An inversion method for separating apparent and intrinsic attenuation in layered media

Abstract

Summary. The method proposed by Menke and Dubendorff for separating the effects of intrinsic and apparent attentuation (due soIely to scattering) is studied. The basic algorithm is shown to be applicable not only to alayered medium, as first proposed, but also to a three-dimensionally heterogeneous medium, as long as the medium possesses a scaling between correlation functions of material properties (compressional and shear velocity, density). The plane layered algorithm is analysed in detail. A rigorous derivation is presented that demonstrates that the inversion formula is unique. The validity of one of the fundamental assumptions of the method, the additivity of intrinsic and apparent attenuation, is discussed, and is shown to be valid in the context of mean field theory. The influence of random noise and of limited bandwidth on the solution are investigated through fdter theory and numerical simulations.