An improved pure quasi-P-wave equation for complex anisotropic media

An accurate pure qP-wave equation in TI media and its efficient and stable implementation are valuable for seismic imaging and inversion. Owing to the complexity of the qP-wave phase velocity expression in anisotropic media, it is difficult to construct such a pure qP-wave equation. In this paper, we combine the Taylor expansion and scalar operator methods to formulate an efficient and stable pure qP-wave equation in TI media. First, the Taylor expansion method is used to convert the square-root term into a fractional term in the qP-wave phase velocity expression. We further improve the approximation accuracy of the resulting equation by a correction technique. Then, the scalar operator is applied to scalarize the equivalent form of the fractional term in the approximated dispersion equation, deriving a simple and easy-to-implement pure qP-wave equation. We utilize the optical flow method to compute the direction of wave propagation, which improves the calculation accuracy of the scalar operators. Numerical experiments with representative models demonstrate that the new method has higher accuracy and better adaptability to models with strong anisotropy, complex structure, and rapid variation of the tilt angle than previous methods.