Generalized stack operator for diffraction tomography

The problem of determining the acoustic properties of a layered background in which unknown weakly scattering components are imbedded is addressed within the context of diffraction tomography. The theory is developed using a generalized slant stack operator and the distorted wave Born approximation analogy to the development of diffraction tomography (DT) for constant backgrounds. It is shown that the reconstruction algorithms of DT for constant backgrounds can be directly applied to layered backgrounds after suitable preprocessing of a set of line source data by the generalized slant stack operator that is derived here