Common-angle migration and oriented waves

From the 3D phase-shift extrapolation of individual phase-space components, we derive for prestacked data a vector relation between $mathbfk_h$, the horizontal offset wavenumber, and $k_z$, the vertical one. While in 2D this relation depends only on the tangent of the scattering angle $theta$ and not on the structural deep, in 3D, in general, this is no longer true. The resulting vector formula takes into account the orientation of the scattering plane containing the slowness vectors $mathbfp_s$ and $mathbfp_r$, one describing the down-going wave and the other the up-going one. For scattering events taking place on vertical planes, we recover the expected 2D result. In this special case, we have a complete theory, first, to construct the angle-domain, common-image gathers, one for each scattering angle $theta$, and, second, to retrieve from those the textitmedium structure by adequately summing over all values of $theta$.

@TechReport{Bon07,
  author       = {Bonomi, E.},
  title        = {Common-angle migration and oriented waves},
  institution  = {CRS4, Center for Advanced Studies, Research and Development in Sardinia},
  number       = {09/47},
  month        = {june},
  year         = {2007},
  address      = {Cagliari, Italy},
  type         = {techreport},
  keywords     = {angle-domain common-image gathers, oriented migration},
  url          = {https://publications.crs4.it/pubdocs/2007/Bon07},
}