next up previous print clean
Next: Acknowledgments Up: Choice of regularization and Previous: Shot continuation


Several choices exist in selecting the regularization operator for iterative data regularization.

Splines in tension represent an approach to data regularization suitable for smooth data. The constraint is embedded in a user-specified[*] tension parameter. The two boundary values of tension correspond to cubic and linear interpolation. By applying the method of spectral factorization on a helix, I have been able to define a family of two-dimensional minimum-phase filters, which correspond to the spline interpolation problem with different values of tension. These filters contribute to the collection of useful helical filters. I have used them for preconditioning in data-regularization problems with smooth surfaces. In general, they are applicable for preconditioning various estimation problems with smooth models.

I demonstrate that adaptive local plane-wave destructors with an improved finite-difference design can be a valuable tool in processing multidimensional seismic data. In several examples, I have shown a good performance of plane-wave destructors in application to data regularization. It may be useful to summarize here the similarities and differences between plane-wave destructors and T-X prediction-error filters.


Differences: I have shown that a 3-D plane-wave destruction filter can be designed from a pair of two-dimensional filters by using helix transform and the Wilson-Burg spectral factorization algorithm. A special approach to designing plane-wave destructor filters follows from the general B-spline regularization method.

Differential offset continuation provides a valuable tool for regularization of reflection seismic data. Starting from analytical frequency-domain solutions of the offset continuation differential equation, I have designed accurate finite-difference filters for implementing offset continuation as a local convolutional operator. A similar technique works for shot continuation across different shot gathers.

Differential offset continuation serves as a bridge between integral and convolutional approaches to data interpolation. It shares the theoretical grounds with the integral approach but is applied in a manner similar to that of prediction-error filters in the convolutional approach.

Tests with synthetic and real data demonstrate that the offset-continuation regularization can succeed in complex structural situations where more simplistic methods fail.

next up previous print clean
Next: Acknowledgments Up: Choice of regularization and Previous: Shot continuation
Stanford Exploration Project