Joint inversion of hydraulic head and self‐potential data associated with harmonic pumping tests

Abstract

Harmonic pumping tests consist in stimulating an aquifer by the means of hydraulic stimulations at some discrete frequencies. The inverse problem consisting in retrieving the hydraulic properties is inherently ill posed and is usually underdetermined when considering the number of well head data available in field conditions. To better constrain this inverse problem, we add self‐potential data recorded at the ground surface to the head data. The self‐potential method is a passive geophysical method. Its signals are generated by the groundwater flow through an electrokinetic coupling. We showed using a 3‐D saturated unconfined synthetic aquifer that the self‐potential method significantly improves the results of the harmonic hydraulic tomography. The hydroelectric forward problem is obtained by solving first the Richards equation, describing the groundwater flow, and then using the result in an electrical Poisson equation describing the self‐potential problem. The joint inversion problem is solved using a reduction model based on the principal component geostatistical approach. In this method, the large prior covariance matrix is truncated and replaced by its low‐rank approximation, allowing thus for notable computational time and storage savings. Three test cases are studied, to assess the validity of our approach. In the first test, we show that when the number of harmonic stimulations is low, combining the harmonic hydraulic and self‐potential data does not improve the inversion results. In the second test where enough harmonic stimulations are performed, a significant improvement of the hydraulic parameters is observed. In the last synthetic test, we show that the electrical conductivity field required to invert the self‐potential data can be determined with enough accuracy using an electrical resistivity tomography survey using the same electrodes configuration as used for the self‐potential investigation.

Combining periodic hydraulic tests and surface tilt measurements to explore in situ fracture hydromechanics

“…Such leakage effect could dramatically decrease fracture deformation beyond the intersection. A way to test this hypothesis on the field would be to combine the harmonic hydromechanical test described in this paper, with geophysical methods which are sensitive to subsurface fluid paths like GPR [e.g., Shakas et al , ] or self‐potential data, already used in the periodic test framework by Maineult et al [] and by Soueid Ahmed et al []. Furthermore, we were able to evidence the distinct mechanical responses of the three tested fractures at depth.…”

Improved Characterization of DNAPL Source Zones via Sequential Hydrogeophysical Inversion of Hydraulic‐Head, Self‐Potential and Partitioning Tracer Data

“…Building on the work of Yeh and Zhu (2007) and Soueid Ahmed et al (2016a), we present a sequential hydrogeophysical inversion framework to improve characterization of both K and DNAPL distribution by integrating the self‐potential (SP) and hydraulic tomography (HT) methods for K characterization, with partitioning tracer test inversion for DNAPL saturation characterization. We demonstrate our method in a 3‐D aquifer with realistic DNAPL source zones generated by an invasion percolation model (Koch & Nowak, 2015).…”

Self-potential signals associated with localized leaks in embankment dams and dikes

“…The self-potential method is nowadays extensively used in engineering and in environmental geosciences. For instance, it can be used to map aquifer properties (e.g., Ozaki et al, 2014;Soueid Ahmed et al, 2014, 2016a, 2016b, to delineate coal seam fires (e.g., Karaoulis et al, 2014;Revil et al, 2013;Shao et al, 2016;Soueid Ahmed et al, 2018), for tracking contaminated groundwater (e.g., Abbas et al, 2017;Martínez-Pagán et al, 2010;Naudet et al, 2003), fracking (Mahardika Fig. 1.…”