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
We present a spectral method 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 haft‐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.