Deconvolution of Seismic Data using Homomorphic Filtering
MASSACHUSETTS INST OF TECH CAMBRIDGE RESEARCH LAB OF ELECTRONICS
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Nonlinear systems which obey a principle of superposition under some operation have been termed homomorphic. A class of homomorphic systems which has found wide application is that involving the filtering of signals that have been combined by convolution. The use of homomorphic systems to deconvolve both seismic reflection and teleseismic data has been proposed and explored by a number of researchers with varying success. The resultant strategies may be globally characterized as a deterministic approach to signal analysis in that no account is made for realistic deviations of the data from the idealized time- invariant seismic models. Several novel results are presented in this paper. A new class of systems, called band-pass homomorphic systems, is discussed, which are matched to the band-pass nature of seismic signals. The implementation of homomorphic systems is improved and made more reliable, through the use of a new phase unwrapping technique. Finally, the concept of short-time homomorphic analysis is introduced and new strategies for wavelet estimation by homomorphic filtering are proposed.
- Numerical Mathematics