f High-order spectral element method (SPEM) for acoustic wave propagation

The most widespread of the discrete numerical methods for modelling seismic wave propagation, are the finite difference (FDM), the Fourier or pseudo-spectral (FSM), and the finite clement (FEM) methods (Boore, 1972; Kelly et al., 1976; Lysmer, 1972; Gazdag, 1981; Kosloff, 1982; Kosloff et al., 1984; Marfurt, 1984), Even though based on different mathematical approaches, all three methods rely on the space discretization of the geological structure to be modelled. In particular, the pseudo-spectral rnethod can he seen as a limiting case of the finito difference methods of increasing orders and accuracies (Fornberg, 1987).