This dissertation addresses the problem of interpolating irregularly spaced seismic exploration data to regular spatial locations. 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.