Dept. of Elec. Eng., Queen's Univ., Kingston, Ontario K7L 3N6, Canada
David J. Thomson
Defence Res. Estab. Pacific, FMO Victoria, BC V0S 1B0, Canada
Density variations are easily analyzed in the context of finite difference parabolic equation (PE) solvers by discretization of an appropriate differential operator. In split-step Fourier solution algorithms, however, variations in the density (rho) are instead modeled by adding terms to the refractive index. Since these extra terms depend on derivatives of (rho), geoacoustic density profiles must be smoothed appropriately to remove any step discontinuities. In this paper, a new hybrid method is proposed for treating density inhomogeneities in the split-step PE. This approach involves splitting the differential operator into density-independent and density-dependent components. While the former component is propagated using the split-step Fourier technique, the influence of density changes is computed through a finite difference procedure. Such an algorithm is especially attractive as it may be transparently incorporated into the recently proposed hybrid split-step/finite-difference and split-step/Lanczos solvers [J. Acoust. Soc. Am. 96, 396--405 (1994)]. Both the hybrid and the standard finite-difference procedures are applied to a shallow-water test case involving jump discontinuities in both the sound speed and the density and are found to be in excellent agreement with reference solutions.