Application of Large-Scale Inversion Algorithms to Hydraulic Tomography in an Alluvial Aquifer

Large-scale inversion methods have been recently developed and permitted now to considerably reduce the computation time and memory needed for inversions of models with a large amount of parameters and data. In this work, we have applied a deterministic geostatistical inversion algorithm to a hydraulic tomography investigation conducted in an experimental field site situated within an alluvial aquifer in Southern France. This application aims to achieve a 2-D large-scale modeling of the spatial transmissivity distribution of the site. The inversion algorithm uses a quasi-Newton iterative process based on a Bayesian approach. We compared the results obtained by using three different methodologies for sensitivity analysis: an adjoint-state method, a finite-difference method, and a principal component geostatistical approach (PCGA). The PCGA is a large-scale adapted method which was developed for inversions with a large number of parameters by using an approximation of the covariance matrix, and by avoiding the calculation of the full Jacobian sensitivity matrix. We reconstructed high-resolution transmissivity fields (composed of up to 25,600 cells) which generated good correlations between the measured and computed hydraulic heads. In particular, we show that, by combining the PCGA inversion method and the hydraulic tomography method, we are able to substantially reduce the computation time of the inversions, while still producing high-quality inversion results as those obtained from the other sensitivity analysis methodologies.