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See detailCovariance-constrained difference inversion of time-lapse electrical resistivity tomography data
Hermans, Thomas ULg; Kemna, Andreas; Nguyen, Frédéric ULg

in Geophysics (in press)

Hydrogeophysics has become a major field of research in the past two decades and time-lapse electrical resistivity tomography (ERT) is one of the most popular techniques to monitor passive and active ... [more ▼]

Hydrogeophysics has become a major field of research in the past two decades and time-lapse electrical resistivity tomography (ERT) is one of the most popular techniques to monitor passive and active processes in shallow subsurface reservoirs. Time-lapse inversion schemes have been developed to refine inversion results, but they mostly still rely on a spatial regularization procedure based on the standard smoothness constraint. In this paper, we propose to apply a covariance-based regularization operator in the time-lapse ERT inverse problem. We first illustrate the method for surface and cross-hole ERT with two synthetic cases and compare the results with the smoothness-constrained inversion (SCI). The examples show that the covariance–constrained inversions (CCI) better image the anomaly both in terms of shape and amplitude. Although more important in low-sensitivity zones, improvements are observed everywhere in the tomograms. Those synthetic examples also show that an error made in the range or in the type of the variogram model has a limited impact on the resulting image, which still remains better than SCI. The method is then applied to cross-borehole ERT field data from a heat tracing experiment, where the comparison with direct measurements shows a strong improvement of the breakthrough curves retrieved from ERT. The proposed method could be extended to the time dimension which would allow the use of CCI in 4D inversion schemes. [less ▲]

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See detailAssessing heat tracing experiment data sets for direct forecast of temperature evolution in subsurface models: an example of well and geophysical monitoring data
Hermans, Thomas ULg; Oware, Erasmus; Klepikova, Maria et al

Scientific conference (2016, May 04)

Hydrogeological inverse modeling is used for integrating data and calibrating subsurface model parameters. On one hand, deterministic approaches are relatively fast but fail to catch the uncertainty ... [more ▼]

Hydrogeological inverse modeling is used for integrating data and calibrating subsurface model parameters. On one hand, deterministic approaches are relatively fast but fail to catch the uncertainty related to the spatial distribution of model parameters. On the other hand, stochastic inverse modeling is time-consuming and sampling the full high-dimensional parameter space is generally impossible. Even then, the end result is not the inverted model itself, but the forecast built from such models. In this study, we investigate a prediction-focused approach (PFA) in order to derive a direct statistical relationship between data and forecast without explicitly calibrating any models to the data. To derive this relationship, we first sample a limited number of models from the prior distribution using geostatistical methods. For each model, we then apply two forward simulations: the first corresponds to the forward model of the data (past), the second corresponds to the forward model of the forecast (future). The relationship between observed data and forecast is generally highly non-linear, depending on the complexity of the prior distribution and the differences in the two forward operators. In order to derive a useful relationship, we first reduce the dimension of the data and the forecast through principal component analysis (PCA) related techniques in order to keep the most informative part of both sets. Then, we apply canonical correlation analysis (CCA) to establish a linear relationship between data and forecast in the reduced space components. If such a relationship exists, it is possible to directly sample the posterior distribution of the forecast with a multi-Gaussian framework. In this study, we apply this methodology to forecast the evolution with time of the distribution of temperature in a control panel in an alluvial aquifer. We simulate a heat tracing experiment monitored with both well logging probes and electrical resistivity tomography. We show (1) that the proposed method can be used to quantify the uncertainty on the forecast both spatially and temporally and (2) that spatially-distributed data acquired through geophysical methods help to significantly reduce the uncertainty of the posterior. [less ▲]

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See detailAssessment of a design to monitor the influence of crop residue management on the dynamics of soil water content with ERT
Chelin, Marie ULg; Hiel, Marie-Pierre ULg; Hermans, Thomas ULg et al

Poster (2016, April 21)

Choices related to crop residue management affect the soil structure. As a consequence, they may determinethe spatio-temporal dynamics of water content and eventually the crop yields. In order to better ... [more ▼]

