Determination of the principal directions of azimuthal anisotropy from P-wave seismic data

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 692-706 ◽  
Author(s):  
Subhashis Mallick ◽  
Kenneth L. Craft ◽  
Laurent J. Meister ◽  
Ronald E. Chambers
Keyword(s):  
Anisotropic Medium ◽  
Seismic Data ◽  
Principal Direction ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Amplitude Variation ◽  
S Waves ◽  
Wave Data ◽  
Principal Directions ◽  
Qualitative Measure

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.

Determination of the principal directions of azimuthal anisotropy from P-wave seismic data

1996 ◽  
Author(s):  
S. Mallick ◽  
K. L. Craft ◽  
L. J. Meister ◽  
R. E. Chambers
Keyword(s):  
Seismic Data ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Principal Directions

Computation of principal directions of azimuthal anisotropy from P‐wave seismic data

1996 ◽  
Author(s):  
Subhashis Mallick ◽  
Kenneth L., Craft ◽  
Laurent J. Meister ◽  
Ron E. Chambers
Keyword(s):  
Seismic Data ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Principal Directions

Computation of Principal Directions of Azimuthal Anisotropy From P-Wave Seismic Data

1997 ◽  
Vol 28 (4) ◽  
pp. 379-382 ◽  
Author(s):  
Subhashis Mallick ◽  
Kenneth L. Craft ◽  
Laurent J. Meister ◽  
Ron E Chambers
Keyword(s):  
Seismic Data ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Principal Directions

Kirchhoff elastic wave migration for the case of noncoincident source and receiver

Geophysics ◽  
1984 ◽  
Vol 49 (8) ◽  
pp. 1223-1238 ◽  
Author(s):  
John T. Kuo ◽  
Ting‐fan Dai
Keyword(s):  
Elastic Wave ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Horizontal Layer ◽  
P Wave ◽  
Seismic Section ◽  
S Waves ◽  
Surface Data ◽  
Marine Seismic ◽  
Wave Migration

In taking into account both compressional (P) and shear (S) waves, more geologic information can likely be extracted from the seismic data. The presence of shear and converted shear waves in both land and marine seismic data recordings calls for the development of elastic wave‐migration methods. The migration method presently developed consists of simultaneous migration of P- and S-waves for offset seismic data based on the Kirchhoff‐Helmholtz type integrals for elastic waves. A new principle of simultaneously migrating both P- and S-waves is introduced. The present method, named the Kirchhoff elastic wave migration, has been tested using the 2-D synthetic surface data calculated from several elastic models of a dipping layer (including a horizontal layer), a composite dipping and horizontal layer, and two layers over a half‐space. The results of these tests not only assure the feasibility of this migration scheme, but also demonstrate that enhanced images in the migrated sections are well formed. Moreover, the signal‐to‐noise ratio increases in the migrated seismic section by this elastic wave migration, as compared with that using the Kirchhoff acoustic (P-) wave migration alone. This migration scheme has about the same order of sensitivity of migration velocity variations, if [Formula: see text] and [Formula: see text] vary concordantly, to the recovery of the reflector as that of the Kirchhoff acoustic (P-) wave migration. In addition, the sensitivity of image quality to the perturbation of [Formula: see text] has also been tested by varying either [Formula: see text] or [Formula: see text]. For varying [Formula: see text] (with [Formula: see text] fixed), the migrated images are virtually unaffected on the [Formula: see text] depth section while they are affected on the [Formula: see text] depth section. For varying [Formula: see text] (with [Formula: see text] fixed), the migrated images are affected on both the [Formula: see text] and [Formula: see text] depth sections.

P-wave and S-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell‐Altamont Field, Utah

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1312-1328 ◽  
Author(s):  
Heloise B. Lynn ◽  
Wallace E. Beckham ◽  
K. Michele Simon ◽  
C. Richard Bates ◽  
M. Layman ◽  
...  
Keyword(s):  
Azimuthal Anisotropy ◽  
P Wave ◽  
Fracture Density ◽  
Wave Reflections ◽  
S Wave ◽  
Gas Reservoir ◽  
Green River ◽  
Wave Data ◽  
Reflection Data ◽  
Naturally Fractured

