When modeling rocks using effective medium theory, or really any
approach, it is important to minimize the number of choices (size and
shape of the inclusions, etc.) available to the modeler. Especially
when dealing with cracks and
simultaneously with partial and patchy saturation, the number of
possible scenarios multiplies rapidly. For example, it would be
entirely realistic to assume that there is a distribution of both crack aspect
ratios and sizes present in the rocks. But since this distribution is
surely not known, we will assume instead that there is only a single
aspect ratio of crack present and choose values to lie in the range
-0.1. The decision to have only one aspect ratio is
arbitrary. But it is motivated by the need to minimize the
nonuniqueness inherent in the enterprise of fitting these data.
Occam's razor applies here: we try to use the simplest possible model
(a single aspect ratio), and if we cannot fit the data then we have
learned something about the rock. We will find however that the
simplest model is always sufficient when fitting the velocity data
alone. The range of values that are considered sensible are based in
part on the data of Hadley (1976) on Westerly granite, where it was
observed that ranged from 10^{-4} all the way up to unity,
with a mode around 10^{-3}.

11/11/2002