Choices related to crop residue management affect the soil structure. As a consequence, they may determinethe spatio-temporal dynamics of water content and eventually the crop yields. In order to better understand the influence of these strategies on hydraulic processes occurring at the plot scale, we opted for the use electrical resistivity tomography (ERT). This approach presents the advantage to limit soil disturbance but is still faced to important challenges when applied in an agricultural field context. Especially changing soil-electrode contact has to be considered, as it can lead to bad quality data, especially for setups with small electrodes and small inter-electrode distance. The objective of this study was to test the efficiency of a high-resolution 3-D field measurement design to properly assess the dynamics of soil water content. ERT measurements were conducted in a Cutanic Siltic Luvisol in Gembloux, Belgium, on two plots of 2m^2 ploughed in Oct 2014 at a depth of 25 cm and sown with maize in April 2015. The plants were removed on one of the plots in order to obtain a bare soil reference. A grid of 98 surface stainless steel electrodes was layed-out on each plot and four sticks supporting each eight stainless steel electrodes were vertically inserted into the soil up to 1.20 m to get more detailed information in depth. The experiments were performed between Jul and Oct 2015, in order to get measurements both in dry and wet periods. For surface and borehole monitoring, a dipole-dipole array configuration including in-line and cross-line measurements was adopted. Normal and reciprocal measurements were performed systematically to assess the data quality: only the datasets with a mean reciprocal error lower than 3% were considered for the data inversion. This contribution will show the first inverted results showing the complexity of experimental design and data analysis for high-resolution, timelapse ERT in field conditions. Based on these results, we will draw conclusions about a minimal data set to be obtained in our upcoming field experiments. [less ▲]

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See detailTime lapse imaging of water content with geoelectrical methods: on the interest of working with absolute water content data
Dumont, Gaël ULg; Pilawski, Tamara ULg; Robert, Tanguy et al

Poster (2016, April 21)

The electrical resistivity tomography is a suitable method to estimate the water content of a waste material and detect changes in water content. Various ERT profiles, both static data and time-lapse ... [more ▼]

The electrical resistivity tomography is a suitable method to estimate the water content of a waste material and detect changes in water content. Various ERT profiles, both static data and time-lapse, where acquired on a landfill during the Minerve project. In the literature, the relative change of resistivity ( Delta rho/rho ) is generally computed. For saline or heat tracer tests in the saturated zone, the Delta rho/rho can be easily translated into pore water conductivity or underground temperature changes (provided that the initial salinity or temperature condition is homogeneous over the ERT panel extension). For water content changes in the vadose zone resulting of an infiltration event or injection experiment, many authors also work with the Delta rho/rho or relative changes of water content Delta theta /theta (linked to the change of resistivity through one single parameter: the Archie’s law exponent “m”). This parameter is not influenced by the underground temperature and pore fluid conductivity ( rho_w) condition but is influenced by the initial water content distribution. Therefore, you never know if the loss of / signal is representative of the limit of the infiltration front or more humid initial condition. Another approach for the understanding of the infiltration process is the assessment of the absolute change of water content ( Delta theta ). This requires the direct computation of the water content of the waste from the resistivity data. For that purpose, we used petrophysical laws calibrated with laboratory experiments and our knowledge of the in situ temperature and pore fluid conductivity parameters. Then, we investigated water content changes in the waste material after a rainfall event ( Delta theta = Delta theta /theta * theta ). This new observation is really representatives of the quantity of water infiltrated in the waste material. However, the uncertainty in the pore fluid conductivity value may influence the computed water changes ( Delta theta =k*m*(rho_w)^1/2 ; where “m” is the Archie’s law exponent). Using these two complementary approaches, we analyzed the effect a major rainfall (20-30 mm in 2 hours) that occurred on the test site, characterized by a vegetalized and relatively dry zone and a devegatelized and humid zone. We intended to prove that most of the information contained in the Delta theta /theta distribution is the initial water content distribution in the ground.Water addition in dry zones resulting in large relative changes. The computation of the Delta theta is necessary to demonstrate preferential infiltration through the capping in a restricted zone of the vegetalized area. [less ▲]

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See detailAssessing heat tracing experiment data sets for direct forecast of temperature evolution in subsurface models: an example of well and geophysical monitoring data
Hermans, Thomas ULg; Klepikova, Maria; Caers, Jef

Conference (2016, April 21)

Hydrogeological inverse modeling is used for integrating data and calibrating subsurface model parameters. On one hand, deterministic approaches are relatively fast but fail to catch the uncertainty ... [more ▼]

