The wavefront synthesis algorithm implicitly assumes that a data set is collected with a source spacing short enough to avoid aliasing and with a large receiver cable that is long enough to avoid artifacts caused by a truncated aperture. The ideal acquisition geometry for wavefront synthesis is a fixed-split spread with an infinite aperture. In practice, however, a moving one-side spread with a finite receiver length is the typical acquisition geometry in marine surveys. The moving one-side spread acquisition leaves missing traces at near and far offsets. These missing traces cause artifacts in image from place to place according to the reflector geometry and the angle of plane wave synthesized.
If we are only interested in structural imaging, weak or broken images are not a major problem. Such image defects will disappear after the stacking of several images generated by a different plane-wave synthesis. If we are interested in angle-dependent reflectivity, however, each image from a different plane-wave needs to be analyzed separately. Therefore, the missing traces should be interpolated to produce a complete image without defects in it.
In chapter 3, I introduce an interpolation scheme for missing traces in near and far offset, which uses iteratively-reweighted, least-squares inversion.