The effect of velocity uncertainty on migrated reflectors: Improvements from relative-depth imaging

We have studied the problem of uncertainty quantification for migrated images. A traditional migrated image contains deterministic reconstructions of subsurface structures. However, input parameters used in migration, such as reflection data and a velocity model, are inherently uncertain. This uncertainty is carried through to the migrated images. We have used Bayesian analysis to quantify the uncertainty of the migrated structures by constructing a joint statistical distribution of the location of these structures. From this distribution, we could deduce the uncertainty in any quantity derived from these structures. We have developed the proposed framework using a simple model with velocity uncertainty in the overburden, and we estimated the absolute positions of the horizons and the relative depth of one horizon with respect to another. By quantifying the difference in the corresponding uncertainties, we found that, in this case, the relative depths of the structures could be estimated much better than their absolute depths. This analysis justifies redatuming below an uncertain overburden for the purposes of the uncertainty reduction.