Rays in transversely isotropic media
P. F. Daley
The theory of characteristics related to the solution of partial differential equations of the hyperbolic type is applied to the coupled qP - qSV wave propagation problem in a transversely isotropic (T.I.) medium. The characteristics or rays are the paths along which energy is transported from one point to another in any media type. The determination of ray paths in such a media type is often a preliminary step in addressing more complex problems in anisotropic wave propagation such as amplitude computations and the related polarization vectors, quantities that are significantly more difficult to obtain in any type of anisotropic medium when compared with the isotropic case.
Equations for tracing the progress of a ray through a homogeneous T.I. medium, which has applications in several areas of seismology, will be presented. The problem of reflection and refraction at an interface separating two T.I. media has been treated in an earlier report. Used with the results presented here, a method will be developed to explore two-point ray propagation in media where the rotationally invariant axis of the T.I. wave front is not aligned with the interfaces separating two media and some simple results shown.