Adaptive Seismic Deconvolution via the Canonical Variate Analysis

Abstract

The seismic deconvolution problem is posed here as that of estimating an input white-noise sequence of an unknown linear, state variable model from a given output sequence y^kdata adaptive solution of the problem is then offered via a two step approach. A canonical variate analysis is first used to generate a sequence of Markovian state vectors which best fits the given seismic data. These state vectors, in turn, can be used either for a direct estimation of the input white noise sequence, or for an indirect estimation via extraction of the seismic wavelet shape. The method may be regarded as a complement to the white-noise estimators of Mendel in that no prior knowledge of the seismic wavelet is used and the entire data is used for a “block” estimation of the reflectivity sequence. The method is shown to yield good deconvolution performance on synthetic seismograms.

Indexing terms:

• Seismic deconvolution
• Markovian state vector
• Canonical variates