ABSTRACT
Underwater Acoustics D. J. Thomson, 733 Lomax Road, Victoria, BC, Canada V9C 4A4, drdjt@shaw.ca
G. H. Brooke, General Dynamics Canada, 3785 Richmond Road, Ottawa, ON, Canada K2H 5B7, Gary.Brooke@gdcanada.com
For over 30 years, one-way wave equations that are derived from applying paraxial approximations to the reduced wave equation have been used to model underwater sound propagation in the ocean [73, 77]. Two criteria that underly the widespread use of parabolic approximations in this context are: (1) long-range sound propagation in the ocean waveguide is dominated by energy travelling at small angles to the horizontal, and (2) backscattered energy can be neglected compared to forward-scattered energy. When these criteria are met, the resulting one-way wave equations are first order in range and therefore admit accurate and efficient numerical solution by marching outward in range in a stepwise manner. Because of this range-stepping procedure, numerical solvers of one-way wave equations are faster and more memory efficient than numerical solvers that are applied directly to the reduced wave equation, e.g., the second order equation. In addition, parabolic equation (PE) models have the inherent capability for accommodating wave propagation in ocean waveguides where the material properties vary along the direction of propagation. Similar one-way propagation criteria are also relevant in other disciplines, e.g., in exploration seismology [15] and radar [57].
