relationship between data space and model space

Data space can be related to model space with the following formula:  

$$\textbf{d}\left( \vec{m}, \vec{h},\omega \right) =L\textbf{m... ..., \gamma \left( \alpha , \varphi \right), n\triangle z \right),$$ (1)

where the modeling operator L is can be a Green's function, a one-way or two-way wave equation, or a more complex wave equation suitable for wavefield extrapolation or modeling. Wavefield extrapolation and modeling operators were exhaustively studied by many authors (, , , , , , , , , , ). However, prestack depth migration imaging is mostly implemented with one-way acoustic wave equations, which is one of the reasons it cannot achieve true-amplitude images. If a one-way wave equation is used for migration imaging, all wave phenomena except the primary reflection wave are processed as noise. In fact, if quantitative reflectivity is the objective of imaging, a two-way acoustic, or even elastic, wave equation should be used (, , ).