The limitations of time migration and trace stretch in the presence of lateral velocity gradients

Abstract

This paper quantifies the imaging errors that result from the assumptions of time migration and a preliminary, laterally-variable ``stretch' of the data, in the presence of lateral velocity gradients. The analysis is restricted to media that are approximately homogeneous in the vertical direction, with dip in the same direction as for the velocity gradient. It is shown that a time migration that explicitly recognizes the lateral variation in velocity results in underestimation of steep dips by only a few degrees, even for large gradients of 0.1 s-1. A preliminary stretch of the data, followed by time migration and stretch removal, however, results in a net overestimation of moderate dips by a few degrees and overestimation of steep dips by 15° or more. The errors increase with increasing gradient and decreasing average velocity.