Generalization of Snell's Law for the propagation of acoustic waves in elliptically anisotropic media

Luis M. Pedruelo-González; Juan L. Fernández-Martínez; Luis M. Pedruelo-González; Juan L. Fernández-Martínez

doi:10.3934/math.2024726

AIMS Mathematics

2024, Volume 9, Issue 6: 14997-15007. doi: 10.3934/math.2024726

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Generalization of Snell's Law for the propagation of acoustic waves in elliptically anisotropic media

Group of Inverse Problems, Optimization and Machine Learning, Department of Mathematics, Universidad de Oviedo, Oviedo, Spain

Received: 02 January 2024 Revised: 13 April 2024 Accepted: 19 April 2024 Published: 25 April 2024
MSC : 86-XX

In seismic data processing, both in inversion (Inverse Processing) and modeling (Direct Processing), it is essential to consider anisotropy to unravel the geological structure of the subsoil. Besides, in most cases, the macroscopic model of anisotropy in 2D seismic surveys is elliptical and weak, with ratios of anisotropy close to one. Therefore, it is crucial to have at disposal the analytical formulas for acoustic wave propagation in elliptical anisotropic media. We presented the generalization of the Snell's Law for the case of acoustic wave propagation in elliptically anisotropic media. The generalization of the Snell's Law for acoustic anisotropic media had different applications in digital processing, raytracing, and acoustic inversion to properly consider elliptical anisotropy.
- transmission tomography,
- elliptical anisotropic media,
- inverse problems
Citation: Luis M. Pedruelo-González, Juan L. Fernández-Martínez. Generalization of Snell's Law for the propagation of acoustic waves in elliptically anisotropic media[J]. AIMS Mathematics, 2024, 9(6): 14997-15007. doi: 10.3934/math.2024726

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Abstract

In seismic data processing, both in inversion (Inverse Processing) and modeling (Direct Processing), it is essential to consider anisotropy to unravel the geological structure of the subsoil. Besides, in most cases, the macroscopic model of anisotropy in 2D seismic surveys is elliptical and weak, with ratios of anisotropy close to one. Therefore, it is crucial to have at disposal the analytical formulas for acoustic wave propagation in elliptical anisotropic media. We presented the generalization of the Snell's Law for the case of acoustic wave propagation in elliptically anisotropic media. The generalization of the Snell's Law for acoustic anisotropic media had different applications in digital processing, raytracing, and acoustic inversion to properly consider elliptical anisotropy.

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