Reconstruction of the S-Wave Velocity via Mixture Density Networks With a New Rayleigh Wave Dispersion Function

How to determine the velocity of an S-wave from measured seismic data is an important topic in seismology. A modern technique for obtaining the S-wave velocity is to solve an inverse problem so that the simulated dispersion curve (the relation between the frequencies and phase velocities) coincides with the actual experimental results. In this work, by using the seismic impedance tensor, we propose a new function describing Rayleigh wave dispersion in the layered medium model of the Earth, which offers an efficient way to compute the dispersion curve. With this newly established forward model, based on mixture density networks (MDNs), we develop a physics-informed neural network, named MDN based on a physics informed forward model (FW-MDN), to estimate the S-wave velocity from dispersion curves. The FW-MDN method deals with the nonuniqueness issue encountered in the inversion of dispersion curves for the crust and upper mantle models, and attains satisfactory performance on an artificial dataset with various noise structures. Numerical simulations are performed to show that the FW-MDN offers easy calculation, efficient computation, and high precision for model characterization.