Minimum apertures and Fresnel zones in migration and demigration

Abstract

The size of the aperture has an important influence on the results of (Kirchhoff‐type) migration and demigration. For true‐amplitude imaging, it is crucial not to have apertures below a certain size. For both the minimum migration and demigration apertures, theoretical expressions are established. Both minimum apertures depend on each other and, although a time‐domain concept, are closely related to the frequency‐dependent Fresnel zone on the searched‐for subsurface reflector. This relationship sheds new light on the role of Fresnel zones in the seismic imaging of subsurface reflectors by showing that Fresnel zones are not only important in resolution studies but also for the correct determination of migration amplitudes. It further helps to better understand the intrinsic interconnection between prestack migration and demigration as inverse procedures of the same type. In contrast to the common opinion that it is always the greatest possible aperture that yields the best signal‐to‐noise enhancement, it is in fact the selection of a minimum aperture that should be desired in order to (a) enhance the computational efficiency and reduce the cost of the summation, (b) improve the image quality by minimizing the noise on account of summing the smallest number of traces, and (c) to have a better control over boundary effects. This paper demonstrates these features rather than addressing the question of how to achieve them technically.