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Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data Hermans, Thomas ; ; Nguyen, Frédéric 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 ▲] Detailed reference viewed: 35 (5 ULg)Data-driven selection of the minimum-gradient support parameter in time-lapse focused electrical imaging Nguyen, Frédéric ; ; 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 ▲] Detailed reference viewed: 81 (17 ULg)Time-lapse inversion of ERT monitoring data using variogram-based regularization Hermans, Thomas ; Dumont, Gaël ; 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 ▲] Detailed reference viewed: 44 (2 ULg)Coupling of hydrogeological models with hydrogeophysical data to characterize seawater intrusion and shallow geothermal systems Beaujean, Jean ; ; et al Conference (2013, December 12) While coastal aquifers are being stressed due to climate changes and excessive groundwater withdrawals require characterizing efficiently seawater intrusion (SWI) dynamics, production of geothermal energy ... [more ▼] While coastal aquifers are being stressed due to climate changes and excessive groundwater withdrawals require characterizing efficiently seawater intrusion (SWI) dynamics, production of geothermal energy is increasingly being used to hinder global warming. To study these issues, we need both robust measuring technologies and reliable predictions based on numerical models. SWI models are currently calibrated using borehole observations. Similarly, geothermal models depend mainly on the temperature field at few locations. Electrical resistivity tomography (ERT) can be used to improve these models given its high sensitivity to TDS and temperature and its relatively high lateral resolution. Inherent geophysical limitations, such as the resolution loss, can affect the overall quality of the ERT images and also prevent the correct recovery of the desired hydrochemical property. We present an uncoupled and coupled hydrogeophysical inversion to calibrate SWI and thermohydrogeologic models using ERT. In the SWI models, we demonstrate with two synthetic benchmarks (homogeneous and heterogeneous coastal aquifers) the ability of cumulative sensitivity-filtered ERT images using surface-only data to recover the hydraulic conductivity. Filtering of ERT-derived data at depth, where resolution is poorer, and the model errors make the dispersivity more difficult to estimate. In the coupled approach, we showed that parameter estimation is significantly improved because regularization bias is replaced by forward modeling only. Our efforts are currently focusing on applying the uncoupled/coupled approaches on a real life case study using field data from the site of Almeria, SE Spain. In the thermohydrogeologic models, the most sensitive hydrologic parameters responsible for heat transport are estimated from surface ERT-derived temperatures and ERT resistance data. A real life geothermal experiment that took place on the Campus De Sterre of Ghent University, Belgium and a synthetic case are tested. They consist in a thermal injection and storage of water in a shallow sandy aquifer. The use of a physically-based constraint accounting for the difference in conductivity between the formation and the tap injected water and based on the hydrogeological model calibrated first on temperatures is necessary to improve the parameter estimation. Results suggest that time-lapse ERT data may be limited but useful information for estimating groundwater flow and transport parameters for both the convection and conduction phases. [less ▲] Detailed reference viewed: 83 (8 ULg)The state of the science and vision of the future: Report from the Hydrogeophysics Workshop ; ; et al in Leading Edge (2013), 32(7), 814-818 In July 2012, 72 hydrogeophysicists from around the world gathered at the Hydrogeophysics Workshop in Boise, Idaho, USA. This was the first workshop to be jointly sponsored by the Society of Exploration ... [more ▼] In July 2012, 72 hydrogeophysicists from around the world gathered at the Hydrogeophysics Workshop in Boise, Idaho, USA. This was the first workshop to be jointly sponsored by the Society of Exploration Geophysicists (SEG) and the American Geophysical Union (AGU), and brought together members from both societies, primarily from the Near-Surface Geophysics Section of SEG and the Near-Surface Focus Group and Hydrology Section of AGU. The intent of the workshop was to address current hydrogeophysical approaches for determining, predicting, and studying hydrologic properties and processes in both the saturated and unsaturated zones, at scales ranging from centimeters to watersheds. [less ▲] Detailed reference viewed: 29 (13 ULg)Inversion of multi-temporal geoelectrical field data sets: insights on noise characterization and regularization Nguyen, Frédéric ; ; Robert, Tanguy et al Poster (2012, July 11) Inversion of geoelectrical time-lapse data sets is increasingly growing as monitoring systems are being used in more applications such as seawater intrusion, landslides, remediation of contaminated sites ... [more ▼] Inversion of geoelectrical time-lapse data sets is increasingly growing as monitoring systems are being used in more applications such as seawater