The spectral element method is based on a weak elastic mechanism equation and combines the geometrical flexibility of the finite element method with the accuracy of the pseudospectral method.Hence the method is called the high-order FEM or the domain decomposition of pseudospectral method.It is a new tool for numerical modeeling of elastic wave propagation.Here

the theory and the deducing process of the SEM based on the Legendre polynomials are shown.The Legendre SEM can get diagonal mass matrix relative to the Chebychev SEM

which leads to a very simple explicit time difference scheme with high efficiency.A few of numerical tests are simulated and approved that the SEM is a effective method for modelling of seismic wave propagation.