Autocorrelogram migration: Theory

We present the equations for migrating inversevertical-seismic-profile-while-drilling and common-midpoint autocorrelograms. These equations partly generalize the 1D autocorrelation imaging methods of Katz and Claerbout to 2D and 3D media, and also provide a formal mathematical procedure for imaging the reflectivity distribution from autocorrelograms. The imaging conditions are designed to migrate specific events in the autocorrelograms, either the direct-primary correlations or the direct-ghost correlations. Here, direct stands for direct wave, primary stands for primary reflections, and ghost denotes free-surface ghost reflections. The main advantage in migrating autocorrelograms is that the source wavelet does not need to be known, which is the case for seismic data generated by a rotating drill bit or for vibroseis data with a corrupted pilot signal. Another advantage is that the source and receiver static problems are mitigated by autocorrelation migration. Two limitations are that autocorrelation of traces amplifies coherent noise such as surface waves, and produces undesirable coherent noise denoted as "virtual multiples." Similar to "physical multiples," such noise can, in principle, be partially suppressed by filtering and stacking of migration images obtained from many different shot gathers. Results with both synthetic and field data validate this conjecture, and show that autocorrelogram migration can be a viable alternative to standard migration when the source signal is not adequately known or there are severe static problems.