Generalized finite difference forward modeling for the first-order qP-wave equation in TTI media based on the new acoustic approximation

Abstract The pseudo-acoustic wave equation has been widely used in anisotropic migration and inversion. However, there exist S wave artifacts and unstable phenomena in the forward wavefields for the acoustic approximation equation. To solve these issues, we formulate the vertically incident S-wave velocity with the qSV-wave phase velocity of zero and incorporate auxiliary operators. Then we derive a new first-order qP-wave equation for tilted transversely isotropic (TTI) media based on the new acoustic approximation (hereinafter referred to as the new acoustic approximation equation). In addition, the conventional finite difference method (FDM) suffers from artificial scattering waves caused by staircase grid discretization when handling undulating interfaces, which decreases numerical simulation accuracy. Regarding this problem, we introduce the generalized finite difference method (GFDM) to forward modeling for the qP-wave equation to eliminate the staircase scattering. Numerical results demonstrate that the new acoustic approximation equation effectively eliminates S wave artifacts and remains stable with anisotropy parameters $\varepsilon \ge \delta $ or $\varepsilon < \delta $, and GFDM successfully suppresses staircase scattering and improves forward modeling accuracy, which is suitable for complex TTI media simulations.