Seismic migration and velocity analysis

Migration using an erroneous velocity gives a curve along which the energy is smeared. Associated with this curve is the caustic enveloped by the normal rays. It is possible to compensate for an erroneous velocity by a simple modification of the imaging principle. Formulae are derived for the general case when the velocity changes laterally, and the position of the caustic suggests how to modify the imaging principle so as to obtain an estimate of the NMO velocity. A synthetic example is used to illustrate the results of the analysis.