Aplicação de deconvolução homomórfica a dados sísmicos

Abstract

A seismic record is often represented as the convolution of a wavelet with the impulse response relative to the reflection path. The process of separating these two components of the convolution is termed deconvolution. There are a number of approaches for carrying out a deconvolution. One of the most common is the use of linear inverse filtering, that is, processing the composite signal through a linear filter, whose frequency response is the reciprocal of the Fourier transform of one of the signal components. Obviously, in order to use inverse filtering, such components must be known or estimated. In this work, we deal with the application to seismic signals, of a nonlinear deconvolution technique, proposed by Oppenheim (1965), which uses the theory of a class of nonlinear systems, that satisfy a generalized principle of superposition, which are termed homomorphic systems. Such systems are particularly useful in separating signals which have been combined through the convolution operation. The homomorphic deconvolution algorithm transforms the convolutional process into an additive superposition of its components, with the result that the single parts can be separated more easily. This class of filtering techniques represent a generalization of linear filtering problems. This method offers the considerable advantage that no prior assumption about the nature of the seismic wavelet or the impulse response of the reflection path need be made, that is, it does not require the usual assumptions of a minimum-phase wavelet and a random distribution of impulses, although the quality of the results obtained by the homomorphic analysis is very sensible to the signal/noise ratio, as demonstrated.