Simultaneous correction for divergence and deconvolution without changing industrial practice

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.