Our ongoing quest for hydrocarbons requires that we improve our ability to image the earth's subsurface. This is particularly true in areas around salt bodies, which can be good hydrocarbon traps but cause poor seismic illumination in the surrounding subsurface. Conventional imaging techniques such as migration cannot provide an adequate picture of these poorly illuminated areas Muerdter et al. (1996); Prucha et al. (1998). In such areas, random noise and processing artifacts can easily obscure the small amount of signal that exists. A common type of artifact seen in these areas is caused by multipathing. Many authors have reduced these artifacts by generating images through Kirchhoff-type migration that create angle domain common image gathers Xu et al. (2001). The artifacts are even better handled by downward continuation migration Prucha et al. (1999a); Stolk and Symes (2004).
However, reducing multipathing artifacts does not significantly improve the image where illumination is poor. If we wish to try to gain information on rock properties through amplitude analysis de Bruin et al. (1990), we will have to deal with both these artifacts and the poor illumination. To improve the image and potentially recover accurate information on rock properties, we must move beyond migration.
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. An intelligent and fairly safe choice 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). I refer to this as ``geophysical'' regularization. This process will help to reduce artifacts and improve the image, but its impact on possible amplitude variation with angle (AVA) analysis must be considered. Kuehl and Sacchi (2002) found that a similar regularization scheme used to compensate for incomplete data rather than the problem of poor illumination could still provide accurate AVA information.
In this paper, I examine the effects of geophysically regularized inversion on a simple synthetic dataset with known AVA. I begin by reviewing the theory of Regularized Inversion with model Preconditioning (RIP). Then I explain the regularization operator used for geophysical RIP. I apply this RIP algorithm to the simple synthetic, using varying numbers of iterations and different strengths of regularization to evaluate the impact of the regularization on the AVA.