Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness

Abstract

Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment.

Shallow Water Propagation

“…A key physical and computational difficulty is that the energy spectrum is much broader in wave number space than for fluid sediments. Our latest PE method [1] evolved from a series of steps: formulating with non-standard dependent variables; applying coordinate rotations at ranges of bathymetry slope changes; using single scattering corrections at stair step approximations of changes in sediment interfaces and volume parameters; and incorporating a procedure to reduce large changes at stair steps by introducing artificial interfaces ("slices") as needed. The capabilities of the method continue to increase, for example by accommodating both topography and stratigraphy in beach, island, and coastal environments [2].…”

“…(A) The first propagation method that combines a single scattering approximation with a coordinate rotation technique provides a major new capability [1] for accurately and efficiently handling ocean seismo-acoustic problems with range-dependent bathymetry and variable thickness sediment layers. An extension is developed for elastic media with topographic variations as in beach, island, and coastal problems [2], for which Scholte interface waves can evolve into Rayleigh waves.…”

Convergence of a linearized second-order BDF-FEM for nonlinear parabolic interface problems

“…Parabolic interface problems often occur when the computational domain consists of two different media, which have applications in many physical and engineering problems, such as underground water flow [1], seismo-acoustics [2], and flow in porous media [3]. Due to the discontinuity of the coefficients along the interface, the global regularity of the solution is very low [4], though the solution is smooth in each subdomain.…”

Experimental testing of the variable rotated elastic parabolic equation

“…The variable rotated parabolic equation method is an effective approach for handling rangedependent problems, 1,2 and the accuracy of this approach has been established for a limited set of seismo-acoustics problems through numerical and experimental benchmarking. 3,4 Spectral solutions are also being considered to treat these types of problems. [5][6][7][8][9] In this paper, results are presented from the second of a series of experiments designed to compare elastic variable rotated parabolic equation solutions with data from an experiment involving a slab of polyvinyl chloride (PVC) suspended in water.…”