Enhancing the information content of geophysical data for nuclear site characterisation

Our knowledge and understanding to the heterogeneous structure and processes occurring in the Earth’s subsurface is limited and uncertain. The above is true even for the upper 100m of the subsurface, yet many processes occur within it (e.g. migration of solutes, landslides, crop water uptake, etc.) are important to human activities. Geophysical methods such as electrical resistivity tomography (ERT) greatly improve our ability to observe the subsurface due to their higher sampling frequency (especially with autonomous time-lapse systems), larger spatial coverage and less invasive operation, in addition to being more cost-effective than traditional point-based sampling. However, the process of using geophysical data for inference is prone to uncertainty. There is a need to better understand the uncertainties embedded in geophysical data and how they translate themselves when they are subsequently used, for example, for hydrological or site management interpretations and decisions. This understanding is critical to maximize the extraction of information in geophysical data. To this end, in this thesis, I examine various aspects of uncertainty in ERT and develop new methods to better use geophysical data quantitatively. The core of the thesis is based on two literature reviews and three papers. In the first review, I provide a comprehensive overview of the use of geophysical data for nuclear site characterization, especially in the context of site clean-up and leak detection. In the second review, I survey the various sources of uncertainties in ERT studies and the existing work to better quantify or reduce them. I propose that the various steps in the general workflow of an ERT study can be viewed as a pipeline for information and uncertainty propagation and suggested some areas have been understudied. One of these areas is measurement errors. In paper 1, I compare various methods to estimate and model ERT measurement errors using two long-term ERT monitoring datasets. I also develop a new error model that considers the fact that each electrode is used to make multiple measurements. In paper 2, I discuss the development and implementation of a new method for geoelectrical leak detection. While existing methods rely on obtaining resistivity images through inversion of ERT data first, the approach described here estimates leak parameters directly from raw ERT data. This is achieved by constructing hydrological models from prior site information and couple it with an ERT forward model, and then update the leak (and other hydrological) parameters through data assimilation. The approach shows promising results and is applied to data from a controlled injection experiment in Yorkshire, UK. The approach complements ERT imaging and provides a new way to utilize ERT data to inform site characterisation. In addition to leak detection, ERT is also commonly used for monitoring soil moisture in the vadose zone, and increasingly so in a quantitative manner. Though both the petrophysical relationships (i.e., choices of appropriate model and parameterization) and the derived moisture content are known to be subject to uncertainty, they are commonly treated as exact and error‐free. In paper 3, I examine the impact of uncertain petrophysical relationships on the moisture content estimates derived from electrical geophysics. Data from a collection of core samples show that the variability in such relationships can be large, and they in turn can lead to high uncertainty in moisture content estimates, and they appear to be the dominating source of uncertainty in many cases. In the closing chapters, I discuss and synthesize the findings in the thesis within the larger context of enhancing the information content of geophysical data, and provide an outlook on further research in this topic

Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter

Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world casestudy. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3 km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much larger number of conditioning piezometric heads, multiple point geostatistics and ERT could improve aquifer characterization. This shows that state of the art stochastic methods need to be supported by abundant and high-quality subsurface data

Facies discrimination with electrical resistivity tomography using a probabilistic methodology: Effect of sensitivity and regularization

peer reviewedElectrical resistivity tomography (ERT) has become a standard geophysical method in the field of hydrogeology, as it has the potential to provide important information regarding the spatial distribution of facies. However, inverted ERT images tend to be grossly smoothed versions of reality because of the regularization of the inverse problem. In this study, we use a probabilistic methodology based upon co-located measurements to assess the utility of ERT to identify hydrofacies in alluvial aquifers. With this methodology, ERT images are interpreted in terms of the probability of belonging to pre-defined hydrofacies. We first analyze through a synthetic study the ability of ERT to discriminate between different facies. As ERT data suffer from a loss of sensitivity with depth, we find that low sensitivity regions are more affected by misclassification. To counteract this effect, we adapt the probabilistic framework to include the spatially varying data sensitivity. We then apply our learning to a field case. For the latter, we consider two different regularization procedures. In contrast to the data sensitivity which affects the facies probability to a limited amount, the regularization can affect the probability maps more considerably because it has a strong influence on the spatial distribution of inverted resistivity. We find that a regularization strategy based on the most realistic prior information tends to offer the most reliable discrimination of facies. Our results confirm the ability of ERT surveys, when properly designed, to detect facies variations in alluvial aquifers. The method can be easily extended to other contexts

Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

Most geophysical inverse problems are non-linear and rely upon numerical forward solvers involving discretization and simplified representations of the underlying physics. As a result, forward modelling errors are inevitable. In practice, such model errors tend to be either completely ignored, which leads to biased and over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we rely on deep generative neural networks to learn problem-specific low-dimensional probabilistic representations of the discrepancy between high-fidelity and low-fidelity forward solvers. These representations are then used to probabilistically invert for the model error jointly with the target geophysical property field, using the computationally cheap, low-fidelity forward solver. To this end, we combine a Markov chain Monte Carlo (MCMC) inversion algorithm with a trained convolutional neural network of the spatial generative adversarial network (SGAN) type, whereby at each MCMC step, the simulated low-fidelity forward response is corrected using a proposed model-error realization. Considering the crosshole ground-penetrating radar traveltime tomography inverse problem, we train SGAN networks on traveltime discrepancy images between: (1) curved-ray (high fidelity) and straight-ray (low fidelity) forward solvers; and (2) finite-difference-time-domain (high fidelity) and straight-ray (low fidelity) forward solvers. We demonstrate that the SGAN is able to learn the spatial statistics of the model error and that suitable representations of both the subsurface model and model error can be recovered by MCMC. In comparison with inversion results obtained when model errors are either ignored or approximated by a Gaussian distribution, we find that our method has lower posterior parameter bias and better explains the observed traveltime data. Our method is most advantageous when high-fidelity forward solvers involve heavy computational costs and the Gaussian assumption of model errors is inappropriate. Unstable MCMC convergence due to non-linearities introduced by our method remain a challenge to be addressed in future work

Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

Fluid flow in a charged porous medium generates electric potentials called streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, global sensitivity analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase.GSA is used through variance-based sensitivity indices, calculated using sparse polynomial chaos expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap information criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov chain Monte Carlo (MCMC) method and the first-order approximation (FOA) approach based on the Levenberg–Marquardt algorithm. The comparison between both approaches allows us to check whether FOA can provide a reliable estimation of parameters and associated uncertainties for the highly nonlinear hydrogeophysical problem investigated.GSA results show that in short time periods, the saturated hydraulic conductivity (Ks) and the voltage coupling coefficient at saturation Csat are the most influential parameters, whereas in long time periods, the residual water content (θs), the Mualem–van Genuchten parameter n and the Archie saturation exponent na become influential, with strong interactions between them. The Mualem–van Genuchten parameter α has a very weak influence on the SP signals during the whole experiment.Results of parameter estimation show that although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (Ks, θs, α, n) and geophysical parameters (na, Csat) can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.</p

Hydrogeophysical characterisation for improved early warning of landslides

Landslides are gravity driven movements of earth material that can have major economic and societal consequences. Most of these movements are driven by changes in subsurface moisture, usually resulting from rainfall and consequently are likely to become more frequent in regions where more extreme wetting events occur due to climate change. This work focuses on moisture-driven landslides in clay rich unstable slopes. Conventional methods of characterising landslides include intrusive sampling methods, such as boreholes and point samples; however, these are only sensitive to discrete portions of the subsurface. Remote sensing can be used to map the external geometry of landslides but offers little information on internal structure and condition. Geophysical methods can enhance the internal characterisation of landslides as they are spatially sensitive to subsurface properties like electrical resistivity and seismic wave speed. Furthermore, repeated geophysical surveys can reveal how these properties change with time. Here the use of direct current (DC) electrical resistivity measurements for monitoring landslides is explored, as near-surface changes in moisture tend to drive changes in electrical resistivity. The research is applied to the Hollin Hill Landslide Observatory, composed of Jurassic rocks in the north of England, as this site is representative of many vulnerable slopes in the United Kingdom. By their nature, landslides move downslope. This continuous movement poses a challenge for the long-term processing of data from permanently installed sensors entrained within these slopes. Here the goal is to process long term DC resistivity data using time-lapse Electrical Resistivity Imaging (ERI) to aid understanding seasonal moisture content dynamics and internal geometry of the Hollin Hill landslide. The topography of the slope and locations of the electrodes at the surface move with landslide movements, which introduces artefacts in conventional ERI processing results. Global positioning systems (GPS) were used to track landslide movements via permanently deployed markers (pegs) on the slope. A thin plate spline algorithm was used to interpolate changes to the slope topography and electrode locations through time, allowing for geophysical modelling to account for changes of the slope surface. These efforts culminate in a time series of geophysical models with a dynamic surface that captures both geomorphological and electrical resistivity changes at Hollin Hill, useful for illuminating landslide moisture content dynamics. Time series ERI models show low resistivities, linked to sustained high moisture contents, are present in an area of the landslide actively undergoing movement during this study. Clay rich rocks are particularly susceptible to landslides due to their low resistance to shearing at high moisture contents. Petrophysical relationships between electrical resistivity and moisture content have been established for decades, hence ERI can facilitate volumetric imaging of moisture content in the field. Such a conversion is useful as it presents geophysical properties in an engineering context and makes geophysical models more accessible for decision makers (or engineers). Electrical resistivity is sensitive to formation lithology, porosity, moisture content, pore fluid conductivity, and temperature. Clay formations have some unusual properties from a petrophysical perspective as they conduct electricity, and their porosity can increase as the clay grains swell with increasing moisture content. It is found that accounting for the swelling of clay is necessary for reliably fitting established petrophysical models. Relationships between matric potential, or negative pore pressure, and electrical resistivity are also explored as the former can be directly related to the unsaturated shear strength of a geological formation. Although, volumetric models of matric potential derived from ERI processing are not always realistic, tending towards negative or negligible matric potentials. Hydrological models of landslides can be used to understand fluid dynamics within slopes and predict crucial hydro-mechanical parameters controlling slope stability. Given the relationship between electrical resistivity and moisture content, electrical resistivity measurements can be used to calibrate hydrological parameters in these models. The soil retention parameters controlling unsaturated fluid flow are calibrated via coupled geophysical and hydrological (hydrogeophysical) modelling, in two formations at the Hollin Hill landslide. Parameter sampling is achieved using a Markov chain Monte-Carlo approach to find most likely soil retention parameters. The workflow is firstly tested against a synthetic case study with known parameters and then applied to Hollin Hill. The results are promising and show agreement with other (conventional) methods of determining these parameters, demonstrating that hydrogeophysical modelling can be used successfully for calibrating landslide models. However, there are limitations with this approach as assumptions with petrophysical relationships and modelling domain must be made. Overall ERI is a valuable tool for enhancing the understanding of landslide structures and moisture content conditions. Time-lapse processing can illuminate moisture content dynamics, and with appropriate petrophysical calibration ERI volumes can be mapped into moisture content and matric potential. Coupled hydrogeophysical approaches can be further used to constrain unsaturated fluid flow parameters in landslide models. As such, geoelectrical monitoring of landslides is a viable tool, alongside pre-existing conventional methods, for continued assessment of unstable slopes and model construction

Thermal conductivity of unsaturated clay-rocks

The parameters used to describe the electrical conductivity of a porous material can be used to describe also its thermal conductivity. A new relationship is developed to connect the thermal conductivity of an unsaturated porous material to the thermal conductivity of the different phases of the composite, and two electrical parameters called the first and second Archie's exponents. A good agreement is obtained between the new model and thermal conductivity measurements performed using packs of glass beads and core samples of the Callovo-Oxfordian clay-rocks at different saturations of the water phase. We showed that the three model parameters optimised to fit the new model against experimental data (namely the thermal conductivity of the solid phase and the two Archie's exponents) are consistent with independent estimates. We also observed that the anisotropy of the effective thermal conductivity of the Callovo-Oxfordian clay-rock was mainly due to the anisotropy of the thermal conductivity of the solid phase

Sequential approach to joint flow-seismic inversion for improved characterization of fractured media

Seismic interpretation of subsurface structures is traditionally performed without any account of flow behavior. Here we present a methodology for characterizing fractured geologic reservoirs by integrating flow and seismic data. The key element of the proposed approach is the identification—within the inversion—of the intimate relation between fracture compliance and fracture transmissivity, which determine the acoustic and flow responses of a fractured reservoir, respectively. Owing to the strong (but highly uncertain) dependence of fracture transmissivity on fracture compliance, the modeled flow response in a fractured reservoir is highly sensitive to the geophysical interpretation. By means of synthetic models, we show that by incorporating flow data (well pressures and tracer breakthrough curves) into the inversion workflow, we can simultaneously reduce the error in the seismic interpretation and improve predictions of the reservoir flow dynamics. While the inversion results are robust with respect to noise in the data for this synthetic example, the applicability of the methodology remains to be tested for more complex synthetic models and field cases.Eni-MIT Energy Initiative Founding Member ProgramKorea (South). Ministry of Land, Transportation and Maritime Affairs (15AWMP-B066761-03

Regional-scale integration of multiresolution 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 distance