Optimum multichannel velocity filters

Abstract

Abstract Optimum systems have been developed to correspond to the sub-optimum moveout discrimination systems presented previously by several authors.The seismic data on the lth trace is assumed to be additive signal S with moveout tau l , coherent noise N with moveout tau l , and incoherent noise U l , expressed byEquationwhere S, N, and U l are independent, second order stationary random processes and tau l and tau l are random variables with prescribed probability density functions. The signal estimate S is produced by filtering each trace with its corresponding filter G l and summing the outputsEquationWe choose the system of filters to make the signal estimate optimum in the Wiener sense (minimum mean-square error of the signal ensemble).For the special cases discussed, the moveouts are linear functions of the trace number l determined by the moveout/trace tau for signal and tau for noise. Thus, the optimum system is determined by the probability densities of tau and tau together with the noise/signal power spectrum ratios R N (f) and R U (f). In comparison, suboptimum systems are controlled completely by the cut-off moveout/trace tau c . Events whose moveout/trace falls within + or -tau c of the expected dip moveout/trace are accepted, and those falling outside this range are suppressed. Suboptimum systems can be derived from optimum systems by choosing probability densities for tau and tau that are uniform within the above ranges and letting R U be very large. Optimum systems have increased flexibility over suboptimum systems due to control over the probability density functions and the power spectrum ratios and allow increased noise suppression in selected regions of f-k space.