Abstract

In 1978 Mendel and Kormylo (see, also, Kormylo and Mendel, 1980; and Mendel, 1983) proposed a technique for simultaneously correcting for spherical divergence and performing deconvolution. We showed that when the traditional starting point for deconvolution, namely, the convolutional sum model of a seismogram, is cast into state-variable format, so that deconvolution can be performed by Kalman filtering and optimal smoothing techniques, e.g., minimum-variance deconvolution (MVD) or maximum-likelihood deconvolution (MLD), then one should not make the commonly made divergence correction on the data. Instead, that correction, which is a time-varying one, should be put into the state-variable model for deconvolution. This is possible because MVD and MLD are applicable to time-varying and/or nonstationary systems.

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