An efficient Helmholtz solver for acoustic  transversely isotropic media

Wu, Zedong; Alkhalifah, Tariq Ali

An efficient Helmholtz solver for acoustic transversely isotropic media

Files

geo2017-0618.1.pdf (473.7 KB)

Type

Article

Authors

Wu, Zedong

Alkhalifah, Tariq Ali

KAUST Department

Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Seismic Wave Analysis Group

Online Publication Date

2017-12-22

Print Publication Date

2018-03

Date

2017-12-22

Abstract

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and depend on less medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we propose to separate the quasi-P wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the non-elliptic-anisotropic components, which form a pseudo-differential operator. We, then, develop a separable approximation of the dispersion relation of non-elliptic-anisotropic components, specifically for transversely isotropic (TI) media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the non-elliptical terms represented in the Fourier domain. A frequency domain Helmholtz formulation of the approach renders the iterative implementation efficient as the cost is dominated by the Lower-Upper (LU) decomposition of the impedance matrix for the simpler elliptical anisotropic model. Also, the resulting wavefield is free of S-wave artifacts and has balanced amplitude. Numerical examples show that the method is reasonably accurate and efficient.

Citation

Wu Z, Alkhalifah T (2017) An efficient Helmholtz solver for acoustic transversely isotropic media. GEOPHYSICS: 1–20. Available: http://dx.doi.org/10.1190/geo2017-0618.1.

Acknowledgements

We thank KAUST for its support and the SWAG group for the collaborative environment. Especially, we thank Zhendong Zhang for useful discussions. We also thank Hemang Shah, Faqi Liu, Scott Morton, Hess Corporation and BP Exploration Operation for providing the benchmark model. The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. We also thank the associate editor Dimitri Komatitsch, assistant editor Arthur Cheng, Jiubing Cheng and another anonymous reviewer for their fruitful suggestions and comments.