On the limited aperture migration in two dimensions

Abstract

Migration of incomplete data aperture is an important problem in exploration seismology because both the location and the size of the migration aperture affect the quality of migration. In 2-D cases, a stationary phase (high‐frequency) analysis concludes that a finitely large migration aperture results in a migrated image with three components. One comes from the tangent point between the traveltime curves of reflected and point‐diffracted rays and gives migration signal. The others are from the two endpoints of the migration aperture and result in migration noise. To guarantee the true‐amplitude reconstruction as well as to remove the migration noise, the migration aperture should be positioned so its central part contains the tangent point mentioned above, and the true‐amplitude weight function should be modified so it tapers the input data near the boundary of the migration aperture. Also, the central part of the migration aperture should be not smaller than the interval confined by the points where the difference between the traveltimes of reflected and point‐diffracted rays equals the half‐duration of the recorded seismic pulse. If the central part of the migration aperture is equal to the interval described here, the whole migration aperture should be confined by the points where the difference between the traveltimes of reflected and point‐diffracted rays equals the duration of the recorded seismic pulse. A migration aperture larger than this size does not improve the migration quality. Furthermore, for the migration apertures suggested here, the form of the taper function is not essential for migration. These results apply to both time and depth (poststack and prestack) migration.