Hydrogeological inverse modeling is used for integrating data and calibrating subsurface model parameters. On one hand, deterministic approaches are relatively fast but fail to catch the uncertainty related to the spatial distribution of model parameters. On the other hand, stochastic inverse modeling is time-consuming and sampling the full high-dimensional parameter space is generally impossible. Even then, the end result is not the inverted model itself, but the forecast built from such models. In this study, we investigate a prediction-focused approach (PFA) in order to derive a direct statistical relationship between data and forecast without explicitly calibrating any models to the data. To derive this relationship, we first sample a limited number of models from the prior distribution using geostatistical methods. For each model, we then apply two forward simulations: the first corresponds to the forward model of the data (past), the second corresponds to the forward model of the forecast (future). The relationship between observed data and forecast is generally highly non-linear, depending on the complexity of the prior distribution and the differences in the two forward operators. In order to derive a useful relationship, we first reduce the dimension of the data and the forecast through principal component analysis (PCA) related techniques in order to keep the most informative part of both sets. Then, we apply canonical correlation analysis (CCA) to establish a linear relationship between data and forecast in the reduced space components. If such a relationship exists, it is possible to directly sample the posterior distribution of the forecast with a multi-Gaussian framework. In this study, we apply this methodology to forecast the evolution with time of the distribution of temperature in a control panel in an alluvial aquifer. We simulate a heat tracing experiment monitored with both well logging probes and electrical resistivity tomography. We show (1) that the proposed method can be used to quantify the uncertainty on the forecast both spatially and temporally and (2) that spatially-distributed data acquired through geophysical methods help to significantly reduce the uncertainty of the posterior. [less ▲]

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See detailHeat tracer test in an alluvial aquifer: field experiment and inverse modelling
Klepikova, Maria; Wildemeersch, Samuel; Jamin, Pierre ULg et al

Poster (2016, April 20)

Using heat as an active tracer for aquifer characterization is a topic of increasing interest. In this study, we investigate the potential of using heat tracer tests for characterization of a shallow ... [more ▼]

Using heat as an active tracer for aquifer characterization is a topic of increasing interest. In this study, we investigate the potential of using heat tracer tests for characterization of a shallow alluvial aquifer. A thermal tracer test was conducted in the alluvial aquifer of the Meuse River, Belgium. The tracing experiment consisted in simultaneously injecting heated water and a dye tracer in a piezometer and monitoring the evolution of groundwater temperature and tracer concentration in the recovery well and in monitoring wells. To get insights in the 3D characteristics of the heat transport mechanisms, temperature data from a large number of observation wells distributed throughout the field site (space-filling arrangement) were used. Temperature breakthrough curves in observation wells are contrasted with what would be expected in an ideal layered aquifer. They reveal strongly unequal lateral and vertical components of the transport mechanisms. The observed complex behavior of the heat plume was explained by the groundwater flow gradient on the site and heterogeneity of hydraulic conductivity field. Moreover, due to high injection temperatures during the field experiment a temperature-induced fluid density effect on heat transport occurred. By using a flow and heat transport numerical model with variable density coupled with the pilot point inverse approach, main preferential flow paths were delineated. [less ▲]

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See detailData-driven selection of the minimum-gradient support parameter in time-lapse focused electrical imaging
Nguyen, Frédéric ULg; Kemna, Andreas; Robert, Tanguy et al

in Geophysics (2016), 81(1), 1-5

We have considered the problem of the choice of the minimum-gradient support (MGS) parameter in focused inversion for time-lapse (TL) electric resistivity tomography. Most existing approaches have relied ... [more ▼]

We have considered the problem of the choice of the minimum-gradient support (MGS) parameter in focused inversion for time-lapse (TL) electric resistivity tomography. Most existing approaches have relied either on an arbitrary choice of this parameter or one based on the prior information, such as the expected contrast in the TL image. We have decided to select the MGS parameter using a line search based on the value of the TL data root-mean-square misfit at the first iteration of the nonlinear inversion procedure. The latter was based on a Gauss-Newton scheme minimizing a regularized objective function in which the regularization functional was defined by the MGS functional. The regularization parameter was optimized to achieve a certain target level, following the Occam principles. We have validated our approach on a synthetic benchmark using a complex and heterogeneous model and determined its effectiveness on electric tomography TL data collected during a salt tracer experiment in fractured limestone. Our results have determined that the approach was successful in retrieving the focused anomaly and did not rely on prior information. [less ▲]

