Jardani, A, J.P. Dupont, A. Revil, N. Massei, M. Fournier and B. Laignel, 2012 : Geostatistical inverse modeling of the transmissivity field of a heterogeneous alluvial aquifer under tidal influence. Journal of Hydrology, 472-473, P287-300. (pdf)

The record of the head fluctuations of an alluvial aquifer connected to the estuary of a river submitted to tidal influence can be used to reconstruct the transmissivity field of the aquifer. A Markov chain Monte Carlo (McMC) sampler is used to invert the transmissivity field at a set of pilot points. Our approach is first successfully benchmarked on a synthetic case study. Then, we present a real case study in which both a semi-confined aquifer and a shallow unconfined aquifer are connected to the estuary of the Seine River in the western-north of France. These aquifers experience strong tidal variations up to 8.4 m. This test site is equipped with a series of seventeen wells in which the temporal fluctuations of water heads associated with megatidal forcing were recorded during several years. In addition to the use of the pilot points method, a zoning parameterization with 45 zones is used to determine the vertical leakage coefficient from the semi-confined aquifer into the shallow unconfined aquifer. The distribution of the vertical leakage coefficient is determined by inverting the hydraulic head at a set of wells localized in thesemi-confined aquifer. We determine jointly the distribution of the hydraulic transmissivity and the vertical leakage from the semi-confined into the unconfined aquifer using 72 pilot points. The storage coefficient is assumed to be constant over the whole domain. Its value is determined from three pumping tests that show a consistent value for this parameter (log10S = ÿ5 and 0.11 as a variance). In our approach, there are 119 model parameters (72 transmissivity values at the pilot points, 45 values of the vertical leakage coefficient, and two parameters (sill and range) for the isotropic variogram). The spatial distribution of the hydraulic transmissivity agrees qualitatively with the soil texture variations observed in the semi-confined aquifer and core samples analysis.

Wang, X, A. Jardani, H. Jourde, L. Lonergan, J. Cosgrove, O. Gosselin and G, Massonnat, 2016: Characterisation of the transmissivity field of a fractured and karstic aquifer, Southern France. Advances in Water Resources, Volume: 87, Pages: 106-121. (pdf)

Geological and hydrological data collected at the Terrieu experimental site north of Montpellier, in a confined carbonate aquifer indicates that both fracture clusters and a major bedding plane form the main flow paths of this highly heterogeneous karst aquifer. However, characterising the geometry and spatial location of the main flow channels and estimating their flow properties remain difficult. These challenges can be addressed by solving an inverse problem using the available hydraulic head data recorded during a set of interference pumping tests. We first constructed a 2D equivalent porous medium model to represent the test site domain and then employed regular zoning parameterisation, on which the inverse modelling was performed. Because we aim to resolve the fine-scale characteristics of the transmissivity field, the problem undertaken is essentially a large-scale inverse model, i.e. the dimension of the unknown parameters is high. In order to deal with the high computational demands in such a large-scale inverse problem, a gradient-based, non-linear algorithm (SNOPT) was used to estimate the transmissivity field on the experimental site scale through the inversion of steady-state, hydraulic head measurements recorded at 22 boreholes during 8 sequential cross-hole pumping tests. We used the data from outcrops, borehole fracture measurements and interpretations of inter-well connectivities from interference test responses as initial models to trigger the inversion. Constraints for hydraulic conductivities, based on analytical interpretations of pumping tests, were also added to the inversion models. In addition, the efficiency of the adopted inverse algorithm enables us to increase dramatically the number of unknown parameters to investigate the influence of elementary discretisation on the reconstruction of the transmissivity fields in both synthetic and field studies.By following the above approach, transmissivity fields that produce similar hydrodynamic behaviours to the real head measurements were obtained. The inverted transmissivity fields show complex, spatial heterogeneities with highly conductive channels embedded in a low transmissivity matrix region. The spatial trend of the main flow channels is in a good agreement with that of the main fracture sets mapped on outcrops in the vicinity of the Terrieu site suggesting that the hydraulic anisotropy is consistent with the structural anisotropy. These results from the inverse modelling enable the main flow paths to be located and their hydrodynamic properties to be estimated.