An Inverse Procedure to Estimate Transmissivit from Heads and SP Signals by Salvatore Straface 1 , Carmine Fallico 2 , Salvatore Troisi 2 , Enzo Rizzo 3 , and Andre ´ Revil 4 Abstract Experimental hydraulic heads and electrical (self-potential) signals associated with a pumping test we in an inverse model to estimate the transmissivity distribution of a real aquifer. Several works reported in ature show that there is a relatively good linear relationship between the hydraulic heads in the aquifer an cal signals measured at the ground surface. In this experimental test field, first,the current coupling coefficient was determined by the best fit between experimental and modeled self-potential signals at the end of the phase. Soon afterward, with the hydraulic heads obtained from the self-potential signals, the transmissivit bution of the aquifer was conditioned by means an inverse model based on the successive linear estimato To further substantiate the estimated T field from the SLE analysis, we analyzed the drawdown rate, the d of the drawdown with respect to the ln(t), because the drawdown rate is highly sensitive to the variability in the transmissivity field. In our opinion, these results show that self-potential signals allow the monitoring of sub- surface flow in the course of pumping experiments, and that electrical potentials serve as a good complement to piezometric observations to condition and characterize the transmissivity distribution of an aquifer. Introduction Characterizing the spatial distribution of hydraulic properties of porous media is a necessary step toward high-resolution predictions of waterflow and contami- nanttransport in an aquifer. Over the past few decades, the characterization of aquifers has relied on traditional aquifertestmethods (i.e., cross-hole tests: pumping at one well and observing the response at another well, and the use of Theis’ or Jacob’s analysis) or slug tests. Tradi- tional aquifer tests are thought to yield averaged hydraulic properties over a large volume of geologic media (Butler and Liu 1993).In reality,the classicalanalysisfor aquifer tests yields spurious average transmissivity values thatare difficultto interpret (Wu etal. 2005).On the other hand, they yield storage coefficient estimates that reflectthe localgeology between the pumping and the observation well. Similarly,Beckie and Harvey (2002) have questioned the validity of storage coefficients esti- mated from slug tests. In spite of these controversies, high-density measurements of the hydraulic properties of an aquiferusing traditional aquifertestmethodsover a large basin are deemed cost-prohibitive and impractical Generally speaking, measurements of waterlevel re- sponses (i.e.,well hydrographs) of an aquiferare less costly and relatively abundant. Making use ofthe well hydrographs to characterize the spatial distribution of hydraulic properties of an aquifer is therefore rational. This approach isknown asinverse modeling in sub- surface hydrology. Nevertheless, withoutsufficientdata to meet necessary and sufficient conditions of the inverse problem, the problem can be ill posed, and its solution will be nonunique. In this context, the interest of the hydrologist is to eitherincrease the number of aquifer responses or improve geostatistical techniques to solve the inverse problem. 1 Corresponding author: Dipartimento di Difesa del Suolo, Universita ` della Calabria, Via P.Bucci42B,87036 Rende (CS), Italy;139-0984496572; fax 139-0984494050; straface@dds. unical.it 2 Dipartimento di Difesa del Suolo, Universita ` della Calabria, 87036 Rende (CS), Italy; fallico@dds.unical.it, troisi@dds.unical.it 3 CNR-IMAA,Hydrogeophysics Laboratory, 85052Marsico Nuovo (PZ), Italy. 4 CNRS-CEREGE, De ´partement d’Hydroge ´ophysique et Milieux Poreux, Universite ´ PaulCe ´zanne, BP80,13545 Aix-en-Provence, cedex 4, France; revil@cerege.fr Received April 2006, accepted January 2007. Copyright ª 2007 The Author(s) Journal compilation ª 2007 National Ground Water Association. doi: 10.1111/j.1745-6584.2007.00310.x 420 Vol. 45, No. 4—GROUND WATER—July–August 2007 (pages 420–428)