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See detailStockage de chaleur en aquifère et flexibilité de la demande électrique: quelles possibilités?
Paulus, Claire; Bolly, Pierre-Yves; Hermans, Thomas ULg et al

in Proceedings des 34e rencontres universitaires du Génie Civil de l'AUGC (2016)

In the context of energy demand side management (EDSM) and heat storage in aquifers, the design and functioning of aquifer thermal energy storage (ATES) systems have strong interconnections with the ... [more ▼]

In the context of energy demand side management (EDSM) and heat storage in aquifers, the design and functioning of aquifer thermal energy storage (ATES) systems have strong interconnections with the geology of the site which may be complex and heterogeneous, making predictions difficult. In this context, we developed a subsurface monitoring methodology to better characterize heat transfer in the subsurface with the help of 4D electrical resistivity tomography (ERT), multiple hydrological measurements in wells, and a short-term heat storage experiment conducted for the purpose in a confined alluvial aquifer. Results clearly show the ability of ERT to delimit the thermal plume growth during injection, the diffusion and decrease of temperature during storage, and the decrease in size after heat recovery. Energy balance shows that up to 70% of the energy can be easily recovered with an adapted strategy in the context of DSM. Short-term heat storage in alluvial aquifer is efficient and ERT is a valuable tool to image and estimate the temperature distribution in the subsurface. [less ▲]

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See detailEvaluating the performance of short-term heat storage in alluvial aquifer with 4D electrical resistivity tomography and hydrological monitoring
Robert, Tanguy; Paulus, Claire; Bolly, Pierre-Yves et al

Poster (2015, December 14)

In the context of energy demand side management (DSM), energy storage solutions are needed to stock energy during high production periods and recover energy during high demand periods. Among currently ... [more ▼]

In the context of energy demand side management (DSM), energy storage solutions are needed to stock energy during high production periods and recover energy during high demand periods. Among currently studied solutions, storing energy in the subsurface through heat pumps and/or exchangers (thermal energy storage) is relatively simple with low investment costs. However, the design and functioning of such systems have strong interconnections with the geology of the site which may be complex and heterogeneous, making predictions difficult. In this context, local temperature measurements are necessary but not sufficient to model heat flow and transport in the subsurface. Electrical resistivity tomography (ERT) provides spatially distributed information on the temperature distribution in the subsurface. In this study, we monitored, with 4D ERT combined with multiple hydrological measurements in available wells, a short-term heat storage experiment in a confined alluvial aquifer. We injected heated water (ΔT=30K) during 6 hours with a rate of 3 m³/h, stored during 3 days, and then we pumped it back to estimate the energy balance. We collected ERT data sets using 9 parallel profiles of 21 electrodes and cross-lines measurements. Inversion results clearly show the ability of ERT to delimit the thermal plume growth during injection, the diffusion and decrease of temperature during storage, and the decrease in size after pumping. Quantitative interpretation of ERT is difficult at this stage due to strong spatial variations of the total dissolved solid content in the aquifer, due to historical chloride contamination of the site. Energy balance shows that up to 75% of the energy can be easily recovered with an adapted strategy in the context of DSM. Short-term heat storage in alluvial aquifer is efficient and ERT is a valuable tool to image and estimate the temperature distribution in the subsurface. [less ▲]

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See detailTime-lapse inversion of ERT monitoring data using variogram-based regularization
Hermans, Thomas ULg; Dumont, Gaël ULg; Kemna, Andreas et al

Conference (2015, November 24)

Hydrogeophysics has become a major field of research in the past two decades and time-lapse electrical resistivity tomography (ERT) is one of the most popular techniques to monitor passive and active ... [more ▼]

