A separable strong-anisotropy approximation for pure qP-wave propagation in transversely isotropic media

The wave equation can be tailored to describe wave propagation in vertical-symmetry axis transversely isotropic (VTI) media. The qP- and qS-wave eikonal equations derived from the VTI wave equation indicate that in the pseudoacoustic approximation, their dispersion relations degenerate into a single one. Therefore, when using this dispersion relation for wave simulation, for instance, by means of finite-difference approximations, both events are generated. To avoid the occurrence of the pseudo-S-wave, the qP-wave dispersion relation alone needs to be approximated. This can be done with or without the pseudoacoustic approximation. A Padé expansion of the exact qP-wave dispersion relation leads to a very good approximation. Our implementation of a separable version of this equation in the mixed space-wavenumber domain permits it to be compared with a low-rank solution of the exact qP-wave dispersion relation. Our numerical experiments showed that this approximation can provide highly accurate wavefields, even in strongly anisotropic inhomogeneous media.

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Anisotropic viscoacoustic wave modelling in VTI media using frequency-dependent complex velocity

Journal of Geophysics and Engineering ◽

10.1093/jge/gxaa023 ◽

2020 ◽

Author(s):

Yabing Zhang ◽

Yang Liu ◽

Shigang Xu

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Wave Equations ◽

Transversely Isotropic ◽

P Wave ◽

Low Rank ◽

Transversely Isotropic Media ◽

Isotropic Media ◽

Rank Decomposition ◽

Low Rank Decomposition

Abstract Under the conditions of acoustic approximation and isotropic attenuation, we derive the pseudo- and pure-viscoacoustic wave equations from the complex constitutive equation and the decoupled P-wave dispersion relation, respectively. Based on the equations, we investigate the viscoacoustic wave propagation in vertical transversely isotropic media. The favourable advantage of these formulas is that the phase dispersion and the amplitude dissipation terms are inherently separated. As a result, we can conveniently perform the decoupled viscoacoustic wavefield simulations by choosing different coefficients. In the computational process, a generalised pseudo-spectral method and a low-rank decomposition scheme are adopted to calculate the wavenumber-domain and mixed-domain propagators, respectively. Because low-rank decomposition plays an important role in the simulated procedure, we evaluate the approximation accuracy for different operators using a linear velocity model. To demonstrate the effectiveness and the accuracy of our method, several numerical examples are carried out based on the new pseudo- and pure-viscoacoustic wave equations. Both equations can effectively describe the viscoacoustic wave propagation characteristics in vertical transversely isotropic media. Unlike the pseudo-viscoacoustic wave equation, the pure-viscoacoustic wave equation can produce stable viscoacoustic wavefields without any SV-wave artefacts.

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Migration of P‐wave reflection data in transversely isotropic media

Geophysics ◽

10.1190/1.1443619 ◽

1994 ◽

Vol 59 (4) ◽

pp. 591-596 ◽

Cited By ~ 3

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.

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An efficient Helmholtz solver for acoustic transversely isotropic media

Geophysics ◽

10.1190/geo2017-0618.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. C75-C83 ◽

Cited By ~ 6

Author(s):

Zedong Wu ◽

Tariq Alkhalifah

Keyword(s):

Wave Equation ◽

Transversely Isotropic ◽

Anisotropic Media ◽

P Wave ◽

Seismic Exploration ◽

S Wave ◽

P Waves ◽

Transversely Isotropic Media ◽

Isotropic Media ◽

Separable Approximation

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute most of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and they depend on fewer medium parameters. However, conventional solutions of the acoustic-wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we separate the quasi-P-wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the nonelliptic anisotropic components, which form a pseudodifferential operator. We then develop a separable approximation of the dispersion relation of nonelliptic-anisotropic components, specifically for transversely isotropic media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the nonelliptical terms represented in the Fourier domain. A frequency-domain Helmholtz formulation of the approach renders the iterative implementation efficient because the cost is dominated by the lower-upper decomposition of the impedance matrix for the simpler elliptical anisotropic model. In addition, the resulting wavefield is free of S-wave artifacts and has a balanced amplitude. Numerical examples indicate that the method is reasonably accurate and efficient.

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