Comparison of Measured and Calculated Normal-Mode Amplitude Functions for Acoustic Waves in Shallow Water

Wave theory predicts that acoustic propagation in bounded media may occur in discrete normal modes. Each modal field has a distinctive pressure-amplitude distribution and propagation velocity. Also, the strength of mode excitation depends on source depth. Experimental tests of the theory were conducted in a shallow-water area of the ocean. Individual modes were resolved by projecting short pulses and listening at long ranges such that the differing group velocities of propagation among modes temporally separated modal arrivals. Modal fields were sampled from near the surface to near the bottom as the depth of the source was changed incrementally. Data were obtained at frequencies of 400 and 750 Hz and for prevailing sound speed profiles in the water layer having positive, negative, and near zero gradients. Results were compared with wave theory calculations applied to an idealized model of the area. Pressure-amplitude distributions of the modal fields for the first- and second-order modes agreed well with calculated distributions. The dependence of modal field strength on source depth also was examined experimentally. In these measurements, a spatial filtering technique was used to enhance the resolution of modal fields. The predicted dependence of field strength on source depth was confirmed for the first-, second-, and in one case the third-order modes. Higher-order modes, possibly being more highly attenuated, were not observed.