The theory of automatic detection at a seismic array by means of an F-statistic is extended to a network of such arrays. The results are generally valid for detection using other statistics. The arrays may have equal or different expected signal-to-noise ratios. Two techniques are discussed: (1) the voting detector in which K out of M arrays must detect; K is determined to be optimum; (2) an incoherent detector which detects on the sum of the subarray detection outputs. For small variation of signal and noise amplitudes between arrays, the detectors are found to be nearly equal in detection capability.
If the standard deviation of log10 (signal/noise) is 0.3, the incoherent detector becomes substantially superior to the voting detector and approaches the capability of a perfect beam of well-correlated signals. This result is in agreement with the few available empirical data.