| The aim of this dissertation is to contribute towards a better understanding of acoustic pulse propagation in shallow-water environments. Propagation models and implementations based on the parabolic equation method are developed.;In the first problem, a time-domain model that describes nonlinear wide-angle propagation from a strong, pulsed source is developed. Derivations of wide-angle paraxial approximations are based on a new approach that iterates on a narrow-angle approximation of the two-way equation. The wide-angle equation is solved numerically by splitting into components representing distinct physical processes, and using a high-order upwind flux-correction method to handle the nonlinearity. Numerical results are presented for adiabatic propagation in a shallow, isospeed channel. It is demonstrated that nonlinear effects are significant, even at small ranges, if the peak source pressure is high enough.;In the second problem, a numerical implementation is developed to treat physical mechanisms such as sediment absorption and dispersion in addition to nonlinearity. The wide-angle equation from the first problem is first split into linear and nonlinear component equations. The linear component is solved in the frequency domain where sediment absorption and dispersion are conveniently incorporated using a complex wave number that ensures causality. The nonlinear equation is solved in the time-domain. Examples that demonstrate the need to include both dispersion and nonlinearity are presented.;In the third problem, an implementation is developed for pulse propagation in environments with elastic sediments. A broadband source is decomposed into frequency components which are marched in range using the split-step Pade method. Stable and accurate solutions are guaranteed by the use of improved Pade coefficients calculated using a rotated branch cut for the square-root operator. Numerical examples that demonstrate compressional, shear, and interface waves in elastic sediments are presented and compared with corresponding calculations using fluid sediments. |
