A stable TTI reverse time migration and its implementation

Abstract

We propose a stable TTI acoustic wave equation system by revisiting the anisotropic elastic equations. A VTI equation system which is equivalent to its elastic counterpart is derived and the self‐adjoint differential operators in rotated coordinates are introduced to stabilize the TTI acoustic wave equations. Compared with conventional formulations, the new equation system does not add numerical complexity and a stable solution can be found by either a pseudo‐spectral or a high‐order explicit finite‐difference scheme. We show examples that our method provides stable and high quality TTI reverse time migration images.