3D time-domain induced polarization tomography: a new approach based on a source current density formulation

International audienceInduced polarization (IP) of porous rocks can be associated with a secondary source current density, which is proportional to both the intrinsic chargeability and the primary (applied) current density. This gives the possibility of reformulating the time domain induced polarization (TDIP) problem as a time-dependent self-potential-type problem. This new approach implies a change of strategy regarding data acquisition and inversion, allowing major time savings for both. For inverting TDIP data, we first retrieve the electrical resistivity distribution. Then, we use this electrical resistivity distribution to reconstruct the primary current density during the injection/retrieval of the (primary) current between the current electrodes A and B. The time-lapse secondary source current density distribution is determined given the primary source current density and a distribution of chargeability (forward modelling step). The inverse problem is linear between the secondary voltages (measured at all the electrodes) and the computed secondary source current density. A kernel matrix relating the secondary observed voltages data to the source current density model is computed once (using the electrical conductivity distribution), and then used throughout the inversion process. This recovered source current density model is in turn used to estimate the time-dependent chargeability (normalized voltages) in each cell of the domain of interest. Assuming a Cole-Cole model for simplicity, we can reconstruct the 3-D distributions of the relaxation time τ and the Cole-Cole exponent c by fitting the intrinsic chargeability decay curve to a Cole-Cole relaxation model for each cell. Two simple cases are studied in details to explain this new approach. In the first case, we estimate the Cole-Cole parameters as well as the source current density field from a synthetic TDIP data set. Our approach is successfully able to reveal the presence of the anomaly and to invert its Cole-Cole parameters. In the second case, we perform a laboratory sandbox experiment in which we mix a volume of burning coal and sand. The algorithm is able to localize the burning coal both in terms of electrical conductivity and chargeability

Induced polarization of volcanic rocks. 4. Large-scale induced polarization imaging

International audienceThanks to the emergence of new technologies developed with the goal of performing largescale galvanometric induced polarization surveys and thanks a better understanding of the underlying physics of induced polarization, this geophysical method can now be applied in the field of volcanology and geothermal resources assessment. A new approach is developed here for directly inverting the primary and secondary electric fields recorded at a set of independent stations when injecting a primary current. The use of independent stations to measure the primary and secondary electrical fields improves the quality of the data by reducing the capacitive coupling effects inherent to systems based on long cables. It avoids issues associated with using the same electrodes for both current injection and voltage measurements and negative apparent resistivity and chargeability values. With such acquisitions, we can perform true 3-D surveys in areas characterized by complex topography such as volcanoes. The numerical scheme we developed returns as output the electrical conductivity and chargeability fields. The implemented methodology presents several advantages. The first is the use of data types at the stations, for example the electric field intensity, that are independent from the local geometrical station parameters such as electrode spacing and dipole orientation. The second advantage lies in the suitability of the proposed approach to perform large-scale applications since we use a matrix-free approach that does not require the assembly of the Jacobian matrices. The third concerns the possibility of performing the inversion on complex geometries through a consistent use of the finite element method on unstructured meshes in combination with algebraic multigrid preconditioning for the regularization and the solution of the forward and adjoint problems. The computation of 3-D sensitivity maps can also be a real asset in survey design. After validating our approach with a benchmark synthetic case study, we test it on a large-scale induced polarization survey that mimic true field conditions on a volcanic environment with rough topography. Our tests demonstrate the high potential of this electric field approach in volcanology especially for deep (3 km) imagining of the internal structure of volcanoes, which in turn could improve our understanding of hydrothermal systems and allow the monitoring of active volcanoes and the potential risk of collapse

Electrical conductivity and induced polarization investigations at Krafla volcano, Iceland

International audienceElectrical conductivity and polarization properties of 6 samples from Krafla volcano (Iceland) were measured in the frequency range 1 mHz-45 kHz and compared to the data obtained on various basaltic rock samples from Ha-waii. The results indicate that for altered samples, the surface conductivity, normalized chargeability, and quad-rature conductivity of the core samples scales linearly with the cation exchange capacity, taken as a proxy of the alteration facies. The surface conductivity of fresh samples is also controlled by the cation exchange capacity but their normalized chargeability is influenced by the presence of magnetite, especially for unaltered samples. The temperature dependence of quadrature conductivity and normalized chargeability can be modeled with an Ar-rhenius equation with an activation energy of 16-19 kJ mol −1. The experimental results agree with a model in which the polarization of the metallic and non-metallic grains are both considered in a unified framework. These results are used to interpret two 3D induced polarization surveys performed in the South and East parts of Krafla volcano using two 1.3 km-long cables with 32 electrodes each. The electrical conductivity is in the range 0.3 (clay cap) to 5 × 10 −5 S m −1 (unaltered rock) while the normalized chargeability is typically comprised between 10 −2 (clay cap) and 10 −5 S m −1 (unaltered rock). Induced polarization is used to image porosity and the cation exchange capacity. A long 5.6 km electrical conductivity profile was also performed connecting the two 3D sites and crossing a rhyolitic obsidian ridge called Hrafntinnuhryggur. Hrafntinnuhryggur is characterized by very low conductivity values on the order of 10 −4 S m −1. The long conductivity profile shows the position of the inner and outer caldera rims and the feeder dike of Hrafntinnuhryggur. A self-potential survey performed along this long profile shows no shallow active geothermal features in this area, as expected from the low perme-ability of the clay cap

