Stochastic inversion of three-dimensional discrete fracture network structure with hydraulic tomography

Abstract

We introduce an approach for the stochastic characterization of the geometric and hydraulic parameters of a three-dimensional (3D) discrete fracture network (DFN) and for estimating their uncertainty based on data from hydraulic tomography experiments. The inversion approach relies on a Bayesian framework and the resulting posterior distribution is characterized by generating samples by Markov chain Monte Carlo (MCMC) methods. The inversion method is evaluated for four synthetic test cases related to the Grimsel test site in Switzerland. Comparison of original and reconstructed DFN models shows that the presented approach is suitable for identifying variable fracture locations and orientations. This is especially the case for those fractures that represent the preferential flow paths in the simulated experiments. It is also revealed that the Bayesian framework is useful to discriminate fractures based on the reliability of the inversion, which is illustrated by fracture probability maps taken as sections through the studied rock mass. Moreover, it is demonstrated that the hydraulic apertures can be calibrated together with the fracture geometries. A premise for applicability in practice, however, is that the hydraulic measurements are complemented by additional information to sufficiently constrain the value ranges of the geometric and hydraulic parameters to be inverted together. The presented work expands the applicability of a previously presented promising two-dimensional procedure based on transdimensional inversion to field-based 3D problems. The theoretical findings here open the door for highly flexible structural characterization in practice based on hydraulic tomography, as well as alternative or complementary tomographic methods.