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Joint inversion of hydraulic head and self‐potential data associated with harmonic pumping tests
Author(s) -
Soueid Ahmed A.,
Jardani A.,
Revil A.,
Dupont J. P.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr019058
Subject(s) - aquifer , hydraulic head , inverse problem , underdetermined system , test data , groundwater flow , mathematics , groundwater , mathematical analysis , mechanics , geology , geotechnical engineering , algorithm , computer science , physics , programming language
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.