the data sets.
A generalized form of Snell’s law in anisotropic media
Authors: Slawinski Michael A. , Slawinski Raphaël A. , Brown R. James , Parkin John M.
Published: October 2002

We have reformulated the law governing the refraction of rays at a planar interface separating two anisotropic media in terms of slowness surfaces. Equations connecting ray directions and phase‐slowness angles are derived using geometrical properties of the gradient operator in slowness space. A numerical example shows that, even in weakly anisotropic media, the ray trajectory governed by the anisotropic Snell’s law is significantly different from that obtained using the isotropic form. This could have important implications for such considerations as imaging (e.g., migration) and lithology analysis (e.g., amplitude variation with offset). Expressions are shown specifically for compressional (qP) waves but they can easily be extended to SH waves by equating the anisotropic parameters (i.e., ε = δ ⇒ γ) and to qSV and converted waves by similar means. The analytic expressions presented are more complicated than the standard form of Snell’s law. To facilitate practical application, we include our Mathematica code.
Rigorous absorbing boundary conditions for 3-D one‐way wave extrapolation
Authors: Zhou Hongbo , McMechan George A.
Published: October 2002

Absorbing boundary conditions play an important role in one‐way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist’s 2-D absorbing boundary conditions for one‐way wave extrapolation by depth stepping in the frequency domain are extended to three dimensions using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45° one‐way wave equation.
Color‐encoding multifrequency acoustic data for near‐bottom studies
Authors: Dunbar John A. , Allen Peter M. , Higley Paul D.
Published: October 2002

In this paper we describe color encoding methods for combining acoustic data in widely separate spectral bands into composite displays. These new display methods better image the near‐bottom is interval in fine‐grained depositional environments. In fine‐grained depositional environments the water bottom is typically not a discrete surface but is a transition zone spanning 1–3 m. This near‐bottom interval is not completely imaged by either fathometers or subbottom profilers alone. Multiple acoustic frequencies spanning both the fathometer and subbottom bands are needed for applications in which the details of the near bottom are critical. Such applications include surveys of water reservoirs, scour around bridge piers, and predredging surveys in harbors. To make effective use of the multifrequency data, we combine three or more signal frequencies into composite false color displays by adapting multispectral photography methods used in optical remote sensing. One approach is to encode amplitudes of traces recorded with three different source frequencies as the red, green, and blue intensities of the false color display. In a second approach, more than three signal frequencies are combined by computing weights for red, green, and blue for each frequency through a principal‐component transformation of the data. We use both color encoding approaches in a field example from a water reservoir and in simulated examples based on a convolutional model of near‐bottom reflectivity. In these examples, color‐encoded displays of multifrequency data improve resolution of interfaces within the near‐bottom interval over that of the corresponding single‐frequency displays. Changes in the near‐bottom frequency response with sediment type also suggest that color encoding of different signal bands has the potential for improved sediment type classification within the near‐bottom interval. The principal component display approach offers a method for automatically adjusting the frequency content within a single display to account for widely varying bottom conditions.
Compressional‐wave velocities in attenuating media: A laboratory physical model study
Authors: Molyneux Joseph B. , Schmitt Douglas R.
Published: October 2002

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.
GPR imaging using the generalized Radon transform
Authors: Wang Tsili , Oristaglio Michael L.
Published: October 2002

A new algorithm for imaging ground‐penetrating radar (GPR) data follows from the theory of the generalized Radon transform (GRT), which was developed and has been used extensively for seismic imaging. The algorithm enables separate reconstructions (to first‐order accuracy) of subsurface permittivity and conductivity images. A pseudovector inverse adapts the original scalar Radon transform theory for vector electromagnetic data. Synthetic examples show that the algorithm can image plastic and metallic pipes buried in a half‐space. In the examples, the half‐space is 100 ohm-m with a relative permittivity of 10. The pipes are 2 cm thick and 15 cm in outer diameter and are buried at a depth of 2 m. The plastic pipes are assumed to be pure insulators, whereas the metallic pipes are assumed to be pure conductors with a conductivity value of 106 S/m. The transmitter waveform has a peak frequency of 200 MHz with a 500-MHz bandwidth. The results show that quantitative images are obtained for plastic pipes, whose scattering is weak (so the Born approximation is accurate). Good images are also obtained for metallic pipes. As with most imaging algorithms, a sharp image requires good estimates of the properties of the background medium.
Acoustic crosswell imaging using asymptotic waveforms
Authors: Keers Henk , Johnson Lane R. , Vasco Don W.
Published: October 2002

