Resolution analysis of tomographic slug test head data: Two‐dimensional radial case

Hydraulic tomography inverse problems, which are solved to estimate aquifer hydraulic properties between wells, are known to be ill-conditioned and a priori information is often added to regularize numerical inversion of head data. Because both head data and a priori information have effects on the inversed solution, assessing the meaningful information contained in head data alone is required to ensure comprehensive interpretation of inverse solutions, whether they are regularized or not. This study thus aims to assess the amount of information contained in tomographic slug tests head data to resolve heterogeneity in Kh, Kv/Kh, and Ss. Therefore, a resolution analysis based on truncated singular value decomposition of the sensitivity matrix with a noise level representative of field measurements is applied using synthetic data reflecting a known littoral aquifer. As an approximation of the hydraulic behavior of a real aquifer system, synthetic tomographic experiments and associated sensitivity matrices are generated using a radial flow model accounting for wellbore storage to simulate slug tests in a plane encompassing a stressed well and an observation well. Although fine-scale resolution of heterogeneities is limited by the diffusive nature of the groundwater flow equations, inversion of tomographic slug tests head data holds the potential to uniquely resolve coarse-scale heterogeneity in Kh, Kv/Kh, and Ss, as inscribed in the resolution matrix. This implies that tomographic head data can provide key information on aquifer heterogeneity and anisotropy, but that fine-scale information must be supplied by a priori information to obtain finer details.