bluuebunny/crossref_metadata_2025 huggingface dataset:
The WIM method for refraction statics
Authors: Zanzi Luigi
Published: October 2002

We know that first breaks may be efficiently inverted in the wavenumber‐offset domain to determine a robust estimate of the near‐surface model. This domain is indicated particularly for regularly covered surveys so that data can be Fourier transformed without interpolation problems. However, it usually happens that data are collected with irregular spacing of the source points. In this case the initial interpolation may bias the solution. An efficient method to prevent bias consists of an iterative model‐driven interpolation. The database is decomposed and recomposed iteratively according to a linear approach to fill in the data space with model‐consistent first arrivals. The method is proved to converge to the unbiased solution and will be called the wavenumber iterative modeling (WIM) method. Experiments, both on synthetic and real data, show that convergence occurs after few iterations so that the procedure is still quite efficient. Moreover, the WIM method can be extended easily to automatically detect and remove the mispicks and suppress coherent and incoherent noise. Simple linear operators are also available for the conversion of the solution to the generalized reciprocal method (GRM) if the interpreter intends to guide the final optimization of the model.
Compressional head waves in attenuative formations: Forward modeling and inversion
Authors: Liu Qing‐Huo , Chang Chung
Published: October 2002

We develop a method of forward modeling and inverting formation attenuation data from sonic compressional head waves in a fluid‐filled borehole using a branch‐cut integration (BCI) technique to calculate individual acoustic arrivals. We validate this approach with a real‐ axis integration (RAI) method that does not separate the individual arrivals. We show that the straightforward application of the original BCI method for lossless media gives erroneous results for attenuative formations. With a choice of the Riemann sheets satisfying the radiation condition, the new BCI method gives correct results for most lossy and lossless formations. However, modeling very slow formations needs to include the contribution of a leaky pole near the vertical branch cut. With a constant‐Q assumption, we develop a simple processing scheme to extract the formation compressional Q factor from the P head‐wave arrivals. We used experimental data from laboratory‐scale borehole measurements to invert for the compressional Q value of a Lucite block. The inverted results agree within 4.5% of an independent ultrasonic transmission measurement of Q.
Predicting porosity from acoustic velocities in siliciclastics: A new look
Authors: Vernik Lev
Published: October 2002

Two principally different mechanisms of porosity reduction‐induced elastic stiffening of siliciclastic rocks are recognized, which, in the domain of grain‐supported siliciclastics with less than 15% volume clay, result in two linear trends with different slopes in the acoustic velocity‐porosity plane. Transition between the two mechanisms occurs at about 30% porosity and roughly coincides with the transition from (1) early diagenesis, characterized by mechanical compaction and initial intergranular bonding, to (2) advanced chemical diagenesis caused by pressure solution and cementation. Peculiarities of velocity‐stress relations in each of these diagenetic domains suggest that while the stress factor is important in loose sandstones, it has practically very little effect on the frame moduli of consolidated (less than about 30% porosity) sandstones at stress magnitudes beyond the closure stress of microcracks introduced by natural or coring‐related processes. Appropriate grain contact and effective medium theories have been used to model the framework stiffening in the two diagenetic domains, respectively. It is shown that realistic, petrographically observed evolution of pore geometries in consolidated sandstones can be successfully modeled, resulting in a quasi‐linear velocity‐porosity relationship deviating from linearity within the accuracy of velocity measurements. A new look at the compilation of experimental data on acoustic velocities in clay matrix‐supported siliciclastics (more than 15% volume clay), including 45 shales and 19 wackes, accounts for their distinct stress‐sensitivity and anisotropy and suggests that their bedding‐normal elastic stiffness varies nonlinearly in the whole range of porosity reduction from around 80% to almost zero. However, in the velocity‐porosity plane below about 30% porosity, shales also show strong linear relationships with slopes subparallel to those of the grain‐supported rocks.
Semi‐automatic analysis of rock fracture orientations from borehole wall images
Authors: Thapa Bhaskar B. , Hughett Paul , Karasaki Kenzi
Published: October 2002

We develop a semiautomatic method of identifying rock fractures and analyzing their orientations from digital images of borehole walls. This method is based on an algorithm related to the Hough transform which is modified to find sinusoidal rather than linear patterns. The algorithm uses the high‐intensity contrast between the fracture aperture and the rock wall, as well as the sinusoidal trajectory defined by the intersection of the borehole and the fracture. The analysis rate of the algorithm itself is independent of fracture contrast and network complexity. The method has successfully identified fractures both in test cases containing several fractures in a noisy background and in real borehole images. The analysis rate was 0.3–1.2 minutes/m of input data, compared to an average of 12 minutes/m using an existing interactive method. An automatic version under development should open new possibilities for site characterization, such as real‐time exploration and analysis of tunnel stability and support requirements as construction proceeds.
Dynamic smoothing in crosswell traveltime tomography
Authors: Nemeth Tamas , Normark Egon , Qin Fuhao
Published: October 2002

