My novel contributions in this dissertation are the following:
Conventional TTI coupled equations are investigated and implemented based on a previous
isotropic RTM code. The complexity, numerical instability and computational intensity of
the TTI RTM algorithm associated with the coupled equations are analyzed. In addition,
several practical problems regarding stability challenges are addressed and mitigated.
A set of new pseudo-differential TTI decoupled equations for the P-wave and SV-wave components
in acoustic TTI media are derived.
As a result, stable TTI modeling and migration are now achievable with the decoupled P-wave equation.
The TTI decoupled P-wave equation is rewritten in a form that reduces the
number of FFTs per time step. A new hybrid pseudospectral/finite-difference scheme
is proposed to solve
it, where wavenumber operators are replaced by inexpensive finite-difference spatial operators.
The computational costs of the hybrid TTI RTM algorithm are reduced by about 30 percent
of the original costs using the pseudospectral method.
The above novel schemes for TTI modeling and migration are numerically tested for 2D and 3D models. Results show the stability and efficiency advantages of this method compared to the standard methods. This dissertation has resulted in two papers
with myself as the first author, one published in Geophysics and the other in
Journal of Geophysics and Engineering. A third paper based on this dissertation will
soon be submitted for publication.