Reply to comment by D. Gibert and P. Sailhac on “Self‐potential signals associated with preferential groundwater flow pathways in sinkholes”

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Jardani et al. [2006a] analyzed self-potential signals associated with the shallow groundwater flow in sinkholes. These signals were electrokinetic in nature resulting from the percolation of water in the ground and the drag of the excess of electrical charge that is present in the bulk pore water [e.g., Leroy and Revil, 2004]. Using the formulation of the electrokinetic coupling introduced by Revil and Leroy [2004] (and extended rece tly to unsaturated flow by Revil et al. [2007] and Linde et al. [2007] and to the inertial laminar flow regime by Bole've et al. [2007]), the electrical potential can be obtained from the solution of the Poisson equation. In this equation, the source term is equal to the divergence of the streaming current density, which in turn is equal to the excess of charge per unit pore volume time the seepage velocity. Generalizing the work by Revil et al. [2003b], Jardani et al. [2006a] used a cross-correlation method to reconstruct the possible shapes of the water table and to locate sinkholes at depth. [2] Numerical simulations of self-potential signals associated with the flow of the groundwater shows the dipolar character of the source [e.g., Revil et al., 1999; Bole've et al., 2007]. In a multipole development of the self-potential field, the monopole contribution is equal to zero because of the global electroneutrality condition prevailing in porous materials. Therefore the leading term is the dipolar field. [3] If the support volume of the source is small or if the sources are located along an interface (like the water table), it is possible to use the cross-correlation method to determine the position of the source or to image this interface by optimizing the semblance between the selfpotential anomaly, normalized by its power, and the signal modeled with the appropriate Green function [see Birch, 1993, 1998]. The Green's function can be computed analytically for a homogeneous ground but it can be also computed numerically accounting for the real (or inverted) electrical resistivity distribution and appropriate boundary conditions for the self-potential field. The cross-correlation approach has been used as a source localization method in acoustic [e.g., Omologo and Svaizer, 1994; Thomann, 1996], in seismology [e.g., Saccorotti and Del Pezzo, 2000], in magnetoencephalography [e.g., Cao et al., 2002], and in the localization of contaminant plumes in the atmosphere [e.g., Roussel et al., 2002], just to cite few of them. This is therefore not a new approach. We discuss below the validity of this approach to self-potential data. Note that this approach was also used very successfully by Revil et al. [2001], Iuliano et al. [2002], and Revil et al. [2003a, 2003b] and recently by Jardani et al. [2006b] and Bhattacharyal et al. [2007] to localize the causative source of self-potential anomalies. Finally, we will discuss briefly future exciting trends in the inversion of self-potential signals.