Variable‐size (dynamic) smoothing operator constraints are applied in crosswell traveltime tomography to reconstruct both the smooth‐ and fine‐scale details of the tomogram. In mixed and underdetermined problems a large number of iterations may be necessary to introduce the slowly varying slowness features into the tomogram. To speed up convergence, the dynamic smoothing operator applies adaptive regularization to the traveltime prediction error function with the help of the model covariance matrix. By so doing, the regularization term has a larger weight at initial iterations and the prediction error term dominates the final iterations with a small regularization term weight. In addition, it is shown that adaptive regularization acts by reweighting the adjoint modeling operator (preconditioning) and by providing additional damping. Comparisons of two dynamic smoothing operators, the low‐pass filter smoothing and the multigrid technique, with the fixed‐size (static) smoothing operators show that the dynamic smoothing operator yields more accurate velocity distributions with greater stability for larger velocity contrasts. Consequently, it is a preferred choice for regularization.
Minimum apertures and Fresnel zones in migration and demigration
Authors: Schleicher Jörg , Hubral Peter , Tygel Martin , Jaya Makky S.
Published: October 2002

The size of the aperture has an important influence on the results of (Kirchhoff‐type) migration and demigration. For true‐amplitude imaging, it is crucial not to have apertures below a certain size. For both the minimum migration and demigration apertures, theoretical expressions are established. Both minimum apertures depend on each other and, although a time‐domain concept, are closely related to the frequency‐dependent Fresnel zone on the searched‐for subsurface reflector. This relationship sheds new light on the role of Fresnel zones in the seismic imaging of subsurface reflectors by showing that Fresnel zones are not only important in resolution studies but also for the correct determination of migration amplitudes. It further helps to better understand the intrinsic interconnection between prestack migration and demigration as inverse procedures of the same type. In contrast to the common opinion that it is always the greatest possible aperture that yields the best signal‐to‐noise enhancement, it is in fact the selection of a minimum aperture that should be desired in order to (a) enhance the computational efficiency and reduce the cost of the summation, (b) improve the image quality by minimizing the noise on account of summing the smallest number of traces, and (c) to have a better control over boundary effects. This paper demonstrates these features rather than addressing the question of how to achieve them technically.
Rapid multi‐wave‐type ray tracing in complex 2-D and 3-D isotropic media
Authors: Mao Weijian , Stuart Graham W.
Published: October 2002

We describe a method for seismic ray tracing in complex 2-D and 3-D heterogeneous isotropic media. Both the interface geometry and the horizontal velocity field are parameterized by using nonuniformly spaced cubic B‐spline nodes. In particular, we present a modified cubic B‐spline method for modeling discontinuities. This model parameterization scheme facilitates tomographic inversion of traveltimes and can represent any realistic geological structure that is continuously varying with embedded discontinuities. Many wave types, such as transmitted, reflected, refracted, mode‐converted, diffracted, and turning waves, are desirable for complex geological models. We select rays of various wave types by choice of initial paths and refine them by applying Fermat's minimum time principle. Since the raypath is piecewise linear between interfaces, we solve a system of linearized equations by iteration to produce the actual raypath between source and receiver. The method is fast and unifies the ray‐tracing procedure for various wave types and multiple paths between a source‐receiver pair. Ray amplitudes can be also evaluated by existing analytical formulae. Several examples show that the method is computationally accurate and effective. The method is practicable for multiphase traveltime tomography and 3-D ray‐trace seismic modeling.
A least‐squares approach to depth determination from self‐potential anomalies caused by horizontal cylinders and spheres
Authors: Abdelrahman El‐Sayed Mohamed , Sharafeldin Sharafeldin Mahmoud
Published: October 2002

We have developed a least‐squares approach to depth determination from self‐potential anomalies caused by horizontal cylinders and spheres. By defining the zero‐anomaly distance and the anomaly value at the origin on the profile, the problem of depth determination from self‐potential data has been transformed into finding a solution to a nonlinear equation. Procedures are also formulated to estimate the electric dipole moment and the polarization angle. The error in the depth parameter estimation introduced by data errors was also studied through imposing 1 to 10% errors in the zero‐anomaly distance and the anomaly value at the origin in one synthetic profile caused by a sphere. When the zero‐anomaly distance and the anomaly value at the origin possess errors of equal magnitude and of the same signs, the results will not differ much from the true values. When errors have opposite signs, the maximum error in depth is 10%. Finally, the validity of the method is tested on a field example from Ergani Copper district, Turkey.
Forward problem of nonlinear Fredholm integral equation in reference medium via velocity‐weighted wavefield function
Authors: Fu Li‐Yun , Mu Yong‐Guang , Yang Huey‐Ju
Published: October 2002

