On the elastic wave equation in weakly anisotropic VTI media

Bloot, Rodrigo; Schleicher, Jörg; Santos, Lúcio Tunes

doi:10.1093/gji/ggs066

Cited by 12 publications

(8 citation statements)

References 21 publications

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“…where the eigenvalues must all be Λ ¼ 1. The explicit expressions for the elements of the Christoffel matrix Γ can be found in Bloot et al (2013). They also show that the three eigenvalues Λ of Γ can be calculated exactly as…”

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 92%

“…We start at the approximate elastic wave equation for VTI media with small δ, as specified by Bloot et al (2013). It reads,…”

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 99%

“…as defined by Bloot et al (2013). Note that the derivation of equation 1 involved linearization in δ.…”

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 99%

“…Still according to Bloot et al (2013), substitution of a zero-order ray ansatz (Červený, 1985, 2001) of the form, uðx 1 ; x 2 ; x 3 ; tÞ ¼ Uðx 1 ; x 2 ; x 3 Þgðt − Tðx 1 ; x 2 ; x 3 ÞÞ; (5) with U denoting a vectorial amplitude and T denoting the traveltime into the VTI wave equation without a source term yields the familiar ray-tracing eigenvalue problem:…”

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 99%

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

Schleicher

Costa

2016

GEOPHYSICS

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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 qPwave dispersion relation. Our numerical experiments showed that this approximation can provide highly accurate wavefields, even in strongly anisotropic inhomogeneous media.

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Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 92%

“…We start at the approximate elastic wave equation for VTI media with small δ, as specified by Bloot et al (2013). It reads,…”

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 99%

“…as defined by Bloot et al (2013). Note that the derivation of equation 1 involved linearization in δ.…”

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 99%

Section: Elastic Wave Propagation In a Vti Mediummentioning

confidence: 99%

See 2 more Smart Citations

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

Schleicher

Costa

2016

GEOPHYSICS

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“…where c P := λ + 2μ ρ , c S := μ ρ . (17) are the compressional and shear-wave velocities. The vector Eq.…”

Section: Elastic Wave Equationmentioning

confidence: 99%

Numerical modeling of mechanical wave propagation

Seriani

Oliveira

2020

Riv. Nuovo Cim.

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The numerical modeling of mechanical waves is currently a fundamental tool for the study and investigation of their propagation in media with heterogeneous physical properties and/or complex geometry, as, in these cases, analytical methods are usually not applicable. These techniques are used in geophysics (geophysical interpretation, subsoil imaging, development of new methods of exploration), seismology (study of earthquakes, regional and global seismology, accurate calculation of synthetic seismograms), in the development of new methods for ultrasonic diagnostics in materials science (non-destructive methods) and medicine (acoustic tomography). In this paper we present a review of numerical methods that have been developed and are currently used. In particular we review the key concepts and pioneering ideas behind finite-difference methods, pseudospectral methods, finite-volume methods, Galerkin continuous and discontinuous finite-element methods (classical or based on spectral interpolation), and still others such as physics-compatible, and multiscale methods. We focus on their formulations in time domain along with the main temporal discretization schemes. We present the theory and implementation for some of these methods. Moreover, their computational characteristics are evaluated in order to aid the choice of the method for each practical situation.

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