The uneven illumination of reflectors can lead to misinterpretation of their amplitudes after migration. This can be due to the seismic experiment acquisition geometry (incomplete data), or to energy focusing or defocusing caused by obstacles in the wave path. In the worst case, this problem can create shadow zones at reservoir depths Muerdter et al. (1996); Prucha et al. (1998).
Some attempts to solve this subsurface imaging problem have used the power of geophysical inverse theory Tarantola (1987). It compensates for the experimental deficiencies (acquisition geometry, obstacles, etc.) while being consistent with the acquired data. Usually the inversion is implemented by using iterative least-squares algorithms Duquet and Marfurt (1999); Kuehl and Sacchi (2001); Nemeth et al. (1999); Prucha et al. (2000); Ronen and Liner (2000). The main inconvenient of this approach is that it is computationally expensive since it iteratively apply the seismic modeling and migration operators to build the whole image.
Since reflection amplitudes are more important at reservoir depths, we propose to apply a target-oriented shot-profile one-way wave equation inversion strategy. Instead of recursively computing the Green functions at each depth step and at each inversion iteration, they could be computed from the surface to the target and from the target to the surface during the first iteration, stored, and reused in subsequent iterations. In that way, the computational cost could be kept reasonable.
In this paper, we first discuss how a target-oriented least-squares inversion could help to improve the image amplitudes while keeping computational cost reasonable. We also review target-oriented modeling by shot-profile extrapolation with the one-way wave equation.