The Parabolic Equation Method Applied to an Ocean Duct with a Parabolic Index of Refraction Squared

The parabolic equation (PE) method is a range dependent, wave theoretic model. Both the modeling and the numerical limitations of this method are investigated for a range independent ocean duct with parabolic index of refraction squared implemented using the split step Fourier algorithm. Equations are given for determining the minimum number of depth sampling points, and the error due to range step size. The error due to range step size is dependent on the sound speed gradient, frequency, and the cube of the range increment. With an appropriate range step size and number of depth sampling points, the numerical errors are negligible. However, in multi-mode propagation, phase and group velocity errors cause the resulting range-versus-loss curve to be shifted in range. This is due to modeling limitations in the parabolic equation which cannot be changed without further theoretical work.