A new approach to absorbing layers for the modelling of local seismic response in 1D and 2D domains

This work proposes a new absorbing-layer formulation for elastic wave simulations in unbounded domains, based on a rheological gradient of Rayleigh/Caughey damping coefficients. Unlike classical methods — such as Lysmer–Kuhlemeyer damping, paraxial conditions, or PMLs — which may suffer from parameter sensitivity, grazing-incidence instabilities, or high computational cost, the proposed model provides a simple and physically interpretable alternative. By treating the sponge layer as a stratified viscoelastic medium with smoothly increasing dissipation, the method ensures progressive absorption without impedance discontinuities. Numerical tests in 1D and 2D using quadratic damping profiles demonstrate very low reflection levels (|R| ≤ 0.03, |R|² < 10⁻³) and stable performance even for oblique waves, while requiring no modification to standard FEM, FDM, or SEM schemes. Overall, the rheological-gradient approach offers an effective, robust, and computationally efficient solution for realistic seismic wave-propagation modelling.