Numerical stability of absorbing layers using increasing damping in Central Difference scheme for modelling seismic wave propagation

Absorbing Layers with Increasing Damping (ALID) associated with Central Difference (CD) scheme could be an efficient solution for modelling seismic wave propagation in unbounded domains, owing to simple displacement-based finite element formulation and computational efficiency of CD scheme. However, the critical time step in CD scheme is usually significantly reduced by the introduction of damping matrix, compromising the computational time. In this paper, the numerical stability of ALID in CD scheme is investigated for two types of damping: Rayleigh damping and Kosloff damping. A dedicated stability analysis confirms the preservation of the critical time step for Kosloff damping in wave propagation problem, in contrast to classical Rayleigh damping. The influence of each damping on the critical time step in CD scheme and the robustness of two ALIDs have been also evaluated in MATLAB through different numerical examples, such as Lamb’s test and seismic wave propagation in stratified soil, using three types of excitations: a Ricker incident wave, a synthetic Ormsby wavelet and a real seismic input introduced via Lagrange multiplier. The advantage of Kosloff damping is highlighted in reducing both spurious reflected waves and CPU time, providing a frequency-independent and time-efficient approach to simulate seismic wave propagation in unbounded domains.