Suchergebnisse

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.

The results of the application of the variational ray tracing algorithm to study the possibilities and limitations of one of the methods for solving the inverse kinematic problem of seismic exploration — the method of homogeneous functions developed at the Department of Seismometry and Geoacoustics of Moscow State University are presented. As a result of the calculations carried out on synthetic models and field material, conclusions were drawn about the exploration possibilities and areas of application of the method of homogeneous functions. Model examples show that the method of homogeneous functions gives correct results only for simple media: vertically inhomogeneous or layered with slightly inclined boundaries, and folds or inclusions can be restored only at a qualitative level. When working with real field data, the method of homogeneous functions correctly restores the velocity structure of the section to a depth of 1/3-1/2 of the maximum depth of ray penetration. At the same time, it makes sense to interpret only large anomalies with contrasting velocity values on the obtained velocity sections.