Mathematical modeling of seismic wave kinematics in complex media

Abstract

A variational method of mathematical modeling of seismic wave kinematics has been developed at the Department of Seismometry and Geoacoustics of the Faculty of Geology of Lomonosov Moscow State University for studying the kinematics of seismic waves of different types in two-dimensional isotropic media (gradient and layered) is presented. The problem of determining the trajectories of seismic rays was solved by integrating using the Runge-Kutta method a system of differential equations with given initial conditions. The algorithm was studied in order to verify the accuracy and correctness of the solutions obtained, as well as its testing on a number of theoretical models of heterogeneous media. The developed ray tracing method was used to study the effect of the velocity gradient and the geometry of seismic boundaries on the kinematics of reflected waves in multilayer media. Based on the results of mathematical modeling of the kinematics of reflected waves, conclusions were drawn about the limits of applicability of simplified models of horizontally layered media, which often approximate complex inhomogeneous media.