The boundary integral equation and boundary element methods are not suitable for near-surface regions with large velocity contrasts ( Bouchon et al., 1995). The pseudo-spectral method is limited to a free surface with smoothly varying topography and leads to inaccuracies for models with strong heterogeneity or sharp boundaries ( Tessmer et al., 1992). However, the classical finite element method suffers from a high computational cost, and, on the other hand, a smaller spectral element than the one required by numerical dispersion is required to describe a highly curved topography, as demonstrated in seismic modeling of a hemispherical crater ( Komatitsc and Tromp, 1999). 3D surface and interface topographies can be modeled using curved piecewise elements. Both the spectral element and the finite element methods satisfy boundary conditions on the free surface naturally. These schemes include finite element method ( Rial et al., 1992 Toshinawa and Ohmachi, 1992), spectral element method ( Komatitsch and 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 Hestholm and 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). In the last two decades, several approaches have been proposed to simulate wave propagation in heterogeneous medium with irregular topography. In oil/gas seismic exploration, seismologists also have a similar problem with the undulating topography along the survey line.
For example, in the context of the deep seismic soundings to explore the crustal structure, seismic experiments are usually carried out across: (a) orogenic belts for understanding the mechanisms (b) basins to understand the formation mechanisms (c) transition zones for the study of its interaction ( Al-Shukri et al., 1995 Ashford et al., 1997 Boore, 1972 Jih et al., 1988 Levander, 1990 Robertsson, 1996 Zhang et al., 2010). Rough topography is very common and we have to deal with it during the acquisition, processing and interpretation of seismic data.