With the advent of high-speed digital electronics, it has become feasible to use digital computers and special purpose digital processors to perform the computational tasks associated with signal reception using an antenna or directional array. The purpose of this paper is mainly tutorial, to describe mathematically and intuitively the fundamental relationships necessary to understand digital array processing. It is hoped that those readers with a background in antenna theory or array processing will see some of the advantages digital processing can offer, while those with a background in digital signal processing recognize the array processing area as a potential application for multi-dimensional signal processing theory.

Fundamentals of digital array processing

Earthquake magnitude — recent research and current trends

The spac (Spatial autocorrelation) method to analyze ambient vibration records was introduced by Aki (1957). Currently, this method is being used for the analysis of microtremor data from an array of stations: crosscorrelation functions are computed between pairs of stations, and then averaged for different station pairs, at the same interstation distance but with different orientation. In this article we propose the idea of exploiting recordings of microtremors over long times as a substitute for spatial averaging, as was suggested in Aki (1957). This idea has several advantages. The two most important are, first, that it is not required to obtain simultaneous recordings using an array of stations, whose locations must obey a very rigid scheme; and second, the ability to obtain results for a large number of closely-spaced distance intervals. Our proposal is tested using data from the Parkway, Wainuiomata, temporary array. These data are supplemented with additional measurements performed during February 2003, to resolve an uncertainty regarding the low-frequency part of our results. Given the irregular distribution of our array, we are able to obtain results for many different station pairs. The phase-velocity dispersion curves we derive from our measurements, interpreted with the spac method, are compared with previous results in this sedimentary basin. Our results suggest that the spac method is more general than appears in recently published papers.

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An Alternative Approach to the spac Analysis of Microtremors: Exploiting Stationarity of Noise

An investigation has been made of the multipath propagation of Rayleigh waves by using data obtained from the large aperture seismic array (LASA). The use of the LASA in conjunction with a high-resolution analysis technique provides a greater angular resolution and accuracy than was previously possible for the analysis of the multipath propagation. Measurements have been made of this phenomenon for the Rayleigh waves of 26 events distributed at various azimuths and distances from LASA. On the bas of these measurements reasonably good conjectures are made concerning the actual propagation paths for groups in the 20- to 40-sec period range. It is shown that in almost all cases these propagation paths can be associated with refractions and reflections at the continental margins.

/pdf/analysis-of-rayleigh-wave-multipath-propagation-at-lasa-4zomq7w90g.pdf

Analysis of rayleigh-wave multipath propagation at lasa*

Signal Processing and Frequency-Wavenumber Spectrum Analysis for a Large Aperture Seismic Array*

Processing of seismic data from LASA can be accomplished by simple delay and sum or beam forming, weighted delay and sum or by maximum‐likelihood filtering. It is found that band‐pass prefiltering the data has a considerable effect on the results. The extra gain produced by maximum likelihood filtering does not justify use of this process on‐line, but could justify off‐line processing in special cases. The spurious precursor introduced by maximum‐likehood processing, and shown to be caused primarily by the signal amplitude scatter within a subarray, can be effectively reduced by using amplitude equalization. The signal amplitude scatter within a subarray, and between subarrays, does not degrade seriously the performance of the signal processing. The effectiveness of the processing depends not only on the array spatial filtering ability, but on differences in absolute level of the noises in the various sensors. Our experience in processing a weak event whose apparent magnitude, as averaged over the LASA wa...

Long-period signal processing results for the large aperture seismic array.

: The signal-to-noise ratio improvement obtained with delay-and-sum (DS) processing is discussed for short-period seismic data. It is shown that at least 3 km spacing should be maintained between seismometers at the Large Aperture Seismic Array (LASA) or at another site with a similar noise environment. It is shown that noise coherency measurements are of use in determining the sensor spacing at a new array location. The parameters required for a site survey coherency measurement, such as length of data and resolution, are also presented. The design of subarrays of approximately 20 km aperture is described and array patterns are given.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0655142&Location=U2&doc=GetTRDoc.pdf

R. T. Lacoss

Papers

Long-period signal processing results for the large aperture seismic array.

Design seismic arrays for efficient on-line beamforming