Discussion

Not surprisingly, the two methods generally represented by Equation (17) produce significantly different results. Although our analysis in this paper does not cover all cases and possibilities, we can make several observations:

• The general form in Equation (17) is not unique, meaning that other forms of equal generality exist. Moreover, we have presented and compared just two members of our general form, although many others exist. The obvious question, for which we do not have a definite answer, is which is the optimal form? Is there such thing, or do we need to consider different forms for different situations? These questions remain the subject of future research.
• The target image fitting (TIF) approach is an attractive alternative because it can, in principle, be driven in the desired direction given by the target image. However, if the constraints presented by the Born approximation are not observed (i.e. the target is too far from the actual image), then inversion may diverge Sava and Fomel (2002). We also need to create the actual target, an improved image, which is not a trivial task.
• The differential semblance optimization (DSO) approach is also attractive for other reasons. The objective function is smooth and unimodal, at least for certain simplified cases Symes (1999). However, even DSO is not guaranteed to converge when the data are aliased or when they are polluted with residual multiples or converted waves.