The first step of shot-profile modeling with the one-way wave equation consists of downward continuation of the source wavefield (for each shot, at each frequency), which is done by using the following equation:
p+(z0) = f,
The Green functions can be computed recursively at each depth step (from zi to zi+1) (Figure 1), or precomputed and stored to allow jumps (from zi to zi+j) (Figure 2). The equations (2) and (3) can be written also in matrix form (see APPENDIX A).
Figure 1 Downward continuation of the source wavefield by recursive computation of the Green functions at each depth step.
Figure 2 Downward continuation of the source wavefield with the precomputed Green functions.
Including all the frequencies and all the shot positions in the data, it follows from equation (15) that the source wavefield () can be computed as a function of the source signature (), as follows: