A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms

Abstract

A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.

Modal propagation of ocean acoustic waves generated by earthquakes

“…It is vertically divided between a fluid ocean with a 3000 m mean depth and a solid crust 7 km thick. All sides, except the top sea-surface, are Perfectly Matched absorbing Layers (PML), which avoid unwanted reflections that would pollute the results [8]. The crust with the absorbing layer at ).…”

Calculation of Hydroacoustic Propagation and Conversion to Seismic Phases at T-Stations

“…Calculations are performed using the two-dimensional spectral element code SPECFEM2D 1 (Tromp et al 2008;Xie et al 2016). We place a point explosion source at the distance shown in Table 1 Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00024-020-02556-3) contains supplementary material, which is available to authorized users.…”

“…In these earlier projects, we used the finite difference code TRES2D (McLaughin and Day 1994) for this purpose. For this project we are using the spectral element code SPECFEM2D (Bottero et al 2016;Xie et al 2016). SPECFEM2D is a higher order code that uses the Message Passing Interface (MPI) 2 to divide the calculation across multiple processors, so it enables much larger problems to be solved in a reasonable time.…”

An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics

“…However, finite-element models have the drawback of requiring large computational resources compared to approximate numerical methods that do not solve the full-wave equation, for instance the parabolic approximation 35 . Despite the recent development of very efficient perfectly matched absorbing layers for the study of wave propagation in fluid-solid regions 45 , which allows for a drastic reduction of the size of the computational domain, performing realistic 3D simulations in ocean acoustics still turns out to be difficult because of the high computational cost incurred. The main reason for this lies in the size of the domains classically studied in ocean acoustics that often represent thousands of wavelengths.…”

“…The main reason for this lies in the size of the domains classically studied in ocean acoustics that often represent thousands of wavelengths. A first attempt was presented at low frequency in Xie et al 45 , but when higher frequencies are required in the context of full-wave simulations, 2D simulations are currently still the only option. In previous work 8 on underwater acoustics, we used a 2D Cartesian (plane strain) version of the spectral-element method.…”