Depth focusing analysis is a methodology for velocity estimation based on the fact that the total wave propagation time is invariant: the total traveltime from the real reflection point obtained with the real propagation velocity is equivalent to the total traveltime obtained from the focus reflection image obtained with a wrong propagation migration velocity plus a residual time related with the error in velocity. This residual time, in a horizontal stratified media case with constant velocity Vr (see Figure 2), is equal to a vertical time associated with a depth error a paraxial approximation MacKay and Abma (1992):
Figure 3 presents the migration of a dipping reflector with the media velocity and with a wrong velocity Vm. Keeping the notation for the migration velocity Vm, real velocity Vr, and the downward continued point with the migration velocity to the imaging condition m=(xm,ym,Zm), the real position of the dipping reflector point is r=(xr,yr,zr) and the focusing point is f=(xf,yf,Zf). The total time tT can be related to the focus time tf by the following equation MacKay and Abma (1992):
The focusing analysis methodology for 3D data is equivalent to 2-D methodology. The depth error panel is built by extracting the zero offset trace from every downward continuation step of prestack data recorded at the surface. In this paper, the downward operator is a 3-D phase-shift in CMP domain operator.
It is important to point out, that in 3-D the focusing point has associated a depth error and lateral position error in in-line and cross line directions. Therefore, to apply equation (6) and (2), it is necessary to perform a residual migration of depth error gather, then the focusing point, the migrated point and the real point are along the same normal ray.