Impact of controlled changes in grain size and pore space characteristics on the hydraulic conductivity and spectral induced polarization response of "proxies" of saturated alluvial sediments

Understanding the influence of pore space characteristics on the hydraulic conductivity and spectral induced polarization (SIP) response is critical for establishing relationships between the electrical and hydrological properties of surficial unconsolidated sedimentary deposits, which host the bulk of the world's readily accessible groundwater resources. Here, we present the results of laboratory SIP measurements on industrial-grade, saturated quartz samples with granulometric characteristics ranging from fine sand to fine gravel, which can be regarded as proxies for widespread alluvial deposits. We altered the pore space characteristics by changing (i) the grain size spectra, (ii) the degree of compaction, and (iii) the level of sorting. We then examined how these changes affect the SIP response, the hydraulic conductivity, and the specific surface area of the considered samples. In general, the results indicate a clear connection between the SIP response and the granulometric as well as pore space characteristics. In particular, we observe a systematic correlation between the hydraulic conductivity and the relaxation time of the Cole-Cole model describing the observed SIP effect for the entire range of considered grain sizes. The results do, however, also indicate that the detailed nature of these relations depends strongly on variations in the pore space characteristics, such as, for example, the degree of compaction. The results of this study underline the complexity of the origin of the SIP signal as well as the difficulty to relate it to a single structural factor of a studied sample, and hence raise some fundamental questions with regard to the practical use of SIP measurements as site- and/or sample-independent predictors of the hydraulic conductivity.

A non-linear Bayesian approach for upscaling local-scale hydraulic conductivity measurements based on local- and regional-scale geophysical data

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed an upscaling procedure based on a Bayesian sequential simulation approach. This method is then applied to the stochastic integration of low-resolution, regional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this upscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Quantitative integration of geophysical and hydraulic data : from the local towards the regional scale range

