A .Djibrilla Saley*, A. Jardani, A. Soueid Ahmed, A. Raphael, J.P. Dupont., 2016: Hamiltonian Monte Carlo algorithm for the characterization of hydraulic conductivity from the heat tracing data. Advances in Water Resources, Volume 97, November 2016, Pages 120–129.

(* Advised PhD student)

Estimating spatial distributions of the hydraulic conductivity in heterogeneous aquifers has always been an important and challenging task in hydrology. Generally, the hydraulic conductivity field is determined from hydraulic head or pressure measurements. In the present study, we propose to use temperature data as source of information for characterizing the spatial distributions of the hydraulic conductivity field. In this way, we performed a laboratory sandbox experiment with the aim of imaging the heterogeneities of the hydraulic conductivity field from thermal monitoring. During the laboratory experiment, we injected a hot water pulse, which induces a heat plume motion in the sandbox. The induced plume was followed by a set of thermocouples placed in the sandbox. After the temperature data acquisition, we performed a hydraulic tomography using the stochastic Hybrid Monte Carlo approach, also called the Hamiltonian Mont Carlo (HMC) algorithm to invert the temperature data. This algorithm is based on a combination of the Metropolis Monte Carlo method and the Hamiltonian dynamics approach. The parameterization of the inverse problem was done with the Karhunen-Loève (KL) expansion to reduce the dimensionality of the unknown parameters. Our approach has provided successful reconstruction of the hydraulic conductivity field with low computational effort

Jardani. A, A. Revil, A. Bolève , and J.P. Dupont, 2008 : Pattern of groundwater flow inferred from the three-dimensional inversion of self potential data and application to geothermal fields. Journal of Geophysical Research., 113, B09204, doi:10.1029/2007JB005302. (pdf)

We propose an algorithm to invert self-potential signals measured at the ground surface of the Earth to localize hydromechanical disturbances or to the pattern of groundwater flow in geothermal systems. The self-potential signals result from the divergence of the streaming current density. Groundwater flow can be either driven by topography of the water table, free convection, or deformation of the medium. The algorithm includes the electrical resistivity distribution of the medium obtained independently by DC resistance tomography or electromagnetic methods or by coding the assumed geology in terms of distribution of the electrical resistivity accounting for the effect of the temperature and salinity distributions and possibly constraints from borehole measurements. An application is presented to the geothermal field of Cerro Prieto, Baja California, Mexico, using literature data. Inversion of the self-potential and resistivity data allows observing a plume of hot groundwater rising to the ground surface in the central part of the investigated area and discharging to the ground surface in the southwest part. The temperature anomaly associated with the existence of this plume is independently observed by interpolating borehole temperature measurements. We found a good agreement between the distribution of the temperature and the inverted source current density. The proposed method appears therefore as a noninvasive method for remote detection and three-dimensional mapping of subsurface groundwater flow.

Jardani, A. and A. Revil, 2009: Stochastic joint inversion Joint inversion of temperature and self-potential data.Geophysical Journal International,doi:1.1111/j.1365-246X.2009.04295.x (pdf)

The flow of the ground water is responsible for both thermal and self-potential anomalies. Temperature is usually recorded in boreholes while self-potential is usually recorded at the ground surface of the Earth. This makes the joint inversion of temperature and self-potential data together an attractive approach to invert permeability. We use an Adaptive Metropolis Algorithm to determine the posterior probability densities of the material properties of different geological formations and faults by inverting jointly self-potential and temperature data. The algorithm is tested using a synthetic case corresponding to a series of sedimentary layers overlying a low-permeability granitic substratum. The flow of the ground water (computed in steady-state condition) is mainly localized in two faults acting as preferential fluid flow pathways. The first fault is discharging warmed ground water near the ground surface while the second fault acts as a recharge zone of cold water (a classical scenario in geothermal systems). The joint inversion algorithm yield accurate estimate of the permeability of the different units only if both temperature and self-potential data are jointly inverted. An application using real data is also performed. It concerns the upwelling of a hydrothermal plume through a set of faults and permeable formations at the Cerro Prieto geothermal field in Baja California. The optimized permeabilities are in close agreement with independent hydrogeological estimates.