Stacking of noisy seismic traces via maximum entropy with a correlation coefficient constraint

A method is developed for stacking a gather of seismic traces in cases where there is a wide variation in the noise power of the traces. Each trace in the stack is weighted by a probability. The entropy of the probability distribution is maximized subject to the constraint that the expected value of the correlation coefficient of each trace with respect to the rest of the gather is fixed. A simple technique for estimating the best maximum entropy result is proposed. Results are presented showing that for a 64-fold variation in noise power across the gather, the method yields a best result which is up to five times more effective than a brute stack in suppressing random noise, while for this same case the estimate of this result is up to three and one-half times more effective than the brute stack. For this case, with a gather 3-4 times smaller, the maximum entropy stack gives as good a signal-to-noise ratio as a brute stack.