Pure quasi-P-wave modeling and imaging using an approximated space-domain pseudo-differential operator in vertical transverse isotropy media

Abstract

Incorporating anisotropy in seismic modeling and imaging is important to produce the correct locations of subsurface reflectors. Traditional wave equations for quasi-P-wave in transverse isotropic media either suffer from S-wave artifacts or require complicated and expensive computation strategies. To mitigate this issue, we develop a novel pure quasi-P-wave equation with an approximated space-domain pseudo-differential operator in the vertical transverse isotropic (VTI) medium. For the pure quasi-P-wave equation, we first simplify it to an elliptical anisotropy equation with an additional pseudo-differential correction term. Then, we directly approximate the pseudo-differential term with a space-domain convolution operator that is calculated by solving a nonlinear inverse problem. Phase-velocity analysis and numerical modeling show that the new space-domain pseudo-differential operator has good accuracy in describing wave propagation in the VTI medium. In addition, it is more suitable for parallel computation with domain-decomposition than the Fourier transform, which is necessary for solving traditional pseudo-differential operators. Finally, we apply our quasi-P-wave propagator to reverse time migration to correct the anisotropic effects in seismic imaging. Numerical experiments for the benchmark models and a land survey demonstrate the feasibility and adaptability of our method.