The Integral Solution of the Sound Field in a Multilayered Liquid-Solid Half-Space with a Liquid Bottom

Abstract

The integral solution of the wave equation is derived by matrix methods for point sources of harmonic waves in a liquid layer of a multilayered half space of interbedded liquid and solid layers. The solution is in a form convenient for numerical computation on a high-speed digital computer. The integral over wavenumber has singularities in the integrand for guided propagation and is conveniently transformed into the complex plane. By a suitable choice of contours, complex poles are displaced to an unused sheet of the two-leaved Riemann surface, and the integral solution for the multilayered system reduces to a sum of normal modes plus the sum of two integrals, one along the real axis and the other along the imaginary axis. These integrals are evaluated by a Gaussian quadrature formula. Numerical computations are presented for propagation in the ice covered Arctic Ocean.