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Ref.: Journal of Acoustical Society of America, Vol142(1), pp. 55-60, June 2017 (doi).
Abstract: The array invariant theory was generalized by incorporating the waveguide invariant Beta, referred to as the generalized array invariant. In this paper, the generalized array invariant is extended to mildly range-dependent environments with a sloping bottom where the waveguide invariant is variable in range. Assuming knowledge of the bottom slope, the array invariant can be applied iteratively to estimate the source range starting with Beta=1 (i.e., range-independent), which converges toward the correct source range by updating Beta at the previously estimated range. The iterative array invariant approach is demonstrated using a short-aperture vertical array (2.8-m) in a sloping-bottom shallow-water waveguide from the Random Array of Drifting Acoustic Receivers 2007 experiment, where a high-frequency source (2–3.5 kHz) close to the surface (6-m) was towed between 0.5 and 5 km in range with the water depth varying from 80 to 50 m