Parabolic equation modeling of anisotropic waves in heterogeneous media.

Abstract

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.]

Shallow Water Propagation

“…Our approach is based on the Biot poro-elastic theory, which is the most common model for ocean sediments. The only published poro-elastic PE appeared over a decade and a half ago, and even with an extension for sediment anisotropy [5], its computational capabilities are too limited for applications. It is essential that recent progress for elastic sediments be generalized to layered poro-elastic media.…”

“…(2) New calculations for elastic and poro-elastic sediments • Range-dependent transversely isotropic elastic sediments, which are a feature of many coastal regions, are treated by a PE new formulation [5] that enables evaluation of the relative significance of anisotropic effects on propagation.…”

“…• Continuing projects with Dr. Michael Collins include [5] and a monograph on new parabolic wave equation models and applications [21], for which the principal research results are nearly complete and chapter drafts are prepared.…”

Shallow Water Propagation

“…• Generalization of the PE method permits treatment of range-dependent transversely isotropic elastic sediments [4] which occur in many coastal regions, and examples of anisotropic effects on propagation are provided.…”

Shallow Water Propagation

“…The accuracy of the approach is verified by comparisons with benchmarks for problems with large changes in shear and compressional sound speeds and with waves on range-dependent elastic interfaces [4], and selection rules are provided for computational parameters. An additional capability is added to the method for handling range-dependent transversely isotropic elastic sediments [5] that occur in many coastal regions. The first propagation model with rangedependent capabilities for a class of transversely isotropic poro-elastic sediments [6] shows the feasibility of PE approaches.…”