Approaches for handling sloping fluid-solid interfaces with the parabolic equation method

TL;DR

This paper evaluates various numerical methods for modeling sloping fluid-solid interfaces with the elastic parabolic equation, highlighting their accuracy, limitations, and suitability for different problem scenarios.

Contribution

It systematically compares multiple approaches for handling sloping interfaces, identifying their strengths and weaknesses in different physical and geometrical conditions.

Findings

Single-scattering approach is accurate but fails with large contrast and Scholte waves.

Energy conservation condition breaks down with Scholte wave propagation.

Treating part of the fluid as a solid with low shear speed handles Scholte waves effectively.

Abstract

Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the contrast across the interface is sufficiently large and when there is a Scholte wave. An approximate condition for conserving energy breaks down when a Scholte wave propagates along a sloping interface but otherwise performs well for a large class of problems involving gradual slopes, a wide range of sediment parameters, and ice cover. An approach based on treating part of the fluid layer as a solid with low shear speed handles Scholte waves and a wide range of sediment parameters accurately, but this approach needs further development. The variable rotated parabolic equation is not effective for problems involving frequent or continuous changes in slope, but it provides a high level of accuracy for most of the test cases, which have regions of constant slope. Approaches based on a coordinate mapping and on using a film of solid material with low shear speed on the rises of the stair steps that approximate a sloping interface are also tested and found to produce accurate results for some cases.