Linear inverse theory and deconvolution

Publisher Website
Google Scholar
Abstract
Seismic source wavelet deconvolution can be treated within the framework of the Backus‐Gilbert (BG) inverse theory. A time shift‐invariant version of this theory leads to the Wiener shaping filter, which has enjoyed widespread use for source wavelet deconvolution in exploration seismology. The model of the BG theory is the ground impulse response, the BG mapping kernel is the source wavelet, and the BG resolving kernel is the convolution between the source wavelet and the Wiener shaping filter. BG inversion involves the minimization of an optimality criterion under a set of constraints. The application of the BG “filter energy” or “noise output power” constraint to Wiener filter design leads to the familiar prewhitening parameter that stabilizes the filter on the one hand, but degrades resolution on the other. The BG “unimodular” constraint produces an unbiased estimate of the model, or ground impulse response. These constraints provide novel insights into the performance of deconvolution filters.

This publication has 0 references indexed in Scilit: