Processing a Partially Coherent Large Seismic Array for Discrimination

A stochastic model has been proposed to characterize the teleseismic short period P-wave signal variations observed within a Large Aperture Seismic Array (LASA). The model asserts that, in the frequency domain, the received signal is equal to some average signal multiplied by a random gain and phase. Within a Montana LASA subarray the mean value of the modulus squared of the random term can be roughly approximated by 1 + 0.18f, where f is frequency. For sensors drawn from the full LASA aperture the value is approximated by 1 + 2. Of. An incoherent signal processing method, spectraforming, is introduced as a viable alternative to beamforming for obtaining spectral information at frequencies above about 1.0 Hz. The spectraform is essentially the average power in sensors with a correction subtracted for background noise power contributions. It is demonstrated that although beamforming will give more noise rejection than spectraforming the latter can be superior in terms of output signal to noise ratio when input signal variations between sensors are large. Expressions have been obtained for the signal power spectral density expected from various modes of processing. Spectra from subarray beams and sums, spectra from array beams and beams of subarray sums, and spectraforms are all considered. Results show for example that the event power output from spectraforming, beamforming of individual sensors, and beamforming of subarray sums will decrease in that order. In the case of actual events considered,the amounts of loss at 3. 0 Hz, relative to spectraforming, are about 10 and 20 dB respectively. Accepted for the Air Force Joseph R. Waterman, Lt. Col., USAF Chief, Lincoln Laboratory Project Office