Advanced Electrical Resistivity Modelling and Inversion using Unstructured Discretization

In this dissertation an approach is presented for the three-dimensional electrical resistivity tomography (ERT) using unstructured discretizations. The geoelectrical forward problem is solved by the finite element method using tetrahedral meshes with linear and quadratic shape functions. Unstructured meshes are suitable for modelling domains of arbitrary geometry (e.g., complicated topography). Furthermore, the best trade-off between accuracy and numerical effort can be achieved due to the capability of problem-adapted mesh refinement. Unstructured discretizations also allow the consideration of spatial extended finite electrodes. Due to a corresponding extension of the forward operator using the complete electrode model, known from medical impedance tomography, a study about the influence of such electrodes to geoelectrical measurements is given. Based on the forward operator, the so-called triple-grid-technique is developed to solve the geoelectrical inverse problem. Due to unstructured discretization, the ERT can be applied by using a resolution dependent parametrization on arbitrarily shaped two-dimensional and three-dimensional domains. A~Gauss-Newton method is used with inexact line search to fit the data within error bounds. A global regularization scheme is applied using special smoothness constraints. Furthermore, an advanced regularization scheme for the ERT is presented based on unstructured meshes, which is able to include a-priori information into the inversion and significantly improves the resulting ERT images. Structural information such as material interfaces known from other geophysical techniques are incorporated as allowed sharp resistivity contrasts. Model weighting functions can define individually the allowed deviation of the final resistivity model from given start or reference values. As a consequent further development the region concept is presented where the parameter domain is subdivided into lithological or geological regions with individual inversion and regularization parameters. All used techniques and concepts are part of the open source C++ library GIMLi, which has been developed during this thesis as an advanced tool for the method-independent solution of the inverse problem

Geophysics for Mineral Exploration

This Special Issue contains ten papers which focus on emerging geophysical techniques for mineral exploration, novel modeling, and interpretation methods, including joint inversions of multi physics data, and challenging case studies. The papers cover a wide range of mineral deposits, including banded iron formations, epithermal gold–silver–copper–iron–molybdenum deposits, iron-oxide–copper–gold deposits, and prospecting forgroundwater resources

Structural joint inversion of electrical and seismic tomography data

This research project has been focused on the achievement of the structural joint inversion of two geophysical methods. The final target is to obtain a high resolution characterization of the shallow subsurface. The aim of determining petrophysical properties, structural boundaries, etc, can be obtained through the integration of different information that derives from various geophysical methods. In fact, since each method is sensitive to a specific physical property, their integration can lead to an accurate final model. However, if such integration is conducted individually inverting the data sets, the final model will be affected by the resolution limitations of each method. For this reason, an important tool has been developed in geophysical applications: the joint inversion. Two different approaches can be used to carry out the joint inversion: the petrophysical one, in which a petrophysical relationship is used, and the structural one, in which a structural similarity between models is imposed (Gallardo and Meju, 2004). Specifically, I decided to implement the algorithm for the structural joint inversion and specifically the structural approach developed by Gallardo and Meju (2003, 2004), since from literature it results to be the most robust method in the joint inversion (Moorkamp, 2017). In this process, an objective function that includes the objective function of each geophysical method is build and simultaneously minimized. In conclusion, the joint inversion may improve the resolution of each geophysical model and bring to models that are more accurate and easier to interpret. Specifically, in this thesis, the electrical resistivity tomography (ERT) and the seismic refraction tomography (SRT) have been used to carry out the joint inversion. Both these high-resolution methods can be crucial in environmental and engineering applications, as for the geotechnical characterization of a site or for the detection of hydrological resources. Since the resistivity range overlaps for the different materials, resistivity measurements cannot be related to a specific soil or rock. Because of that, it would be better to obtain other information, for example from the seismic tomography. In fact, this method allows not only the reconstruction of the seismic wave velocities with depth, but also to obtain a good lateral resolution. Instead, the Ground Penetrating Radar (GPR) has not been considered since it presents some limits in the investigation depth, due to the high attenuation of electromagnetic energy in porous conductive media. In addition to the integrated inversion, another goal has been obtained in this thesis: the implementation of the forward modeling for the seismic method and specifically, the Multistencils Fast Marching Method (MSFMM). This method can be seen as an extension of the FMM, that is considered from literature the fastest and the most efficient method for the solution of the eikonal equation and accordingly for the computation of the first arrivals traveltimes. In particular, the MSFMM improves the accuracy and the efficiency of the FMM, since it considers also the information that derives from the diagonal directions. Both the algorithms, the one of the joint inversion and the one of the forward modeling for the seismic method, have been implemented in Python language and integrated in the open-source software pyGIMLi

