Full Green?s functions between image points and the recording surface are crucial to constructing accurate subsurface wavefields and images beyond the single-scattering assumption. A direct approach to do so is offered by utilizing the recorded data combined with a background imaging velocity. The process includes extrapolating the recorded data back in time followed by a simple interferometric cross-correlation of the back-propagated wavefield with the recorded data. This interferometric step offers the opportunity to extract subsurface Green?s functions with first-order scattering forming the transmission component, and the second-order scattering becoming the leading scattering term. A cross-correlation of the resulting, assumed upgoing, wavefield with a forward modelled down going wavefield highlights the doublescattered reflectivity in a process referred to as the generalized internal multiple imaging (GIMI). The resulting image is vulnerable to cross-talk between different order multiples interacting with each other. Thus, we develop the adjoint GIMI operation that takes us from the image to the data, and use it to formulate a least-squares optimization problem to fit the image to the data. The result is reduced cross-talk and cleaner higher resolution multiscattered images.We also extract space extensions of the image, which offers the opportunity to evaluate the focusing capability of the velocity model, and formulate updates for that model based on double scattering. We show the features of this approach on the modified Marmousi model.