Prestack partial migration is a mapping of prestack data to zero-offset data. This mapping can be divided in two steps:
For zero-offset, the time and space coordinates are (t0,x0); v represents the velocity; th represents the source-receiver travel time for a constant offset; represents the dip angle and h is the half-offset. The parameters V, a and b are
For the constant velocity medium, the analytical formulation for the PSPM operator as expressed by Popovici and Biondi, (1989)is
The equations (1) are the parametric equations (functions of the dip angle )of the DMO ellipse containing the velocity-time truncation. In the constant velocity case the PSPM operator is equivalent to NMO followed by DMO. The form of the PSPM operator is identical to the form of the DMO operator, as NMO introduces merely a time shift. Equations (1) are velocity dependent, and the velocity truncation has to be determined for each medium with a given velocity.