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The calculated complex sound field cj for sensor j at depth zj and range rj from a sound source of frequency ω and depth z0 can be written in the normal-mode form as cj= (2π/rj) 1/2 ΣmUm (z0) Um (zj) expi (kmrj−ωt). Here, km is the horizontal wavenumber of mode m and Um is the depth function of the mth mode. It is proposed that the detection factor DF=ΣJj=1 cjc*k〈 (c0jc0k*) *〉 is a reasonable measure for determination of whether a set of sound pressure measurements c0j for j=1, 2, ⋅⋅⋅, J is a good fit to calculated values of cj for an assumed location of the sound source. Here 〈 〉 denotes a time average and * denotes complex conjugate. Several examples are shown where a set of c0j are calculated for a given source location in a typical shallow water channel and values of DF are then calculated for a grid of range depth or range azimuth locations. Subject Classification: 4360. 20; 4330. 82.
Homer P. Bucker (1976) studied this question.