Imaging In Anisotropic Media Research Articles

A new qP-wave approximation in tilted transversely isotropic media and its reverse time migration for areas with complex overburdens

During seismic imaging in anisotropic media, undesired SV waves may be detected when conventional wave equations are used for wavefield simulation, which will contaminate the final seismic image. A pure qP-wave equation that is free of S-wave artifacts is desired, such that crosstalk introduced from the interference of different waves can be eliminated. We have developed a new fully decoupled P-wave equation in transversely isotropic media with titled symmetry axis that avoids unwanted energy during migration. The qP and qSV phase velocities for the new approximations are plotted and compared with the exact solution and some other approximations and indicate high accuracy for various anisotropic models (from low to high degrees of anisotropy). During wavefield simulation, the finite-difference and pseudospectral methods also are combined to accelerate the computation. Moreover, a hybrid perfectly matched layer (H-PML) that combines two different perfectly matched layers for second-order wave equations in the wavenumber domain also is proposed and applied to eliminate the artificial boundary reflections. Comparisons of different absorbing boundary layers also are illustrated to validate the wavenumber domain H-PML. Finally, the new proposed wave approximation together with the new absorbing layer is further incorporated in a new 3D anisotropic reverse time migration (RTM). We test the RTM on the 3D synthetic SEG Advanced Modeling Corporation data and offshore field data with a complicated overburden (salt and gas overburden) and obtain seismic images with high resolution. Benchmarks against commercial implementations also are demonstrated, which proves that the positioning of the reflectors is more reliable and accurate with the new algorithm.

Separating quasi-P-wave in transversely isotropic media with a vertical symmetry axis by synthesized pressure applied to ocean-bottom seismic data elastic reverse time migration

Quasi-P (qP)-wavefield separation is a crucial step for elastic P-wave imaging in anisotropic media. It is, however, notoriously challenging to quickly and accurately obtain separated qP-wavefields. Based on the concepts of the trace of the stress tensor and the pressure fields defined in isotropic media, we have developed a new method to rapidly separate the qP-wave in a transversely isotropic medium with a vertical symmetry axis (VTI) by synthesized pressure from ocean-bottom seismic (OBS) data as a preprocessing step for elastic reverse time migration (ERTM). Another key aspect of OBS data elastic wave imaging is receiver-side 4C records back extrapolation. Recent studies have revealed that receiver-side tensorial extrapolation in isotropic media with ocean-bottom 4C records can sufficiently suppress nonphysical waves produced during receiver-side reverse time wavefield extrapolation. Similarly, the receiver-side 4C records tensorial extrapolation was extended to ERTM in VTI media in our studies. Combining a separated qP-wave by synthesizing pressure and receiver-side wavefield reverse time tensorial extrapolation with the crosscorrelation imaging condition, we have developed a robust, fast, flexible, and elastic imaging quality improved method in VTI media for OBS data.

Effect of errors in the migration velocity model of PS-converted waves on traveltime accuracy in prestack Kirchhoff time migration in weak anisotropic media

We investigated the effect of errors in the migration-velocity model of PS-converted waves on the traveltime calculated in prestack Kirchhoff time migration in weak anisotropic media. The prestack-Kirchhoff-time-migration operator contains four parameters: the PS-converted-wave velocity, the vertical velocity ratio, the effective velocity ratio, and the anisotropic parameter. We derived four error factors that correspond to those parameters. Theoretical and numerical analyses of the error factors show them all to be inversely proportional to the velocity and to traveltime. Traveltime errors for shallow events usually are larger than for deep events. Error in PS-converted-wave velocity causes the largest traveltime error, and error in the vertical velocity ratio causes the smallest traveltime error. For a small horizontal-distance/depth ratio, the error in the effective velocity ratio affects traveltime more than does the anisotropic-parameter error. However, the anisotropic-parameter error affects traveltime more when the horizontal-distance/depth ratio is larger. Traveltime errors caused by errors in effective velocity ratio and the anisotropic parameter mainly stem from the converted-S-wave raypath of the PS-converted waves. To save processing time and cost, PS-wave velocity can be estimated accurately without an accurate vertical velocity ratio, effective velocity ratio, and anisotropic parameter. These findings are useful for understanding PS-wave behavior and for PS-wave imaging in anisotropic media.