intrusion, landslides, remediation of contaminated sites, landfill operation, shallow geothermal systems, or management of water resources. To date, several inversion strategies exist for taking into account the temporal dimension of the data. The most used nowadays are the independent inversion of multi-temporal data sets, the difference inversion, the temporally-constrained inversion, and the more recent process-based inversion. However, difference inversion schemes generally assume that part of the noise contained in the data cancels out when working with temporal data differences. Temporally-constrained inversion on the other hand assumes that the changes are localized and minor. Process-based inversion requires a more advanced knowledge of the system prior the inversion. In this study we demonstrate that the resolution of the time-lapse inversion scheme is mostly dependent on the quantification of the temporal behavior of the data error, on the resolution of the model-dependent pattern of the survey, and not on the regularization strategy. Our study is based on the imaging results of different data sets with different time and spatial scales, and with different degrees of geological complexity and resistivity contrast, The considered sites are a shallow sandy aquifer and a fractured hard rock aquifer where tracer experiments were performed and monitored using surface arrays. The two studied transport processes are advection, with velocities on the order of 10 m/hour and slower advection/diffusion processes. The strongest improvements were brought by using the data difference and a quantitative estimation of the data error. We found in particular a dependence of the time-lapse data error to the measured resistance (i.e., signal-to-noise-ratio), permitting to formulate an error model to describe the data error present in time-lapse data sets. We used minimum gradient support regularization to invert for model changes with enhanced contrast and found this technique more suited to time-lapse studies than for static images. Noise characterization and error models appear therefore as essential and the most impacting for a successful inversion both for static and time-lapse data whereas different spatio-temporal regularization techniques allowed to decrease artefacts but needs to be coherent with the process. [less ▲] Detailed reference viewed: 70 (10 ULg)Imaging artificial salt water infiltration using electrical resistivity tomography constrained by geostatistical data Hermans, Thomas ; ; et al in Journal of Hydrology (2012), 438-439 Electrical resistivity tomography is a well-known technique to monitor fresh-salt water transitions. In such environments, boreholes are often used to validate geophysical results but rarely used to ... [more ▼] Electrical resistivity tomography is a well-known technique to monitor fresh-salt water transitions. In such environments, boreholes are often used to validate geophysical results but rarely used to constrain the geoelectrical inversion. To estimate the extent of salt water infiltration in the dune area of a Natural Reserve (Westhoek, Belgium), electrical resistivity tomography profiles were carried out together with borehole electromagnetic measurements. The latter were used to calculate a vertical variogram, representative of the study site. Then, a geostatistical constraint, in the form of an a priori model covariance matrix based on the variogram, was imposed as regularization to solve the electrical inverse problem. Inversion results enabled to determine the extension of the salt water plume laterally and at depth, but also to estimate the total dissolved solid content within the plume. These results are in agreement with the hydrogeological data of the site. A comparison with borehole data showed that the inversion results with geostatistical constraints are much more representative of the seawater body (in terms of total dissolved solids, extension and height) than results using standard smoothness-constrained inversion. The field results obtained for the Westhoek site emphasize the need to go beyond standard smoothness-constrained images and to use available borehole data as prior information to constrain the inversion. [less ▲] Detailed reference viewed: 180 (54 ULg)Incorporation of prior information in the regularized inversion of ERT data with CRTomo Hermans, Thomas ; Caterina, David ; et al Conference (2012, February 03) The electrical resistivity tomography (ERT) inverse problem is ill-posed leading to non-uniqueness of its solution. A possible way to reduce the amount of mathematical solutions to more geologically ... [more ▼] The electrical resistivity tomography (ERT) inverse problem is ill-posed leading to non-uniqueness of its solution. A possible way to reduce the amount of mathematical solutions to more geologically plausible models is to incorporate priori information in the inversion process. In this presentation, we describe the implementation of three different techniques ways to go beyond standard Occam’s inversion for ERT with the code CRTomo : a simple reference model weighted by a user-defined parameter, a structural constraint defined by modifying the construction of the roughness matrix compared to standard Occam’s inversion and a geostatistical constraint