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

Détermination de la conductivité hydraulique à saturation d'un sol non saturé par suivi d'infiltration à l'aide de la tomographie de résistivité électrique

RÉSUMÉ Nous présentons le développement d'une nouvelle méthodologie qui permet d'estimer la conductivité hydraulique à saturation en utilisant la tomographie de résistivité électrique lors d'un suivi d'infiltration dans un sol non-saturé ainsi que le développement d'une nouvelle méthode de maillage pour le problème d’inversion en tomographie de résistivité électrique. Cette thèse inclut deux articles qui ont été soumis dans des revues scientifiques reconnues internationalement----------ABSTRACT We present the development of a new methodology to estimate the saturated hydraulic conductivity using electrical resistivity tomography to monitor water infiltration in an unsaturated soil, and the development of a new intelligent meshing technique for electrical resistivity tomography inversion problems. This thesis includes two articles that were submitted to international refereed scientific journals

Study on 3D forward modeling & inversion of surface-borehole electromagnetic data.

The purpose of this research is to develop an interpretive tool to meet the requirements of deep mineral exploration. Therefore, we carried out a series of research work as part of a doctoral training program and achieved the relevant objectives below. The core of this doctoral thesis is the development of 3D modeling tools to interpret the electromagnetic data collected in boreholes. First, a 3D model creation tool is designed, with which we can easily build a 3D geological model from sections and quickly discretize it. The sections could be true geological cross-sections or from a conceptual geological model. The utility of this tool is to facilitate the tests of the algorithms developed within the framework of this thesis, in order to model the electromagnetic responses in various geological situations and allow to easily change the parameters of the geophysical measurement system. Two parallelization algorithms, MPI-based and hybrid MPI/OpenMP-based methods, are designed for surface borehole time domain electromagnetic (BHTEM) forward modeling. The BHTEM responses are calculated from anomalous regions distributed in a 3D model (discretized into cells). The forward modeling additionally uses multiple meshes, fine meshes are used for the anomalous region in the high-frequency range and coarser meshes for geological background in the low-frequency range. Based on varying meshes for different frequency ranges, the parallel computation greatly reduces the computation time of the TEM forward modeling. An optimal survey design benefits from quick forward modeling. We found that the target BHTEM response depends upon the transmitting pulse width, target time constant, and the duration of measurement time. We proposed the formula with respect to the three variables to design optimal pulse widths in advance for different off-times in order to maximize the efficiency of TEM measurement in the field. Finally, a 3D BHTEM inversion algorithm is developed based on the Gauss-Newton method with high spatial resolution. By introducing the isosurface, neighborhood anomalies search, 3D trace envelope, and false targets elimination into the inversion process, the predicted model is improved through iterations and interactions between the computation and the user intervention

Three-dimensional individual and joint inversion of direct current resistivity and electromagnetic data

