GEOPHYSICAL DIFFRACTION TOMOGRAPHY IN A LAYERED BACKGROUND

The problem of determining the acoustic properties of a geological formation from cross-well tomographic experiments is addressed for formations consisting of a known, plane parallel, layered background in which are imbedded unknown weakly scattering components. The theory is developed using the distorted wave Born approximation along lines analogous to the development of geophysical diffraction tomography (DT) for homogeneous backgrounds. It is shown that the reconstruction algorithms of DT for homogeneous backgrounds can be directly applied to layered backgrounds after suitable preprocessing of a set of line source data by a certain linear operator that is derived in the paper. The paper includes results from a computer simulation illustrating the new reconstruction procedure.