Solution of the equations of dynamic elasticity by a Chebychev spectral method

A spectral method is presented for solving the two-dimensional equations of dynamic elasticity, based on a Chebychev expansion in the vertical direction and a Fourier expansion for the horizontal direction. The technique can handle the free-surface boundary condition more rigorously than the ordinary Fourier method. The algorithm is tested against problems with known analytic solutions, including Lamb's problem of wave propagation in a uniform elastic half-space, reflection from a solid-solid interface, and surface wave propagation in a half-space containing a low-velocity layer. Agreement between the solutions is very good. A fourth example of wave propagation in a laterally heterogeneous structure is also presented. Results indicate that the method is very accurate and only about a factor of two slower than the Fourier method. -Authors