Accurate simulations of pure quasi-P-waves in complex anisotropic media

Abstract

Reverse time migration (RTM) in complex anisotropic media requires calculation of the propagation of a single-mode wave, the quasi-P-wave. This was conventionally realized by solving a [Formula: see text] system of second-order partial differential equations. The implementation of this [Formula: see text] system required at least twice the computational resources as compared with the acoustic wave equation. The S-waves, an introduced auxiliary function in this system, were treated as artifacts in the RTM. Furthermore, the [Formula: see text] system suffered numerical stability problems at the places in which abrupt changes of symmetric axis of anisotropy exist, which brings more challenges to real data implementation. On the other hand, the Alkhalifah’s equation, which governs the pure quasi-P-wave propagation, was hard to solve because it was a pseudodifferential equation. We proposed a pure quasi-P-wave equation that can be easily implemented within current imaging framework. Our new equation was obtained by decomposing the original pseudodifferential operator into two numerical solvable operators: a differential operator and a scalar operator. The combination of these two operators yielded an accurate phase of quasi-P-wave propagation. Our solution was S-wave free and numerically stable for very complicated models. Because only one equation was required to resolve numerically, the new proposed scheme was more efficient than those conventional schemes that solve the [Formula: see text] second-order differential equations system. For tilted transverse isotropy (TTI) RTM implementation, the required increase of numerical cost was minimal, and we could expect at least a factor of two of improvement of efficiency. We showed the effectiveness and robustness of our method with numerical examples with simple and very complicated TTI models, the SEG Advanced Modeling (SEAM) model. Further extension of our approach to orthorhombic anisotropy or tilted orthorhombic anisotropy was straightforward.