based on a vertical correlation length deduced from borehole data to build the model covariance matrix and use it to regularize the inversion. With several examples, we show that the traditional smoothness constraint yield small contrasts of resistivity, far from the reality revealed by borehole measurements. Incorporating prior information from boreholes clearly or from another geophysical technique (like GPR or seismic refraction) improves the misfit with logging data. The choice of the prior information incorporation technique highly depends on which king of information is available and further developments are needed to extend the techniques to more complex cases. [less ▲] Detailed reference viewed: 302 (16 ULg)Inversion of multi-temporal geoelectrical data sets: insights from several case studies Nguyen, Frédéric ; ; Robert, Tanguy et al Conference (2011, December) Time-lapse inversion of geoelectrical data is increasingly growing as remote monitoring systems are being used in more applications such as seawater intrusions, landslides, bioremediation of contaminated ... [more ▼] Time-lapse inversion of geoelectrical data is increasingly growing as remote monitoring systems are being used in more applications such as seawater intrusions, landslides, bioremediation of contaminated sites, landfill operations, shallow geothermal systems, or water resources. To date, several inversion strategies exist for taking into account the temporal dimension of the data. Among the most used ones are the independent inversion of multi-temporal data sets, the difference inversion, the temporally-constrained inversion, and the more recent process-based inversion. The success of a particular time-lapse inversion scheme depends on the validity of several assumptions made by these inversion schemes. Difference inversion schemes generally assume that part of the noise contained in the data cancels out when working with temporal data differences. Process-based inversion requires a more advanced knowledge of the system prior the inversion. Temporally-constrained inversion on the other hand assumes that the changes are localized and minor. We show in this paper using data sets with different time and spatial scales, and with different degrees of geological complexity and resistivity contrasts, that the particular success of a time-lapse inversion scheme is highly dependent on the temporal behaviour of the noise estimation in the time-lapse data set and of the model-dependent resolution pattern of the survey. We attempt to provide guidelines for successful quantitative interpretation of time-lapse data sets whenever possible. [less ▲] Detailed reference viewed: 96 (31 ULg)How to incorporate prior information in geophysical inverse problems: deterministic and geostatistical approaches. Hermans, Thomas ; Caterina, David ; et al in EarthDoc - Near Surface 2011 - 17th European Meeting of Environmental and Engineering Geophysics (2011, September 13) Many geophysical inverse problems are ill-posed leading to non-uniqueness of the solution. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by ... [more ▼] Many geophysical inverse problems are ill-posed leading to non-uniqueness of the solution. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the inverse problem and incorporating all available prior information in the inversion process. We compare three different ways to go beyond standard Occam’s inversion for electrical resistivity tomography (ERT) using electromagnetic logging data in the context of salt water infiltration: a simple reference model, a structural constraint and a geostatistical constraint based on a vertical correlation length. Results with the traditional smoothness constraint yield small contrasts of resistivity, far from the reality revealed by borehole measurements. Incorporating prior information from boreholes clearly improves the misfit with logging data. If a good reference model can always be used, it can lead to misinterpretation if its weight is too strong. When the computation of the correlation length is possible, the geostatistical inversion gives satisfactory results everywhere in the section. In this specific case, the geostatistical approach seems to be a more robust way to incorporate prior information. The structural constraint seems to be more indicated when integrating information from other geophysical methods such as GPR or seismic. [less ▲] Detailed reference viewed: 332 (26 ULg)Using geostatistical constraints in electrical imaging for improved reservoir characterization ; ; Hermans, Thomas et al Conference (2010, December 14) Developing predictive models of reservoirs is often complicated by the spatial heterogeneities and the different scales which control flow and transport processes. In numerous studies over the past two ... [more ▼] Developing predictive models of reservoirs is often complicated by the spatial heterogeneities and the different scales which control flow and transport processes. In numerous studies over the past two decades, geophysical imaging techniques have proved very useful for reservoir characterization. However, the loss of resolution and the non-uniqueness of standard solutions to inverse problems strongly limit the use of such deterministic imaging approaches. On