具有强性质起伏的非均匀弹性介质的多重散射理论：理论基础和应用
Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation: theoretical fundamentals and applications
摘要：
本文建立了具有强性质涨落的非均匀弹性介质的多重散射模型，并在一阶光滑近似下得到了由Dyson方程导出的色散方程的精确解。该模型建立了微观结构特性与相干波传播参数之间的精确定量关系，可用于微观结构的表征或反演。作为新模型的应用，计算了相干波在地球岩石圈、多孔和两相合金以及人体皮质骨中的色散和衰减曲线。详细分析表明，该模型能够反映出主要的色散和衰减特性，如纵波和横波Q因子及其比值、两种传播模式的存在、反常负色散、非线性衰减-频率关系，甚至相干波的消失。此外，它有助于获得一系列长期存在的问题，如地震衰减的主导机制和Mohorovic不连续的存在新的见解。这项工作提供了一个通用的和准确的理论框架，定量表征的微观结构在一个广泛的异质材料，预计在地震学，超声无损评价和生物医学超声有重要的应用。
英文摘要：
In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the first-order smoothing approximation. The model establishes accurate quantitative relation between the microstructural properties and the coherent wave propagation parameters and can be used for characterization or inversion of microstructures. As applications of the new model, dispersion and attenuation curves for coherent waves in the Earth lithosphere, the porous and two-phase alloys, and human cortical bone are calculated. Detailed analysis shows the model can capture the major dispersion and attenuation characteristics, such as the longitudinal and transverse wave Q-factors and their ratios, existence of two propagation modes, anomalous negative dispersion, nonlinear attenuation-frequency relation, and even the disappearance of coherent waves. Additionally, it helps gain new insights into a series of longstanding problems, such as the dominant mechanism of seismic attenuation and the existence of the Mohorovicic discontinuity. This work provides a general and accurate theoretical framework for quantitative characterization of microstructures in a broad spectrum of heterogeneous materials and it is anticipated to have vital applications in seismology, ultrasonic nondestructive evaluation and biomedical ultrasound.
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