Improved ray calculations in shallow water

Abstract

The lateral displacement of a bounded beam which is totally reflected from an interface is well-known. This beam displacement is used to modify the ray paths in a ray model of shallow water propagation in the simple Pekeris channel. Inclusion of the beam displacement for total reflection at the bottom greatly alters the eigenray distribution. Coherent summation of pulses traveling along each eigenray yields a series of arrivals with the depth dependence characteristic of normal modes. The calculations are in good agreement with experimental data obtained at 5.1-km range in water 50 m deep for four cycle pulse transmissions in the range 60–140 Hz. There is also good agreement with the results of normal mode calculations and exact analytic expressions for the mode eigenvalues and group velocities are obtained using the actual eigenrays of the problem. The improved ray method appears to be as good as normal mode theory for practical calculations in shallow water.