No abstract

Several alternative parabolic approximations to the reduced wave equation and their numerical solution are investigated for underwater acoustics applications. Parabolic approximations are derived by splitting the wave equation into transmitted and reflected components. An exact splitting operator is found, and further parabolic approximations for the transmitted fields are based on approximations to this operator. For the case of a range-independent environment, the resulting parabolic approximations are compared with normalmode theory. The efficiency with which numerical results can be obtained is discussed, and an example of propagation from shallow to deep water is given.Subject Classification: 30.20, 20.15; 20.40.

A perturbation technique is applied to derive a composite-roughness theory for acoustic scattering from the sea surface. The leading term in the expansion obtained is the well-known result obtainable using ad hoc arguments. Higher order terms are evaluated to assess their contribution to the high-frequency monostatic backscattering strength of the sea. It is concluded that the leading term in the perturbation expansion provides an excellent approximation.

Variations of seabed parameters, particularly the acoustic compressional velocity relative to that of the water column, have a very strong effect on the predicted magnitude of the propagated acoustic field. In many cases, the sensitivity of the predicted losses to the assumed seabed parameters is sufficiently severe to render the predictions meaningless. In this article, coupled-mode theory is employed to study how the presence of lateral seabed inhomogeneities affects this sensitivity. The dependence of predicted propagation losses on sediment sound speed is first examined for horizontally stratified sediments; then a rough layered structure of clay-silt interbedded with sand is assumed. With the introduction of rough sub-bottom layering, coupling occurs between modes, so that the conversion of energy into progressively higher-order modes, which attenuate rapidly, becomes an important loss mechanism. The extent to which acoustic energy penetrates the seabed and interacts with the sub-bottom inhomogeneities is governed by the sediment sound speed. Hence, the mode coupling that is induced is simply another loss mechanism dependent on sediment sound speed, leading to an increase in sensitivity to this parameter. Studies to determine the effect of inhomogeneous sediment layering on the transverse horizontal spatial coherence of the propagated field reveal that, even in the presence of mode coupling, the coherence remains high over many acoustic wavelengths, in agreement with measured data trends.

An elegant finite-difference technique applicable to the parabolic wave equation is developed to handle the boundary conditions at the interface between two media with different sound speeds and densities. Continuity of pressure and continuity of the normal component of particle velocity are preserved at the interface. The method is designed to be implicit and is unconditionally stable. A complete mathematical treatment for the case of a horizontal interface is described.