Converted‐wave imaging in anisotropic media: theory and case studies

ABSTRACTCommon‐conversion‐point binning associated with converted‐wave (C‐wave) processing complicates the task of parameter estimation, especially in anisotropic media. To overcome this problem, we derive new expressions for converted‐wave prestack time migration (PSTM) in anisotropic media and illustrate their applications using both 2D and 3D data examples.The converted‐wave kinematic response in inhomogeneous media with vertical transverse isotropy is separated into two parts: the response in horizontally layered vertical transverse isotrophy media and the response from a point‐scatterer. The former controls the stacking process and the latter controls the process of PSTM. The C‐wave traveltime in horizontally layered vertical transverse isotrophy media is determined by four parameters: the C‐wave stacking velocity VC2, the vertical and effective velocity ratios γ0 and γeff, and the C‐wave anisotropic parameter χeff. These four parameters are referred to as the C‐wave stacking velocity model. In contrast, the C‐wave diffraction time from a point‐scatterer is determined by five parameters: γ0, VP2, VS2, ηeff and ζeff, where ηeff and ζeff are, respectively, the P‐ and S‐wave anisotropic parameters, and VP2 and VS2 are the corresponding stacking velocities. VP2, VS2, ηeff and ζeff are referred to as the C‐wave PSTM velocity model. There is a one‐to‐one analytical link between the stacking velocity model and the PSTM velocity model. There is also a simple analytical link between the C‐wave stacking velocities VC2 and the migration velocity VCmig, which is in turn linked to VP2 and VS2.Based on the above, we have developed an interactive processing scheme to build the stacking and PSTM velocity models and to perform 2D and 3D C‐wave anisotropic PSTM. Real data applications show that the PSTM scheme substantially improves the quality of C‐wave imaging compared with the dip‐moveout scheme, and these improvements have been confirmed by drilling.

Plane-wave depth migration

We present fast and efficient plane-wave migration methods for densely sampled seismic data in both the source and receiver domains. The methods are based on slant stacking over both shot and receiver positions (or offsets) for all the recorded data. If the data-acquisition geometry permits, both inline and crossline source and receiver positions can be incorporated into a multidimensional phase-velocity space, which is regular even for randomly positioned input data. By noting the maximum time dips present in the shot and receiver gathers and constant-offset sections, the number of plane waves required can be estimated, and this generally results in a reduction of the data volume used for migration. The required traveltime computations for depth imaging are independent for each particular plane-wave component. It thus can be used for either the source or the receiver plane waves during extrapolation in phase space, reducing considerably the computational burden. Since only vertical delay times are required, many traveltime techniques can be employed, and the problems with multipathing and first arrivals are either reduced or eliminated. Further, the plane-wave integrals can be pruned to concentrate the image on selected targets. In this way, the computation time can be further reduced, and the technique lends itself naturally to a velocity-modeling scheme where, for example, horizontal and then steeply dipping events are gradually introduced into the velocity analysis. The migration method also lends itself to imaging in anisotropic media because phase space is the natural domain for such an analysis.

Depth imaging in anisotropic media by symmetric non‐stationary phase shift

ABSTRACTWe present a new depth‐imaging method for seismic data in heterogeneous anisotropic media. This recursive explicit method uses a non‐stationary extrapolation operator to allow lateral velocity variation, and it uses the relationship between phase angle and the spectral coordinates of seismic data to allow velocity variation with phase angle. A qualitative comparison of migration impulse responses suggests that, for an equivalent cost, the symmetric non‐stationary phase‐shift (SNPS) operator is superior to the phase‐shift plus interpolation (PSPI) operator, for very large depth intervals. To demonstrate the potential of the new method, seismic data from a physical model acquired over a transversely isotropic medium are imaged using a shot‐record migration based on the SNPS operator.

