Energy-Conserving Parabolic Wave Equations

摘要

Energy-conserving versions of the parabolic wave equation model used forunderwater sound propagation are derived for stratified media and variable coefficients (depth-dependent and range-dependent). The energy-conserving PWE models are first given for time-dependent problems, showing the difference between exact and approximate energy conservation rules and the corresponding error growth equations most clearly. In the following sections, corresponding PWE models are derived for the Helmholz equation and finite-difference schemes. For problems with sloping interfaces, a simple transformation to a new coordinate system is introduced. Such a modification is shown to be necessary for higher-order PWE models, but also for low-order models, it simplifies the formulation of appropriate interface conditions.