Evaluation of two‐pass three‐dimensional migration

Abstract

The theoretically correct way to perform a three‐dimensional (3-D) migration of seismic data requires large amounts of data manipulation on the computer. In order to alleviate this problem, a true, one‐pass 3-D migration is commonly replaced with an approximate technique in which a series of two‐dimensional (2-D) migrations is performed in orthogonal directions. This two‐pass algorithm produces the correct answer when the velocity is constant, both horizontally and vertically. Here I analyze the error due to this algorithm when the velocities vary vertically. The analysis has two parts: first, a theoretical analysis is performed in which a formula for the error is derived; and second, a field data comparison between one‐pass and two‐pass migrations is shown. My conclusion is that two‐pass 3-D migration is, in general, a very good approximation. Its errors are usually small, the exceptions being when both the reflector dip is large (in practice this typically means greater than about 25 to 40 degrees) and the orientation of the reflector is in neither the inline nor the crossline direction. Even then the error is the same order of magnitude as that due to the uncertainty in the migration velocities. These conclusions are still valid when there is lateral velocity variation, as long as this variation is accounted for by trace stretching. The analysis presented here deals with time migration; no claims are made regarding depth migration.