Use of calculated sound fields and matched-field detection to locate sound sources in shallow water

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) exp[i (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: [43]60.20; [43]30.82.