Abstract
I develop an efficient modeling technique for transversely isotropic, inhomogeneous media using a mix of analytical equations and numerical calculations. The analytic equation for the raypath in a factorized transversely isotropic (FTI) media with linear velocity variation, derived by Shearer and Chapman, is used to trace rays between two points. In addition, I derive an analytical equation for geometrical spreading in FTI media that aids in preserving program efficiency; however, the traveltimes are calculated numerically. I then generalize the method to treat general transversely isotropic (TI) media that are not factorized anisotropic inhomogeneous by perturbing the FTI traveltimes, following the perturbation ideas of Cerveny and Filho. A Kirchhoff-summation-based program relying on Trorey's diffraction method is used to generate synthetic seismograms for such a medium. For the type of velocity models treated, the program is much more efficient than finite-difference or general ray-trace modeling techniques.