Reflection P- and S-wave data were used in an investigation to determine the relative merits and strengths of these two data sets to characterize a naturally fractured gas reservoir in the Tertiary Upper Green River formation. The objective is to evaluate the viability of P-wave seismic to detect the presence of gas‐filled fractures, estimate fracture density and orientation, and compare the results with estimates obtained from the S-wave data. The P-wave response to vertical fractures must be evaluated at different source‐receiver azimuths (travelpaths) relative to fracture strike. Two perpendicular lines of multicomponent reflection data were acquired approximately parallel and normal to the dominant strike of Upper Green River fractures as obtained from outcrop, core analysis, and borehole image logs. The P-wave amplitude response is extracted from prestack amplitude variation with offset (AVO) analysis, which is compared to isotropic‐model AVO responses of gas sand versus brine sand in the Upper Green River. A nine‐component vertical seismic profile (VSP) was also obtained for calibration of S-wave reflections with P-wave reflections, and support of reflection S-wave results. The direction of the fast (S1) shear‐wave component from the reflection data and the VSP coincides with the northwest orientation of Upper Green River fractures, and the direction of maximum horizontal in‐situ stress as determined from borehole ellipticity logs. Significant differences were observed in the P-wave AVO gradient measured parallel and perpendicular to the orientation of Upper Green River fractures. Positive AVO gradients were associated with gas‐producing fractured intervals for propagation normal to fractures. AVO gradients measured normal to fractures at known waterwet zones were near zero or negative. A proportional relationship was observed between the azimuthal variation of the P-wave AVO gradient as measured at the tops of fractured intervals, and the fractional difference between the vertical traveltimes of split S-waves (the “S-wave anisotropy”) of the intervals.

Traveltime and relative geometric spreading approximation in elastic orthorhombic medium

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. C153-C162 ◽  
Author(s):  
Shibo Xu ◽  
Alexey Stovas ◽  
Hitoshi Mikada
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
P Wave ◽  
Form Expression ◽  
Amplitude Variation ◽  
Rational Form ◽  
Amplitude Variation With Offset ◽  
Practical Applications ◽  
Numerical Tests ◽  
Geometric Spreading

Wavefield properties such as traveltime and relative geometric spreading (traveltime derivatives) are highly essential in seismic data processing and can be used in stacking, time-domain migration, and amplitude variation with offset analysis. Due to the complexity of an elastic orthorhombic (ORT) medium, analysis of these properties becomes reasonably difficult, where accurate explicit-form approximations are highly recommended. We have defined the shifted hyperbola form, Taylor series (TS), and the rational form (RF) approximations for P-wave traveltime and relative geometric spreading in an elastic ORT model. Because the parametric form expression for the P-wave vertical slowness in the derivation is too complicated, TS (expansion in offset) is applied to facilitate the derivation of approximate coefficients. The same approximation forms computed in the acoustic ORT model also are derived for comparison. In the numerical tests, three ORT models with parameters obtained from real data are used to test the accuracy of each approximation. The numerical examples yield results in which, apart from the error along the y-axis in ORT model 2 for the relative geometric spreading, the RF approximations all are very accurate for all of the tested models in practical applications.

Quartic reflection moveout in a weakly anisotropic dipping layer

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. D1-D13 ◽  
Author(s):  
Vladimir Grechka ◽  
Andrés Pech
Keyword(s):  
General Formula ◽  
Anisotropic Medium ◽  
Seismic Data ◽  
Wave Reflection ◽  
P Wave ◽  
Weak Anisotropy ◽  
Effective Anisotropy ◽  
Isotropic Solid ◽  
Strike Direction

Deviations of P-wave reflection traveltimes from a hyperbola, called the nonhyperbolic or quartic moveout, need to be handled properly while processing long-spread seismic data. As observed nonhyperbolic moveout is usually attributed to the presence of anisotropy, we devote our paper to deriving and analyzing a general formula that describes an azimuthally varying quartic moveout coefficient in a homogeneous, weakly anisotropic medium above a dipping, mildly curved reflector. To obtain the desired expression, we consistently linearize all quantities in small stiffness perturbations from a given isotropic solid. Our result incorporates all known weak-anisotropy approximations of the quartic moveout coefficient and extends them further to triclinic media. By comparing our approximation with nonhyperbolic moveout obtained from the ray-traced reflection traveltimes, we find that the former predicts azimuthal variations of the quartic moveout when its magnitude is less than 20% of the corresponding hyperbolic moveout term. We also study the influence of reflector curvature on nonhyperbolic moveout. It turns out that the curvature produces no quartic moveout in the reflector strike direction, where the anisotropy-induced moveout nonhyperbolicity is usually nonnegligible. Thus, the presence of nonhyperbolic moveout along the reflector strike might indicate effective anisotropy.

scholarly journals Physical and numerical modeling of tuning and diffraction in azimuthally anisotropic media

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1613-1621 ◽  
Author(s):  
Richard L. Gibson ◽  
Stephen Theophanis ◽  
M. Nafi Toksöz
Keyword(s):  
Numerical Modeling ◽  
Fractured Reservoirs ◽  
Homogeneous Model ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Fractured Reservoir ◽  
Sh Wave ◽  
Wave Data ◽  
Ray Methods

