In Chapter 2, I implemented a TTI RTM by solving the coupled equations. Numerical tests show that a stable TTI RTM is achievable by selecting and equating anisotropic parameters in the model to reduce the contrast between epsilon and delta in areas of rapid changes along the symmetry axes. From the numerical results, it is obvious that TTI RTM has the ability to produce a more accurate image than isotropic RTM, especially in areas with anisotropy and strong variations of dip angles of the interfaces.
To deal with the intrinsic problems in the TTI RTM algorithm using coupled equations, such as numerical instabilities and shear wave artifacts, I have derived a new TTI decoupled P-wave equation in Chapter 3, starting from the exact dispersion relation with a square root approximation. 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. High quality, accurate TTI RTM images are therefore achieved with the decoupled P-wave equation.
Intensive computational cost is a critical problem in solving the decoupled P-wave equation. In Chapter 4, I have rewritten the TTI decoupled P-wave equation in a form which reduces the number of FFTs per time step, and propose a hybrid pseudospectral and finite-difference scheme to solve it. Computational examples demonstrate that the hybrid strategy demands less computation time and is faster than using the pseudospectral method alone.