Multidimensional computation and visualisation for marine controlled source electromagnetic methods

The controlled source electromagnetic method is improving the search for oil and gas in marine settings and is becoming an integral component of many exploration toolkits. While the level of detail and benefit obtained from recorded electromagnetic data sets is limited to the tools available, interpretation is fundamentally restricted by non-unique and equivalent solutions. I create the tools necessary to rapidly compute and visualise multi-dimensional electromagnetic fields generated for a variety of controlled source electromagnetic surveys. This thesis is divided into two parts: the creation of an electromagnetic software framework and the electromagnetic research applications.The creation of a new electromagnetic software framework is covered in Part I. Steps to create and test a modern electromagnetic data structure, three-dimensional visualisation and interactive graphical user interface from the ground up are presented. Bringing together several computer science disciplines ranging from parallel computing, networking and computer human interaction to three-dimensional visualisation, a package specifically tailored to marine controlled source electromagnetic compuation is formed. The electromagnetic framework is comprised of approximately 100,000 lines of new Java code and several third party libraries, which provides low-level graphical, network and execution cross-platform functionality. The software provides a generic framework to integrate most computational engines and algorithms into the coherent global electromagnetic package enabling the interactive forward modelling, inversion and visualisation of electromagnetic data.Part II is comprised of several research applications utilising the developed electromagnetic software framework. Cloud computing and streamline visualisation are covered. These topics are covered to solve several problems in modern controlled source electromagnetic methods. Large 3D electromagnetic modelling and inversion may require days or even weeks to be performed on a single-threaded personal computers. A massively parallelised electromagnetic forward modelling and inversion methods can dramatically was created to improve computational time. The developed ’macro’ parallelisation method facilitated the reduction in computational time by several orders of magnitude with relatively little additional effort and without modification of the internal electromagnetic algorithm. The air wave is a significant component of marine controlled source electromagnetic surveys however there is controversy and confusion over its defintion. The airwave has been described as a reflected, refracted, direct or diffusing wave, which has lead to confusion over its physical reality

Multimodal Imaging of Anisotropic Hierarchical Materials

The thesis is focused on studying the nanostructure of natural and synthetic hierarchical materials with biological applications, using X-ray scattering imaging and birefringence microscopy. The term "hierarchical materials" is used for structures composed of sub-units organised in different length scales that create the building blocks for the next level. Hierarchical materials are commonly found in nature, with diverse structures and functionalities. In the first part of this thesis, the nanostructure of mineralised tissue, such as tusk and bone, was the focus. Scanning SAXS, SAXS tensor tomography and birefringence microscopy were used to study the helicoidal structure of narwhal tusk. A high degree of anisotropy was found, in which the dentine and cementum have a very highly organised nanostructure with a preferential orientation along the tusk. However, those two main components differ in the deviations from that primary orientation, which revealed a complex helical pattern that could be the source of its anisotropic mechanical properties. A layered structure was also observed using X-ray fluorescence spectroscopy, indicating tusk growth layers that reflect the animal history. Those methods were also applied to study the anisotropic nanostructure of regenerated bone in biodegradable scaffolds and titanium implants in vivo, successfully demonstrating that the scaffold or implant architecture influence the new bone formation. Scaffolds with aligned fibres led to well-structured bone and a faster regeneration process, while scaffolds with randomly oriented fibres only created a callus around the damaged area with poor growth of new tissue.In the second part of this thesis, the anisotropy of self-assembled lyotropic liquid crystals for 3D printing of bone-mimetic composites was studied. This work aimed to understand the fundamental processes and mechanisms that induce the alignment of the self-assembled crystalline units to create composites with more anisotropic mechanical properties. In that study, an in situ characterisation of the nanostructure during flow in the 3D printer was done using scanning SAXS and birefringence microscopy to correlate the manufacturing process with the observed structural alignment of the material. The results demonstrated the role of the shear stress in such liquid crystals, highlighting the effect it has on the anisotropy and morphological transitions in the self-assembled structures. The importance of time and environmental conditions during 3D printing is also shown, which may affect the final structure and orientation

