Although migration is not sufficient to image the subsurface in areas with poor illumination Muerdter et al. (1996); Prucha et al. (1998), we can use migration as an imaging operator in an iterative 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).
Selecting proper imaging operators and regularization operators is difficult enough, but there are still two more small but important details. We must select an appropriate value for the regularization parameter to balance the data and model residuals and decide how many iterations (niter) to carry out for this problem. There is no well established way to decide on either of these, and their values will vary depending on the data and inversion operators.
In this paper, I will explain my methodology for selecting and niter for a regularized inversion using wavefield continuation migration as the imaging operator and a steering filter as the regularization operator. I will begin by explaining the inversion scheme. I will then explain a criteria for an optimum and niter. Finally, I will show the effects of and niter on a simple synthetic with well defined illumination problems.