Des progrès significatifs ont été réalisés dans le domaine de l'intégration quantitative des données géophysique et hydrologique l'échelle locale. Cependant, l'extension à de plus grandes échelles des approches correspondantes constitue encore un défi majeur. Il est néanmoins extrêmement important de relever ce défi pour développer des modèles fiables de flux des eaux souterraines et de transport de contaminant. Pour résoudre ce problème, j'ai développé une technique d'intégration des données hydrogéophysiques basée sur une procédure bayésienne de simulation séquentielle en deux étapes. Cette procédure vise des problèmes à plus grande échelle. L'objectif est de simuler la distribution d'un paramètre hydraulique cible à partir, d'une part, de mesures d'un paramètre géophysique pertinent qui couvrent l'espace de manière exhaustive, mais avec une faible résolution (spatiale) et, d'autre part, de mesures locales de très haute résolution des mêmes paramètres géophysique et hydraulique. Pour cela, mon algorithme lie dans un premier temps les données géophysiques de faible et de haute résolution à travers une procédure de réduction déchelle. Les données géophysiques régionales réduites sont ensuite reliées au champ du paramètre hydraulique à haute résolution. J'illustre d'abord l'application de cette nouvelle approche dintégration des données à une base de données synthétiques réaliste. Celle-ci est constituée de mesures de conductivité hydraulique et électrique de haute résolution réalisées dans les mêmes forages ainsi que destimations des conductivités électriques obtenues à partir de mesures de tomographic de résistivité électrique (ERT) sur l'ensemble de l'espace. Ces dernières mesures ont une faible résolution spatiale. La viabilité globale de cette méthode est testée en effectuant les simulations de flux et de transport au travers du modèle original du champ de conductivité hydraulique ainsi que du modèle simulé. Les simulations sont alors comparées. Les résultats obtenus indiquent que la procédure dintégration des données proposée permet d'obtenir des estimations de la conductivité en adéquation avec la structure à grande échelle ainsi que des predictions fiables des caractéristiques de transports sur des distances de moyenne à grande échelle. Les résultats correspondant au scénario de terrain indiquent que l'approche d'intégration des données nouvellement mise au point est capable d'appréhender correctement les hétérogénéitées à petite échelle aussi bien que les tendances à gande échelle du champ hydraulique prévalent. Les résultats montrent également une flexibilté remarquable et une robustesse de cette nouvelle approche dintégration des données. De ce fait, elle est susceptible d'être appliquée à un large éventail de données géophysiques et hydrologiques, à toutes les gammes déchelles. Dans la deuxième partie de ma thèse, j'évalue en détail la viabilité du réechantillonnage geostatique séquentiel comme mécanisme de proposition pour les méthodes Markov Chain Monte Carlo (MCMC) appliquées à des probmes inverses géophysiques et hydrologiques de grande dimension . L'objectif est de permettre une quantification plus précise et plus réaliste des incertitudes associées aux modèles obtenus. En considérant une série dexemples de tomographic radar puits à puits, j'étudie deux classes de stratégies de rééchantillonnage spatial en considérant leur habilité à générer efficacement et précisément des réalisations de la distribution postérieure bayésienne. Les résultats obtenus montrent que, malgré sa popularité, le réechantillonnage séquentiel est plutôt inefficace à générer des échantillons postérieurs indépendants pour des études de cas synthétiques réalistes, notamment pour le cas assez communs et importants où il existe de fortes corrélations spatiales entre le modèle et les paramètres. Pour résoudre ce problème, j'ai développé un nouvelle approche de perturbation basée sur une déformation progressive. Cette approche est flexible en ce qui concerne le nombre de paramètres du modèle et lintensité de la perturbation. Par rapport au rééchantillonage séquentiel, cette nouvelle approche s'avère être très efficace pour diminuer le nombre requis d'itérations pour générer des échantillons indépendants à partir de la distribution postérieure bayésienne. - Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending corresponding approaches beyond the local scale still represents a major challenge, yet is critically important for the development of reliable groundwater flow and contaminant transport models. To address this issue, I have developed a hydrogeophysical data integration technique based on a two-step Bayesian sequential simulation procedure that is specifically targeted towards larger-scale problems. The objective is to simulate the distribution of a target hydraulic parameter based on spatially exhaustive, but poorly resolved, measurements of a pertinent geophysical parameter and locally highly resolved, but spatially sparse, measurements of the considered geophysical and hydraulic parameters. To this end, my algorithm links the low- and high-resolution geophysical data via a downscaling procedure before relating the downscaled regional-scale geophysical data to the high-resolution hydraulic parameter field. I first illustrate the application of this novel data integration approach to a realistic synthetic database consisting of collocated high-resolution borehole measurements of the hydraulic and electrical conductivities and spatially exhaustive, low-resolution electrical conductivity estimates obtained from electrical resistivity tomography (ERT). The overall viability of this method is tested and verified by performing and comparing flow and transport simulations through the original and simulated hydraulic conductivity fields. The corresponding results indicate that the proposed data integration procedure does indeed allow for obtaining faithful estimates of the larger-scale hydraulic conductivity structure and reliable predictions of the transport characteristics over medium- to regional-scale distances. The approach is then applied to a corresponding field scenario consisting of collocated high- resolution measurements of the electrical conductivity, as measured using a cone penetrometer testing (CPT) system, and the hydraulic conductivity, as estimated from electromagnetic flowmeter and slug test measurements, in combination with spatially exhaustive low-resolution electrical conductivity estimates obtained from surface-based electrical resistivity tomography (ERT). The corresponding results indicate that the newly developed data integration approach is indeed capable of adequately capturing both the small-scale heterogeneity as well as the larger-scale trend of the prevailing hydraulic conductivity field. The results also indicate that this novel data integration approach is remarkably flexible and robust and hence can be expected to be applicable to a wide range of geophysical and hydrological data at all scale ranges. In the second part of my thesis, I evaluate in detail the viability of sequential geostatistical resampling as a proposal mechanism for Markov Chain Monte Carlo (MCMC) methods applied to high-dimensional geophysical and hydrological inverse problems in order to allow for a more accurate and realistic quantification of the uncertainty associated with the thus inferred models. Focusing on a series of pertinent crosshole georadar tomographic examples, I investigated two classes of geostatistical resampling strategies with regard to their ability to efficiently and accurately generate independent realizations from the Bayesian posterior distribution. The corresponding results indicate that, despite its popularity, sequential resampling is rather inefficient at drawing independent posterior samples for realistic synthetic case studies, notably for the practically common and important scenario of pronounced spatial correlation between model parameters. To address this issue, I have developed a new gradual-deformation-based perturbation approach, which is flexible with regard to the number of model parameters as well as the perturbation strength. Compared to sequential resampling, this newly proposed approach was proven to be highly effective in decreasing the number of iterations required for drawing independent samples from the Bayesian posterior distribution.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.

