Abstract:
Wave propagation in range-dependent ocean environments is often treated by dividing the domain into a sequence of range-independent regions. One-way techniques, such as the parabolic equation method, are applied to efficiently solve the wave equation in each region. The reduced order of one-way wave equations limits the number of boundary conditions that may be imposed at the vertical interfaces between regions. This can result in significant errors as well as instabilities. Accurate solutions may be obtained for many problems by a conserving energy flux at the vertical interfaces [M. B. Porter et al., J. Acoust. Soc. Am. 89, 1058--1067 (1991)]. The standard expressions for energy flux are of limited practical use because they are nonlinear. It is possible to obtain equivalent linear conditions by writing the energy flux integrand as a perfect square involving roots of operators. The acoustic case has been resolved and some progress has been made for the elastic case. Problems currently under investigation include energy-flux conditions for poroelastic and poroacoustic media as well as corrections for problems involving different types of layers. [Work supported by the NRC and ONR.]