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.
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.