Array filters for attenuating coherence interference in the presence of random noise

Array filters are derived for processing recorded measurements of an array of sensors in order to extract a desired signal buried in a background of interfering coherent and random noises. The intersensor travel times and relative amplitudes of the coherent noise and the statistics of the random noise are assumed to be known. The derivation of the filters is done in two steps. First, the family of array filters which best attenuate the coherent noise and satisfy an all-pass requirement for the desired signal is characterized. Second, the unique member (of array filters) in this family which best attenuates the random noise is determined. These filters are best suited for applications (such as in seismic signal processing) where the coherent noise is predominant over the random noise and, consequently, its suppression is more important.