Scalable subsurface inverse modeling of huge data sets with an application to tracer concentration breakthrough data from magnetic resonance imaging

Characterizing subsurface properties is crucial for reliable and cost-effective groundwater supply management and contaminant remediation. With recent advances in sensor technology, large volumes of hydrogeophysical and geochemical data can be obtained to achieve high-resolution images of subsurface properties. However, characterization with such a large amount of information requires prohibitive computational costs associated with big data'' processing and numerous large-scale numerical simulations. To tackle such difficulties, the principal component geostatistical approach (PCGA) has been proposed as a Jacobian-free'' inversion method that requires much smaller forward simulation runs for each iteration than the number of unknown parameters and measurements needed in the traditional inversion methods. PCGA can be conveniently linked to any multiphysics simulation software with independent parallel executions. In this paper, we extend PCGA to handle a large number of measurements (e.g., 106 or more) by constructing a fast preconditioner whose computational cost scales linearly with the data size. For illustration, we characterize the heterogeneous hydraulic conductivity (K) distribution in a laboratory-scale 3-D sand box using about 6 million transient tracer concentration measurements obtained using magnetic resonance imaging. Since each individual observation has little information on the K distribution, the data were compressed by the zeroth temporal moment of breakthrough curves, which is equivalent to the mean travel time under the experimental setting. Only about 2000 forward simulations in total were required to obtain the best estimate with corresponding estimation uncertainty, and the estimated K field captured key patterns of the original packing design, showing the efficiency and effectiveness of the proposed method.