Properly imaging the subsurface in areas that are structurally complex is a daunting task. The migration algorithms typically used for imaging are unable to provide satisfactory images where shadow zones are common, particularly around salt bodies Muerdter et al. (1996); Prucha et al. (1998). Since salt can make a good hydrocarbon trap, these areas are where we would really like to obtain good images.
There have been many improved migration algorithms that ameliorate the effects of the complex subsurface. Several authors have demonstrated that wave equation migration methods can provide better images than Kirchhoff migration methods Geoltrain and Brac (1993); O'Brien and Etgen (1998). Additionally, some artifacts commonly seen in complex areas are caused by seismic energy that arrives at the receivers at the same time, but follow different paths through and reflect at different points in the subsurface ten Kroode et al. (1994). These artifacts can be reduced by creating images with angle-domain common image gathers (ADCIGs). Methods that produce ADCIGs through Kirchhoff techniques Xu et al. (2001) may partially reduce artifacts caused by multipathing, but still have difficulties Stolk and Symes (2002). Wave equation methods to create ADCIGs Mosher and Foster (2000); Prucha et al. (1999) handle multipathing better Stolk and De Hoop (2001); Stolk and Symes (2004). However, regardless of how a migration algorithm is formulated, migration is generally insufficient to image poorly illuminated areas Prucha et al. (2001).
To improve our seismic imaging in areas of poor illumination, we can use migration as an imaging operator in a least-squares inversion scheme Duquet and Marfurt (1999); Kuehl and Sacchi (2001); Nemeth et al. (1999); Prucha and Biondi (2002b); Ronen and Liner (2000). In areas with poor illumination, the inversion problem is ill-conditioned; therefore, it is wise to regularize the inversion 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 (2002a).
In this paper, we will begin by reviewing a scheme for iterative regularized inversion. We will implement an inversion scheme that regularizes amplitudes along offset ray parameters (reflection angles) on a real 2-D seismic line from the Gulf of Mexico. We will also discuss how our regularized inversion scheme that can be applied to the real 3-D dataset from which we extracted the 2-D line.