Hydrogeophysics has become a major field of research in the past two decades and time-lapse electrical resistivity tomography (ERT) is one of the most popular techniques to monitor passive and active processes in subsurface reservoirs. Time-lapse inversion schemes have been developed to refine inversion results; but, in contrast with static inversion, they mostly still rely on the spatial regularization procedure based on the standard smoothness constraint. In this contribution, we propose to apply a variogram-based regularization operator in the time-lapse ERT inverse problem, using the model difference covariance matrix to replace the standard smoothing operator. The variogram of resistivity variations can be computed through independent borehole data, such as electromagnetic logs or hydrogeological monitoring, which is often available during monitoring experiments. We first illustrate the method for surface ERT with a synthetic case and compare the results with the standard smoothness constraint solution. This example shows that the variogram-based constraint images better the assumed anomaly both in terms of shape and amplitude. The improvement is largely higher than the one obtained with more classical anisotropic smoothness constraint. This synthetic example also shows that an error made in the range of the variogram has a limited impact on the resulting image, which still remains better than the smoothness constraint result. Anomalies located in various part of the tomograms were tested. Although more crucial in low-sensitivity zones, improvements are observed everywhere in the tomograms. The method is then applied to cross-borehole ERT field data from a heat tracing experiment, where the comparison with direct temperature measurements shows a strong improvement of the breakthrough curves retrieved from ERT. Using the variogram-based regularization, it is possible to reduce the smoothing of resistivity variations in low sensitivity zones and therefore to avoid overestimation of temperatures. The proposed method could be extended to the time dimension which would allow the use of variogram-based constraints in 4D inversion schemes. [less ▲]

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See detailERT monitoring of water infiltration process through a landfill cover layer
Dumont, Gaël ULg; Pilawski, Tamara ULg; Robert, Tanguy et al

in Berichte der Geologischen Bundesanstalt, 112 (2015, November)

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See detailAssessing electrical resistivity tomography for hydrofacies detection using a sensitivity dependent probabilistic methodology
Hermans, Thomas ULg; Irving, James

in EarthDoc - Near Surface Geosciences 2015 (2015, September 08)

Alluvial aquifers are generally composed of several facies with complex architectures and interconnections depending on the fluvial system. In this context, electrical resistivity tomography (ERT) may ... [more ▼]

Alluvial aquifers are generally composed of several facies with complex architectures and interconnections depending on the fluvial system. In this context, electrical resistivity tomography (ERT) may provide important information on the spatial distribution of hydrogeological parameters. However, ERT inversion introduces some bias in the resulting resistivity distribution due to regularization and resolution issues. In this study, we refine ERT inversions by incorporating prior information in order to improve the identification of facies through a probabilistic relationship derived from collocated measurements. We then analyze with synthetic cases the effect of spatially varying sensitivity on the probabilistic relationship. As expected, when sensitivity decreases, the distributions of resistivity for the different facies tend to be superimposed. A mean distribution thus overestimates the ability of surface ERT to discriminate hydrofacies in depth. [less ▲]

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See detailUse and utility of combined solute and heat tracer tests for characterizing hydrogeothermal properties of an alluvial aquifer
Klepikova, Maria; Wildemeersch, Samuel; Jamin, Pierre ULg et al

Conference (2015, June 05)

Using heat as a tracer together with a solute tracer is interesting for characterizing hydrogeothermal properties of the underground. These properties are particularly needed to dimension any low ... [more ▼]

Using heat as a tracer together with a solute tracer is interesting for characterizing hydrogeothermal properties of the underground. These properties are particularly needed to dimension any low temperature geothermal project using an open doublet system (pumping-reinjection) in a shallow aquifer. The tracing experiment, conducted in the alluvial aquifer of the River Meuse (Hermalle near Liège), consisted in injecting simultaneously heated water at 40°C and a dye tracer in a piezometer and monitoring the evolution of temperature and tracer concentration in the recovery well and in nine monitoring piezometers located in three transects with regards to the main groundwater flow direction. The breakthrough curves measured in the recovery well showed that heat transfer in the alluvial aquifer is slower. All measured results show also that the heat diffusivity is larger than the solute dispersion. These contrasted behaviours are stressed in the lower permeability zones of the aquifer. Inverse modelling is applied for calibrating the numerical simulation of the groundwater flow, heat and solute transport. First results are presented showing that the density effect must be taken into account and that, as expected, the most important parameter to be calibrated accurately is the hydraulic conductivity. [less ▲]

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See detailUncertainty in Training-Image Based Inversion of Hydraulic Head Data Constrained to ERT Data : Workflow and Case Study
Hermans, Thomas ULg; Nguyen, Frédéric ULg; Caers, Jef

Scientific conference (2015, May 06)

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In ... [more ▼]