Uncertainty Quantification for low-frequency Maxwell equations with stochastic conductivity models

Uncertainty Quantification (UQ) has been an active area of research in recent years with a wide range of applications in data and imaging sciences. In many problems, the source of uncertainty stems from an unknown parameter in the model. In physical and engineering systems for example, the parameters of the partial differential equation (PDE) that model the observed data may be unknown or incompletely specified. In such cases, one may use a probabilistic description based on prior information and formulate a forward UQ problem of characterising the uncertainty in the PDE solution and observations in response to that in the parameters. Conversely, inverse UQ encompasses the statistical estimation of the unknown parameters from the available observations, which can be cast as a Bayesian inverse problem. The contributions of the thesis focus on examining the aforementioned forward and inverse UQ problems for the low-frequency, time-harmonic Maxwell equations, where the model uncertainty emanates from the lack of knowledge of the material conductivity parameter. The motivation comes from the Controlled-Source Electromagnetic Method (CSEM) that aims to detect and image hydrocarbon reservoirs by using electromagnetic field (EM) measurements to obtain information about the conductivity profile of the sub-seabed. Traditionally, algorithms for deterministic models have been employed to solve the inverse problem in CSEM by optimisation and regularisation methods, which aside from the image reconstruction provide no quantitative information on the credibility of its features. This work employs instead stochastic models where the conductivity is represented as a lognormal random field, with the objective of providing a more informative characterisation of the model observables and the unknown parameters. The variational formulation of these stochastic models is analysed and proved to be well-posed under suitable assumptions. For computational purposes the stochastic formulation is recast as a deterministic, parametric problem with distributed uncertainty, which leads to an infinite-dimensional integration problem with respect to the prior and posterior measure. One of the main challenges is thus the approximation of these integrals, with the standard choice being some variant of the Monte-Carlo (MC) method. However, such methods typically fail to take advantage of the intrinsic properties of the model and suffer from unsatisfactory convergence rates. Based on recently developed theory on high-dimensional approximation, this thesis advocates the use of Sparse Quadrature (SQ) to tackle the integration problem. For the models considered here and under certain assumptions, we prove that for forward UQ, Sparse Quadrature can attain dimension-independent convergence rates that out-perform MC. Typical CSEM models are large-scale and thus additional effort is made in this work to reduce the cost of obtaining forward solutions for each sampling parameter by utilising the weighted Reduced Basis method (RB) and the Empirical Interpolation Method (EIM). The proposed variant of a combined SQ-EIM-RB algorithm is based on an adaptive selection of training sets and a primal-dual, goal-oriented formulation for the EIM-RB approximation. Numerical examples show that the suggested computational framework can alleviate the computational costs associated with forward UQ for the pertinent large-scale models, thus providing a viable methodology for practical applications

The assessment of time lapse marine controlled-source electromagnetics (CSEM) for dynamic reservoir characterisation