The objective of our studies is the combination of electromagnetic and direct current (DC) resistivity methods in a joint inversion approach to improve the reconstruction of a given conductivity distribution. We utilize the distinct sensitivity patterns of different methods to enhance the overall resolution power and ensure a more reliable imaging result. In order to simplify the work with more than one electromagnetic method and establish a flexible and state-of-the-art software basis, we developed new DC resistivity and electromagnetic forward modeling and inversion codes based on finite elements of second order on unstructured grids. The forward operators are verified using analytical solutions and convergence studies before we apply a regularized Gauss-Newton scheme and successfully invert synthetic data sets. Finally, we link both codes with each other in a joint inversion. In contrast to most widely used joint inversion strategies, where different data sets are combined in a single least-squares problem resulting in a large system of equations, we introduce a sequential approach that cycles through the different methods iteratively. This way, we avoid several difficulties such as the determination of the full set of regularization parameters or a weighting of the distinct data sets. The sequential approach makes use of a smoothness regularization operator which penalizes the deviation of the model parameters from a given reference model. In our sequential strategy, we use the result of the preceding individual inversion scheme as reference model for the following one. We successfully apply this approach to synthetic data sets and show that the combination of at least two methods yields a significantly improved parameter model compared to the individual inversion results.Ziel der vorliegenden Arbeit ist die gemeinsame Inversion (\"joint inversion\") elektromagnetischer und geoelektrischer Daten zur Verbesserung des rekonstruierten Leitfähigkeitsmodells. Dabei nutzen wir die verschiedenartigen Sensitivitäten der Methoden aus, um die Auflösung zu erhöhen und ein zuverlässigeres Ergebnis zu erhalten. Um die Arbeit mit mehr als einer Methode zu vereinfachen und eine flexible Softwarebasis auf dem neuesten Stand der Forschung zu etablieren, wurden zwei Codes zur Modellierung und Inversion geoelektrischer als auch elektromagnetischer Daten neu entwickelt, die mit finiten Elementen zweiter Ordnung auf unstrukturierten Gittern arbeiten. Die Vorwärtsoperatoren werden mithilfe analytischer Lösungen und Konvergenzstudien verifiziert, bevor wir ein regularisiertes Gauß-Newton-Verfahren zur Inversion synthetischer Datensätze anwenden. Im Gegensatz zur meistgenutzten \"joint inversion\"-Strategie, bei der verschiedene Daten in einem einzigen Minimierungsproblem kombiniert werden, was in einem großen Gleichungssystem resultiert, stellen wir schließlich einen sequentiellen Ansatz vor, der zyklisch durch die einzelnen Methoden iteriert. So vermeiden wir u.a. eine komplizierte Wichtung der verschiedenen Daten und die Bestimmung aller Regularisierungsparameter in einem Schritt. Der sequentielle Ansatz wird über die Anwendung einer Glättungsregularisierung umgesetzt, bei der die Abweichung der Modellparameter zu einem gegebenen Referenzmodell bestraft wird. Wir nutzen das Ergebnis der vorangegangenen Einzelinversion als Referenzmodell für die folgende Inversion. Der Ansatz wird erfolgreich auf synthetische Datensätze angewendet und wir zeigen, dass die Kombination von mehreren Methoden eine erhebliche Verbesserung des Inversionsergebnisses im Vergleich zu den Einzelinversionen liefert

Electric resistivity and seismic refraction tomography: a challenging joint underwater survey at Äspö Hard Rock Laboratory

Tunnelling below water passages is a challenging task in terms of planning, pre-investigation and construction. Fracture zones in the underlying bedrock lead to low rock quality and thus reduced stability. For natural reasons, they tend to be more frequent at water passages. Ground investigations that provide information on the subsurface are necessary prior to the construction phase, but these can be logistically difficult. Geophysics can help close the gaps between local point information by producing subsurface images. An approach that combines seismic refraction tomography and electrical resistivity tomography has been tested at the Äspö Hard Rock Laboratory (HRL). The aim was to detect fracture zones in a well-known but logistically challenging area from a measuring perspective. The presented surveys cover a water passage along part of a tunnel that connects surface facilities with an underground test laboratory. The tunnel is approximately 100 m below and 20 m east of the survey line and gives evidence for one major and several minor fracture zones. The geological and general test site conditions, e.g. with strong power line noise from the nearby nuclear power plant, are challenging for geophysical measurements. Co-located positions for seismic and ERT sensors and source positions are used on the 450 m underwater section of the 700 m profile. Because of a large transition zone that appeared in the ERT result and the missing coverage of the seismic data, fracture zones at the southern and northern parts of the underwater passage cannot be detected by separated inversion. Synthetic studies show that significant three-dimensional (3-D) artefacts occur in the ERT model that even exceed the positioning errors of underwater electrodes. The model coverage is closely connected to the resolution and can be used to display the model uncertainty by introducing thresholds to fade-out regions of medium and low resolution. A structural coupling cooperative inversion approach is able to image the northern fracture zone successfully. In addition, previously unknown sedimentary deposits with a significantly large thickness are detected in the otherwise unusually well-documented geological environment. The results significantly improve the imaging of some geologic features, which would have been undetected or misinterpreted otherwise, and combines the images by means of cluster analysis into a conceptual subsurface model