Other possibilities can be explored using the mathematical formalism in this paper. It is straightforward to develop a non-linear inverse methodology by using crosscorrelation misfit functions and obtaining its gradient.
It is interesting to note the analogy of inverting correlograms with that of constructing holograms. Light intensity images are used to reconstruct holograms, which are images of the object polluted by noisy interference terms. Seismic correlograms can also be used to reconstruct images of the object, but the other terms in equation (3) suggest that the data are polluted by noisy interference terms. However, we can design migration operators to reconstruct the object function (e.g., reflectivity) or information from the interference terms (e.g., source locations). An alternative is to simultaneously reconstruct both coherent noise and signal models with least squares migration filtering.