Pure qP-wave reverse time migration using low rank finite difference method with spherical difference stencil
YANG Lisheng1, HUANG Jinqiang1,2, GAO Guochao1,2, XIA Peng1,2, HE Yunchuan2, WU Hao1
1. College of Resources and Environmental Engineering, Guizhou University, Guiyang, Guizhou 550025, China; 2. Key Laboratory of Karst Georesoucres and Environment (Guizhou University), Ministry of Education, Guiyang, Guizhou 550025, China
Abstract：Pseudo shear-wave artifacts and numerical instability exist in forward modeling and reverse time migration of quasi-acoustic equations for anisotropic media, producing poor imaging quality. Meanwhile, computational efficiency is an important factor in anisotropic reverse time migration. Therefore, a pure qP-wave reverse time migration method is proposed, where both imaging quality and computational efficiency are taken into account. Firstly, based on the pseudo-analytic solution of the wave equation and the exact anisotropic dispersion relation, the wave field continuation formula of the pseudo-analytic solution of pure qP-wave in VTI and TTI media is constructed respectively, which avoids the derivation of the explicit wave equation and does not need to square the dispersion relation, thus eliminating the pseudo-shear wave artifacts existing in the wave field simulation. Then, by designing a three-dimensional (3D) spherical or two-dimensional (2D) circular difference stencil and solving the difference coefficients appropriate to the model with the help of the low-rank finite difference method, a pure qP-wave field continuation formula based on low-rank finite difference is derived, which reduces the computational complexity by eliminating the need for multiple Fourier transforms during continuation along the time direction. On this basis, the GPU is used to calculate the forward and backward seismic wave fields in parallel, which improves the imaging efficiency of the reverse time migration. The experimental results of typical 2D and 3D models show that the proposed method can eliminate the pseudo shear-wave artifacts, ensure the stability of the calculation process, and have strong adaptability and high computational efficiency in both 2D and 3D anisotropic media.
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