“…These schemes include finite element method (Rial et al, 1992;Toshinawa and Ohmachi, 1992), spectral element method Tromp, 1999, 2002), pseudo-spectral method (Nielsen et al, 1994;Tessmer et al, 1992;Tessmer and Kosloff, 1994), boundary element method (Bouchon et al, 1989;Campillo and Bouchon, 1985;Sánchez-Sesma and Campillo, 1993;Sánchez-Sesma et al, 2006), finite difference method (Frankel and Vidale, 1992;Gao and Zhang, 2006;Ruud, 1994, 1998;Jih et al, 1988;Lombard et al, 2008;Robertsson, 1996;Zhang and Chen, 2006), and also a hybrid approach which combines the staggered-grid finite difference scheme with the finite element method (Galis et al, 2008;Moczo et al, 1997). Both the spectral element and the finite element methods satisfy boundary conditions on the free surface naturally.…”