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A constructive deconvolution procedure of bandpass signals by homomorphic analysis

A convolution may be represented as x(.)=r(.)*w(.). The goal of deconvolution is to extract r(.) and w(.) from knowledge of x(.), and 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 particularly efficient for those cases where x(.) is known to be full-band. This paper presents a robust constructive procedure for efficient homomorphic deconvolution for those cases where x(.) is a bandpass signal. Analysis and comparison with other methods for deconvolving bandpass signals on measured seismic traces (including the Novaya Zemlya event) illustrate the improvement in the deconvolution.