Seismic waveforms are inverted using an asymptotic method. The asymptotic method models amplitudes correctly at the caustics and takes nonstationary raypaths into account when computing the waveforms, and thus is an extension of geometrical ray theory. Using numerical differencing, partial derivatives of the data with respect to the model are computed. As expected, these partial derivatives (or sensitivity functions) are concentrated along, but not confined to, raypaths. The sensitivity functions enable the formulation of a waveform inversion algorithm, which is applied to a synthetic crosswell experiment and a laboratory crosswell experiment. The synthetic experiment shows the advantages of the waveform inversion method over conventional traveltime inversion methods. Boundaries of anomalies are better defined, and smearing is reduced. The waveform inversion produces a much lower misfit than the traveltime inversion. The goal of the laboratory experiment was the detection of a nonaqueous phase liquid (NAPL) in water saturated sand. The sand was imaged before and after injection of the NAPL. Using the waveform inversion method, low‐velocity anomalies were imaged that correlate well with post‐experiment determination of NAPL concentrations. The low‐velocity anomaly defocuses the seismic energy. However, the amplitude reduction due to the low‐velocity anomaly is not enough to explain the observed low amplitudes. We suggest that other mechanisms (such as multiple scattering, 3-D effects, or intrinsic attenuation) not included in the asymptotic waveform modeling play an important role in decreasing the amplitude.
A dual‐grid nonlinear inversion technique with applications to the interpretation of dc resistivity data
Authors: Torres‐Verdín Carlos , Druskin Vladimir L. , Fang Sheng , Knizhnerman Leonid A. , Malinverno Alberto
Published: October 2002

We develop a solution to the nonlinear inverse problem via a cascade sequence of auxiliary least‐squares minimizations. The auxiliary minimizations are nonlinear inverse problems themselves, except that they are implemented with an approximate forward problem that is at least an order of magnitude faster to solve than the algorithm used to simulate the measurements. Any given auxiliary minimization in the cascade is fully selfcontained and yields a solution of the unknown model parameters. This solution, in turn, is used to perform a numerical simulation of the data to quantify its agreement with the input measurements. If the difference between the measured data and the simulated data is above the estimated noise threshold, it is input as data to the subsequent auxiliary inverse problem in the cascade. Otherwise, the inversion is brought to a successful completion. We describe the theory and operating conditions under which this cascade inversion approach converges to a solution equivalent to that of a single inversion implemented with the original forward problem. Depending on the choice of approximate forward problem and regardless of the computer algorithm employed to solve the inversion, the cascade sequence of auxiliary minimizations can be made many times more efficient than a single inversion performed with the original forward problem. In this paper, we consider a practical and flexible way to construct the approximate forward problem by using a subset of the finite‐difference grid used to simulate the measurements numerically, i.e., a dual‐grid construction approach. Numerical examples of performance are described based on the inversion of cross‐ and single‐well 2.5-D direct‐current (dc) resistivity data. Our results suggest that the proposed dual‐grid minimization technique may be able to improve greatly the performance of even the most effective multidimensional nonlinear inversion procedures currently in use.
Crosshole seismic imaging for sulfide orebody delineation near Sudbury, Ontario, Canada
Authors: Wong Joe
Published: October 2002

Crosshole seismic instrumentation based on a piezoelectric source and hydrophone detectors were used to gather seismograms between boreholes at the McConnell orebody near Sudbury, Ontario. High‐frequency seismograms were recorded across rock sections 50 to 100 m wide containing a continuous zone of massive sulfide ore. First‐arrival traveltimes obtained from a detailed scan were used to create a P-wave velocity tomogram that clearly delineated the ore zone. Refraction ray tracing on a discrete layer model confirmed the main features of the tomogram. The survey demonstrated that it is possible to conduct cost‐effective, high‐resolution crosshole seismic surveys to delineate ore bodies on a scale useful for planning mining operations.