Estimation Of A Time-varying Seismic Autocorrelation Function†Paper presented at the 41st Annual International SEG Meeting, November 11, 1971, Houston, Texas. Manuscript received by the Editor February 24, 1972; revised manuscript received July 26, 1972.-

Abstract The autocorrelation function of a seismic trace provides information about the generating wavelet needed for optimal processing. The classical time-averaging technique used to estimate the autocorrelation, however, fails for the commonly encountered time-varying autocorrelation resulting from progressive wavelet distortion. To estimate a time-varying autocorrelation, an iterative computational procedure is proposed from which a sequence of progressively improved estimates of the autocorrelation is obtained. In the time-invariant case, the algorithm reduces to the usual time-average procedure applied to several different “windows” along the trace, and convergence occurs on the first step. For a “slowly” varying autocorrelation, however, the procedure tends to iteratively correct the bias error resulting from time averaging. It is proven that if the time variation for each “lag” value can be modeled by a polynomial of degree N, the sequence of estimates converges (in expected value) to the solution in no more than the integer part of (N+2)/2 steps. Examples are included to illustrate the procedure.