Wave-equation time migration

Abstract

Time migration, as opposed to depth migration, suffers from two well-known shortcomings: (1) approximate equations are used for computing Green’s functions inside the imaging operator and (2) in case of lateral velocity variations, the transformation between the image-ray coordinates and the Cartesian coordinates is undefined in places where the image rays cross. We have found that the first limitation can be removed entirely by formulating time migration through wave propagation in image-ray coordinates. Our approach constructs a time-migrated image without relying on any kind of traveltime approximation by formulating an appropriate geometrically accurate acoustic wave equation in the time-migration domain. The advantage of this approach is that the propagation velocity in image-ray coordinates does not require expensive model building and can be approximated by quantities that are estimated in conventional time-domain processing. Synthetic and field data examples demonstrate the effectiveness of the proposed approach and show that the proposed imaging workflow leads to a significant uplift in terms of image quality and can bridge the gap between time and depth migrations. The image obtained by the proposed algorithm is correctly focused and mapped to depth coordinates; it is comparable to the image obtained by depth migration.