Publisher Summary This chapter discusses various ways in which homomorphic filtering has been explored for use with seismic data processing. Homomorphic filtering represents an alternative approach to the deconvolution of the seismic signal. This class of filtering techniques represents a generalization of linear filtering to encompass a variety of nonlinear filtering problems. One particular class of nonlinear filtering problems to which it has been successfully applied in a number of applications is that of deconvolution. Within the context of seismic signal processing, a number of approaches have been explored for the application of this class of nonlinear filtering techniques. One consists of applying the method directly to extract the reflector series from the received signal. A second corresponds to using homomorphic filtering to estimate the source pulse. From this estimate, an inverse filter is then designed using one of several possible techniques including Wiener inverse filter design.

Application of homomorphic filtering to seismic data processing

Interactive computing and graphics in the interpretation of geomagnetic spectra

: This research is concerned with two log spectral estimators in the context of both stationary and nonstationary signals. They differ because in one smoothing is realized before the logarithmic transformation, while the other is smoothed in the logarithmic domain. It is shown that for stationary signals the two estimators are similar, differing in expected value by only a universal constant. The first estimator, however, is smoother. For nonstationary signals, the estimators are biased by different amounts dependent upon the nonstationarity. The difference between the estimators is shown to be a sensitive test for nonstationarity. The estimators are used in the analysis and implementation of two solutions to the problem of blind deconvolution. It is found that the methods are equivalent for stationary signals, but differ markedly for nonstationary signals in the presence of stationary background noise. Recommendations are made for the practical digital implementation of the log spectral estimators.

Robert Bergstrom Ingebretsen

Papers

Log Spectral Estimation for Stationary and Nonstationary Processes