Parabolic equation solution for a transitional solid seafloor

Abstract

The study of sound propagation in the ocean has a wide range of applications and is interesting from a mathematical perspective. Parabolic equation solutions, resulting from factoring the parabolic wave equation, have been formulated for sound propagation in a variety of propagation environments. In this work, an idealized environment, that of a water layer, overlying a denser fluid sediment layer (termed a transitional solid), overlying an elastic basement is considered. Parabolic equation solutions for the acoustic pressure field are advantageous as they accurately handle range dependence and are computationally efficient. Using rational-linear approximations for the depth operator, which arises in the parabolic factorization, in an azimuthally symmetric outgoing wave equation gives accurate and efficient results for wide propagation angles. Parabolic equation solutions for sound propagation in the ocean differ in their treatment of the layered seafloor. Solutions that treat the sediment as a fluid and elastic, poro-elastic, and poro-acoustic solids are in use. An improved model is developed and implemented for a stratified environment with transitional solid sediments, sediments that may accurately be treated as a fluid. This involves strictly enforcing interface conditions, accomplished numerically by eliminating nonphysical values that appear near the interface in a Galerkin-inspired discretization of a parabolic equation range-marching solution. The implementation is verified by comparing it to existing models that treat the sediment as a fluid or as an elastic solid. Comparisons are drawn between fluid, elastic, and poro-elastic sediment treatments.