Second-order seismic wave simulation in the presence of a free-surface by pseudo-spectral method

In this paper second-order seismic wave equations are adopted to simulate the wave propagation in the presence of a free-surface. In the simulations, horizontal and vertical spatial derivatives are solved by Fourier and Chebyshev pseudo-spectral algorithms respectively. In addition, Fourier-Chebyshev pseudo-spectral method is also used to solve the boundary conditions of the free-surface, which are Neumann boundaries. That makes results at the free-surface keep same high precision with inner domain. The new scheme is tested against Lamb's problem in a uniform elastic half space. Agreement between numerical and analytical results is every good. Compared with the former simulation scheme based first-order velocity-stress equations, the new scheme based on second-order equations is more efficient because it has fewer controlling equations.