Dispersive staggered grid finite difference modelling of Rayleigh waves

Abstract

Non-destructive surface wave-based ground exploration techniques such as multichannel analysis of surface wave (MASW) require a rigorous numerical model to predict the soil properties accurately. The staggered grid finite difference (SGFD) method is widely used to simulate elastic wave propagation due to its stability and ease of implementation. However, in the presence of low-velocity layers, the SGFD method requires computationally expensive high spatial grid resolution to accurately model the surface waves. On the other hand, velocity dependent grid approaches become unstable for the highly irregular soil profile. In order to overcome these challenges, a vertically non-uniform dispersive staggered grid scheme is proposed that significantly reduces the computing time without sacrificing accuracy. The proposed non-uniform discretization strategy is based on the Rayleigh wave dispersion relation, where the penetration depth of each frequency is assumed to be roughly one and half of the wavelength. Based on the above assumption, an exponential relationship between grid size and grid number is developed. The proposed method calculates continuously increasing grid length while ensuring grid points at the exact layer interface. Five different soil profiles: a homogenous elastic half-space, an irregularly dispersive crustal level profile, a low velocity layer at a deeper depth model, a real-world model, and a lateral heterogeneous model are used to demonstrate the efficacy of the proposed approach. For all the cases, the results of the proposed dispersive grid match those of the uniform grid with a correlation coefficient value (R) > 0.99. Compared to the uniform and velocity dependent grid approaches, the proposed dispersive grid scheme requires ½ to 1/4th of elements and CPU time. Furthermore, unlike the velocity dependent grid scheme, the proposed method does not become unstable for a highly irregular profile. Results indicate that the proposed method is superior to the traditional uniform and velocity dependent grid approaches for modelling elastic waves in layered media.