Prediction and subtraction of multiple diffractions

A system, comprising:

• an analysis hardware engine configured to transform previously acquired seismic data acquired at a plurality of locations from a time-space domain to a transformed domain using a dictionary of asymptote- and apex-shifted hyperbolic radon transform (AASHRT) basis functions and a dictionary of Green's functions;
• a separation hardware engine configured to separate, within the transformed previously acquired seismic data, a first portion and a second portion of the transformed previously acquired seismic data based on an asymptote shift parameter associated with the dictionary of AASHRT basis functions and a firing delay parameter associated with the dictionary of Green's functions;
• a prediction hardware engine configured to predict, a plurality of multiple diffractions based on the separated first and second portions;
• a subtraction hardware engine configured to adaptively subtract the predicted multiple diffractions from the previously acquired seismic data;
• and
• a synthesis hardware engine configured to inverse transform a particular seismic data set from the transformed domain to the time-space domain such that the separated diffractive portion is synthesized at denser locations than the previously acquired seismic data,
• wherein the denser locations are more compact with respect to one another as compared to the plurality locations during acquisition of the previously acquired seismic data.