On the weakness of a multiple scattering theory for weak ultrasound scattering

2Department of Engineering Sciences and Mechanics, Pennsylvania State University, University Park, PA, 16802 We report an in-depth look into commonly applied theories describing the propagation of ultrasound in polycrystalline materials. The analysis indicates that integrals involving multiple spatial derivatives on the tensor of the Green's function were inappropriately defined as a result of neglecting its singularity. The subsequent impact is demonstrated via an instability in the dispersion relations for two-phase polycrystals having locally isotropic constituents. Evaluation of the dispersion relation reveals non-physical values of negative attenuation in certain cases. Correcting these terms accounts for strong property fluctuations and provides quantitative error estimates for the velocity dispersion and attenuation constants.