scholarly journals Simulating propagation of decomposed elastic waves using low-rank approximate mixed-domain integral operators for heterogeneous transversely isotropic media

2014 ◽  
Author(s):  
Jiubing Cheng ◽  
Zedong Wu ◽  
Tariq Alkhalifah
Keyword(s):  
Elastic Waves ◽  
Integral Operators ◽  
Transversely Isotropic ◽  
Low Rank ◽  
Domain Integral ◽  
Transversely Isotropic Media ◽  
Isotropic Media

scholarly journals Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. T63-T77 ◽  
Author(s):  
Jiubing Cheng ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Peng Zou ◽  
Chenlong Wang
Keyword(s):  
Elastic Waves ◽  
Vector Fields ◽  
Integral Operators ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Low Rank ◽  
Elastic Displacement ◽  
Low Rank Approximation ◽  
Time Step ◽  
Domain Integral

In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly because the operators involved are dependent on the velocity, and thus they are not stationary. We have developed an efficient pseudospectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We have applied [Formula: see text]-space adjustment to the pseudospectral solution to allow for a relatively large extrapolation time step. The low-rank approximation was, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models showed that our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields for elastic wave modeling, imaging, and inversion.

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.

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