sgr ms thesis - University of Maine

to place a minimum size limit when measuring clasts (Blenkinsop, 1991; Clark
and James, 2003; Barnett, 2004).
CSD data are commonly presented with respect to 3-dimensional space. If
an object is fractal in 2-dimensions, it is also fractal in 3-dimensions, and
(5.5)
This conversion is validated by the fact that D s refers to the line, surface, or
space that dissects the object. An increase in Euclidean dimension requires the
same increase in D s (e.g. Sammis et al., 1987). This conversion is justified for a
breccia made of a homogeneous, isotropic material, but error can be introduced
if this assumption is used on anisotropic materials (e.g. Barnett, 2004; Farris and
Paterson, 2007). To reduce this potential error, outcrops with 3 dimensional
exposures can be used. Clast distribution can also be expressed as a function of
clast frequency versus mass (e.g. Hartmann, 1969; Blenkinsop, 1991), or percent
sample by weight versus diameter (see Schoutens, 1979), both of which are
directly related to a 3-dimensional distribution. These results also pertain to
power law distributions and therefore their slopes are proportional and can be
converted to D s (Blenkinsop, 1991; Perfect, 1997).
5.3.2. The Fractal Dimension-Brecciation Mechanism Link for Clast
Size Distribution (CSD)
Understanding the brecciation mechanism will provide important
information on the mechanical response to subsurface volcanic eruption. As CSD
results are a function of the self-similar manner by which fractures proliferate
54