Contributions

1.

Preconditioning by recursive filtering as a general method for accelerating the convergence of iterative data regularization.

2.

A general approach to iterative data regularization using B-spline forward interpolation.

3.

New choices for the regularization filters:

(a)

tension-spline filters for regularizing smooth two-dimensional surfaces,

(b)

local plane-wave-destructor filters for regularizing seismic images,

(c)

offset and shot continuation filters for regularizing prestack seismic data.

4.

A comprehensive theory of differential offset continuation, which serves as a bridge between integral and convolutional approaches.

The most innovative part of this dissertation is the theory and practical implementation of differential offset continuation. The theory captures the intrinsic connection among different parts of seismic reflection data. The practical implementation transforms differential offset continuation into a local efficiently computed regularization operator.