Choice of regularization and numerical results

  This chapter addresses the problem of choosing appropriate regularization and preconditioning operators. Such a choice plays a crucially important role in iterative data regularization. I discuss three strategies appropriate for different kinds of data:

1.

Smoothly varying surfaces are regularized with recursive helical smoothers based on the tension-spline theory.

2.

The local plane-wave model is often suitable for characterizing different kinds of seismic data. Such data are successfully regularized with plane-wave destructor filters.

3.

Seismic reflection data exhibit additional degrees of predictability because of multiple coverage. They can be regularized with finite-difference offset continuation filters. Among the three methods being discussed, the offset continuation approach is the most innovative. The theory behind it is explained in Chapter .

Combining the constructed regularization operator $\bold{D}$ with the appropriate forward operator $\bold{L}$, discussed in Chapter , we obtain a complete problem formulation in the form of system () or (). This chapter is the culmination of this dissertation. It contains final numerical experiments that test and illustrate the main concepts developed in other chapters.