A nonlinear Fredholm integral equation of the first kind for the perturbation potential can be derived by interpreting the acoustic velocity as a perturbation of a reference velocity. We present an accurate and efficient method to formulate and numerically solve this equation with no restriction on the size of the perturbation by introducing a velocity‐weighted wavefield function (i.e., the scalar product of the potential function with the perturbed velocity function inside a scatterer), which is an intermediate function associating the observed wavefield with the perturbed velocity function. We start with a singularity analysis of the Fredholm integral equation when the observation point coincides with the scattering point to establish a linear singular integral equation with respect to the velocity‐weighted wavefield function. Then we formulate the relation between the velocity‐weighted wavefield and scattered field in the f‐k domain. A numerical scheme is developed to solve the forward problem for the velocity‐weighted wavefield inside a scatterer. Then the observed wavefield can be calculated through back substitutions of the Fredholm integral equation. The total wavefield and scattered field from a triangular object in a host medium observed from four sides are computed and compared with those given by the boundary‐element (BE) method and the approach using Born approximation. A second model computes both the common shot‐point (CSP) and common depth‐point (CMP) records of three velocity layers in a host medium. In addition, theoretical analyses and numerical experiments show that we can also use the singular integral equation to decompose accurately the velocity‐weighted wavefield given by inverse algorithms to recover the perturbed velocity function.
Pushing the limits of seismic imaging, Part I: Prestack migration in terms of double dynamic focusing
Authors: Berkhout A. J.
Published: October 2002

In this paper, the author proposes to extend the synthesis of areal sources (controlled emission) to the synthesis of areal detectors (controlled detection) such that the concept of numerical focusing can be formulated as a special version of target‐oriented synthesis. As a consequence, the insight in the complex prestack migration process can be improved significantly by making use of the concepts “focusing in emission” and “focusing in detection.” Focusing in emission transforms shot records into so‐called common focus‐point (CFP) gathers. Focusing in detection transforms CFP gathers into the prestack migration result. If structural information is sought, the focus point in emission is chosen equal to the focus point in detection: confocal version of CFP migration. If rock and pore information is required as well, the focus point in emission is chosen different from the focus point in detection: bifocal version of CFP migration. Errors in the underlying macro velocity model can be better analysed than before by using CFP gathers as an intermediate migration output. The error analysis involves a comparison between each CFP gather and its related focusing operator. The quality (amplitude accuracy, noise content, resolution) of prestack migration results can be evaluated effectively at each subsurface grid point by analysing the two focused beams involved (pre‐evaluation) and by analyzing the so‐called grid‐point gather (post‐evaluation). The proposed pre‐evaluation method may lead to an improved way of coping with “acquisition footprints” of relatively sparse source and receiver coverage.
Pushing the limits of seismic imaging, Part II: Integration of prestack migration, velocity estimation, and AVO analysis
Authors: Berkhout A. J.
Published: October 2002

The author proposes an operator‐driven prestack migration scheme that is based on the synthesis of common focus‐point (CFP) gathers. Each CFP gather represents the response of a synthesized source array that aims at the illumination of one subsurface gridpoint (focus point). The involved synthesis operator is referred to as the focusing operator. If the time‐reversed focusing operator and its related focus‐point response have equal traveltimes, then the underlying macro velocity model is correct and the focus‐point response in the CFP gather is stacked by weighted addition along the common traveltime curve (CFP‐stacking), yielding the prestack migration result at the subsurface grid point under consideration. If the time‐reversed focusing operator and its related focus‐point response have different traveltimes, then the underlying macro velocity model is incorrect and the correct focusing operator can be derived from the two traveltime curves. A simple updating procedure is proposed. The total CFP migration process of synthesis, updating, and stacking is repeated for all subsurface grid points of interest, leading to the prestack migration result in one‐way image time together with a distribution of updated focusing operators. In a postprocessing step, all operator traveltime information can be used to derive a velocity model for the time‐to‐depth conversion process. Hence, in the presented “CFP technology” the author proposes to estimate the velocity model from the correct focusing operators by a global inversion process after the migration process has been carried out (“beyond depth migration”). For each subsurface grid point, the amplitudes along the pairs of updated traveltime curves provide amplitude‐versus‐offset (AVO) information. In addition, by introducing the grid‐point gather with the aid of an extension of the second focusing process, the author shows that this gather leads to the extraction of pre‐ and postcritical amplitude‐versus‐ray parameter (AVP) information at each grid point. Finally, just as a velocity model can be estimated from all grid‐point‐oriented traveltime information, a lithology model can be estimated from all grid‐point—oriented amplitude information by a postimaging global inversion process.
Inversion of 4-C borehole flexural waves to determine anisotropy in a fractured carbonate reservoir
Authors: Tichelaar Bart W. , Hatchell Paul J.
Published: October 2002

