Pseudo-acoustic wave equations are usually used in reverse-time migration (RTM) for TI media. The acoustic wave equations for TTI media are much more complicated than those for isotropic and VTI media. To ensure a stable computation, the pseudo-S velocity along the symmetry axis is set to a non-zero value, which may induce more remarkable undesired S component one would like to eliminate before imaging. We propose a cost-effective filtering process to suppress the S component before applying the imaging condition. Furthermore second-order mixed spatial derivatives are involved in the acoustic TTI wave equations which are much more expensive to compute than a second-order non-mixed spatial derivative. We present a FD scheme to compute a second-order mixed spatial derivative by two non-mixed derivatives in a rotated coordinate system. It requires much less floating point operations and memory at each grid point, and is numerically simpler. Numerical examples are included to show the validity of the algorithm.

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