Applications of short-time homomorphic signal analysis to seismic wavelet estimation

The use of homomorphic systems to deconvolve seismic reflection and teleseismic data has been proposed and explored by a number of researchers with varying success. A careful study of the methods employed reveals a number of problems involving both the class of characteristic systems used and their numerical implementation. Furthermore, the analysis strategies used introduce deterministic constraints on the estimation of the seismic wavelet which may lead to serious problems in determining the earth impulse response. Several novel results are presented in this paper. A class of homomorphic systems matched to the bandpass nature of seismic signals is discussed and improved and more reliable implementation algorithms are developed. The concept of short-time wavelet estimation by homomorphic filtering is introduced. This technique takes into account the specific time-varying characteristics of seismic traces. Strategies for homomorphic wavelet estimation are proposed and illustrated. The recovery of the earth impulse response may then be accomplished by combining homomorphic wavelet estimation with parametric inverse filtering.