An experimental test of P-wave anisotropy in stratified media

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 374-378 ◽  
Author(s):  
Patrick J. Melia ◽  
Richard L. Carlson
Keyword(s):  
Layer Thickness ◽  
Field Measurements ◽  
Transversely Isotropic ◽  
Compressional Wave ◽  
P Wave ◽  
Stratified Media ◽  
Layer Spacing ◽  
Long Wave ◽  
Significant Difference ◽  
Isotropic Media

In theory, stratified media in which the layers are elastically homogeneous and isotropic approximate transversely isotropic media with an axis of symmetry perpendicular to layering when the seismic wavelength is sufficiently longer than the layer spacing. The phenomenon has apparently been observed in field measurements, and acoustic anisotropy in deep‐sea sediments, measured in the laboratory, has been attributed to fine‐scale bedding laminations. However, to the best of our knowledge, no rigorous test of the theory has been made. We have made a partial test by making laboratory measurements of compressional‐wave velocities parallel and perpendicular to layering in fabricated samples consisting of glass and epoxy. We found no statistically significant difference between observation and theory in this limited test. Further, having used several frequencies, we found that the velocities progressively change from the long‐wave values toward those predicted by the time‐average relation, as expected. Finally, it has been proposed that the long‐wave approximation holds when the ratio of the seismic wavelength to layer thickness (λ/d) is 10–100. We found that the minimum ratio was highest in the midrange of composition (half glass, half epoxy), even though the samples in that range have the smallest combined layer thickness. This result suggests that the frequency dependence of anisotropy in layered media is a function of the proportions of the materials as well as the thickness of the layers.

Long‐wave anisotropy in stratified media: A numerical test

Geophysics ◽  
1991 ◽  
Vol 56 (2) ◽  
pp. 245-254 ◽  
Author(s):  
J. M. Carcione ◽  
D. Kosloff ◽  
A. Behle
Keyword(s):  
Layer Thickness ◽  
Numerical Test ◽  
Transversely Isotropic ◽  
Seismic Signal ◽  
Layer Spacing ◽  
Wave Approximation ◽  
Numerical Tests ◽  
Long Wave ◽  
Long Wave Approximation ◽  
Minimum Ratio

When a seismic signal propagates in a stratified earth, there is anisotropy if the dominant wavelength is long enough compared to the layer thickness. In this situation, the layered medium can be replaced by an equivalent nondispersive transversely isotropic medium. Theoretical and experimental analyses of the required minimum ratio of seismic wavelength to layer spacing based on kinematic considerations yield different results, with a much higher value in the experimental test. The present work investigates the effects of layering by wave simulation and attempts to establish quantitatively the minimum ratio for which the long‐wave approximation starts to be valid. We consider two‐constituent periodically layered media and analyze the long‐wave approximation for different material compositions and different material proportions in 1-D and 2-D media. The evaluation of the minimum ratio compares snapshots and synthetic seismograms visually and through a measure of coherence. Layering induces scattering with wave dispersion or anisotropy depending upon the wavelength‐to‐layer thickness ratio. The modeling confirms the dispersive characteristics of the wave field, the scattering effects in the form of coda waves at short wavelengths, and the smoothed transversely isotropic behavior at long wavelengths. 1-D numerical tests for different media indicate that the minimum ratio is highest for the midrange of compositions, i.e., equal amount of each material, and for stronger reflection coefficients between the constituents. For epoxy‐glass, the value is around R = 8, while for sandstone‐limestone, it is between R = 5 and R = 6. Recent wave‐propagation experiments done in epoxy‐glass also imply a highest minimum ratio for midrange of composition; however, the 1-D numerical tests confirm the long‐wave approximation at shorter wavelengths than experimentally. The 2-D case shows that the more anisotropic the equivalent medium, the higher the minimum ratio, and that the approximation depends upon the propagation angle with longer wavelengths required in the direction of the layering.

scholarly journals The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T51-T62 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Analytic Representation ◽  
Velocity Inversion ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Time Domains ◽  
Isotropic Media ◽  
Hti Media

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

Long‐wave elastic anisotropy in transversely isotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 896-917 ◽  
Author(s):  
James G. Berryman
Keyword(s):  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Seismic Signal ◽  
Perturbation Scheme ◽  
Low Velocity ◽  
Compressional Waves ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality [Formula: see text] derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limestone and one‐quarter sandstone. It is concluded that anisotropic effects are greatest in areas where the layering is quite thin (10–50 ft), so that the wavelengths of the seismic signal are greater than the layer thickness and the layers are of alternately high‐ and low‐velocity materials.

On: “Long‐wave elastic anisotropy in transversely isotropic media” by J. G. Berryman, and “Seismic velocities in transversely isotropic media” by F. K. Levin (GEOPHYSICS, v. 44, May 1979, p. 896–917 and p. 918–936, respectively).

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 336-338 ◽  
Author(s):  
Felix M. Lyakhovitskiy
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Thin Layers ◽  
Poisson's Ratio ◽  
Seismic Velocities ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Berryman and Levin made an assumption about constancy or limited variations of Poisson’s ratio in the thin layers, in their analyses of elastic anisotropy in thin‐layered media. Berryman states (p. 913): “Rare cases can occur with large variations in Poisson’s ratio.” However, on p. 911 Berryman does point out (with reference to Benzing) that range of variations of the parameter γ = VS/VP from 0.45 to 0.65 is typical of rocks. That corresponds to a range of variations of Poisson’s ratio of 0.373 to 0.134 (i.e., almost three times as much).

Migration of P‐wave reflection data in transversely isotropic media

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 591-596 ◽  
Author(s):  
Suhas Phadke ◽  
S. Kapotas ◽  
N. Dai ◽  
Ernest R. Kanasewich
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Limited Range ◽  
Horizontal Velocity ◽  
P Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Wave propagation in transversely isotropic media is governed by the horizontal and vertical wave velocities. The quasi‐P(qP) wavefront is not an ellipse; therefore, the propagation cannot be described by the wave equation appropriate for elliptically anisotropic media. However, for a limited range of angles from the vertical, the dispersion relation for qP‐waves can be approximated by an ellipse. The horizontal velocity necessary for this approximation is different from the true horizontal velocity and depends upon the physical properties of the media. In the method described here, seismic data is migrated using a 45-degree wave equation for elliptically anisotropic media with the horizontal velocity determined by comparing the 45-degree elliptical dispersion relation and the quasi‐P‐dispersion relation. The method is demonstrated for some synthetic data sets.

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

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C295-C307 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng ◽  
Chenlong Wang
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Wave Imaging ◽  
Obs Data

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.

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