Several methods have been developed for computing optimum multichannel filters for use with short-period arrays, but these methods are not widely used. The most commonly used method is delay and sum (DS) followed by high-pass filtering. This, however, fails to exploit fully the spatial-filtering properties of arrays, which if used should reduce the need for frequency filtering. To compute spatial filters requires the auto- and cross-correlation of functions of the noise. Here the correlation functions are specified using noise models rather than the observed noise in an interval (the fitting interval) preceding signal onset. With noise models, it is found that problems of signal distortion and “supergain” are avoided, supergain being excessive noise reduction in the fitting interval, with little reduction or even amplification of the noise outside the interval. Using minimum power (MP) filters, which minimize the noise at the output yet pass signals undistorted, it is shown using data from the 20-element array at Eskdalemuir, Scotland, that signal-to-noise improvements of up to 7 can be obtained during periods when noise levels are above average, the improvement with simple delay-and-sum processing for the same noise sample being only 1.7. The use of noise models allows stable and effective wave-number filters to be rapidly estimated and applied. For those seismograms for which the signal and noise after MP processing have obvious differences in predominant frequency, it is shown that optimum frequency filters can sometimes be used to further improve signal-to-noise ratio (S/N) without significant loss of bandwidth.

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