Selecting an optimal aperture in Kirchhoff migration using dip-angle images |

For insight into the appearance of reflector images in the dip-angle domain, let us consider the case of a hyperbolic reflector (Fomel and Kazinnik, 2013). A special property of hyperbolic reflectors is that they can transform to plane dipping reflectors or point diffractors with an appropriate choice of parameters.
Reflector depth is given by the function

When the reflector is imaged by time migration in the dip-angle domain (Sava and Fomel, 2003) using velocity , point in the data domain migrates to in the image domain according to

where is the migration dip angle. Eliminating from equations A-3 and A-4, we arrive at the equation

where and . Equation A-5 describes the shape of the image of the hyperbolic reflector (A-1) in the dip-angle domain.

When the dip of the migrated event, imaged at a correct velocity (),

We can specify these conditions for two special cases described next.

Selecting an optimal aperture in Kirchhoff migration using dip-angle images |

2014-03-25