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In recent years, many efforts have been done to assess the posterior distribution of a given problem with reasonable computational costs through inversion techniques such as McMC. The derived posterior distribution is always dependent on the prior distribution. However, most of the studies ignore modeling the prior with realistic uncertainty. In this paper, we propose a workflow to assess the uncertainty of inversion of hydraulic heads data through the addition of electrical resistivity tomography (ERT) constraining data. The workflow is divided in three successive steps: 1) Construction of prior: we generate multiple alternative geological scenarios from literature data (architecture of facies) as well as site specific data (proportions of facies). Spatial uncertainty within each scenario is integrated hierarchically through geostatistics (multiple-point statistics simulation of facies constrained by ERT data as soft data). 2) Validation of prior scenarios: we transform prior facies scenarios into resistivity distribution scenarios through forward and inverse modeling. The scenarios are validated by comparison with field ERT data. The comparison is made through distance calculation and projection into a low dimensional space to calculate the probability of each scenario given field ERT data. 3) Matching dynamical data: we use the probability perturbation method, within each scenario, to integrate hydraulic heads to our models. We account for scenario probabilities, calculated in 2, in determining how many models per scenario we have to consider for building a reliable posterior distribution. The method is first applied on synthetic cases where the "true" model is known. Then, it is apllied a field case study in an alluvial aquifer (Belgium) where we consider prior uncertainty related to the type of elements (gravel channels or bars) and to their size. This study shows the importance of considering the uncertainty of the prior in inverse problems as it has a strong influence on model predictions and decision-making problems. [less ▲]

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See detailRegularized focusing inversion of time-lapse electrical resistivity data: an approach to parametrize the minimum gradient support functional
Nguyen, Frédéric ULg; Hermans, Thomas ULg

Poster (2015, April 15)

Inversion of time-lapse resistivity data allows obtaining ‘snapshots’ of changes occurring in monitored systems for applications such as aquifer storage, geothermal heat exchange, site remediation or ... [more ▼]

Inversion of time-lapse resistivity data allows obtaining ‘snapshots’ of changes occurring in monitored systems for applications such as aquifer storage, geothermal heat exchange, site remediation or tracer tests. Based on these snapshots, one can infer qualitative information on the location and morphology of changes occurring in the subsurface but also quantitative estimates on the degree of changes in certain property such as temperature or total dissolved solid content. Analysis of these changes can provide direct insight into flow and transport and associated processes and controlling parameters. However, the reliability of the analysis is dependent on survey geometry, measurement schemes, data error, and regularization. Survey design parameters may be optimized prior to the monitoring survey. Regularization, on the other hand, may be chosen depending on available information collected during the monitoring. Common approaches consider smoothing model changes both in space and time but it is often needed to obtain a sharp temporal anomaly, for example in fractured aquifers. We here propose to use the alternative regularization approach based on minimum gradient support (MGS) (Zhdanov, 2002) for time-lapse surveys which will focus the changes in tomograms snapshots. MGS will limit the occurrences of changes in electrical resistivity but will also restrict the variations of these changes inside the different zones. A common difficulty encountered by practitioners in this type of regularization is the choice of an additional parameter, the so-called , required to define the MGS functional. To the best of our knowledge, there is no commonly accepted or standard methodology to optimize the MGS parameter . The inversion algorithm used in this study is CRTomo (Kemna 2000). It uses a Gauss-Newton scheme to iteratively minimize an objective function which consists of a data misfit functional and a model constraint functional. A univariate line search is performed at each Gauss-Newton iteration step to find the optimum value of the regularization parameter  which minimizes the data misfit as a function of  while the data misfit is above the desired value and yields the desired target misfit (root-mean square value of error-weighted data misfit equal to 1) at the last iteration for a maximum value of . We propose here to optimize the  of the MGS functional by considering a univariate line search at the first iteration to find the  that minimizes the data misfit. The parameter is then kept constant during the Gauss-Newton iterative scheme. In this contribution, we validate our approach on a numerical benchmark and apply it successfully on a case study in the context of salt tracers in fractured aquifers. Zhdanov M.S. 2002. Geophysical Inverse Theory and Regularization Problems. Elsevier, Amsterdam, 628 p. Kemna A. 2000. Tomographic Inversion of Complex Resistivity - Theory and Application. PhD Thesis, Ruhr University Bochum. [less ▲]