Hydrogeophysical data integration at larger scales: Application of Bayesian sequential simulation for the characterization of heterogeneous alluvial aquifers

Knowledge of the spatial distribution of hydraulic conductivity (K) within an aquifer is critical for reliable predictions of solute transport and the development of effective groundwater management and/or remediation strategies. While core analyses and hydraulic logging can provide highly detailed information, such information is inherently localized around boreholes that tend to be sparsely distributed throughout the aquifer volume. Conversely, larger-scale hydraulic experiments like pumping and tracer tests provide relatively low-resolution estimates of K in the investigated subsurface region. As a result, traditional hydrogeological measurement techniques contain a gap in terms of spatial resolution and coverage, and they are often alone inadequate for characterizing heterogeneous aquifers. Geophysical methods have the potential to bridge this gap. The recent increased interest in the application of geophysical methods to hydrogeological problems is clearly evidenced by the formation and rapid growth of the domain of hydrogeophysics over the past decade (e.g., Rubin and Hubbard, 2005).

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Developing a predictive understanding of subsurface flow and transport is complicated by the disparity of scales across which controlling hydrological properties and processes span. Conventional techniques for characterizing hydrogeological properties (such as pumping, slug, and flowmeter tests) typically rely on borehole access to the subsurface. Because their spatial extent is commonly limited to the vicinity near the wellbores, these methods often cannot provide sufficient information to describe key controls on subsurface flow and transport. The field of hydrogeophysics has evolved in recent years to explore the potential that geophysical methods hold for improving the quantification of subsurface properties and processes relevant for hydrological investigations. This chapter is intended to familiarize hydrogeologists and water-resource professionals with the state of the art as well as existing challenges associated with hydrogeophysics. We provide a review of the key components of hydrogeophysical studies, which include: geophysical methods commonly used for shallow subsurface characterization; petrophysical relationships used to link the geophysical properties to hydrological properties and state variables; and estimation or inversion methods used to integrate hydrological and geophysical measurements in a consistent manner. We demonstrate the use of these different geophysical methods, petrophysical relationships, and estimation approaches through several field-scale case studies. Among other applications, the case studies illustrate the use of hydrogeophysical approaches to quantify subsurface architecture that influence flow (such as hydrostratigraphy and preferential pathways); delineate anomalous subsurface fluid bodies (such as contaminant plumes); monitor hydrological processes (such as infiltration, freshwater-seawater interface dynamics, and flow through fractures); and estimate hydrological properties (such as hydraulic conductivity) and state variables (such as water content). The case studies have been chosen to illustrate how hydrogeophysical approaches can yield insights about complex subsurface hydrological processes, provide input that improves flow and transport predictions, and provide quantitative information over field-relevant spatial scales. The chapter concludes by describing existing hydrogeophysical challenges and associated research needs. In particular, we identify the area of quantitative watershed hydrogeophysics as a frontier area, where significant effort is required to advance the estimation of hydrological properties and processes (and their uncertainties) over spatial scales relevant to the management of water resources and contaminants.

Multiple-scale hydrological and geophysical data integration through non-linear Bayesian sequential simulation

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the scale of a field site represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed downscaling procedure based on a non-linear Bayesian sequential simulation approach. The main objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity logged at collocated wells and surface resistivity measurements, which are available throughout the studied site. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariatekernel density function. Then a stochastic integration of low-resolution, large-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities is applied. The overall viability of this downscaling approach is tested and validated by comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure allows obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Regional-scale integration of multi-scale hydrological and geophysical data using a two-step Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale for the purpose of improving predictions of groundwater flow and solute transport. However, extending corresponding approaches to the regional scale still represents one of the major challenges in the domain of hydrogeophysics. To address this problem, we have developed a regional-scale data integration methodology based on a two-step Bayesian sequential simulation approach. Our objective is to generate high-resolution stochastic realizations of the regional-scale hydraulic conductivity field in the common case where there exist spatially exhaustive but poorly resolved measurements of a related geophysical parameter, as well as highly resolved but spatially sparse collocated measurements of this geophysical parameter and the hydraulic conductivity. To integrate this multi-scale, multi-parameter database, we first link the low- and high-resolution geophysical data via a stochastic downscaling procedure. This is followed by relating the downscaled geophysical data to the high-resolution hydraulic conductivity distribution. After outlining the general methodology of the approach, we demonstrate its application to a realistic synthetic example where we consider as data high-resolution measurements of the hydraulic and electrical conductivities at a small number of borehole locations, as well as spatially exhaustive, low-resolution estimates of the electrical conductivity obtained from surface-based electrical resistivity tomography. The different stochastic realizations of the hydraulic conductivity field obtained using our procedure are validated by comparing their solute transport behaviour with that of the underlying ?true? hydraulic conductivity field. We find that, even in the presence of strong subsurface heterogeneity, our proposed procedure allows for the generation of faithful representations of the regional-scale hydraulic conductivity structure and reliable predictions of solute transport over long, regional-scale distances.

Use of high-resolution geophysical data to characterize heterogeneous aquifers: influence of data integration method on hydrological predictions

The integration of geophysical data into the subsurface characterization problem has been shown in many cases to significantly improve hydrological knowledge by providing information at spatial scales and locations that is unattainable using conventional hydrological measurement techniques. The investigation of exactly how much benefit can be brought by geophysical data in terms of its effect on hydrological predictions, however, has received considerably less attention in the literature. Here, we examine the potential hydrological benefits brought by a recently introduced simulated annealing (SA) conditional stochastic simulation method designed for the assimilation of diverse hydrogeophysical data sets. We consider the specific case of integrating crosshole ground-penetrating radar (GPR) and borehole porosity log data to characterize the porosity distribution in saturated heterogeneous aquifers. In many cases, porosity is linked to hydraulic conductivity and thus to flow and transport behavior. To perform our evaluation, we first generate a number of synthetic porosity fields exhibiting varying degrees of spatial continuity and structural complexity. Next, we simulate the collection of crosshole GPR data between several boreholes in these fields, and the collection of porosity log data at the borehole locations. The inverted GPR data, together with the porosity logs, are then used to reconstruct the porosity field using the SA-based method, along with a number of other more elementary approaches. Assuming that the grid-cell-scale relationship between porosity and hydraulic conductivity is unique and known, the porosity realizations are then used in groundwater flow and contaminant transport simulations to assess the benefits and limitations of the different approaches.

Integration of high-resolution geophysical data for the characterization of alluvial aquifers : new approaches and implications for hydrological predictions

