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ROYAL NORWEGIAN COUNCIL FOR SCIENTIFIC AND INDUSTRIAL RESEARCH NORWEGIAN SEISMIC ARRAY, P.O. BOX 51, N-2007 KJELLER, Norway
DEPARTMENT OF STATISTICS UPPSALA UNIVERSITY, UPPSALA, Sweden
Abstract
In the 1960's, Lincoln Laboratory, Texas Instruments, and Teledyne-Geotech research groups were assigned tasks related to the design of the large-aperture arrays LASA and NORSAR resulting in a number of sophisticated processing techniques for additional signal-to-noise ratio (SNR) enhancements relative to conventional delay-and-sum processing (or beamforming). At that time, these techniques (essentially variations of Wiener filtering theory) did not prove a great success, and part of the lame was attributed to inadequate computing power for handling large data volumes in a nontrivial manner. However, with the present advent of miniarrays and relatively much faster computers, optimum array processing techniques are again in vogue. In this respect, we have examined different weighting schemes based on the noise structure as manifested in the noise covariance matrix using data from the prototype NORESS array in Norway. Results are as follows: (i) with strong correlations between sensors the processing gain is obtained essentially by deleting "redundant" sensors; (ii) with strong-to-moderate negative correlations, SNR gain in excess of 
is obtained by giving large weights to a few sensors to ensure destructive interference; (iii) with weakly structured noise conventional beamforming is very efficient as expected; and (iv) observed noise correlation curves exhibit rather strong spatial variation, i.e., depend on both phase velocity and azimuth. Also the time stationarity of the noise covariance matrix is rather weak, thus diminishing the expected gain from the optimum weighting schemes in a real-time context. Some experiments were also performed with a simplified maximum-likelihood filtering processor, and in this case approximate gains were obtained even for strongly correlated noise. Because processing gains implicitly reflect sensor geometry, criteria for array configurations are discussed in the light of the results obtained from the optimum processing experiments. Essentially, an array aperture of 3 km, like that of NORESS, represents high-pass filters with a lower cut-off at about 2 to 3 Hz while signal decorrelation and signal beamforming losses ensure that the array acts as a low-pass filter with a cut-off at about 6 Hz. However, using subsets of the array's original 25 sensors with correspondingly smaller apertures, the array's operational bandwidth can efficiently be shifted toward higher frequencies, say 4 to 8 Hz. Besides array aperture, the sensor interspacing distribution is an important parameter for judging array performance. SNR spectra for events with signal paths in oceanic and active tectonic belt regions peak at about 3 Hz, and for shield areas between 5 to 7 Hz. Finally, future array developments are discussed in view of recent initiatives within the seismological community concomitant with advances in communication and microprocessor technologies.
Footnotes
* Present address: Earth Resources Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
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