A review of homomorphic deconvolution

Abstract

The purpose of this paper is to review the definition, to outline advantages and disadvantages, and to present both solved and unsolved problems of homomorphic deconvolution. The advantages of homomorphic deconvolution are that it does not require the assumptions of a minimum‐phase wavelet and of a white random reflection coefficient series. Recognized disadvantages of the method have been difficulties in unwrapping the phase, in dealing with band‐limited signals, and in handling mixed‐phase reflection coefficient series. These difficulties may be overcome by using an “adaptive numerical integration algorithm,” frequency transformations, and exponential weighting of the signal, respectively. Two unresolved problems in homomorphic deconvolution are deciding the cutoff quefrencies in liftering convolutional components and eliminating the effect of additive noise. No theoretical means of recovering one convolutional component of an arbitrary real seismogram which is not contaminated by the other component has been discovered. Additive noise plays an important role in homomorphic deconvolution, so that it is unreliable when the spectral amplitudes of the signal are very small over certain frequency bands in signals of relatively small signal‐to‐noise ratios.