On homomorphic deconvolution of bandpass signals

A convolution may be represented as x(.)=r(.)* w(.). The goal of deconvolution is to extract r(.) and w(.) from a knowledge of x(.) and it finds numerous applications in digital signal processing. Of practical interest in oil exploration is the case where w(.) is a seismic pressure wavelet, x(.) is the observed seismic response, and r(.) is the reflectivity of the Earth. A number of procedures have been proposed, including predictive, deterministic, and homomorphic deconvolution. Homomorphic deconvolution has been found to be particularly efficient for those cases where x(.) is known to be fullband. This paper presents a robust constructive procedure for efficient homomorphic deconvolution for those cases where x(.) is a bandpass signal. Extensive comparisons with other methods for deconvolving bandpass signals on measured seismic data traces (including the Novaya Zemlya event) illustrate the improvement in the deconvolution.