The second step of shot-profile modeling consists of upward continuation of the receiver wavefield to the surface, which is done by using the following equation:
r(z0) = 0,
The Green functions can be computed recursively at each depth step (from zi+1 to zi) (Figure 3), or precomputed and stored to allow jumps (from zi+j to zi) (Figure 4). In addition, the third term in equation (6) must also be stored. Equation (6) can be written also in matrix form (see APPENDIX B).
Figure 3 Upward continuation of the receiver wavefield by recursive computation of the Green functions at each depth step.
Figure 4 Upward continuation of the receiver wavefield with the precomputed Green functions.
Including all the frequencies and all the shot positions in the data, it follows from equation (19) that the receiver wavefield () can be computed as follows: