Direct Green's Function Synthetic Seismograms

They solve the seismic wave equation in a spherically layered isotropic medium using a decomposition into spheroidal and toroidal motions. For each spherical harmonic degree l and azimuthal order number m, the (l,m) response function is deternined subject to jumps in the displacement-stress vector at the source radius, a zero-traction boundary condition at Earth’s surface, and a homogeneous isotropic elastic solid at the base of the specified Earth model. The computation of synthetics is stable at both high and low frequencies, as well as at high and low spherical harmonic degrees.