Page 12 - Winter2014

James F. Lynch and Timothy F. Duda Woods Hole Oceanographic Institution Woods Hole, MA 02543
John A. Colosi
Naval Postgraduate School Monterey, CA 93943
Acoustical Horizontal Array Coherence Lengths and the “Carey Number”
The late Bill Carey came up with the rule of thumb that the horizontal array coherence length in shallow water is, on the average, 30 wavelengths.
Introduction
Though the genesis of this paper is of a somewhat sad origin (the passing of close friend and colleague Bill Carey of Boston University last year) the outcome is repre- sentative of what occurred when people interacted with Bill – he made them think about interesting problems. In organizing and participating in some memorial sessions for Bill (at both the Underwater Acoustics meeting in Corfu, Greece and the upcom- ing Providence ASA meeting), we looked at one of Bill’s signature research areas, horizontal array coherence, and decided to focus on that. It is an area that all of the authors have worked in, and so we thought we could nicely elucidate the physics of one of Bill’s coherence results, specifically that the horizontal array coherence length in shallow water is measured to be ~20-40λ (average 30λ) at frequencies around 400 Hz (Carey, 1998). However, the physical origin of that number, and even the measure- ments of it, were not as simple to summarize as we thought, and so in digging back into Bill’s research, we again were given something to think further about.
Array signal coherence is of interest because it (in part) determines the overall array gain, the amount an array “amplifies” a signal against the noise. Specifically, it determines the signal re- lated part of the array gain. For an N element array, array gain (AG), quoting Urick (1983) “is by definition the ratio, in decibel units, of the signal to noise of the array to the signal to noise of a single element, so that
The gain of the array therefore depends on the sum of the cross-correlation coefficients between all pairs of elements of the array, for both noise and signal.” The array signal gain (ASG), which is the quantity that Carey concentrated on in his work, is the numerator of the above AG expression. The noise effect which appears in the denominator, is also a very interesting and complicated entity, but it is not the focus of what we want to look at here. Regarding
the array gain for a simple case, if the signal is coherent, the ASG against white noise goes as N 2 whereas if the signal is incoherent, it goes as N. The difference between an N and an N 2 dependence can be many dB of gain, so understanding the ASG is of great practical value.
10 | Acoustics Today | Winter 2014