The Chebyshev spectral element method using staggered predictor and corrector for elastic wave simulations

Abstract

Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method (SEM) using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient (PCG)-element by element (EBE) method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method (FDM) for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.