An analytical formulation for the calculation of the range and depth-dependence of propagation loss in isospeed water is introduced. The range-dependent bathymetry is handled with Weston's ray invariant approach, requiring a gradually varying water depth. The depth dependence of propagation loss is formulated using a transformation from an incoherent mode sum to an integral over angle, in the adiabatic approximation, and the results obtained in this way are tested by comparison with a full adiabatic normal mode sum. The validity of the adiabatic approximation itself is then investigated by means of a comparison with parabolic equation and coupled normal mode results for selected test cases from the Weston Memorial Workshop, held at the University of Cambridge in April 2010. Propagation loss calculations based on different methods are compared. The proposed analytical approach provides practical, fast and accurate results.
- Mathematical model
- Propagation losses
- Eigenvalues and eigenfunctions
- depth dependence
- flux theory