Stable Simulating Algorithm of Pure Quasi-P Wavefield in Complex Anisotropic Media

Stable and accurate quasi-P waves simulating has always been a significant aspect in P-wave seismic imaging and inversion. We develop a stable quasi-P wave simulating algorithm based on the elliptic decomposition approach proposed by Xu et al. (2015). The first-order differential equation system of pure quasi-P wave corresponding to the decomposed scalar operator and elliptic differential operator for transverse isotropic (TI) media is derived. In order to ensure stabilities, we introduce self-adjoint operator to generalize the equation to tilted transverse isotropic (TTI) media. Then under Lebedev staggered grid framework, we deduce the high-order finite difference scheme of the equation and discuss specific issues such as calculation accuracy and efficiency of the numerical implementation. We test our algorithm in homogeneous anisotropic model and part of BP TTI model with extremely complex anisotropic parameters. The results show that the quasi-P wavefiled produced by our algorithm is not affected by pseudo-S-waves and anomalous amplitude. In complex TTI media with abrupt changes of the tilted symmetric axis, our algorithm also produces stable and accurate quasi-P wavefield which shows that it has a high tolerance to the spatial variation of anisotropic parameters.