Two-dimensional, three-component wave propagation in a transversely isotropic medium with arbitrary-orientation-finite-element modeling

Numerical modeling of seismic waves in transversely isotropic (TI) media is often restricted to special cases where the plane of isotropy coincides wi th a coordinate plane of the model medium. We remove this special Limitatio n by developing a scheme in which symmetry axes of individual component TI media are oriented arbitrarily with respect to the coordinate axes of the c omposite model. In these general TI media, the elastic constants for each h omogeneous anisotropic region are a 6 x 6 matrix of nonzero elements calcul ated by an arbitrary rotation. Then, 3-D modeling can readily deal with the coupling of the three components of wave motion. However, required compute r memory and execution time may exceed practical limits. Therefore, we implement a finite-element modeling process for TI media in w hich elastic properties vary only in two dimensions but component media hav e planes of isotropy in arbitrary directions. The compute three components of particle motion since the latter are coupled together in these media. Th e computational load is about mice that of the special cases where the plan es of isotropy coincide with the coordinate planes. Three-component synthet ic profiles corresponding to two sample models clearly illustrate the behav ior of seismic waves in anisotropic media, including shear-wave splitting a nd coupling between the in-line and cross-line motion.