The Earth is an heterogeneous complex media from the mineral composition scale (10?6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006
Rücker et al., 2006), diffusive methods (Cognon, 1971
Druskin & Knizhnerman, 1988
Goldman & Stover, 1983
Hohmann, 1988
Kuo & Cho, 1980
Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968
Bolt & Smith, 1976
Dablain, 1986
Kelly et al., 1976
Levander, 1988
Marfurt, 1984
Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields.