Influence of data irregularities on 3D common offset migration

In 3D seismics offset is a vector characterized by the source-receiver distance and azimuth. Due to irregularities in the acquisition (for instance streamer feathering in marine acquisition) common offset data are not available and, in turn, 3D common offset migration does not make sense any longer. We then introduce the concept of migration by offset class: it is a straightforward extension of common offset migration in which we migrate all traces that belong to a given offset class, namely all traces with offset close to a given one. The result of such a migration depends of course on how the offset class is constructed or, in other words, on what is meant with "close". The aint of this paper is to investigate by means of a 3D numerical study how to design offset classes so as to obtain migrated images that can be interpreted without trouble (such an interpretation is a key element for a successful migration velocity analysis). We have to find a trade-off between two extremes: - a too loose offset class that would mix heterogeneous offsets (in particular mixing substantially different azimuths can be dangerous); - a too narrow offset class that would result in sparse seismic traces with, in turn, an inadequate coverage of the reflector. The regularity, within an offset class, of the offset variation as well as the one of the distribution of midpoints are parameters that can have a drastic influence on the quality of the migrated image. It is shown that migration by offset class appears as a robust procedure all the more than the offset varies slowly with the midpoint coordinate within an offset class. Besides. the smaller the mean offset norm, the lower is the contamination of the image due to the mixing of azimuths within an offset class.