简介

Advances in asymptotic methods, computing power, and numerical algorithms have invigorated research in the analysis of wave propagation. Professor Bill Siegmann and a group of doctoral and masters' students work actively together on variety of propagation problems. The principal applications involve acoustic transmission in the ocean, and others have been directed toward both electromagnetic and acoustic waves in the atmosphere. New parabolic wave equations and new solution methods are under development, in order to account for dominant variations of the propagation medium. These methods, like their predecessors constructed in recent decades, are based on accurate asymptotic approximations to scalar and vector wave equations. The continued success and appeal of parabolic approximations result from the very efficient computational marching algorithms that are available for their solution. Applications of our new results include sound transmission through shallow-water regions (especially with substantial changes in the propagation direction, including interactions with beaches and islands), improved procedures for ocean acoustic tomography (in which ocean properties are estimated using acoustic signals), and sound propagation that penetrates the ocean bottom (incorporating effects of the elasticity or pro-elasticity of sediment layers). Increasing the computational efficiencies of high-order parabolic approximations is also under investigation. Other problems concern the prediction of the propagation of pulse signals in complex ocean channels. New methods are being constructed for describing the nonlinear effects of relatively strong pulse sources. Computationally accurate and efficient approximations of parabolic type are providing new capabilities for solutions of these problems. Representing random ocean variablities in novel and efficient ways for estimation of propagation statistics is also under active study.