Several methods of seismic data regularization appear in the geophysical literature and in the practice of seismic exploration.
One group of methods is based on different types of integral (Kirchhoff) continuation operators, such as offset continuation Bagaini and Spagnolini (1996); Chemingui and Biondi (1994); Stovas and Fomel (1993, 1996), shot continuation Bagaini and Spagnolini (1993); Schwab (1993); Spagnolini and Opreni (1996), and azimuth moveout Biondi et al. (1998). Integral continuation operators can be applied directly for missing data interpolation and regularization Bagaini et al. (1994); Mazzucchelli and Rocca (1999). However, they do not behave well for continuation at small distances in the offset space because of limited integration apertures and, therefore, are not well-suited for interpolating neighboring records. Additionally, like all integral (Kirchhoff-type) operators, they suffer from irregularities in the input geometry. The latter problem is addressed by accurate but expensive inversion to common offset Chemingui (1999).
Another group of methods formulates data regularization as an iterative optimization problem with a convolution operator Claerbout (1992, 1999). Convolution with prediction-error filters is a popular choice for interpolating locally plane seismic events Spitz (1991). The method has a comparatively high efficiency, which degrades in the case of large data gaps. Handling non-stationary events presents an additional difficulty. Non-stationary prediction-error filtering leads to an accurate but relatively expensive method with many adjustable parameters Clapp et al. (1999); Crawley (1999).
Methods based on nonuniform discrete Fourier transforms Duijndam et al. (1999); Hindriks et al. (1997) or Radon transforms Ji (1994); Thorson and Claerbout (1985) have some attractive computational properties but do not outperform convolutional optimization methods and have serious limitations with respect to regularizing aliased data.
In this dissertation, I follow Claerbout's iterative optimization framework, extending it in several important ways. The major original contributions of this work are summarized below.