A Bayesian approach for inversion of hydraulic tomographic data

Hydraulic tomography is a promising methodology that shows the potential to map subsurface hydraulic properties at an unprecedented level of detail by interpreting a suite of hydraulic tests. In the present work, we apply the hydraulic tomography concept to a Multiple Pulse Multiple Receiver (MPMR) cross-well configuration, which consists of two boreholes subdivided into intervals by packers. A short pressure (or flow) pulse is applied sequentially to all the intervals, and for each perturbation, the transient heads are recorded at the remaining intervals. The resulting tomograms are inverted within the Bayesian framework by using the pilot point approach. In addition to the values of the hydraulic conductivity at the pilot points, we assume that the stochastic parameters of the spatial variability model (the structural parameters) are unknown. Using synthetic two-dimensional and three-dimensional examples, we demonstrate the effectiveness of the MPMR configuration and the inversion procedure for characterizing the spatial variability of the hydraulic conductivity with limited or no prior information. We observed that increasing the number of source points (the locations at which the pulse is alternatively applied) provides more details on the spatial variability and that the parameters of the hydrogeological model of spatial variability are inferred with an acceptable, although variable, level of accuracy. In particular, the theoretical variance of the log conductivity is estimated with large errors, while the estimate of the anisotropic integral scales depends on the distance between the boreholes. Inversion preserves the overall spatial pattern of hydraulic conductivity, although low conductivity values are less connected in the inferred than in the true conductivity fields.