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NTNF/NORSAR, POST BOX 51, N-2007 KJELLER, Norway
Abstract
Noise at the experimental NORESS miniarray (aperture 2 km) exibits a distinct negative correlation minimum, and regional phases, in particular Lg, are only partly correlated over the array. These features are strongly frequency dependent. It is shown that a negative noise correlation minimum is to be generally expected for propagating noise under the condition of azimuthal symmetry. This noise feature can be exploited to optimize the array geometry with respect to signal-to-noise ratio. Whereas NORESS and similar arrays process regional phases with a signal-to-noise ratio gain well below the standard 
gain (in amplitude), an optimized geometry can lead to gains in excess of . Our optimization procedure is tied to the common beam-forming practice at arrays by maximizing the expected value of a gain function expressed as the ratio of quadratic forms of the signal and noise correlation matrices. By means of examples, we demonstrate the effects of frequency range and type of signal; specifically, we compare results for Pg and Lg in five frequency bands between 0.8 and 4.8 Hz or combinations thereof. Pg has a relatively good correlation so the optimum array geometry is mainly determined by correlation minima of the noise. Lg is relatively poorly correlated, and the optimum geometry forms a compromise between the opposing effects of signal and noise correlation decreasing with increasing intersensor distance. As a result, the optimum array configuration for Lg has a smaller aperture, and the gain is less than that obtained for Pg. In practice, the reduced Lg gain is usually compensated for by the larger amplitude of this phase. The experiments performed so far indicate that optimum arrays tend to specific (frequency and phase dependent) sizes, and this feature can be used to infer an optimum number of sensors for the array.
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