| In seismic data processing, we often need to interpolate and extrapolate missing data at spatial locations. The reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data we attempt to reconstruct the seismic wavefield at locations where measurements were not acquired. This thesis presents a wavefield reconstruction scheme called minimum weighted norm interpolation (MWNI) for spatially band limited signals. The method entails the solution of an inverse problem where a wavenumber domain regularization term is included. The regularization term is not only used to constrain the solution to be spatially band limited but also to impose a priori spectral shape.; The numerical algorithm is quite efficient since the method of conjugate gradients in conjunction with fast matrix-vector multiplication, implemented via the Fast Fourier Transform (FFT), were adopted. In addition, its computational efficiency allows for feasible extensions to higher dimensional interpolation schemes.; In this thesis, the MWNI method is used to interpolate prestack seismic data before wave equation amplitude versus angle imaging. Synthetic data were used to investigate the effectiveness of the 2-D/3-D MWNI scheme at the time of preconditioning seismic data for wave equation AVA imaging where a regular and dense data sampling is required to accurately estimate angle gathers. Two field data examples are presented to illustrate the application of the multi-dimensional MWNI schemes to real-world datasets. |
