P-wave extrapolation in anisotropic media suffers from SVwave artifacts and computational dependency on the complexity of anisotropy. The anisotropic pseudodifferential wave equation cannot be solved using an efficient time-domain finite-difference (FD) scheme directly. The wavenumber domain allows us to handle pseudodifferential operators accurately; however, it requires either smoothly varying media or more computational resources. In the limit of elliptical anisotropy, the pseudodifferential operator reduces to a conventional operator. Therefore, we have developed a hybrid-domain solution that includes a spacedomain FD solver for the elliptical anisotropic part of the anisotropic operator and a wavenumber-domain low-rank scheme to solve the pseudodifferential part. Thus, we split the original pseudodifferential operator into a second-order differentiable background and a pseudodifferential correction term. The background equation is solved using the efficient FD scheme, and the correction term is approximated by the low-rank approximation. As a result, the correction wavefield is independent of the velocity model, and, thus, it has a reduced rank compared with the full operator. The total computation cost of our method includes the cost of solving a spatial FD time-step update plus several fast Fourier transforms related to the rank. The accuracy of our method is of the order of the FD scheme. Applications to a simple homogeneous tilted transverse isotropic (TTI) medium and modified BP TTI models demonstrate the effectiveness of the approach.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank J. Etgen, D. Komatitsch, V. Socco, and three anonymous reviewers for improving the quality of the paper. We thank H. Wang, N. Masmoudi, and Y. Liu for their helpful discussions. We thank King Abdullah University of Science & Technology (KAUST) for its support and specifically the seismic wave analysis group members for their valuable insights. For computer time, this research used the resources of the Supercomputing Laboratory at KAUST in Thuwal, Saudi Arabia.