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

Abstract

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.

Improving hydrogeological understanding through well-test interpretation by diagnostic plot and modelling: a case study in an alluvial aquifer in France

“…geophysics (Bowling et al 2005;Vogelgesang et al 2020), geological correlation between well stratigraphic logs (Durozoy 1972;Borgomano et al 2008;Jazayeri Noushabadi et al 2011) or geostatistical approaches (Meier et al 1998;de Marsily et al 2005;Mariethoz et al 2010). Other methods based on hydraulic tomography provide promising results to describe the heterogeneity of hydraulic conductivity and storage coefficient in fractured rocks, but also require a largeamount of field data (Illman 2014;Yeh et al 2014;Fischer et al 2017). As already mentioned, the pumping test is one of the main methods used to characterize hydrodynamic properties, but in-depth analysis of the data is required to identify the reservoir structure.…”

Temporal sampling and role of flux measurements for subsurface heterogeneous characterization in groundwater basins using hydraulic tomography

“…Over the past two decades, hydraulic tomography (HT) has shown a great potential for high‐resolution subsurface characterization in numerical studies (Cardiff, Bakhos, et al, 2013; Illman et al, 2008; Illman et al, 2010), laboratory sandboxes (Illman et al, 2007; Liu et al, 2007; Zhao et al, 2016), and field‐scale studies (Berg & Illman, 2011; Cardiff et al, 2012; Fischer et al, 2017; Kuhlman et al, 2008; Liu, Yeh, Wang, Hao, et al, 2020; Zha et al, 2016). Many researchers (such as Cardiff et al, 2009; Cho et al, 2020; Illman et al, 2007; Soueid Ahmed et al, 2015; Yeh & Liu, 2000; Zhao & Illman, 2017) have demonstrated steady‐state HT's ability to estimate hydraulic conductivity or transmissivity heterogeneity.…”

Efficient estimation of hydraulic conductivity heterogeneity with non-redundant measurement information

“…For measurements with high correlation and therefore redundancy, the proposed compression approach allows decreasing the computational effort of model inversion. The proposed approach is similar to the method in Fischer et al (2017), but instead of applying PCA to the parameter space and reducing the number of parameters, it is applied to the observation space to express the measurements with a reduced number of fixed measurement component terms, as in Rezaie et al (2012). In meteorological forecasting, PCA has been applied for measurement reduction in data assimilation (Collard et al 2010).…”