PECan is a Canadian N× 2D/3D parabolic equation (PE) underwater sound propagation model that was developed for matched-field processing applications. It is based on standard square-root operator and/or propagator approximations that lead to an alternating direction solution of the 3-D problem. A 2-D split-step Padé approximation is employed for propagation in range. The 3-D azimuthal corrections are computed using either a split-step Fourier method or a Crank–Nicolson finite-difference approximation. It features a heterogeneous formulation of the differential operators on an offset vertical grid, energy conservation, a choice of initial field including self-starter, and both absorbing and nonlocal boundary conditions. Losses due to shear wave conversion in an elastic bottom are handled in the context of a complex density approximation. In this paper, PECan is described and validated against some standard benchmark solutions to underwater acoustics problems. Subsequently, PECan is applied to several single-frequency test cases that were offered for numerical consideration at the SWAM'99 Shallow Water Acoustic Modeling workshop.

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Acoustic shadowing by an isolated seamount has been studied by examining the multipath propagation measurements obtained in a shot run that passed over the seamount peak. Source depths of 24 and 196 m were used in the experiment. In the acoustic shadow, the propagation loss for the shallow 24-m shots increased by 10-15 dB over the loss expected in the absence of the seamount. Examination of the pressure-time history for shots deployed in the shadowing region revealed that the signals consisted of two components. The first and dominant pulse was determined to be a diffracted wave which passed over the seamount by rough-surface forward scattering and diffraction. The subsequent group of weaker pulses was attributed to the energy which had passed over the seamount by a series of surface-bottom interactions. The shadowing loss increased by 3 dB per octave for frequencies greater than 50 Hz, in agreement with theory, but is appreciably greater than the predicted values at lower frequencies. The shadowing loss for the 196-m shots was about 5 dB less than that observed for the shallower shots.

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The acoustic propagation losses between a 230-Hz cw source and a multi-hydrophone receiving system were measured over Dickins Seamount in the Northeast Pacific. The source was towed at depths of 18 and 184 m. The receiving system had hydrophones spaced in depth from 323 to 633 m. The measurements were made to a maximum range of 130 km with the receiver located at a range of 60 km from the seamount peak. The results show that the seamount cast an acoustic shadow over the receiver, increasing the propagation loss by up to 15 dB, when the source was shallow and in a position which enabled the seamount to intercept all of the deep refracted source energy. Back reflections from the seamount with levels 6 to 13 dB below the direct signal level were present when the shallow source was 3 to 5 'km from the seamount peak. Downslope reflections enhanced the direct signal by up to 10 dB when the shallow source was within 3 km of the peak. Acoustic shadowing and reflection effects were minimal in the results for the deep source because most of the source energy propagated along the sound-channel axis above the seamount peak. The analysis indicates that ray theory is adequate for describing the reflection effects of the acoustic propagation but does not account for all of the acoustic energy in the shadow zone.