| Surface waves propagating on the surface of the Earth exhibit path, phase, and amplitude variations due to the lateral heterogeneity. We investigate the path deviation and geometric nature of caustics using both exact ray tracing and linear ray perturbation theory on a smooth, laterally heterogeneous Earth model. A numerically efficient implementation of JWKB theory is developed to calculate synthetic surface wave seismograms on such a model. We illustrate the method by applying it to model S12/WM13; the phase and amplitude anomalies of long-period, fundamental-mode Love and Rayleigh waves are compared with the corresponding results obtained using the great-circle approximation and first-order ray perturbation theory. The most serious discrepancies between these two approximations and full JWKB theory occur for paths with large transverse phase-velocity gradients, which lead to significant deviations away from the source-receiver great circle.;A necessary and sufficient condition for the validity of surface-wave ray theory is ;We propose a spherical surface-spline method that parameterizes a phase-velocity model on a sphere in terms of a local cubic B-spline basis on a set of grids with approximately equal separations. A triangular tessellation technique is developed to configure the grids so that the inter-knot spacing is nearly even on the spherical surface. This spherical surface-spline parameterization enables us to apply the surface-wave JWKB theory to regional studies and has distinct advantage in computational efficiency. |
