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On the aperture effect in 3D Kirchhoff‐type migration
- Source: Geophysical Prospecting, Volume 47, Issue 6, Jan 1999, p. 1045 - 1076
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- 24 Dec 2001
Abstract
It is well known that the migrated image given by a Kirchhoff‐type (diffraction‐stack) migration with limited aperture is always accompanied by some events which depend on the migration aperture. Although these events may severely affect the quality of migration, they have been studied only in 2D cases. Here, the events due to the migration aperture in 3D situations are investigated using a new method of analysing the reconstructed wavefield. It is found that a finite migration aperture results in a reconstructed wavefield with two components. One comes from the tangent points and curves between the traveltime surfaces of reflected and point‐diffracted rays and is independent of the migration aperture, and the other is from the boundary of the migration aperture and depends strongly on the location and size as well as on the shape of the migration aperture. It is this last component that describes the aperture effect in migration. If the migration aperture is not sufficiently large, and if the input for migration is not zero on the boundary of the migration aperture, the boundary component may partially or totally cancel the migration signal. Furthermore, for synthetic data, the aperture effect cannot be eliminated by enlarging the migration aperture because, except for the common‐shotpoint data, the aperture effect always exists however large the migration aperture becomes. This leads to the conclusion that the published Kirchhoff‐type operators are not the exact inverse operators of the Fresnel–Kirchhoff integral if the input data are synthetic.