Seismic Wave Fields in a Spherically Symmetric Earth: An Analytical Solution

An analytical solution was obtained for seismic wave fields in a spherically symmetric Earth. Asymptotics is used for stable calculation of wave fields. It is shown that the classical asymptotics in the case of a sphere of large (in wavelengths) dimensions gives an error in the solution. The original asymptotics is used for efficient calculation of a solution without errors with great detail. Software has been created that makes it possible to carry out calculations for high-frequency (1 Hz and more) teleseismic wave fields in a discrete (layered) sphere of planetary dimensions. Calculations can be carried out on personal computers with OpenMP parallelization. V.Yu. Burmin (2010, 2019) proposed a spherically symmetric model of the Earth. It is characterized by the fact that the outer core in this model has viscosity and, therefore, an effective shear modulus other than zero. For this model of the Earth, a highly detailed calculation was carried out with a carrier frequency of 1 Hz. As a result of the analytical calculation, it was found that low-amplitude high-frequency oscillations, so-called “precursors,” appear ahead of the PKP waves. An analytical calculation showed that the theoretical seismograms for this model of the Earth is in many respects similar to the experimental data. This confirms the correctness of the ideas that form the basis of the model.