Numerical analytic methods for calculating wave fields and restoring the velocity characteristics of inhomogeneous elastic media in the Baikal rift zone

On the basis of a numerical method for solving direct and inverse problems, a method has been developed for tracking the dynamics of the propagation of a seismo-hydroacoustic wave field, constructing model seismograms, and estimating the velocity characteristics of the complex geophysical structure of the Baikal rift zone in the area of the village Babushkin (southeastern Baikal) - the village. Buguldeika (north-western Baikal). The choice of the profile for modeling is due to the experimental work performed here by the Institute of Physics of the Earth Russian Academy of Sciences, the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, the Institute of Geology of the Siberian Branch of the Russian Academy of Sciences in 2021. The algorithm for solving the direct problem of wave field reconstruction is based on the application of the integral Laguerre transformation in time and finite-difference approximation in spatial coordinates. The numerical model of the medium used to calculate the propagation of seismic waves was set taking into account a priori data on the velocity section of the Baikal rift zone, obtained by a number of researchers in the region according to the data of deep seismic sounding of the Earth. The results of direct numerical modeling assume the prediction of the complex structure of the wave field and are intended to facilitate its interpretation. As an approach to solving the inverse problem of restoring the velocity characteristics of an inhomogeneous media, a computational grid algorithm based on the calculation of weighted average velocities in sections of a grid superimposed on the Earth's surface is proposed and tested. By choosing the grid step, the method of approximating the discrete wave travel time curve by cubic splines, and taking into account the curvature of the head wave travel time curve in areas with a pronounced inhomogeneity of the medium structure, it is possible to determine the velocity characteristic with increased accuracy. The consistency of the reconstructed theoretical velocity model of the medium with the experimentally obtained model by the method of deep seismic sounding is shown.