Abstract Accurate characterization of the spatial distribution of hydrological properties in heterogeneous aquifers at a range of scales is a key prerequisite for reliable modeling of subsurface contaminant transport, and is essential for designing effective and cost-efficient groundwater management and remediation strategies. To this end, high-resolution geophysical methods have shown significant potential to bridge a critical gap in subsurface resolution and coverage between traditional hydrological measurement techniques such as borehole log/core analyses and tracer or pumping tests. An important and still largely unresolved issue, however, is how to best quantitatively integrate geophysical data into a characterization study in order to estimate the spatial distribution of one or more pertinent hydrological parameters, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first develop a strategy for the assimilation of several types of hydrogeophysical data having varying degrees of resolution, subsurface coverage, and sensitivity to the hydrologic parameter of interest. In this regard a novel simulated annealing (SA)-based conditional simulation approach was developed and then tested in its ability to generate realizations of porosity given crosshole ground-penetrating radar (GPR) and neutron porosity log data. This was done successfully for both synthetic and field data sets. A subsequent issue that needed to be addressed involved assessing the potential benefits and implications of the resulting porosity realizations in terms of groundwater flow and contaminant transport. This was investigated synthetically assuming first that the relationship between porosity and hydraulic conductivity was well-defined. Then, the relationship was itself investigated in the context of a calibration procedure using hypothetical tracer test data. Essentially, the relationship best predicting the observed tracer test measurements was determined given the geophysically derived porosity structure. Both of these investigations showed that the SA-based approach, in general, allows much more reliable hydrological predictions than other more elementary techniques considered. Further, the developed calibration procedure was seen to be very effective, even at the scale of tomographic resolution, for predictions of transport. This also held true at locations within the aquifer where only geophysical data were available. This is significant because the acquisition of hydrological tracer test measurements is clearly more complicated and expensive than the acquisition of geophysical measurements. Although the above methodologies were tested using porosity logs and GPR data, the findings are expected to remain valid for a large number of pertinent combinations of geophysical and borehole log data of comparable resolution and sensitivity to the hydrological target parameter. Moreover, the obtained results allow us to have confidence for future developments in integration methodologies for geophysical and hydrological data to improve the 3-D estimation of hydrological properties.

Geophysical Investigations for Hydrogeological Characterization at the Kappelen Test Site (Switzerland)

Vertical electric soundings, 2D resistivity imaging and several logging measurements were performed at Kappelen test site to identify the various geolelectric facies that allowed determining the tabular and horizontal structure of the aquifer. The surface-based geoelectric methods allowed for a reliable characterization of the overall structure and the geometry of the aquifer, while geophysical logging methods allowed for inferring detailed hydrogeophysical characteristics, such as the electrical resistivity, total porosity, global and matrix density and hydraulic conductivity. The synoptic interpretation and integration of this broad and diverse database allows for constraining the key hydrological characteristics and hence forms the basis for the detailed hydraulic modelling of flow and transport process.

Calibration of high-resolution geophysical data with tracer test measurements to improve hydrological predictions

Relationships between porosity and hydraulic conductivity tend to be strongly scale- and site-dependent and are thus very difficult to establish. As a result, hydraulic conductivity distributions inferred from geophysically derived porosity models must be calibrated using some measurement of aquifer response. This type of calibration is potentially very valuable as it may allow for transport predictions within the considered hydrological unit at locations where only geophysical measurements are available, thus reducing the number of well tests required and thereby the costs of management and remediation. Here, we explore this concept through a series of numerical experiments. Considering the case of porosity characterization in saturated heterogeneous aquifers using crosshole ground-penetrating radar and borehole porosity log data, we use tracer test measurements to calibrate a relationship between porosity and hydraulic conductivity that allows the best prediction of the observed hydrological behavior. To examine the validity and effectiveness of the obtained relationship, we examine its performance at alternate locations not used in the calibration procedure. Our results indicate that this methodology allows us to obtain remarkably reliable hydrological predictions throughout the considered hydrological unit based on the geophysical data only. This was also found to be the case when significant uncertainty was considered in the underlying relationship between porosity and hydraulic conductivity.

On the use of spatially discrete data to compute energy and mass balance

In many practical applications the state of field soils is monitored by recording the evolution of temperature and soil moisture at discrete depths. We theoretically investigate the systematic errors that arise when mass and energy balances are computed directly from these measurements. We show that, even with no measurement or model errors, large residuals might result when finite difference approximations are used to compute fluxes and storage term. To calculate the limits set by the use of spatially discrete measurements on the accuracy of balance closure, we derive an analytical solution to estimate the residual on the basis of the two key parameters: the penetration depth and the distance between the measurements. When the thickness of the control layer for which the balance is computed is comparable to the penetration depth of the forcing (which depends on the thermal diffusivity and on the forcing period) large residuals arise. The residual is also very sensitive to the distance between the measurements, which requires accurately controlling the position of the sensors in field experiments. We also demonstrate that, for the same experimental setup, mass residuals are sensitively larger than the energy residuals due to the nonlinearity of the moisture transport equation. Our analysis suggests that a careful assessment of the systematic mass error introduced by the use of spatially discrete data is required before using fluxes and residuals computed directly from field measurements.