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 with a coordinate plane of the model medium. We remove this special limitation by developing a scheme in which symmetry axes of individual component TI media are oriented arbitrarily with respect to the coordinate axes of the composite model. In these general TI media, the elastic constants for each homogeneous anisotropic region are a 6 × 6 matrix of nonzero elements calculated by an arbitrary rotation. Then, 3-D modeling can readily deal with the coupling of the three components of wave motion. However, required computer memory and execution time may exceed practical limits. Therefore, we implement a finite‐element modeling process for TI media in which elastic properties vary only in two dimensions but component media have planes of isotropy in arbitrary directions. We compute three components of particle motion since the latter are coupled together in these media. The computational load is about twice that of the special cases where the planes of isotropy coincide with the coordinate planes. Three‐component synthetic profiles corresponding to two sample models clearly illustrate the behavior of seismic waves in anisotropic media, including shear‐wave splitting and coupling between the in‐line and cross‐line motion.