Multiple Scattering Theory for Heterogeneous Elastic Continua with Strong Property Fluctuation: Theoretical Fundamentals and Applications

摘要

In this work, the author developed a multiple scattering model forheterogeneous elastic continua with strong property fluctuation and obtainedthe exact solution to the dispersion equation derived from the Dyson equationunder the first-order smoothing approximation. The model establishes accuratequantitative relation between the microstructural properties and the coherentwave propagation parameters and can be used for characterization or inversionof microstructures. As applications of the new model, dispersion andattenuation curves for coherent waves in the Earth lithosphere, the porous andtwo-phase alloys, and human cortical bone are calculated. Detailed analysisshows the model can capture the major dispersion and attenuationcharacteristics, such as the longitudinal and transverse wave Q-factors andtheir ratios, existence of two propagation modes, anomalous negativedispersion, nonlinear attenuation-frequency relation, and even thedisappearance of coherent waves. Additionally, it helps gain new insights intoa series of longstanding problems, such as the dominant mechanism of seismicattenuation and the existence of the Mohorovicic discontinuity. This workprovides a general and accurate theoretical framework for quantitativecharacterization of microstructures in a broad spectrum of heterogeneousmaterials and it is anticipated to have vital applications in seismology,ultrasonic nondestructive evaluation and biomedical ultrasound.