Observations of anisotropy in fractured carbonate reservoirs can yield important information such as the orientation of aligned crack systems and crack density. A new generation of borehole acoustic tools provides the data necessary to observe anisotropy around the borehole. The flexural waves, excited by two dipole sources operating perpendicularly to each other in these tools, are recorded in two perpendicular directions, resulting in four‐component flexural wave recordings, Superposition of sources and rotation of receivers are the basic elements for the inversion of the waveforms to determine fast or slow mode orientations. Since the two sources are not necessarily of the same strength, a reciprocity‐based source equalization is carried out as part of the inversion. We have inverted four‐component borehole flexural waves, recorded in a vertical well, penetrating three lithologic units of a fractured carbonate reservoir in northern Oman. For the lower unit, a northeast‐southwest azimuth of flexural wave anisotropy is well resolved, which is parallel to the strike of open fractures observed in the borehole, preferential flow directions, and to the regional present‐day in‐situ maximum horizontal stress. Furthermore, the northeast‐southwest direction corresponds with polarization directions of the fast shear wave observed in a multicomponent surface seismic survey over the reservoir. The middle unit is most likely isotropic, except for a depth interval of low gamma readings, where a northeast‐southwest orientation is found for the fast mode. For the upper unit, a north‐south fast mode orientation is found, which does not correspond to the expected northeast‐southwest direction. Borehole geometry data indicate that the shape of the hole is circular for the middle unit but elongated for the upper and lower unit. Caliper orientations track the flexural wave anisotropy azimuths in these two units. Because of the elongation of the borehole, the observed flexural mode orientations, as well as the magnitude of flexural wave anisotropy, cannot be related to formation anisotropy directly, which obscures the determination of fracture orientation and fracture density from four‐component borehole flexural waves.
Attenuation in fine‐grained marine sediments: Extension of the Biot‐Stoll model by the “effective grain model” (EGM)
Authors: Leurer Klaus C.
Published: October 2002

It is postulated that the presence of swelling clay minerals in unconsolidated fine‐grained saturated marine sediments leads to deviations from the normally assumed ideal elasticity of the solid phase. In the proposed “effective grain model” (EGM), the elastic grain material is consequently replaced by an effective medium made up of a homogeneous elastic mineral phase that is isotropically interspersed with cylindrical, “penny‐shaped” inclusions of low aspect ratio representing the intracrystalline water layers in the swelling clay minerals. The two‐phase nature of the grain material thus specified results in a wave‐energy consuming squirt‐flow process from the inclusions into the pore space. Introducing the EGM into the Biot‐Stoll model (BSM) via the complex bulk modulus of the dissipative grain material leads to a better fit to literature data on the attenuation of compressional waves than does the original BSM alone. Since swelling clay minerals occur in nearly all clay‐bearing sediments, it is concluded that the attenuation mechanism of the EGM may represent a universal contribution to the overall intrinsic anelasticity of unconsolidated fine‐grained saturated marine sediments in the frequency range from a few kilohertz to about 1 MHz.
Boundary conditions on a finite grid: Applications with pseudospectral wave propagation
Authors: Wu Huatao , Lees Jonathan M.
Published: October 2002

A new method for calculating boundary conditions at the free surface and along absorbing boundaries of a finite grid is presented. A finite, twice differentiable reduction function that achieves a 99% reduction over three wavelengths is proposed and tested. In the context of pseudospectral wave propagation, this implies a boundary layer of at least six grid nodes. The method is analyzed in one and two dimensions and the problems of waves impinging on corners are addressed. The reduction function recommended is [Formula: see text] where α is a parameter to be determined by optimization. Tests of the performance of the new method versus other common schemes are presented and analyzed. We provide a strategy for determining the optimal parameter in the reduction function. Synthetic Rayleigh waves are observed at the free surface of the simulation. Experiments with a vertical fault plane show the presence of direct, reflected, transmitted, and head waves. The presence of head waves may be used to analyze velocity contrasts across fault zones.
Application of perfectly matched layers to the transient modeling of subsurface EM problems
Authors: Chen Yong H. , Chew Weng Cho , Oristaglio Michael L.
Published: October 2002

