Least-squares data to data migration

Free-surface related multiples can sometimes provide extra illumination of the subsurface and thus have been used in migration procedures. However, most multiples migration approaches need to separate primaries and free-surface related multiples or predict multiples in advance, which is time consuming and prone to errors. Data to data migration (DDM) method migrates free-surface related multiples by forward propagates the recorded field data (containing both primaries and free-surface related multiples), and also backward propagates the recorded field data itself. For DDM, there is no need to predict or separate multiples, but the migration result is suffered from the cross-talks generated by cross-correlations of undesired seismic events, e.g. primaries and second-order free-surface related multiples. We propose a least-squares data to data migration (LSDDM) approach to eliminate the cross-talks generated by DDM. In each iteration, the forward propagated primaries and free-surface related multiples are cross-correlated with backward propagated primary residuals and free-surface related multiple residuals to form the reflectivity gradient. We use the Marmousi model for numerical test and the numerical results validate that LSDDM can provide a migrated image with higher signal to noise ratio and more balanced amplitudes compared with DDM. The LSDDM approach might be significant for general subsurface imaging when the migration velocity is correct and the acquired data has enough recording time.