Data adaptive velocity/depth spectra estimation in seismic wide angle reflection analysis

Abstract

In studying the earth with reflection seismics, one of the major unknowns is the velocity structure of the medium. Techniques used to determine the velocity structure commonly involve multi-channel arrays which measure the spatial as well as the time structure of the returning signals. The application of a data adaptive technique, the Maximum Likelihood Method, to the problem of estimating seismic velocities is described. The peculiar problems of this application are identified and investigated. The windowing of short duration signals is shown to be an important consideration, and the statistics of the MLM estimator for a single observation of the data set are presented. The adaptive estimator is applied to an ideal covariance matrix, to simulated data, and to field data. The results show the MLM velocity/depth estimator to be a valuable tool in seismic analysis, and the windowing and statistical results should have general applications in a variety of fields.