Microlocal Analysis of the Scattering Angle Transform
Stolk, Christiaan C.
The goal of seismic imaging is to map single reflection seismic data to an image of a medium parameter, ie. a reconstruction of the singularities in the medium parameter up to a pseudodifferential factor. Given a smooth model of the medium (background medium), satisfying certain conditions, there is a Fourier integral operator (FIO) mapping seismic data to an image. Under more restrictive conditions the data can be mapped to a family of images, each depending on a different subset of the data. This mapping is used in the determination of the background medium. The canonical relations of these operators consist of data from reflected bicharacteristics in the background medium. When several rays (projections of the bicharacteristics on the base space) connect an acquisition point with a scattering point (multipathing), the conditions for imaging using subsets of data are in general violated. In the geophysical literature scattering angle transforms have been proposed to yield image families in the presence of multipathing. It has been conjectured that an integral operator related to the Kirchhoff migration operator maps seismic data to a family of images. We show that this conjecture is false. The Kirchhoff type angle transform maps seismic data to a sum of a correct image and possible artifacts, ie. singularities in the image that do not correspond to singularities in the medium. We give an explicit example in which such artifacts are present.
Citable link to this pagehttps://hdl.handle.net/1911/101979
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