Berenger's perfectly matched layers (PML) have been found to be very efficient as a material absorbing boundary condition (ABC) for finite‐difference time‐domain (FDTD) modeling of lossless media. In this paper, we apply the PML technique to truncate the simulation region of conductive media. Examples are given to show some possible applications of the PML technique to subsurface problems with lossy media. To apply the PML ABC for lossy media, we first modify the original 3-D Maxwell's equations to achieve PML at the boundaries of the simulation region. The modified equations are then solved by using a staggered grid with a central‐differencing scheme. A 3-D FDTD code has been written on the basis of our PML formulation to simulate the electromagnetic field responses of a dipole source in both lossless and lossy media. The code is first tested against analytical solutions for homogeneous media of different losses and then applied to some subsurface problems, such as a geological fault and a buried gas tank. Very interesting propagation and scattering phenomena are observed from the simulation results. Some analyses are also given to explain the physical phenomena of the calculated waveforms.
Topography can affect linearization in tomographic inversions
Authors: Wiggins Sean M. , Dorman LeRoy M. , Cornuelle Bruce D.
Published: October 2002

Linearized inverse techniques commonly are used to solve for velocity models from traveltime data. The amount that a model may change without producing large, nonlinear changes in the predicted traveltime data is dependent on the surface topography and parameterization. Simple, one‐layer, laterally homogeneous, constant‐gradient models are used to study analytically and empirically the effect of topography and parameterization on the linearity of the model‐data relationship. If, in a weak‐velocity‐gradient model, rays turn beneath a valley with topography similar to the radius of curvature of the raypaths, then large nonlinearities will result from small model perturbations. Hills, conversely, create environments in which the data are more nearly linearly related to models with the same model perturbations.
Ground‐roll suppression using the wavelet transform
Authors: Deighan Andrew J. , Watts Doyle R.
Published: October 2002

Low‐frequency, high‐amplitude ground roll is an old problem in land‐based seismic field records. Current processing techniques aimed at ground‐roll suppression, such as frequency filtering, f-k filtering, and f-k filtering with time‐offset windowing, use the Fourier transform, a technique that assumes that the basic seismic signal is stationary. A new alternative to the Fourier transform is the wavelet transform, which decomposes a function using basis functions that, unlike the Fourier transform, have finite extent in both frequency and time. Application of a filter based on the wavelet transform to land seismic shot records suppresses ground roll in a time‐frequency sense; unlike the Fourier filter, this filter does not assume that the signal is stationary. The wavelet transform technique also allows more effective time‐frequency analysis and filtering than current processing techniques and can be implemented using an algorithm as computationally efficient as the fast Fourier transform. This new filtering technique leads to the improvement of shot records and considerably improves the final stack quality.
Euclid and the art of wavelet estimation, Part I: Basic algorithm for noise‐free data
Authors: Rietsch Eike
Published: October 2002

An algorithm borrowed from polynomial algebra for finding the common factors of two or more polynomials can be used to find the wavelet that several seismic traces have in common. In the implementation described in this first part of a two‐part work, a matrix is constructed from the autocorrelations and crosscorrelations of these seismic traces. The number of zero eigenvalues of this matrix is equal to the number of samples of the wavelet, and the eigenvectors associated with these eigenvalues are related to the reflection coefficients. The method, which works well if the noise is not too high, is illustrated by means of a synthetic example. Part II of this two‐part work shows how this method is affected by noise and gives field‐data examples.
3-D inversion of gravity data
Authors: Li Yaoguo , Oldenburg Douglas W.
Published: October 2002

We present two methods for inverting surface gravity data to recover a 3-D distribution of density contrast. In the first method, we transform the gravity data into pseudomagnetic data via Poisson’s relation and carry out the inversion using a 3-D magnetic inversion algorithm. In the second, we invert the gravity data directly to recover a minimum structure model. In both approaches, the earth is modeled by using a large number of rectangular cells of constant density, and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data. The model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints. We apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information. Applications of the algorithms to synthetic and field data produce density models representative of true structures. Our results have shown that the inversion of gravity data with a properly designed objective function can yield geologically meaningful information.
Shear slowness measurement by dispersive processing of the borehole flexural mode
Authors: Kimball Christopher V.
Published: October 2002

In sonic well logging, the flexural mode generated by a dipole transducer allows measurement of shear slowness in slow formations, that is, formations in which the shear slowness is slower than the borehole fluid speed. The flexural mode is a dispersive borehole mode, but many current processing methods do not account for this dispersion. The approximate semblance equation is derived to explain what happens when a dispersive wave is processed nondispersively. The processing described here is a dispersive analog of the slowness‐time coherence (STC) processing used commonly for array sonic waveforms. It back‐propagates waveforms according to model dispersion curves and calculates semblance. It is a specialized version of the maximum likelihood (ML) and least‐mean‐squared‐error (LMSE) estimator for formation shear slowness. The dispersive analog of STC is too slow for depth‐by‐depth logging but may be a helpful analytic tool. A high‐speed variant, dispersive STC (DSTC), eliminates this difficulty by a new window‐positioning technique and can be faster than STC. DSTC results based on data from a real‐axis integration model show that the technique measures the formation shear slowness with small bias because of windowing and other arrivals. Results are presented from two wells logged with a dipole sonic tool. A log from a fast formation shows that shear slownesses measured from the flexural mode by DSTC agree with monopole results. A log from a slow formation is also presented.
A boundary element method for 2-D dc resistivity modeling with a point current source
Authors: Xu Shi‐Zhe , Zhao Shengkai , Ni Yi
Published: October 2002

