Abstract
For considering elastic seismic wave propagation in large domains, efficient absorbing boundary conditions are required with numerical modelling in finite domains. Since their introduction by Berenger, the perfectly matched layers (PML) has become the state-of-the art method because of its efficiency and ease of implementation. However, for anisotropic media, theoretical analysis and numerical experiments show that the PML method is amplifying, that is it exhibits numerical instabilities. Numerical experiments can also exhibit numerical instabilities of the PML when dealing with long time simulations even for isotropic media, especially for finite element methods in unstructured grids. Recently, a new method, called SMART layers approach, has been proposed. This method is shown to be stable even for anisotropic media. The drawback is that the SMART layers are not perfectly matched. We have implemented this new approach in a discontinuous Galerkin method and we illustrate that this method does not exhibit numerical instabilities while PML do for an isotropic elastodynamic simulation. We show that this approach is also competitive with respect to the PML method in terms of efficiency and computational cost.
Highlights
For seismic wave propagation, we often consider the Earth as a semi-infinite medium
The SMART layers is a robust alternative to perfectly matched layers (PML) approaches for elastodynamic simulations
They are easier to implement and for a given absorbing layer width faster than convolutional PML (C-PML). We showed that they are robust in a case where C-PMLs are unstable
Summary
We often consider the Earth as a semi-infinite medium. for the wavefield numerical computation, the domain of computation must be finite and as small as possible. Cerjan et al (1985) have introduced this strategy where a damping profile is designed inside the sponge layer with a significant efficient performance for grazing angles. This technique induces unwanted reflections between the domain of interest and the absorbing layer. As we have observed that these instabilities may dramatically complicate the design of the numerical modelling (different meshes, absorbing layer size and damping profiles should be tried for avoiding these instabilities in the working time window), we investigate an alternative strategy based on the so-called SMART absorbing layers with nice mathematical properties of bounded discrete energy over time introduced by Halpern et al (2011). We shall compare the SMART layers versus the C-PML approach in a specific example where long time instabilities appear
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