A numerically efficient global matrix approach t o the solution of the wave equation in horizontally stratified environments is presented. The field in each layer is expressed as a superposition of the field produced by the sources within the layer and an unknown field satisfying the homogeneous wave equations, both expressed as integral representations in the horizontal wavenumber. The boundary conditions t o be satisfied at each interface then yield a linear system of equations in the unknown wavefield amplitudes, t o be satisfied a t each horizontal wavenumber. As an alternative t o the traditional propagator matrix approaches, the solution technique presented here yields both improved efficiency and versatility. Its global nature makes it well suited t o problems involving many receivers in range as well as depth and to calculations of both stresses and particle velocities. The global solution technique is developed in close analogy to the finite element method, thereby reducing the number of arithmetic operations t o a minimum and making the resulting computer code very efficient in terms of computation time. These features are illustrated by a number of numerical examples from both crustal and exploration seismology.

Abstruct-Ship noise received on a horizontal array towed behind the ship is shown to he useful as a potentially diagnostic tool for estimating local acoustic bottom properties. In numerical simulations, tow-ship noise which bounces off the bottom is processed on a beamformer that shows the arrival angles; the beamformer output is readily interpreted by relating it to the Green's function of the acoustic wave equation. Simple signal processing is shown to be sufficient to extract the propagation angles of the "trapped" (i.e., propagating) modes of the acoustic waveguide. By relating the trapped modes to a basic geophysical model of the bottom, one can predict acoustic-propagation conditions for a particnlar bottom-interacting ocean acoustic environment.

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