Приближения эффективной среды для описания многокомпонентных композитов

Several generalizations of the approximation of the effective Bruggeman medium using elliptic cells are compared, namely the “uniaxial” anisotropic approximation and two isotropic models averaged over random orientations and random conductivities of particles, allowing one to consider multicomponent composites with different filler particles.

Anisotropic approximations for mudrocks: A seismic laboratory study

An experimental technique for determining the in‐situ elastic properties of mudrocks with (horizontal) alignments in the microstructure is used to study the accuracy of a set of three nested scalar anisotropic approximations for transversely isotropic (TI) media. Each subsequent approximation adds one more velocity parameter and includes the previous as a special case. These approximations are convenient and robust because of their close relationship to standard geophysical measurements. There exists no good theory to predict the effects of an imposed stress on the elasticity of mudrocks. In this study, the tensor of elastic moduli of a single test specimen of mudrock subjected to an anisotropic stress field is determined from ultrasonic group velocity measurements involving pointlike transducers. The mechanical characterization (performed at constant pore pressure) is accompanied by detailed microscopic observations and analysis. The method was used to obtain accurate elastic constants for five well‐defined mudrocks with different degrees of anisotropy. These elastic constants were then used to study the accuracy of the three anisotropic approximations. We have found that mudrocks can be significantly anelliptic. The agreement between the second anisotropic approximation and the exact phase velocity was found to be very good for qP-waves. For qSV-waves agreement was not as good, and the third anisotropic approximation is required to obtain reasonable accuracy.