The simplest algorithm for time-to-depth conversion is to stretch the vertical axis of a time-migrated image in accordance with the relation between the vertical traveltime and depth. Obviously, such an algorithm is valid only for layered media. Assuming that time migration focuses the energy diffracted from a scatterer to a point, Hubral (1977) introduced the concept of the image ray that defines a time-to-depth conversion valid for arbitrary variations of overburden velocities. The cascade of time migration and image-ray corrections was later proposed (Larner et. al., 1981) as an approximation to true depth migration. Experiments with field data show that the image-ray corrections are often important in the presence of lateral velocity variations. Black and Brzostowski (1992) recently studied the errors of time migration and pointed out that the image-ray method is invalid for reflectors of large dips. They suggested that image-ray corrections should be supplemented by additional spatial corrections.
One of the most important applications of the image ray method is in the process of migration-velocity analysis that usually requires an efficient prestack migration algorithm. However, up till now, the concept of image ray is limited to poststack imaging and the computation of image rays is done through ray tracing that is inefficient. In this paper, I present my studies in two aspects of the image-ray method. Assuming that the validity condition of the image ray method holds, I generalize the image-ray concept to prestack imaging. I derive the mapping functions of the image-ray corrections for both profile imaging and constant offset imaging. I also describe how to compute these mapping functions without actually tracing image rays. For the sake of simplicity, I address the problem only in two-dimensional cases although the concepts and algorithms readily generalize to three dimensions.