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See detailVariogram-based inversion of time-lapse electrical resistivity data: development and application to a thermal tracing experiment
Hermans, Thomas ULg; Nguyen, Frédéric ULg

Poster (2015, April 15)

Electrical resistivity tomography (ERT) has become a popular imaging methodology in a broad range of applications given its large sensitivity to subsurface parameters and its relative simplicity to ... [more ▼]

Electrical resistivity tomography (ERT) has become a popular imaging methodology in a broad range of applications given its large sensitivity to subsurface parameters and its relative simplicity to implement. More particularly, time-lapse ERT is now increasingly used for monitoring purposes in many contexts such as water content, permafrost, landslide, seawater intrusion, solute transport or heat transport experiments. Specific inversion schemes have been developed for time-lapse data sets. However, in contrast with static inversions for which many techniques including geostatistical, minimum support or structural inversion are commonly applied, most of the methodologies for time-lapse inversion still rely on non-physically based spatial and/or temporal smoothing of the parameters or parameter changes. In this work, we propose a time-lapse ERT inversion scheme based on the difference inversion scheme. We replace the standard smoothness-constraint regularization operator by the parameter change covariance matrix. This operator takes into account the correlation between changes in resistivity at different locations through a variogram computed using independent data (e.g., electromagnetic logs). It may vary for subsequent time-steps if the correlation length is time-dependent. The methodology is first validated and compared to the standard smoothness-constraint inversion using a synthetic benchmark simulating the injection of a conductive tracer into a homogeneous aquifer inducing changes in resistivity values of known correlation length. We analyze the influence of the assumed correlation length on inversion results. Globally, the method yields better results than the traditional smoothness constraint inversion. Even if a wrong correlation length is assumed, the method performs as well as the smoothness constraint since the regularization operator balances the weight given to the model constraint functional in the objective function. Then the methodology is successfully applied to a heat injection and pumping experiment in an alluvial aquifer. The comparison with direct measurements in boreholes (temperature loggers and distributed temperature sensing optic fibres) shows that ERT-derived temperatures and breakthrough curves image reliably the heat plume through time (increasing part of the curve, maximum and tail are correctly retrieved) and space (lateral variations of temperature are observed) with less spatial smoothing than standard methods. The development of new regularization operators for time-lapse inversion of ERT data is necessary given the broad range of applications where ERT monitoring is used. In many studies, independent data are available to derive geostatistical parameters that can be subsequently used to regularize geophysical inversions. In the future, the integration of spatio-temporal variograms into existing 4D inversion schemes should further improve ERT time-lapse imaging. [less ▲]

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See detailUncertainty in training image-based inversion of hydraulic head data constrained to ERT data: workflow and case study
Hermans, Thomas ULg; Nguyen, Frédéric ULg; Caers, Jef

in Water Resources Research (2015), 51

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the ... [more ▼]

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, most of the studies ignore modeling the prior with realistic geological uncertainty. In this paper, we propose a workflow inspired by a Popper-Bayes philosophy, that data should first be used to falsify models, then only be considered for matching. We propose a workflow consisting of three steps: (1) in defining the prior, we interpret multiple alternative geological scenarios from literature (architecture of facies) and site specific data (proportions of facies). Prior spatial uncertainty is modeled using multiple-point geostatistics, where each scenario is defined using a training image. (2) We validate these prior geological scenarios by simulating electrical resistivity tomography (ERT) data on realizations of each scenario and comparing them to field ERT in a lower dimensional space. In this second step, the idea is to probabilistically falsify scenarios with ERT, meaning that scenarios which are incompatible receive an updated probability of zero while compatible scenarios receive a non-zero updated belief. (3) We constrain the hydrogeological model with hydraulic head and ERT using a stochastic search method. The workflow is applied to a synthetic and a field case studies in an alluvial aquifer. This study highlights the importance of considering and estimate prior uncertainty (without data) through a process of probabilistic falsification. [less ▲]

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See detailQuantitative temperature monitoring of a heat tracing experiment using cross-borehole ERT
Hermans, Thomas ULg; Wildemeersch, Samuel ULg; Jamin, Pierre ULg et al

in Geothermics (2015), 53

The growing demand for renewable energy leads to an increase in the development of geothermal energy projects and heat has become a common tracer in hydrology and hydrogeology. Designing geothermal ... [more ▼]

