[Paper Review] A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains

Jean‐François Semblat, Luca Lenti+1 more|arXiv (Cornell University)|Sep 6, 2010

Geotechnical Engineering and Underground Structures41 references4 citations

TL;DR

This paper proposes a simple, efficient multi-directional absorbing layer method for simulating elastic wave propagation in unbounded domains using Rayleigh/Caughey damping, readily implementable in existing finite element software. It effectively reduces spurious reflections across various wave types and incidence angles, demonstrating performance comparable to PML in 2D heterogeneous models.

ABSTRACT

The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P-waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc).

Motivation & Objective

• Address the challenge of spurious wave reflections at artificial boundaries in numerical simulations of elastic wave propagation.
• Overcome limitations of traditional absorbing boundary conditions and Perfectly Matched Layers (PML) in complex, heterogeneous, or layered media.
• Develop a method compatible with standard finite element software that leverages existing Rayleigh/Caughey damping formulations.
• Ensure robust performance across diverse wave types (P-, S-waves) and incidence angles in 2D configurations.
• Validate the method against PML in both pure P-wave and complex multi-wave scenarios.

Proposed method

• Adapt the Caughey damping formulation as a multi-directional absorbing layer to dissipate outgoing elastic waves.
• Apply the absorbing layer as a damping zone surrounding the computational domain, with spatially varying damping parameters.
• Use a rheological interpretation to model the absorbing layer as a viscoelastic material with frequency-dependent damping.
• Implement the method within standard finite element frameworks by leveraging pre-existing Rayleigh damping capabilities.
• Optimize damping parameters in the layer to minimize wave reflection across multiple directions and wave types.
• Validate the method through 1D and 2D finite element simulations with varying material heterogeneity and wave incidence.

Experimental results

Research questions

• RQ1 Can a Caughey-based absorbing layer effectively suppress spurious reflections in elastic wave simulations for unbounded domains?
• RQ2 How does the method perform in 1D and 2D models with homogeneous and heterogeneous damping distributions?
• RQ3 How does the method compare to the widely used PML in terms of reflection suppression for pure P-waves?
• RQ4 Can the method handle complex wave interactions involving multiple wave types (P- and S-waves) and oblique incidences?
• RQ5 Is the method practical for real-world applications such as seismic wave modeling or machine vibration analysis?

Key findings

• The Caughey absorbing layer method significantly reduces spurious reflections in 1D simulations with both homogeneous and heterogeneous damping.
• In 2D models, the method effectively suppresses reflections across various wave types and incidence angles, including oblique P- and S-waves.
• The method achieves reflection levels comparable to PML in pure P-wave cases, validating its accuracy.
• The approach maintains stability and performance in complex 2D configurations involving multiple wave modes and heterogeneous materials.
• The method is computationally efficient and directly implementable in existing finite element software using standard Rayleigh damping features.
• The rheological interpretation of the absorbing layer provides physical clarity and facilitates parameter tuning.