the other hand, the use of common geostatistical approaches for reservoir characterization, for instance from logging information, may be a difficult task, since accurate variogram information is difficult to obtain (dense sampling in the vertical and lateral directions), and also because a high number of conditioned simulations is needed to remove statistical bias. Combining the high spatial sampling of deterministic geophysical imaging methods with geostatistical constraints, valid in the whole image plane, appears as a very promising approach to enhance reservoir characterization. To do so, we use a parameterized model covariance matrix based on standard variogram functions and a prior model as regularization operator in the inversion of electrical resistance data. This way of including additional data is not restricted to electrical data but the variogram parameters may be also inferred from for example available textural or lithological information. The benefit of the presented approach is twofold: (i) It honors the spatial statistics of the reservoir and (ii) it alters the posterior model by further reducing model ambiguity inherent to the inversion compared to classical (smooth model) regularization. The proof of concept is given by synthetic studies carried out on random fields from Gauss simulations with varying (an)isotropic scale lengths using different model (co)variogram functions. We also demonstrate the approach on electrical field data combined with borehole electromagnetic data from two artificial sea inlets in the nature reserve "The Westhoek" near the French-Belgian border. The electromagnetic logs were used to calculate an experimental vertical variogram characteristic of the study site. The results enabled to determine the extension of the salt water plume laterally, and significantly enhance its extension in depth, but also in terms of total dissolved solid content. These observations are in agreement with the hydrogeological situation at the site. A comparison with borehole data shows that the results are much more plausible than results obtained with a traditional smoothness constraint used as regularization operator. In conclusion, the incorporation of geostatistical information, vertical variograms in our case, in the inverse process improves imaging capabilities for reservoir characterization significantly. [less ▲] Detailed reference viewed: 68 (6 ULg)Joint and sequential inversion of geophysical and hydrogeological data to characterize seawater intrusion models Beaujean, Jean ; Nguyen, Frédéric ; in Teresa Condesso de Melo, Maria; Lebbe, Luc; Virgílio Cruz, José (Eds.) et al Proceedings SWIM21, 21st Salt Water Intrusion Meeting (2010, June) The integrated water resource management problems require studying efficiently seawater intrusion at local and regional scale and identifying in real time the seawater/freshwater interface dynamic ... [more ▼] The integrated water resource management problems require studying efficiently seawater intrusion at local and regional scale and identifying in real time the seawater/freshwater interface dynamic. Hydrogeological modeling is widely used to predict seawater intrusion if additional natural or man‐made factors are modified. These models are currently calibrated using measured heads and salt mass fractions in boreholes, which generally result in sparse data coverage. Within this scope, non to minimally invasive geophysical techniques like electrical resistivity tomography (ERT) or time‐domain electromagnetic method are becoming increasingly popular, given their relatively greater spatial horizontal resolution compared to borehole observations. We present a comparison between both a sequential and joint approach to calibrate seawater intrusion models using ERT. The former consists of constraining hydrogeological parameters using ERT derived parameters and relies on sequential inversions of the geophysical and hydrogeological data using a given petrophysical relationship. The second approach in based on simultaneous inversion of petrophysical and hydrogeological data using electrical resistance data as data. It is performed by coupling an inversion code with two hydrogeological and geophysical modeling codes through a petrophysical conversion. This investigation was performed on a densitydependent flow and transport numerical (three/two‐dimensional) simulation study from complex and realistic heterogeneous models. In the sequential approach, the simulations showed that only the shallow salt concentration of the seawater/freshwater transition zone could be recovered for different time‐lapse, due to poorly resolved regions in depth. The capability of image appraisal indicators (cumulative sensitivity and resolution) has been analyzed to emphasize the discrepancy between the targeted and imaged parameter values. On the other hand, the preliminary coupled inversion avoids the regularization bias introduced by ERT and addresses the non‐stationarity of the petrophysical relationship. [less ▲] Detailed reference viewed: 96 (9 ULg)Detecting preferential flow and transport in soils using electrical resistivity tomography ; ; Garré, Sarah et al Conference (2009) Detailed reference viewed: 53 (1 ULg) |
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