Probing through cloudiness: Theory of statistical inversion for multiply scattered data.

Wave multiple scattering is responsible for making a random medium cloudy in appearance and opaque in the sense of structure delineation. For a randomly layered medium such as the earth's subsurface, however, knowledge about the generic behavior of multiple scattering enables us to construct a theory of statistical inversion which can recover from a single data set the slowly varying mean character of a medium with signal amplitude only ${10}^{\mathrm{\ensuremath{-}}3}$ that of the multiple-scattering noise. Inversion accuracy improves systematically with the availability of statistically redundant data.