Subsurface imaging in complex areas, particularly around salt, is plagued by poor illumination. This poor illumination is caused by seismic energy being lost due to such processes as evanescence, mode conversion, or being directed outside of the recording geometry. In this paper, I am concerned with the seismic energy that is directed outside the bounds of the seismic survey by the complex structures. This energy can be thought of as lost data.
One method for compensating for poor illumination is Regularized Inversion with model Preconditioning (RIP). RIP uses a migration operator and a regularization operator in a least-squares inversion. RIP regularizes the image of the subsurface in a way that is consistent with the recorded data. Since it is trying to compensate for the illumination problems, it is filling in parts of the image that correspond to the energy that left the surface bounds. It is as if RIP is recovering the lost data.
In this paper, I will first explain the theory for regularized inversion with model preconditioning. I will discuss how energy that leaves the survey area affects the inversion process. I will show that by expanding the data space and introducing a weighting operator that accounts for the actual recording geometry, we can account for much of the energy that escapes the survey bounds.