Imaging and inversion of zero-offset seismic data

We present some of the basic problems of seismic inverse theory and some of the basic principles used in solving them. The one-dimensional (1-D) acoustic inverse problem is treated as an introduction to the more important and difficult three-dimensional (3-D) imaging and inverse problems. We argue that certain aspects of seismic data (e.g., CMP stacking and band- and aperture-limiting) are sufficient to prevent a useful generalization to 3-D of some very sophisticated 1-D solution techniques. This leaves such simple and relatively crude methods as Born inversion as useful candidates for generalization from one to three dimensions. A close investigation of 1-D Born inversion yields fairly general principles for overcoming its inadequacies, which are limited accuracy in mapping size and location of reflection events. These principles are based on ray theory, and lead directly to analogous improvements in higher dimensional seismic inversion techniques. These improvements, combined with others which are based on the fact that seismic data reside in the high-frequency regime as far as mapping isolated reflectors is concerned, yield an integral solution of the higher dimensional acoustic inverse problem which has been shown to be useful in practice.