Imaging and Aliasing
The quality of 3D images is influenced strongly by the spatial sampling of the data and by whether the imaging operators properly take into account the data sampling. Strong aliasing artifacts degrade the images when the data are sampled poorly and the imaging operators are not implemented carefully. The sampling problem is more acute in 3D imaging than in 2D imaging, because the spatial axes of 3D data often are sampled sparsely and irregularly. In this chapter, I analyze the problems caused by regular data grids that are sampled too coarsely, although regularly. Chapter 9 discusses the issues related to irregularity of both data acquisition and reflector illumination.
Three types of aliasing are relevant to seismic imaging: data aliasing, image aliasing, and operator aliasing. Data aliasing and image aliasing are fairly straightforward to understand by using standard sampling theory, whereas operator aliasing is more specific to imaging operators and thus requires detailed analysis. From the earliest development of Kirchhoff migration methods (Schneider, 1978), it has been evident that aliasing artifacts appear in the image if one does not consider data and operator aliasing when one implements the summation operator (Gardner et al., 1974). Thus, methods for preventing operator aliasing during Kirchhoff migration are well established (Bevc and Claerbout, 1992; Gray, 1992; Lumley et al., 1994; Abma et al., 1998; Biondi, 2001). In the first part of this chapter, I discuss aliasing for Kirchhoff migration.