Multidomain finite-difference and Chebyshev pseudospectral hybrid method for elastic wave simulation: two-dimensional case

Efficient and accurate seismic wave simulations are important for waveform inversion and strong ground motion simulation in regions with complex surface topography. The finite-difference method (FDM) is widely used for these simulations due to its simplicity and high efficiency. High-order FDM mitigates dispersion and dissipation errors through higher order schemes, allowing the use of larger grid spacings and increasing efficiency. However, achieving a high-order and stable implementation of the free surface boundary condition remains challenging. To address this, this paper introduces a novel multidomain finite-difference and Chebyshev pseudospectral hybrid method (multidomain FDM/PSM) for elastic wave modelling. This method divides the computational domain into multiple subdomains along the vertical direction, employing characteristic boundary conditions for patching subdomains and implementing the free surface boundary condition. Within each subdomain, a high-order finite-difference scheme is applied horizontally, complemented by a Chebyshev pseudospectral scheme based on Chebyshev-Gauss-Lobatto (CGL) points in the vertical direction. To prevent excessive point density at mesh edges and avoid overly small time steps, we only use grid configurations with 13 or less CGL points. Using a hybrid approach that integrates a 13-point central stencil finite-difference scheme with a 9-point Chebyshev pseudospectral scheme, we achieve waveform errors under 0.5 per cent while requiring only four points per wavelength. Numerical examples demonstrate that the multidomain FDM/PSM effectively simulates the propagation of elastic waves in models with complex structures and topography. While this study focuses on 2-D problems, the method can be readily extended to 3-D problems.