Overall properties of heterogeneous material

Abstract

Small‐scale heterogeneity in crustal structure can be very complex and difficult to describe in detail and yet, at the same time, can be very important for the description of, for instance, tectonic stress and porosity. Statistical properties of such heterogeneity can be derived from the properties of waves of relatively large wavelength as they propagate through the crust. The differences between measured wavelengths and attenuation coefficients and those of compact rock and the variations of these quantities in space and time provide, in principle, a means of determining quantities like the density and orientations of microfractures and the nature of crack infill material. The theoretical basis for inferences of this kind is the concept of the ‘effective’ or ‘equivalent’ material based on an averaging process taken over the microstructure. A number of methods have been used to calculate the properties of the effective medium, several of which are described here. Copyright © 1991, Wiley Blackwell. All rights reserved