Hydraulic conductivity field characterization from the joint inversion of hydraulic heads and self‐potential data

Abstract

Pumping tests can be used to estimate the hydraulic conductivity field from the inversion of hydraulic head data taken intrusively in a set of piezometers. Nevertheless, the inverse problem is strongly underdetermined. We propose to add more information by adding self-potential data taken at the ground surface during pumping tests. These self-potential data correspond to perturbations of the electrical field caused directly by the flow of the groundwater. The coupling is electrokinetic in nature that is due to the drag of the excess of electrical charges existing in the pore water. These self-potential signals can be easily measured in field conditions with a set of the nonpolarizing electrodes installed at the ground surface. We used the adjoint-state method for the estimation of the hydraulic conductivity field from measurements of both hydraulic heads and self potential during pumping tests. In addition, we use a recently developed petrophysical formulation of the streaming potential problem using an effective charge density of the pore water derived directly from the hydraulic conductivity. The geostatistical inverse framework is applied to five synthetic case studies with different number of wells and electrodes and thickness of the confining unit. To evaluate the benefits of incorporating the self-potential data in the inverse problem, we compare the cases in which the data are combined or not. Incorporating the self-potential information improves the estimate of hydraulic conductivity field in the case where the number of piezometers is limited. However, the uncertainty of the characterization of the hydraulic conductivity from the inversion of the self-potential data is dependent on the quality of the distribution of the electrical conductivity used to solve the Poisson equation. Consequently, the approach discussed in this paper requires a precise estimate of the electrical conductivity distribution of the subsurface and requires therefore new strategies to be developed for the joint inversion of the hydraulic and electrical conductivity distributions.

A Physically Based Analytical Model to Describe Effective Excess Charge for Streaming Potential Generation in Water Saturated Porous Media

“…Some years later, Jardani et al (2007) proposed a more precise empirical relationship that has been proven to be very useful as it decreases the number of variables to be estimated and provides good estimates of effective excess charge for different types of porous media. This relationship has been used in many studies involving electrokinetic phenomena, such as dam leakage (e.g., Bolève et al, 2009;Ikard et al, 2014), surface-groundwater interaction (e.g., Linde et al, 2011), seismoelectric studies (e.g., Mahardika et al, 2012;Monachesi et al, 2015;Revil et al, 2015), hydraulically active fracture identification (e.g., Roubinet et al, 2016), and permeability field characterization (e.g., Jardani & Revil, 2009;Soueid Ahmed et al, 2014). However, equation (26) has been obtained regardless of pore water composition and other hydraulic parameters of porous media.…”

Exploring the Effect of the Pore Size Distribution on the Streaming Potential Generation in Saturated Porous Media, Insight From Pore Network Simulations

“…Among these works, Jardani et al () propose the following empirical relationship where A 1 =−9.2349 and A 2 =−0.8219 are constant values obtained by fitting equation to a large set of experimental data that includes various lithologies and ionic concentrations. It has been widely used for SP (e.g., Jardani & Revil, ; Linde et al, ; Roubinet et al, ; Soueid Ahmed et al, ) and seismoelectrics (e.g., Jougnot et al, ; Monachesi et al, ; Revil et al, ) applications.…”

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

“…In addition to the PCGA experimental application presented above, several other inversions were also conducted for the same field site but with a smaller number of parameters and using different methods for the computation of sensitivity matrix (input for each inversion is shown in Table ). These numerical experiments allows us to compare (1) the results from PCGA with varied low‐rank truncation and (2) the results from PCGA to those obtained from the GA method with a first‐order finite‐difference Jacobian matrix computation, and an adjoint‐state Jabobian matrix computation (the integral was solved using the Gauss‐Legendre quadratic method as described in Soueid Ahmed et al ) The inversion results are compared with respect to the total computation time and relative accuracy of the results.…”