Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model

Rogister, Yves; Slawiński, Michael A.

doi:10.1190/1.2049347

Cited by 20 publications

(20 citation statements)

References 6 publications

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“…In this paper, we invoke analytic expressions for traveltimes and rays of the abχ model that are formulated by Rogister and Slawinski (2005). The traveltime between a source at (0,0) and a receiver at ðX; ZÞ is…”

Section: Traveltime Datamentioning

confidence: 99%

Bayesian inversion of VSP traveltimes for linear inhomogeneity and elliptical anisotropy

Danek

Slawiński

2012

GEOPHYSICS

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Bayesian interpretation of a three-parameter model of anisotropy and inhomogeneity for a VSP data set obtained in the Western Canada Basin indicates that introduction of the anisotropy parameter is justified by the data to a high grade of evidence. The acquisition geometry is a key factor in the resolving power of the data, and hence in deciding on the appropriate number of pertinent parameters. Herein, we show that the acquisition geometry composed of only two sources and eight receivers might be sufficient. The resolution of the inhomogeneity parameters is higher than the resolution of the anisotropy parameter. Nevertheless, the presence of the last parameter remains strongly justifiable by means of the Bayesian information criterion.

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Section: Traveltime Datamentioning

confidence: 99%

Bayesian inversion of VSP traveltimes for linear inhomogeneity and elliptical anisotropy

Danek

Slawiński

2012

GEOPHYSICS

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“…Rasolofosaon (1998) suggested that the anisotropy induced by stress may be elliptical anisotropy. Therefore, the elliptically anisotropic media is common in the ground which is the anisotropic media with the least parameters observed so far (Gurvich 1940;Kleyn 1956;Levin 1978;Daley and Hron 1979;Rogister and Slawinski 2005;Grechka 2009). The expression of the wavefront velocity (phase velocity) in the elliptically anisotropic media (Rogister and Slawinski 2005) is:…”

Section: Elliptically Anisotropic Mediamentioning

confidence: 99%

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Zhang

Bai

et al. 2017

Earthq Sci

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Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameterization in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in transversely homogeneous elliptically anisotropic media. Seismic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in elliptically anisotropic media with an irregular surface.

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“…Fewer works are found about the derivation of closed-form analytical solutions for anisotropic inhomogeneous distributions. In the field of geophysics, a solution is found for estimation of seismic wave propagation under an idealization, the ab χ model, for linearly inhomogeneous anisotropic media [30,31].…”

Section: Introductionmentioning

confidence: 99%

Closed-form analytical solutions for ray tracing in optically anisotropic inhomogeneous media

Nishidate

2013

J. Opt. Soc. Am. A

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Closed-form analytical solutions are obtained for ray tracing in several types of optically anisotropic inhomogeneous media whose optical properties are characterized by a matrix form of the inhomogeneous dielectric tensor in principal coordinates. The first solution is for anisotropic axial media, the second solution is for meridional rays in epsilon-negative metamaterial, and the third solution is an approximate one for rectangular lenses fabricated by molding procedures. The validation of numerical ray-tracing procedures for optically anisotropic inhomogeneous media was widely ignored since the solution was not available, and thus the present solutions are also useful for the validation. Furthermore, as examples of validation, ray trajectories are calculated by the closed-form solutions, and their results are compared with those obtained by a numerical solution of the geodesic equation which can be interpreted as a generalized ray equation.

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Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model

Cited by 20 publications

References 6 publications

Bayesian inversion of VSP traveltimes for linear inhomogeneity and elliptical anisotropy

Bayesian inversion of VSP traveltimes for linear inhomogeneity and elliptical anisotropy

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Closed-form analytical solutions for ray tracing in optically anisotropic inhomogeneous media

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