Hydraulic tomography using joint inversion of head and flux data

Hydraulic tomography is a state of the art method for inferring hydraulic conductivity fields using head data. Here, a numerical model is used to simulate a steady-state hydraulic tomography experiment by assuming a Gaussian hydraulic conductivity field (also constant storativity) and generating the head and flux data in different observation points. We employed geostatistical inversion using head and flux data individually and jointly to better understand the relative merits of each data type. For the typical case of a small number of observation points, we find that flux data provide a better resolved hydraulic conductivity field compared to head data when considering data with similar signal-to-noise ratios. In the case of a high number of observation points, we find the estimated fields to be of similar quality regardless of the data type. A resolution analysis for a small number of observations reveals that head data averages over a broader region than flux data, and flux data can better resolve the hydraulic conductivity field than head data. The inversions' performance depends on borehole boundary conditions, with the best performing setting for flux data and head data are constant head and constant rate, respectively. However, the joint inversion results of both data types are insensitive to the borehole boundary type. Considering the same number of observations, the joint inversion of head and flux data does not offer advantages over individual inversions. By increasing the hydraulic conductivity field variance, we find that the resulting increased non-linearity makes it more challenging to recover high-quality estimates of the reference hydraulic conductivity field. Our findings would be useful for future planning and design of hydraulic tomography tests comprising the flux and head data.