Wavelet estimation via fourth-order cumulants

Abstract

A recent paper by Lazear (1993) holds out the possibility of directly measuring wavelet phase from seismic data, with no restrictive assumptions on the nature of the phase spectrum. His approach is "4th-order cumulant matching", in which an initial guess for the wavelet is iteratively updated until its 4th-order statistics match those of the data. A relatively large number of traces, several hundred at least, are needed to obtain reliable results, so the process does not readily lend itself to a trace-by-trace or even a shot-by-shot deconvolution. Even so, if reliable wavelet estimates can be obtained in typical circumstances this would be a considerable breakthorough, cutting across a number of existing uncertainties and difficulties in this area. In this paper I investigate the accuracy and the limitations of the 4th-order cumulant approach to wavelet estimation. I propose a procedure that can be used to assess the reliability of the derived wavelets, and I investigate the preprocessing necessary to improve their reliability. I demonstrate the technique as part of a quality control procedure that tracks the seismic wavelet through the different stages of a processing sequence.