Time-domain solutions for Rayleigh and Stoneley waves using the single-scattering parabolic equation method.

Abstract

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.]

Shallow Water Propagation

“…Benchmarking provides essential validation throughout the development, and one paper [2] shows applications to high quality data obtained from an NRL experimental series using elastic slabs. Additional calculations [3] show excellent agreement with benchmarks for problems with relatively large changes in sound speeds and with range-dependent interface waves. An important extension [4] is to range-dependent transversely isotropic (TI) elastic sediments which occur in coastal and shallow regions.…”

“…• Accuracy is also verified by comparing with benchmarks for problems with large changes in sound speeds and with waves on range-dependent elastic interfaces [3], and guidelines for selection of computational parameters are determined.…”

“…• Recent progress for range-dependent elastic sediments is extended to poro-elastic sediments [7], by employing the same propagation variables and computational techniques as in [3].…”

“…• Continuing projects with Dr. Michael Collins [3]- [8] also include a monograph on state of the art parabolic wave equation models and applications [23], for which principal research results are nearly complete and chapter drafts are prepared.…”

Shallow Water Propagation

“…This PE method has improved accuracy over others, as demonstrated by applications [3] to high fidelity data from propagation over an elastic slab with variable bottom slopes in a large NRL tank. 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.…”