A new boundary element method (BEM) is presented for 2-D dc resistivity modeling with a point source. When compared with previously published techniques, the new method has two main features: (1) The normal derivative of potential has been eliminated from the integral equation. The formulation of the present method is simpler and requires less memory and time than the previous published methods. (2) Multiple subsurface inhomogeneous bodies can be modeled. For a simple testing model, the maximum relative error of reciprocity test is 0.24% and the average relative error is 0.05%. For the same model, the maximum relative difference between the BEM solution and the finite‐element method solution is 1.14% and the average relative difference is 0.73%. For a field geoelectrical profile, the responses of the constructed model agree with the observed data quite well.
Radiation patterns for 2-D GPR forward modeling
Authors: Carcione José M.
Published: October 2002

The electromagnetic (EM) radiation of a ground‐penetrating radar (GPR) antenna is affected by the presence of the air‐earth interface and depends on the geometrical and physical characteristics of the antenna. To simulate the radiation pattern with grid methods without the explicit modeling of these features, an equivalent solution is obtained by using a composite source concept. The 2-D analytic solution corresponding to magnetic and electric sources located at the same grid point is computed. This solution constitutes a basis for the construction of a composite source located in a small region of the numerical mesh. The field is obtained for transverse magnetic (TM) and transverse electric (TE) waves in anisotropic media because the use of anisotropic conductivity is an alternative approach to simulating different radar apertures. Realistic radiation patterns are obtained from simple combinations of magnetic and electric sources by analogy with seismic shear stresses. The source parameterization is used for GPR simulation, and single radargram traces obtained with the modeling algorithm are cross checked with the analytic solution.
Exploration in the Shetland‐Faeroe Basin using densely spaced arrays of ocean‐bottom seismometers
Authors: Hughes Stephen , Barton Penny J. , Harrison David
Published: October 2002

Recent exploration activity in the peripheral regions of the Shetland‐Faeroe Basin, offshore northwest Scotland, has led to the discovery of some of the largest oil reserves on the United Kingdom (UK) continental shelf. We present results from two ocean‐bottom seismometer profiles acquired by Mobil North Sea Ltd. across the center of the Shetland‐Faeroe Basin. These data provide a powerful tool for delineating long‐wavelength velocity variations and thus have potential for reducing the nonuniqueness associated with conventional seismic exploration methods. Analysis of the first‐arrival traveltime data using both forward and inverse ray‐based techniques produces a well constrained velocity‐depth model of the basin fill. We estimate that the uncertainty in the velocity structure is ±5% from a series of trial and error perturbations applied to the final models. The velocity structure of the Faeroe Basin has three principal layers: (1) a near‐surface layer with velocities in the range 1.6 to 2.2 km/s, (2) a 3.0–3.2 km/s layer which is characterized by a northwards structural pinch out in the center of the basin, and (3) a deeper laterally heterogeneous layer with velocities in the range 3.8 to 4.2 km/s. In the northwestern portion of the basin, a high velocity (5.0 km/s) basaltic layer is imaged dipping toward the southeast at a depth of 2–3 km. The basement is mapped at a depth of 7–9 km in the center of the basin. Gravity modeling provides independent corroboration of our models through the application of a velocity‐density relationship obtained from a synthesis of physical property measurements. Reflections from the Moho indicate a crustal thickness of 18 ± 3 km, suggesting that the basin is underlain by highly attenuated continental crust, but the velocities in the basement are closer to those of the Faeroe Islands basalts than the expected Lewisian gneiss, suggesting that it may be highly intruded.
Stratal slicing, Part II: Real 3-D seismic data
Authors: Zeng Hongliu , Henry Stephen C. , Riola John P.
Published: October 2002

