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

In studying the earth with reflection seismics, one of themajor 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 adata adaptive technique, the Maximum Likelihood Method, to theproblem of estimating seismic velocities is described. Thepeculiar problems of this application are identified and investigated. The windowing of short duration signals is shown tobe an important consideration, and the statistics of the MLMestimator 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 seismicanalysis, and the windowing and statistical results shouldhave general applications in a variety of fields.

Submitted in partial fulfillment of the requirements for theDegree of Doctor of Philosophy at the Woods Hole Oceanographic Institution and the Massachusetts Institute of Technology July 1977

This study was supported in part by NSF-IDOE Grant GX-4094, NOAA Contract 04-6-158-44081, ONR ContractN00014-77-6-0266, by a fellowship from the Research Laboratoryof Electronics at MIT, and by the MIT/WHOI Joint programin Ocean Engineering.