Although migration is not sufficient to image the subsurface in areas with poor illumination, we can use migration as an imaging operator in a least-squares inversion scheme Duquet and Marfurt (1999); Nemeth et al. (1999); Ronen and Liner (2000). In areas with poor illumination, the inversion problem is ill-conditioned, therefore it is wise to regularize the inversion scheme Tikhonov and Arsenin (1977). The regularization operator can be designed to exploit knowledge we have about the expected amplitude behavior and dip orientation of events in the image Prucha and Biondi (2002).
When using regularized inversion for imaging, the choice of regularization operator is critical. If it were possible for the subsurface to be perfectly illuminated, we would expect the amplitudes of the seismic events to vary smoothly with reflection angle. THerefore, an intelligent and fairly safe choice of regularization is to penalize large amplitude changes as the reflection angle varies for a given point in the subsurface Kuehl and Sacchi (2001); Prucha and Biondi (2002). We refer to this as ``geophysical'' regularization. This process will help to reduce artifacts and improve the image.
In this paper, we examine the effects of geophysically regularized inversion on a real 3-D dataset. We will begin by explaining the basic theory of regularized inversion with model preconditioning (RIP). We will then demonstrate its use on a real 2-D line and the real 3-D volume that the 2-D line is taken from.