Three‐dimensional seismic data from the Gulf of Mexico Tertiary section show a close dependence of seismic events on data frequency. While some events remain frequency independent, many events exhibit different occurrences with changing frequency and, therefore, are not parallel to geologic time surfaces. In the data set we have studied, observed maximum time transgression of seismic events is at least 120 ms traveltime on lower frequency sections. Severe interference in lower frequency data may produce false seismic facies characteristics and obscure the true stratigraphic relationships. This phenomenon has important implications for seismic interpretation, particularly for sequence stratigraphic studies. This time transgression problem is mitigated to a large degree by the stratal slicing technique discussed in Part I of this paper. Stratal slicing on a workstation is done by first tracking frequency‐independent, geologic‐time‐equivalent reference seismic events, then building a stratal time model and an amplitude stratal slice volume on the basis of linear interpolation functions between references. The new volumes have an x-, y-coordinate system the same as the original data, but a z-axis of relative geologic time. Stratal slicing is a useful new tool for basin analysis and reservoir delineation by making depositional facies mapping an easier task, especially in wedged depositional sequences. Examples show that the common depositional facies like fluvial channels, deltaic systems, and submarine turbidite deposits are often imaged from real 3-D data with relatively high lateral resolution.
3-D prestack Kirchhoff depth migration: From prototype to production in a massively parallel processor environment
Authors: Chang Herman , VanDyke John P. , Solano Marcelo , McMechan George A. , Epili Duryodhan
Published: October 2002

Portable, production‐scale 3-D prestack Kirchhoff depth migration software capable of full‐volume imaging has been successfully implemented and applied to a six‐million trace (46.9 Gbyte) marine data set from a salt/subsalt play in the Gulf of Mexico. Velocity model building and updates use an image‐driven strategy and were performed in a Sun Sparc environment. Images obtained by 3-D prestack migration after three velocity iterations are substantially better focused and reveal drilling targets that were not visible in images obtained from conventional 3-D poststack time migration. Amplitudes are well preserved, so anomalies associated with known reservoirs conform to the petrophysical predictions. Prototype development was on an 8-node Intel iPSC860 computer; the production version was run on an 1824-node Intel Paragon computer. The code has been successfully ported to CRAY (T3D) and Unix workstation (PVM) environments.
Determination of the principal directions of azimuthal anisotropy fromP-wave seismic data
Authors: Mallick Subhashis , Craft Kenneth L. , Meister Laurent J. , Chambers Ronald E.
Published: October 2002

In an azimuthally anisotropic medium, the principal directions of azimuthal anisotropy are the directions along which the quasi-P- and the quasi-S-waves propagate as pure P and S modes. When azimuthal anisotropy is induced by oriented vertical fractures imposed on an azimuthally isotropic background, two of these principal directions correspond to the directions parallel and perpendicular to the fractures. S-waves propagating through an azimuthally anisotropic medium are sensitive to the direction of their propagation with respect to the principal directions. As a result, primary or mode‐converted multicomponent S-wave data are used to obtain the principal directions. Apart from high acquisition cost, processing and interpretation of multicomponent data require a technology that the seismic industry has not fully developed. Anisotropy detection from conventional P-wave data, on the other hand, has been limited to a few qualitative studies of the amplitude variation with offset (AVO) for different azimuthal directions. To quantify the azimuthal AVO, we studied the amplitude variation with azimuth for P-wave data at fixed offsets. Our results show that such amplitude variation with azimuth is periodic in 2θ, θ being the orientation of the shooting direction with respect to one of the principal directions. For fracture‐induced anisotropy, this principal direction corresponds to the direction parallel or perpendicular to the fractures. We use this periodic azimuthal dependence of P-wave reflection amplitudes to identify two distinct cases of anisotropy detection. The first case is an exactly determined one, where we have observations from three azimuthal lines for every common‐midpoint (CMP) location. We derive equations to compute the orientation of the principal directions for such a case. The second case is an overdetermined one where we have observations from more than three azimuthal lines. Orientation of the principal direction from such an overdetermined case can be obtained from a least‐squares fit to the reflection amplitudes over all the azimuthal directions or by solving many exactly determined problems. In addition to the orientation angle, a qualitative measure of the degree of azimuthal anisotropy can also be obtained from either of the above two cases. When azimuthal anisotropy is induced by oriented vertical fractures, this qualitative measure of anisotropy is proportional to fracture density. Using synthetic seismograms, we demonstrate the robustness of our method in evaluating the principal directions from conventional P-wave seismic data. We also apply our technique to real P-wave data, collected over a wide source‐to‐receiver azimuth distribution. Computations using our method gave an orientation of the principal direction consistent with the general fracture orientation in the area as inferred from other geological and geophysical evidence.
Traveltime computation by perturbation with FD-eikonal solvers in isotropic and weakly anisotropic media
Authors: Ettrich Norman , Gajewski Dirk
Published: October 2002

