Spectral element method for the solution of viscoelastic seismic wave propagation

This paper considers the Gauss-Legendre-Lobatto spectral element method combined with the Crank-Nicolson (CN) technique to solve the viscoelastic wave equation model. The CN technique is chosen for its unconditional stability and second-order accuracy. Additionally, the convergence order is determined for the time semi-discrete scheme of the problem. The Gauss-Legendre-Lobatto points are used as interpolation nodes and integral quadrature points to discretize the spatial direction with the spectral element method, providing an a priori estimate. Numerical results demonstrate the proposed method's high efficiency and accuracy.