  The geometry of mesoscopic inhomogeneities plays an important role in
determining the macroscopic propagation behaviors of elastic waves in a
heterogeneous medium. Nonequiaxed inhomogeneities can lead to anisotropic wave
velocity and attenuation. Developing an accurate scattering theory to describe
the quantitative relation between the microstructure features and wave
propagation parameters is of fundamental importance for seismology and
ultrasonic nondestructive characterization. This work presents a multiple
scattering theory for strongly scattering elastic media with general triaxial
heterogeneities. A closed analytical expression of the shape dependent
singularity of the anisotropic Green tensor for the homogeneous reference
medium is derived by introducing a proper nonorthogonal ellipsoidal coordinate.
Renormalized Dyson equation for the coherent wave field is then derived with
the help of Feynman diagram technique and the first order smoothing
approximation. The exact dispersion curves and the inverse Q-factors of
coherent waves in several representative medium models for the heterogeneous
lithosphere are calculated numerically. Numerical results for smallscale
heterogeneities with the aspect ratio varying from 1 to 7 show satisfactory
agreement with those obtained from real earthquakes. The results for velocity
dispersion give rise to a novel explanation to the formation mechanism of
different seismic phases. The new model has potential applications in
seismology and ultrasonic microstructure characterization.