Fractured reservoirs are an important target for exploration and production geophysics, and the azimuthal anisotropy often associated with these reservoirs can strongly influence seismic wave propagation. We created a physical model of a fractured reservoir to simulate some of these propagation effects. The reservoir is represented by a phenolite disk that is thin with respect to the elastic wavelengths in the experiment, creating model dimensions that are representative of realistic reservoirs. Phenolite is strongly anisotropic with orthorhombic symmetry, which suggests that azimuthal amplitude versus offset (AVO) effects should be obvious in data. We acquired both SH- and P-wave data in common‐offset gathers with a near offset and a far offset and found that although the SH-wave data show clear azimuthal variations in AVO, the P-wave signals show no apparent changes with azimuth. We then applied numerical modeling to analyze the data. Because ray methods cannot model diffractions from the disk edge, we first used a ray‐Born technique to simulate variations in waveforms associated with such scattering. The synthetic seismograms reproduced variations in the SH-wave waveforms accurately, though the amplitude contrast between acquisition azimuths was overestimated. Assuming a laterally homogeneous model, we then applied ray methods to simulate tuning effects in SH- and P-wave data and confirmed that in spite of the large contrasts in elastic properties, the tuning of the P-wave reflections from the thin disk changed so there was negligible contrast in AVO with azimuth. Models of field scale reservoirs showed that the same effects could be expected for field applications.

Stress-induced seismic azimuthal anisotropy, sand-shale content, and depth trends offshore North West Australia

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. C77-C90 ◽  
Author(s):  
Lisa J. Gavin ◽  
David Lumley
Keyword(s):  
Confining Pressure ◽  
Horizontal Stress ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Model Parameters ◽  
Burial Depth ◽  
3D Seismic ◽  
Depth Limit ◽  
North West ◽  
S Waves

Seismic azimuthal anisotropy is apparent when P-wave velocities vary with source-receiver azimuth and downward-propagating S-waves split into two quasi-S-waves, polarized in orthogonal directions. Not accounting for these effects can degrade seismic image quality and result in erroneous amplitude analysis and geologic interpretations. There are currently no physical models available to describe how azimuthal anisotropy induced by differential horizontal stress varies with sand-shale lithology and depth; we develop a model that does so, in unconsolidated sand-shale sequences offshore North West Australia. Our method naturally introduces two new concepts: “critical anisotropy” and “anisotropic depth limit.” Critical anisotropy is the maximum amount of azimuthal anisotropy expected to be observed at the shallowest sediment burial depth, where the confining pressure and sediment compaction are minimal. The anisotropic depth limit is the maximum depth where the stress-induced azimuthal anisotropy is expected to be observable, where the increasing effects of confining pressure, compaction, and cementation make the sediments insensitive to differential horizontal stress. We test our model on borehole log data acquired in the Stybarrow Field, offshore North West Australia, where significant differential horizontal stress and azimuthal anisotropy are present. We determine our model parameters by performing regressions using dipole shear log velocities, gamma-ray shale volume logs, and depth trend data. We perform a blind test using the model parameters derived from one well to accurately predict the azimuthal anisotropy values at two other wells in an adjacent area. We use our anisotropy predictions to improve the well-tie match of the modeled angle-dependent reflectivity amplitudes to the 3D seismic amplitude variation with offset data observed at the well locations. Future applications of our method may allow the possibility to estimate the sand-shale content over a wide exploration area using anisotropic parameters derived from surface 3D seismic data.

Anisotropic 3D elastic full-wavefield inversion to directly estimate elastic properties and its role in interpretation

2021 ◽  
Vol 40 (4) ◽  
pp. 277-286
Author(s):  
Haiyang Wang ◽  
Olivier Burtz ◽  
Partha Routh ◽  
Don Wang ◽  
Jake Violet ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
P Wave ◽  
Quality Estimation ◽  
Amplitude Variation ◽  
Linear Inversion ◽  
Amplitude Variation With Offset ◽  
P Wave Velocity ◽  
Wavefield Inversion

Elastic properties from seismic data are important to determine subsurface hydrocarbon presence and have become increasingly important for detailed reservoir characterization that aids to derisk specific hydrocarbon prospects. Traditional techniques to extract elastic properties from seismic data typically use linear inversion of imaged products (migrated angle stacks). In this research, we attempt to get closer to Tarantola's visionary goal for full-wavefield inversion (FWI) by directly obtaining 3D elastic properties from seismic shot-gather data with limited well information. First, we present a realistic 2D synthetic example to show the need for elastic physics in a strongly elastic medium. Then, a 3D field example from deepwater West Africa is used to validate our workflow, which can be practically used in today's computing architecture. To enable reservoir characterization, we produce elastic products in a cascaded manner and run 3D elastic FWI up to 50 Hz. We demonstrate that reliable and high-resolution P-wave velocity can be retrieved in a strongly elastic setting (i.e., with a class 2 or 2P amplitude variation with offset response) in addition to higher-quality estimation of P-impedance and VP/VS ratio. These parameters can be directly used in interpretation, lithology, and fluid prediction.

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