Computing Theoretical Seismograms from a Point Source in a Spherical Multilayered Medium

Computing theoretical seismograms from a point source in a given Earth model is essential for modeling and inversion of observed seismic waveforms for Earth’s structure and earthquake source parameters. Here, we derived the propagator matrices and source terms for a spherical multilayered Earth model using the exact earth flattening transformation. We found that their differences from their counterparts in horizontal layered media are inversely proportional to the nondimensional horizontal wavenumber and its higher order. In addition, all the source terms in a spherical layered model have a source-depth dependent scaling factor that differs from in a horizontal layered model by up to 6% for deep earthquakes. The surface displacement produced by a point source can be obtained in a similar form as in horizontal layered media. Computation of theoretical seismograms was implemented using the generalized reflection and transmission coefficients method. Numerical tests show that our formulae and implementation are correct and efficient for computing full-wave seismograms, including the permanent displacements, at teleseismic distances up to 100°. Individual seismic phases can be isolated and analyzed semianalytically because the generalized reflection and transmission method is used. Furthermore, our analytic expression of displacement in terms of the propagator matrices and source terms can be used to derive analytic derivatives of seismograms for full-wave waveform inversion.