  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.
