Introduction

Reverse-time migration Baysal et al. (1984) has some potential advantages with respect to downward-continuation migration. It can migrate overturned and prismatic reflections even in the presence of strong lateral velocity variations Biondi (2002). It also models the amplitude of the transmitted wavefield more accurately than downward-continuation in the presence of sharp interfaces. However, it has the drawback of being computationally intensive. In particular, shot profile migration of overturned events can be extremely expensive because we need to pad the computational domain with a huge number of zero traces to assure that it includes the reflectors that generated the overturned events.

A similar problem of computational-domain size exists for shot profile migration by downward continuation. For marine data, an efficient solution to the problem is migration in midpoint-offset coordinate Biondi and Palacharla (1996). In the midpoint-offset domain the wavefield focuses towards zero offset, and thus we can drastically limit the length of the offset axes (at the limit we can eliminate the cross-line offset altogether by a common-azimuth approximation). It is thus natural to try to derive a reverse-time migration method that backward propagates the data in midpoint-offset coordinates.

In this paper, I derive an equation for backward propagating in time midpoint-offset domain data. The equation is derived from the Double Square Root equation. The proposed method successfully images non-overturned events. Unfortunately, the propagation equation has a singularity for horizontally traveling waves, thus the method does not seem capable of imaging overturned waves. The root of the problem is that the DSR implicitly assumes that the sources and the receivers are at the same depth level (or at least that their vertical offset is constant). This assumptions is clearly unfulfilled by finite-offset overturned events. I speculate that the assumption of null (constant) vertical offset between sources and receiver could be removed. In this case a midpoint-offset domain might be still computationally attractive because the reflected wavefield would still tend to focus towards zero offset as it is back-propagated in time.