Large-Scale Inverse Modeling with an Application in Hydraulic Tomography

Hydraulic tomography has been suggested as a promising method for estimating subsurface hydraulic conductivity distributions - a key prerequisite for performing accurate and realistic flow and transport simulations. This method tends to produce large data sets and requires to resolve variability on a fine grid, which demands inverse modeling methods that can efficiently handle large scale problems, for instance, with millions of unknowns and perhaps hundreds of thousands of observations. We propose in this presentation a Bayesian inverse modeling methodology that is suitable for large-scale problems. This stochastic approach can take advantage of modern computer architectures and high-performance computational techniques. We have applied this methodology to a laboratory hydraulic tomography problem, where we successfully estimated half a million unknowns that represent the hydraulic conductivity field of the sandbox at a very fine scale. The lab experiments were conducted, as part of a different study, at the University of Iowa by Professor Walter Illman and his coworkers. We then compared the results with a few other inverse methods and found that the proposed methodology performed better than the other methods in several aspects, including computation time and memory requirement.