Modeling of reciprocity in the time domain using the parabolic equation method

Transmission loss in the time domain is carefully defined, and it is shown to be reciprocal on the basis of the reduced wave equation in fully range-dependent and lossy oceanic environments when currents and other reciprocity-breaking effects are absent. Under the same conditions, it is shown theoretically that time-domain transmission loss as computed by the two-dimensional parabolic equation (PE) method is reciprocal. In a range-dependent bottom-limited ocean, we have numerically computed the time-domain transmission loss and have independently computed its reciprocal using the parabolic equation method and split-step Fourier algorithm. The numerical results confirm that the PE model is accurately reciprocal.