SP2DINV: A 2 D forward and inverse code for streaming potential problems

International audienceThe self-potentialmethodcorrespondstothepassivemeasurementoftheelectrical field inresponseto the occurrenceofnaturalsourcesofcurrentintheground.Oneofthesesourcescorrespondstothe streaming currentassociatedwiththe flow ofthegroundwater.Wecanthereforeapplytheself- potentialmethodtorecovernon-intrusivelysomeinformationregardingthegroundwater flow.We first solvetheforwardproblemstartingwiththesolutionofthegroundwater flowproblem,thencomputing the sourcecurrentdensity,and finally solvingaPoissonequationfortheelectricalpotential.Weusethe finite-element methodtosolvetherelevantpartialdifferentialequations.Inordertoreducethenumber of (petrophysical)modelparametersrequiredtosolvetheforwardproblem,weintroducedaneffective charge densitytensoroftheporewater,whichcanbedetermineddirectlyfromthepermeabilitytensor for neutralporewaters.Thesecondaspectofourworkconcernstheinversionoftheself-potentialdata using Tikhonovregularizationwithsmoothnessandweightingdepthconstraints.Thisapproachaccounts for thedistributionoftheelectricalresistivity,whichcanbeindependentlyandapproximately determined fromelectricalresistivitytomography.Anumericalcode,SP2DINV,hasbeenimplemented in Matlabtoperformboththeforwardandinversemodeling.Threesyntheticcasestudiesarediscussed

HT2DINV: A 2D forward and inverse code for steady-state and transient hydraulic tomography problems

International audienceHydraulic tomography is a technique used to characterize the spatial heterogeneities of storativity and transmissivity fields. The responses of an aquifer to a source of hydraulic stimulations are used to recover the features of the estimated fields using inverse techniques. We developed a 2D free source Matlab package for performing hydraulic tomography analysis in steady state and transient regimes. The package uses the finite elements method to solve the ground water flow equation for simple or complex geometries accounting for the anisotropy of the material properties. The inverse problem is based on implementing the geostatistical quasi-linear approach of Kitanidis combined with the adjoint-state method to compute the required sensitivity matrices. For undetermined inverse problems, the adjoint-state method provides a faster and more accurate approach for the evaluation of sensitivity matrices compared with the finite differences method. Our methodology is organized in a way that permits the end-user to activate parallel computing in order to reduce the computational burden. Three case studies are investigated demonstrating the robustness and efficiency of our approach for inverting hydraulic parameters

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

International audienceHarmonic 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

Analyse interdisciplinaire de l’instabilité d’une remontée mécanique implantée sur un glacier rocheux dans les Alpes françaises

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Specific storage and hydraulic conductivity tomography through the joint inversion of hydraulic heads and self-potential data

International audienceTransient hydraulic tomography is used to image the heterogeneous hydraulic conductivity and specific storage fields of shallow aquifers using time series of hydraulic head data. Such ill-posed and non-unique inverse problem can be regularized using some spatial geostatistical characteristic of the two fields. In addition to hydraulic heads changes, the flow of water, during pumping tests, generates an electrical field of electrokinetic nature. These electrical field fluctuations can be passively recorded at the ground surface using a network of non-polarizing electrodes connected to a high impedance (> 10 MOhm) and sensitive (0.1 mV) voltmeter, a method known in geophysics as the self-potential method. We perform a joint inversion of the self-potential and hydraulic head data to image the hydraulic conductivity and specific storage fields. We work on a 3D synthetic confined aquifer and we use the adjoint state method to compute the sensitivities of the hydraulic parameters to the hydraulic head and self-potential data in both steady-state and transient conditions. The inverse problem is solved using the geostatistical quasi-linear algorithm framework of Kitanidis. When the number of piezometers is small, the record of the transient self-potential signals provides useful information to characterize the hydraulic conductivity and specific storage fields. These results show that the self-potential method reveals the heterogeneities of some areas of the aquifer, which could not been captured by the tomography based on the hydraulic heads alone. In our analysis, the improvement on the hydraulic conductivity and specific storage estimations were based on perfect knowledge of electrical resistivity field. This implies that electrical resistivity will need to be jointly inverted with the hydraulic parameters in future studies and the impact of its uncertainty assessed with respect to the final tomograms of the hydraulic parameters

3D Hydraulic tomography from joint inversion of the hydraulic heads and self-potential data.

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

International audiencePumping 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