Optimum seismic signal estimation with complicated models of coherent and random noise

Abstract

A method is described for optimally seismic signal with a complicated, more realistic as compared with the conventional one, mathematical model of the multichannel record. The method is based on the Wiener criterion and related multichannel filter. The signal is supposed to be contaminated by random noise and an arbitrary number of coherent noise wavetrains. The signal and coherent noise wavetrains bear individual trace‐ independent waveforms, whereas their amplitudes and arrival times vary from trace to trace an arbitrary manner. Random noise is assumed to be a stationary zero‐mean Gaussian stochastic process uncorrelated in space and with the same to within a scale factor, the variance, autocorrelation function on different channels. The signal and coherent noise waveforms are statistically independent zero‐mean stationary stochastic processes and hence uncorrelated with each other and with random noise. For the method to be feasible, two essentially different approaches, which are based on the same record model, have been suggested to determine the necessary signal and noise parameters. The effectiveness of a simplified version of the method in subtracting severe coherent noise is demonstrated with field data.