This dissertation addresses the problem of interpolating irregularly spaced seismic exploration data to regular spatial locations. This problem arises in practice in three-dimensional seismic exploration in such applications as Kirchhoff prestack migration, multiple elimination, wave-equation migration, and 4-D seismic monitoring.

I formulate data regularization as a linear-estimation problem and solve it with an iterative optimization algorithm. I develop a general method of accelerating the iterative convergence using inverse recursive filtering and show that invertible multidimensional filters can be created by spectral factorization in helical coordinates.

Different choices exist for the regularization operator in iterative data regularization.

- Smoothly varying surfaces are regularized with recursive helical smoothers based on the tension-spline theory.
- The local plane-wave model is suitable for characterizing different types of seismic data. Such data are successfully regularized with plane-wave destructor filters.
- Seismic reflection data exhibit additional degrees of predictability because of multiple coverage. They can be regularized with finite-difference offset and shot continuation filters.

Synthetic and real data tests demonstrate the performance and applicability of the proposed data regularization methods. I show that a local plane-wave continuity of the input data allows for an efficient regularization with plane-wave filters. Increasing the filter accuracy leads to more accurate results. Alternatively, seismic data can be regularized with offset-continuation filters, which operate efficiently in frequency slices and bring information from neighboring offsets. Offset continuation succeeds in structurally complex situations where more simplistic approaches fail. The dataset tested is 3-D marine from the North Sea.

- Introduction (ps.gz 631K) (pdf 1174K) (src 2926K)
- Fundamentals of data regularization (ps.gz 35K) (pdf 62K) (src 5K)
- Forward interpolation (ps.gz 1214K) (pdf 1181K) (src 5989K)
- Iterative data regularization (ps.gz 809K) (pdf 939K) (src 6412K)
- Choice of regularization and numerical results (ps.gz 4266K) (pdf 3609K) (src 20539K)
- Offset continuation for reflection seismic data (ps.gz 286K) (pdf 299K) (src 697K)
- Conclusions (ps.gz 7K) (pdf 12K) (src 1K)
- Second-order reflection traveltime derivatives (ps.gz 46K) (pdf 63K) (src 47K)
- Solving the Cauchy problem
- The kinematics of offset continuation
- REFERENCES
- About this document ...

12/28/2000