Split-step Padé-sine method for wide-angle parabolic equation modeling in penetrable-bottom waveguides

wide-angle parabolic-equation (PE) model based on a split-step Padé-sine method, denoted sspsPE, is developed for underwater acoustic propagation in penetrable-bottom waveguides. The formulation extends Küsel’s propagator factorization to penetrable-bottom waveguides through a hybrid sine pseudospectral/finite-difference evaluation of the leading first-order factor, while the higher-order correction is treated by a Padé approximation. Conservative finite differences account for density variations and discontinuities, and a single-scatter condition accounts for transmission at vertical staircase interfaces. Numerical comparisons with the split-step Padé model (sspPE) and other PE models are performed on the same computational grids in wedge-shaped and Munk waveguides. The sspsPE model generally yields smaller complex-pressure errors over the full water column and better agreement with the reference interference patterns, with improvements most evident in the 300-Hz wedge case and long-range Munk propagation.