• Seismic Reconstruction Interpolation

Seismic data are often irregularly and inadequately sampled spatially due to economic and logistic constraints in in the acquisition stage.
Non-uniform and coarse spatial sampling can introduce noise and artefacts in results from the most commonly used seismic data processing algorithms.
To overcome these problems, several reconstruction methods, with different strengths and weaknesses, are commonly used in the early stages of seismic processing.
The least-squares (LS) Fourier reconstruction method is one possible tool to tackle this problem. LS Fourier econstruction is basically a discrete linear inverse problem that attempts to recover the Fourier spectrum of the seismic wave-field from irregularly sampled data. The estimated Fourier coefficients are then used to reconstruct the data on a regular grid via a standard inverse Fourier transform.
The theory of LS Fourier reconstruction has been well developed in the literature and it is well known that the ill conditioning of the forward operator is the main difficulty in this inverse problem.
In this thesis I describe a numerically stable methods to use and properly weight minimum energy constraints in the LS Fourier estimation that lead to a free-noise spectral estimation. Second I develop a robust method for choosing the optimal spatial bandwidth in the parameterization of the forward operator such that the reconstructed regular data are a good band-limited approximation of the true desired data. Finally I define an efficient method of quality control for the estimated Fourier spectra and the reconstructed regular data. Real data from 3D marine common shot gathers are used to discuss my approach and to show the results of LS Fourier reconstruction with minimum energy constraints.