The design of wavefield extrapolators using projections onto convex sets

In this paper, the design algorithm of explicit depth extrapolation operators using the method of Projections onto Convex Sets (POCS) is presented. The operators are feasible in the sense that they satisfy all required extrapolation design characteristics. In addition, a simple modification of the derived POCS algorithm is proposed that will further enhance the migrated sections and reduce the number of iterations required to design such operators to only 1.64% of that required for the basic POCS design algorithm. Migration impulse response shows that 1-D extrapolation operators of length 29 can be used to accommodate dip angles up to 69^o. Finally, the 1-D extrapolators design algorithm, using POCS for 2-D extrapolation, can be directly extended to the 2-D case where it will suit the 3-D extrapolation process, and we expect that this will result in a perfectly circularly symmetrical migration impulse response.