One-way wave propagation in the ray-centred coordinate system for vertical transversely isotropic media

2021 ◽  
Author(s):  
Bohan Zhang ◽  
Huazhong Wang
Keyword(s):  
Wave Propagation ◽  
Coordinate System ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Approximate dispersion relations for qP-qSV-waves in transversely isotropic media

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 919-933 ◽  
Author(s):  
Michael A. Schoenberg ◽  
Maarten V. de Hoop
Keyword(s):  
Wave Propagation ◽  
Order Approximation ◽  
Transverse Isotropy ◽  
Slight Modification ◽  
Transversely Isotropic ◽  
P Wave ◽  
Slowness Surface ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
First Order Approximation

To decouple qP and qSV sheets of the slowness surface of a transversely isotropic (TI) medium, a sequence of rational approximations to the solution of the dispersion relation of a TI medium is introduced. Originally conceived to allow isotropic P-wave processing schemes to be generalized to encompass the case of qP-waves in transverse isotropy, the sequence of approximations was found to be applicable to qSV-wave processing as well, although a higher order of approximation is necessary for qSV-waves than for qP-waves to yield the same accuracy. The zeroth‐order approximation, about which all other approximations are taken, is that of elliptical TI, which contains the correct values of slowness and its derivative along and perpendicular to the medium’s axis of symmetry. Successive orders of approximation yield the correct values of successive orders of derivatives in these directions, thereby forcing the approximation into increasingly better fit at the intervening oblique angles. Practically, the first‐order approximation for qP-wave propagation and the second‐order approximation for qSV-wave propagation yield sufficiently accurate results for the typical transverse isotropy found in geological settings. After only slight modification to existing programs, the rational approximation allows for ray tracing, (f-k) domain migration, and split‐step Fourier migration in TI media—with little more difficulty than that encountered presently with such algorithms in isotropic media.

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

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C337-C354 ◽  
Author(s):  
Jörg Schleicher ◽  
Jessé C. Costa
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Dispersion Relation ◽  
Transversely Isotropic ◽  
Wave Dispersion ◽  
Low Rank ◽  
S Wave ◽  
Finite Difference Approximations ◽  
Transversely Isotropic Media ◽  
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.

P-wave propagation in transversely isotropic media

2006 ◽  
Vol 156 (1-2) ◽  
pp. 21-40 ◽  
Author(s):  
Marie Calvet ◽  
Sébastien Chevrot ◽  
Annie Souriau
Keyword(s):  
Wave Propagation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media
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