Theory of Reverse-time Migration

If $G({\bf {x}}\vert{\bf {x}}')$ is computed by a finite-difference solution to the wave equation in the frequency domain, then the equation of prestack reverse-time migration (RTM) can be obtained by right shifting the square brackets in equation 

$$m({\bf {x}}) = \sum_{\omega} \sum_r \alpha(\omega,{\bf {x}},{\bf {r}},{\bf {s}})... ...ace{[G({\bf {r}}\vert{\bf {x}})^*D({\bf {r}}\vert{\bf {s}})]}^{back~propagate}.$$ (2)

The traditional implementation of prestack RTM (Stolt and Benson, 1986) is to backpropagate the data and take the zero-lag correlation of it with the forward propagated source wavefield to get $m({\bf {x}})$ . This is illustrated in Figure .

Figure: The standard reverse-time migration (RTM) image is obtained by computing the zero-lag correlation of the forward-propagated source wavefield a) with the back-projected data b). The scattering point at $X'$ shows up in c) after applying the imaging condition.