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 k-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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We would like to thank S. Fomel for sharing his experience in designing low-rank approximate algorithms for wave propagation. The first author appreciates T. F. Wang and J. Z. Sun for their useful discussion in this study. We acknowledge supports from the National Natural Science Foundation of China (no. 41474099) and Shanghai Natural Science Foundation (no. 14ZR1442900). This paper is also based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under award no. 2230. We thank SEG, BP, and HESS Corporation for making the 2D VTI and TTI models available.