Extinction cross-section for elastic wave scattering in energy-absorbing media: revisited

A rigorous derivation of the extinction cross-section for elastic wave scattering by an object in an absorbing medium is given. It is necessary to readdress this problem because the assumption of a small detector made in our previous derivation, which essentially leads to the extinction cross-section that is valid strictly in the short wavelength limit, is found to be unnecessary. The detector is now assumed to be infinitely large. This assumption endows the extinction cross-section with a physical meaning that it is a property of the scatterer, independent of the nature of the detector, and is valid in the entire frequency range. Using an integral representation for scattered wave fields instead of using the wave functions for a specific dimension, two- and three-dimensional scattering problems are treated in a unified way. Numerical results are given to demonstrate why the exact extinction cross-section should be used. Applications of the present result to the analysis of wave propagation in inhomogeneous materials are also discussed.