Angle domain common image gathers

ODCIGs can be transformed into an angle domain representation (ADCIGs) that describe reflectivity as a function of incidence angle at the reflector, $\gamma$ Sava and Fomel (2003). ADCIGs are generated after migration with the relation,

$${\rm tan} \, \gamma = -\frac{k_h}{k_z}.$$ (8)

which uses the Fourier transformed wavenumbers associated with offset and depth.

Angle gathers may be used to examine the accuracy of the imaging velocity model at all subsurface locations. A reflector focused with the correct velocity model should be at a consistent depth for all illumination angles. Deviations in reflector position due to incorrect velocity models result in angle-dependent "smiles" and "frowns", which indicate over- and under-migration, respectively. Corresponding velocity model errors can be estimated from angular moveout through the process of migration velocity analysis (MVA). More importantly, after migration velocity inaccuracy has been minimized, angle-dependent amplitude variations should be attributed to AVA response. However, for GPR images, this will not be the case unless the proper radiation patterns and scattering physics have been taken into account.