Toward a stable iterative migration velocity analysis scheme

Abstract

Migration velocity analysis is a family of methods aiming at automatically recovering large-scale trends of the velocity model from primary reflection data. We studied an image-domain version, in which the model is extended with the subsurface offset and we use the differential semblance optimization objective function. To incorporate first-order surface multiples in this method, the standard migration step is replaced by a least-squares iterative scheme aiming at determining an extended reflectivity model explaining primaries and multiples. Hence, this iterative migration velocity analysis strategy takes the form of a nested optimization problem, with gradient-based minimization techniques for the inner (migration part) and outer loops (macromodel estimation). The behavior of the outer loop gradient is unstable, depending on the number of iterations of the inner loop. This problem is addressed by slightly modifying the outer loop objective function: A “filter” operator attenuating unwanted energy in the extended reflectivity is applied before evaluating the focusing of reflectivity images. Simple synthetic numerical examples illustrate that this modification improves the stability of the gradient. In addition, a less expensive outer gradient computation is proposed, without harming the background velocity updates.