Disk ray theory in transversely isotropic media

The first motion approximation has been used to calculate synthetic seisnograms in transversely isotropic, linear, elastic media. To achieve this end the equations of motion have been solved in a geometrical optics regime. Formally, this has been accomplished by the use of asymptotic propagator matrices. This formalism is important, since the phase of the JWKB reflection coefficient can be easily calculated by consideration of the radiation condition. Calculation of this reflection coefficient has shown that the turning point behaviour is identical to that obtained for an isotropic medium. The similarity of the turning point behaviour is a direct consequence of the physical result that at a turning point the phase and group velocities are in the same direction. To understand the results of the first motion approximation applied to a simple upper mantle model, it is first necessary to understand the basic physics of transversely isotropic media. This has been achieved by examination of the dispersion relation arising from Newton*s Laws for an elastic solid. From the dispersion relation, it has been demonstrated how the Green's Function can be constructed using elementary projective geometry. Subsequently, the nature of the Green's Function has been analyzed. The analysis of the Green's Function (wave surface) is important because it facilitates comprehension of any dynamical results. The synthetic seismograms were calculated using ray parameter versus distance curves. These curves were obtained by integration of the ray equations derived form the dispersion relations. A Gaussian-Kantorovich method was utilized to perform the required integration. This hybrid integration technique proved to be extremely fast and accurate. When the resulting p-delta curve was used to calculate the synthetic seismogram, the main effect of the anisotropic model considered was a kinematic one - the main arrivals were earlier than those for an isotropic model.Science, Faculty ofPhysics and Astronomy, Department ofGraduat