Conclusions

Starting with the exact dispersion relation, new pseudo-differential decoupled equations for the P wave and SV wave components in acoustic TTI media are derived. Separation of the P wave and SV wave modes results in a stable wave propagation in TTI media. Numerical examples show that modeling and migration using the TTI decoupled P wave equation provide a stable P wave propagation even for anisotropic models with strong spatial variations and sharp contrasts. A pseudospectral implementation for all the spatial derivatives and derivative-like terms coupled with REM in time is employed in the numerical implementation to provide accurate and nondispersive wave propagation. I conclude that stable TTI modeling and migration are achievable with the TTI decoupled P wave equation, and numerical implementation of pseudospectral in space coupled with REM in time provides high quality, accurate TTI RTM images.