Aperture effects in 2.5-D Kirchhoff migration

Seismic images obtained by Kirchhoff time or depth migration are always accompanied by some artifacts known as ``migration noise'', ``migration boundary effects'', or ``diffraction smiles'', which may severely affect the quality of the migration result. Most of these undesirable effects are caused by a limited aperture if the algorithms make no special disposition to avoid them. Likewise, strong amplitude variation along reflection events may also cause similar artifacts. All these effects can be explained mathematically by means of the Method of Stationary Phase. However, such a purely theoretical explication is not always easy to understand for applied geophysicists. By relating the terms of the stationary­phase approximation to simple geometrical situations, a more physical interpretation of the migration artifacts can be obtained. A simple numerical experiment for post­stack (zero­offset) data indicates the problem and helps to develop an intuitive understanding of the effects and the methods to avoid them.