The growing demand for renewable energy leads to an increase in the development of geothermal energy projects and heat has become a common tracer in hydrology and hydrogeology. Designing geothermal systems requires a multidisciplinary approach including geological and hydrogeological aspects. In this context, electrical resistivity tomography (ERT) can bring relevant, qualitative and quantitative information on the temperature distribution in operating shallow geothermal systems or during heat tracing experiments. We followed a heat tracing experiment in an alluvial aquifer using cross-borehole time-lapse ERT. Heated water was injected in a well while water of the aquifer was extracted at another well. An ERT section was set up across the main flow direction. The results of ERT were transformed into temperature using calibrated petrophysical relationships. These ERT-derived temperatures were then compared to direct temperature measurements in control piezometers collected with distributed temperature sensing (DTS) and groundwater temperature loggers. Spatially, it enabled to map the horizontal and vertical extent of the heated water plume, as well as the zones where maximum temperatures occurred. Quantitatively, the temperatures and breakthrough curves estimated from ERT were in good agreement with the ones observed directly during the rise and maximum of the curve. An overestimation, likely related to 3D effects, was observed for the tail of the heat breakthrough curve. The error made on temperature can be estimated to be between 10 to 20 %, which is a fair value for indirect measurements. From our data, we estimated a quantification threshold for temperature variation of 1.2°C. These results suggest that ERT should be considered when designing heat tracing experiments or geothermal systems. It could help also to assess the geometrical complexity of the concerned reservoirs. It also appears that ERT could be a useful tool to monitor and control geothermal systems once they are in operation. [less ▲]

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Peer Reviewed
See detailUncertainty in Training-Image Based Inversion of Hydraulic Head Data Constrained to ERT Data: Workflow and Case Study
Hermans, Thomas ULg; Nguyen, Frédéric ULg; Caers, Jef

Conference (2014, December 18)

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In ... [more ▼]

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In recent years, many efforts have been done to assess the posterior distribution of a given problem with reasonable computational costs through inversion techniques such as McMC. The derived posterior distribution is always dependent on the prior distribution. However, most of the studies ignore modeling the prior with realistic uncertainty. In this paper, we propose a workflow to assess the uncertainty of inversion of hydraulic heads data through the addition of electrical resistivity tomography (ERT) constraining data. The workflow is divided in three successive steps: 1) Construction of prior: we generate multiple alternative geological scenarios from literature data (architecture of facies) as well as site specific data (proportions of facies). Spatial uncertainty within each scenario is integrated hierarchically through geostatistics (multiple-point statistics simulation of facies constrained by ERT data as soft data). 2) Validation of prior scenarios: we transform prior facies scenarios into resistivity distribution scenarios through forward and inverse modeling. The scenarios are validated by comparison with field ERT data. The comparison is made through distance calculation and projection into a low dimensional space to calculate the probability of each scenario given field ERT data. 3) Matching dynamical data: we use the probability perturbation method, within each scenario, to integrate hydraulic heads to our models. We account for scenario probabilities, calculated in 2, in determining how many models per scenario we have to consider for building a reliable posterior distribution. As an illustration, the method is applied on a field case study in an alluvial aquifer (Belgium) where we consider prior uncertainty related to the type of elements (gravel channels or bars) and to their size. This study shows the importance of considering the uncertainty of the prior in inverse problems as it has a strong influence on model predictions and decision-making problems. [less ▲]

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Full Text
See detailProspection géophysique de la zone faillée de Hockai dans la région de Malmedy: Rapport des tomographies de résistivité électrique
Hermans, Thomas ULg; Nguyen, Frédéric ULg

Report (2014)

Ce rapport consiste en la présentation des résultats des prospections géophysiques par tomographie de résistivité électrique (ERT) menées sur la zone faillée de Hockai dans la région de Malmedy. Le but ... [more ▼]

Ce rapport consiste en la présentation des résultats des prospections géophysiques par tomographie de résistivité électrique (ERT) menées sur la zone faillée de Hockai dans la région de Malmedy. Le but principal de ces investigations est de juger de la fracturation de la roche dans et en dehors de la Zone de Faille de Hockai (ZFH) et de mettre en évidence les structures liées à cette zone de failles. [less ▲]

Detailed reference viewed: 54 (7 ULg)