A normal mode model for acousto-elastic ocean environments

Abstract

A normal mode method for propagation modeling in acousto-elastic ocean waveguides is described. The compressional (p-) and shear (s-) wave propagation speeds in the multilayer environment may be constant or have a gradient (1/c2 linear) in each layer. Mode eigenvalues are found by analytically computing the downward- and upward-looking plane wave reflection coefficients R1 and R2 at a reference depth in the fluid and searching the complex k plane for points where the product R1R2=1. The complex k-plane search is greatly simplified by following the path along which |R1R2|=1. Modes are found as points on the path where the phase of R1R2 is a multiple of 2π. The direction of the path is found by computing the derivatives d(R1R2)/dk analytically. Leaky modes are found, allowing the mode solution to be accurate at short ranges. Seismic interface modes such as the Scholte and Stonely modes are also found. Multiple ducts in the sound speed profile are handled by employing multiple reference depths. Use of Airy function solutions to the wave equation in each layer when computing R1 and R2 results in computation times that increase only linearly with frequency.