Angular spectrum approach for the computation of group and phase velocity surfaces of acoustic waves in anisotropic materials

The decomposition of an acoustic wave into its angular spectrum representation creates an effective base for the calculation of wave propagation effects in anisotropic media. In this method, the distribution of acoustic fields is calculated in arbitrary planes from the superposition of the planar components with proper phase shifts. These phase shifts depend on the ratio of the distance between the planes to the normal component of the phase slowness vector. In anisotropic media, the phase shifts depend additionally on the changes of the slowness with respect to the direction of the propagation vector and the polarization. Those relations are obtained from the Christoffel equation. The method employing the fast Fourier transformation algorithm is especially suited for volume imaging in anisotropic media, based on holographic detection in transmission of acoustic waves generated by a point source. This technique is compared with measurements on crystals performed by phase-sensitive scanning acoustic microscopy.

Acoustic flux imaging in anisotropic media

A new method for characterizing acoustic flux propagation in anisotropic media is introduced and developed. The technique, which we call ultrasonic flux imaging (UFI), utilizes a pair of water-immersion focused acoustic transducers as a point source and point detector. Raster scanning one transducer produces a transmission pattern which exhibits the anisotropies in acoustic flux known as “phonon focusing” modulated by interference between sheets of the acoustic wave surface. This “internal diffraction” is studied theoretically taking into account the anisotropy of the medium, the boundary conditions between the solid and the water, and the pressure fields produced by the transducers. In addition to bulk effects, the images reveal interesting critical-cone structures associated with the water/solid interface. The theoretical predictions agree well with experimental observations in silicon and a number of other materials, including single-crystal metals, insulators, and semiconductors. All measurements are made at room temperature, in contrast to the cryogenic requirements of previous phononimaging techniques. As a new method, UFI holds promise for examining anisotropies in the vibrational properties, and, possibly, electron-phonon coupling in metals and superconductors. The principles and techniques may also have application to non-destructive characterization of textured polycrystalline and composite materials.

Well Imaging and Fault Detection In Anisotropic Reservoirs

Flow-confining image well location in both isotropic and anisotropic reservoirs can be reduced to one general equation. The equation is presented here, along with analyses of fault-location errors that result presented here, along with analyses of fault-location errors that result from conventional pressure transient studies applied to anisotropic systems. Introduction Engineers and geologists have long been aware of the directional flow properties of natural rocks. Permeabilities measured across the bedding are usually much Permeabilities measured across the bedding are usually much less than those along the bedding. Moreover, a change in flow direction along the plane of bedding will often show a significant change in horizontal permeability. This anisotropic behavior of natural permeability. This anisotropic behavior of natural rocks can pose some major problems for efficient reservoir exploitation. Some degree of horizontal permeability anisotropy is believed to be present, with few exceptions, in bedded rocks and limestones. In general, sandstones do not exhibit permeability ratios, k /k, in excess of 2.0. Homogeneous fractured reservoirs, such as the Spraberry trend field, however, may exhibit ratios as high as 144. In about half of some 10 limestone cores analyzed, Hutchinson reported significant permeability ratios averaging about 16. Arnold et al. and Elkins and Skov developed steady-state and transient pressure methods to evaluate horizontal, anisotropic media. Both the orthogonal permeability ratio and the orientation of the principal permeability ratio and the orientation of the principal axes can be determined by suitable well tests. The effect of anisotropy upon secondary recovery flood patterns has been studied by a number of patterns has been studied by a number of investigators. They conclude that the ease of flow or transmissibility of the fluid in one preferential direction causes premature water breakthrough and poor sweep efficiency with improper choice of pattern geometry and orientation. The combined effects of inhomogeneity and horizontal anisotropy have not been studied extensively. Greenkorn et al. extended the tensor theory of permeability to include heterogeneity for the case of flow permeability to include heterogeneity for the case of flow parallel to the plane of bedding. Merrick considered parallel to the plane of bedding. Merrick considered both anisotropy and stratification in evaluating recovery from gas cycling projects in bounded systems, using steady-state streamline flow solutions. Transient pressure buildup and drawdown tests used to define linear discontinuities within a reservoir should also be affected by anisotropy. Conventional methods of analysis us in their mathematical development the principles of superposition and direct mirror imaging of wells - principles applicable to isotropic systems only. The purpose of this study, therefore, was to:develop a valid technique for well imaging in anisotropic media,verify its use by a study of steady-state streamline patterns about a single well in the vicinity of a linear sealing boundary,devise methods for fault detection and location in anisotropic media, andinvestigate the error incurred by use of isotropic methods of fault location when applied to anisotropic reservoirs. JPT P. 1317