The Limitations and Applicability of the Method of Homogeneous Functions for Solving the Inverse Kinematic Problem of Seismic Exploration

Abstract

The results of the application of the variational ray tracing algorithm to studying the possibilities and limitations of one of the methods for solving the inverse kinematic problem of seismic exploration, namely, 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 sloping boundaries, while 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 one-third to one-half of the maximum depth of ray penetration. At the same time, only large anomalies with contrasting velocity values on the obtained velocity sections are to be identified and interpreted as real geological structures.