First‐order perturbation theory is used for fast 2-D computation of traveltimes. For highest efficiency we implement the perturbation integrals into Vidale’s finite‐difference (FD) eikonal solver. Traveltimes in the unperturbed reference medium are computed with Vidale’s method, while perturbed traveltimes in a slightly deviating perturbed medium are obtained by adding a correction Δt to the traveltimes of the reference medium. To compute Δt, raypaths between source and receivers in the reference medium must be known. In Vidale’s method traveltimes are computed on a discrete grid assuming local plane wavefronts inside the grid cells. Rays are not determined in this method. Therefore, we suggest approximating rays by ray segments corresponding to the plane wavefronts in each cell. We compute Δt along these segments and obtain initial values for Δt at cell boundaries by linear interpolation between the corner points of the cells. The FD perturbation method can be used for simultaneous computations of traveltime to a number of slightly different models and is, therefore, applicable to prestack velocity estimation techniques. Furthermore, using isotropic reference media the FD perturbation method allows very fast traveltime computations for weakly general anisotropic media. For the computation of traveltimes to a large number of subsurface grid points, the FD perturbation method is about three orders of magnitude faster than classical anisotropic ray‐shooting algorithms. Furthermore, we modify Vidale’s FD-eikonal solver for elliptically anisotropic media. Using reference media with elliptical anisotropy allows a higher accuracy of the FD perturbation method and let us consider perturbed models of stronger anisotropy. The extension of the FD-perturbation method to 3-D is straightforward.
Finite‐difference modeling of electromagnetic wave propagation in dispersive and attenuating media
Authors: Bergmann Tim , Robertsson Johan O. A. , Holliger Klaus
Published: October 2002

Realistic modeling of electromagnetic wave propagation in the radar frequency band requires a full solution of Maxwell’s equations as well as an adequate description of the material properties. We present a finite‐difference time‐domain (FDTD) solution of Maxwell’s equations that allows accounting for the frequency dependence of the dielectric permittivity and electrical conductivity typical of many near‐surface materials. This algorithm is second‐order accurate in time and fourth‐order accurate in space, conditionally stable, and computationally only marginally more expensive than its standard equivalent without frequency‐dependent material properties. Empirical rules on spatial wavefield sampling are derived through systematic investigations of the influence of various parameter combinations on the numerical dispersion curves. Since this algorithm intrinsically models energy absorption, efficient absorbing boundaries are implemented by surrounding the computational domain by a thin (⩽2 dominant wavelengths) highly attenuating frame. The importance of accurate modeling in frequency‐dependent media is illustrated by applying this algorithm to two‐dimensional examples from archaeology and environmental geophysics.
3-D seismic attributes using a semblance‐based coherency algorithm
Authors: Marfurt Kurt J. , Kirlin R. Lynn , Farmer Steven L. , Bahorich Michael S.
Published: October 2002

Seismic coherency is a measure of lateral changes in the seismic response caused by variation in structure, stratigraphy, lithology, porosity, and the presence of hydrocarbons. Unlike shaded relief maps that allow 3-D visualization of faults and channels from horizon picks, seismic coherency operates on the seismic data itself and is therefore unencumbered by interpreter or automatic picker biases. We present a more robust, multitrace, semblance‐based coherency algorithm that allows us to analyze data of lesser quality than our original three‐trace cross‐correlation‐based algorithm. This second‐generation, semblance‐based coherency algorithm provides improved vertical resolution over our original zero mean crosscorrelation algorithm, resulting in reduced mixing of overlying or underlying stratigraphic features. In general, we analyze stratigraphic features using as narrow a temporal analysis window as possible, typically determined by the highest usable frequency in the input seismic data. In the limit, one may confidently apply our new semblance‐based algorithm to a one‐sample‐thick seismic volume extracted along a conventionally picked stratigraphic horizon corresponding to a peak or trough whose amplitudes lie sufficiently above the ambient seismic noise. In contrast, near‐vertical structural features, such as faults, are better enhanced when using a longer temporal analysis window corresponding to the lowest usable frequency in the input data. The calculation of reflector dip/azimuth throughout the data volume allows us to generalize the calculation of conventional complex trace attributes (including envelope, phase, frequency, and bandwidth) to the calculation of complex reflector attributes generated by slant stacking the input data along the reflector dip within the coherency analysis window. These more robust complex reflector attribute cubes can be combined with coherency and dip/azimuth cubes using conventional geostatistical, clustering, and segmentation algorithms to provide an integrated, multiattribute analysis.
Smiles and frowns in migration/velocity analysis
Authors: Zhu Jinming , Lines Larry , Gray Sam
Published: October 2002

Reliable seismic depth migrations require an accurate input velocity model. Inaccurate velocity estimates will distort point diffractors into smiles or frowns on a depth section. For both poststack and prestack migrated sections, high velocities cause deep smiles while low velocities cause shallow frowns on migrated gathers. However, for prestack images in the offset domain, high velocities cause deep frowns while low velocities cause shallow smiles. If the velocity is correct, there will be no variation in the depth migration as a function of offset and no smiles or frowns in the offset domain. We explain migration responses both mathematically and graphically and thereby provide the basis for depth migration velocity analysis.