Wave propagation in heterogeneous media can be modeled efficiently with the parabolic equation method, which has been extended to problems with homogeneous anisotropic layers [A. J. Fredricks et al., Wave Motion 31, 139–146 (2000)]. This approach is currently being extended to the heterogeneous case, including piecewise continuous vertical dependence and horizontal dependence that is relatively gradual but which may be large over sufficient distances. Vertical dependence is included by applying appropriate heterogeneous depth operators in the equations of motion. Horizontal dependence is included by extending the single-scattering solution [E. T. Kusel et al., J. Acoust. Soc. Am. 121, 808–813 (2007)] to the anisotropic case. [Work supported by the Office of Naval Research.]

Parabolic equation solutions have recently been improved to increase accuracy for range-dependent problems involving sloping fluid-solid interfaces. One improvement is a formulation using a new set of variables that includes a term proportional to the normal stress at a horizontal interface [J. Acoust. Soc. Am. 127, 1962 (2010)]. These variables lead to horizontal interface conditions with only first-order derivatives, which is valuable for implementing techniques such as energy conservation or single scattering that handle range dependence. This improvement is extended to problems that involve layered poro-elastic media that occur in shallow water environments. An analogous formulation is derived for the field variables in a poro-elastic layer. The horizontal interface conditions have similar characteristics as in the elastic case. Solutions are obtained for layered environments and are benchmarked to confirm accuracy. [Work supported by the ONR.]

The parabolic equation method implemented with the single-scattering correction accurately handles range-dependent environments in elastic layered media. Interfaces between elastic media may be treated efficiently by subdividing into a series of two or more single-scattering problems [Küsel et al., J. Acoust. Soc. Am. 121, 808–813 (2007)]. In addition to environmental waveguide parameters, the procedure uses several computational parameters. The impacts of the number of interfacial scattering problems, an iteration scheme convergence parameter, and the number of iterations for convergence are shown on the accuracy and efficiency of the method. In particular, selection criteria for these parameters are developed. Fourier transforms and syntheses generate time-domain solutions for seismic applications of interest. Examples for model waveguides show features of Rayleigh and Stoneley wave propagation, and comparisons with solutions from other methods are shown. [Work supported by the ONR.]

The parabolic equation method with a single-scattering correction allows for accurate modeling of range-dependent environments in elastic layered media. For problems with large contrasts, accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single-scattering problems. This approach generates several computational parameters, such as the number of interface slices, an iteration convergence parameter τ, and the number of iterations n for convergence. Using a narrow-angle approximation, the choices of n=1 and τ=2 give accurate solutions. Analogous results from the narrow-angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces. The approach is applied to a generic ocean waveguide that includes the generation of a Rayleigh interface wave. Results are presented in both frequency and time domains.

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.