Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: Theoretical fundamentals and applications

Scattering theories of elastic waves in heterogeneous media have broad applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound. This work developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation. The major distinctive feature of the new theory is that the singularity of the Green tensor is properly accounted for, and the renormalized Dyson's equation is reformulated. The dispersion equations for the coherent waves are then obtained by applying Fourier transform to the Dyson equation. Numerical results have shown that the new model is capable of giving a more robust and accurate prediction of velocity and attenuation for both weak and strong scattering materials. To show its applications, dispersion and attenuation curves for coherent waves in the Earth's lithosphere, the porous and two-phase alloys, high-temperature polycrystalline alloys and human cortical bone are calculated. It shows the model can capture the major scattering characteristics, such as the P- and S-wave Q-factors, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and the disappearance of coherent waves.