  The geometry and connectivity of fractures exert a strong influence on the
flow and transport properties of fracture networks. We present a novel approach
to stochastically generate three-dimensional discrete networks of connected
fractures that are conditioned to hydrological and geophysical data. A
hierarchical rejection sampling algorithm is used to draw realizations from the
posterior probability density function at different conditioning levels. The
method is applied to a well-studied granitic formation using data acquired
within two boreholes located 6 m apart. The prior models include 27 fractures
with their geometry (position and orientation) bounded by information derived
from single-hole ground-penetrating radar (GPR) data acquired during saline
tracer tests and optical televiewer logs. Eleven cross-hole hydraulic
connections between fractures in neighboring boreholes and the order in which
the tracer arrives at different fractures are used for conditioning.
Furthermore, the networks are conditioned to the observed relative hydraulic
importance of the different hydraulic connections by numerically simulating the
flow response. Among the conditioning data considered, constraints on the
relative flow contributions were the most effective in determining the
variability among the network realizations. Nevertheless, we find that the
posterior model space is strongly determined by the imposed prior bounds.
Strong prior bounds were derived from GPR measurements and helped to make the
approach computationally feasible. We analyze a set of 230 posterior
realizations that reproduce all data given their uncertainties assuming the
same uniform transmissivity in all fractures. The posterior models provide
valuable statistics on length scales and density of connected fractures, as
well as their connectivity.