Marine controlled-source electromagnetics (CSEM) techniques can be used to detect subsurface resistivity anomalies to discriminate hydrocarbon filled reservoir from the water saturated sediments in pre-drill appraisal of seismic anomalies in hydrocarbon exploration. The governing physics of marine CSEM is electromagnetic induction/diffusion therefore it has poor structural resolution. Current time – lapse CSEM feasibility studies for reservoir monitoring assume that the intrinsic limitation of CSEM has little impact on the dynamic fluid discrimination, as more structural constraining information are available at a producing oilfield. However, basic resistivity model is used without rigorous rock physics model, and is thus lacking in dynamic reservoir characterisation. Recent efforts at utilising simulation models combined with rock physics for realistic water-flooding front did not include reservoir management issues. In this thesis, CSEM is presented from the perspective of a reservoir manager, the end – user of this technology. A review of various hydrocarbon production mechanisms and scenarios showed that water – related mechanisms are ideally suited for time lapse CSEM applications as a complimentary tool to seismic in reservoir monitoring because of the resistivity anomaly generated as water replaces hydrocarbon. Channelized turbidite system for the North Sea oilfield model is used, such that the laminar lithological arrangement of sand and shale indicates that a linear arithmetic summation of resistivities of shale and sand will be a good representative of electrical rock physics model. Using this electrical rock physics model, three hydrocarbon provinces are assessed for the technical risk of time lapse CSEM project, in similar manner as done in 4D seismic projects. The North Sea province has highest technical risk, followed by the Gulf of Mexico, while the West Africa province has the least technical risk. A simulation to electromagnetic (sim2EM) workflow is then incorporated into the simulation to seismic (sim2seis) workflow. The sim2EM workflow is used to first examine the impacts of overburden complexity and sea water resistivity stratification on CSEM data. It is observed that the structural impacts are more pronounced on the static CSEM images than on its dynamic images. Then, coupled forward modelling of inline CSEM data and seismic amplitude data from a 3D fluid flow reservoir simulator is performed. The simulator serves the dual purpose of common oilfield in which production is aided by water injection, and of an interpretational constraint involving correlation of CSEM and seismic anomalies with injection and production activities at well locations (here called dynamic well tie). The time-lapse in-line CSEM amplitude change, modelled using dipole 1D, shows linear correlations of 64 to 68% with the change in water saturation. It is more responsive and consistently more linearly related to the change in water saturation than the seismic, despite the possible detrimental effects of reservoir heterogeneity. This is not surprising as seismic is responsive to a combination of changes in saturation and pressure. Coupled interpretation of seismic and CSEM modelled data show that time – lapse CSEM is a definite indicator of water saturation changes. For instance, when seismic softening due to rise in pressure masks increase in water saturation, or when seismic hardening due to pressure drop gives false increase in water saturation. The importance of brine mixing on the acoustic and electrical properties, during secondary and tertiary oil recovery, is examined. The seismic and EM rock physics are adjusted to cater for effective mixed brine resistivity, bulk modulus and bulk density, as functions of temperature and salinity for the injected and formation brines. Modelling of three scenarios of different combinations of injected and formation brines around the world, calibrated with a reference model in which brine properties were kept constant, indicate that EM is more responsive than the seismic, to the brine chemistry. Fluid flow modelling of sea water injection in the North Sea field shows that temperature effect is restricted to the vicinity of injector; while salinity effect travels farther from the injector along the water flooding front. The time-lapse EM could theoretically distinguish extreme brines. For instance, low salinity water injected into oil-wet reservoir with saline formation water; or moderately saline subsurface aquifer water injected into very saline formations of the Middle Eastern carbonates produced between -15 and 7% change in inline CSEM amplitude. In this thesis, 1D dipole forward modelling has generally highlighted values of EM in reservoir monitoring and management. Finally, repeat 3D EM data modelling produced time-lapse amplitude change of 0.3%, which is too small to be detected by the current CSEM acquisition. Thus, high precision EM field sensor will be required for practical application of 4D CSEM to reservoir monitoring. Only about 46% of this small 4D signature is interpretable for the change in transverse resistance of between -800Ωm2 and -1050Ωm2 (equivalent to resistivity reduction of between 13Ωm to 18Ωm). Broad qualitative information about the water flooded areas is provided, but fine detailed information about bypassed oil and early warning of water breakthrough could not be properly imaged

Numerical Modelling of the Influence of Lower Boundary Roughness on Turbulent Sedimentary Flows

Numerical computations have been performed to evaluate the influence of bedform roughness on turbulent transport of sediments in geophysical flows. Special attention is paid to turbidity currents, which are responsible for the transport of sedimentary rocks far into the deep ocean. It has been suggested that enhanced turbulence mixing in flows over rugose topography contributes to the unexpectedly large runout lengths of naturally occurring turbidity currents. One of the objectives of this study is to provide evidence for against this conjecture. We perform computations over a wide range of periodic arrays of rectangular roughness elements, We find that a strong peak in turbulent mixing occurs when the width-to-height ratio equals a critical value of seven. We also find that a strong peak in resistance to flow occurs at the same critical value. These are competing effects, with the former acting to promote, and the latter acting to diminish runout length. So we are not able to conclude definitively that the enhancement of mixing is responsible for long runout lengths. We continue by considering flows over periodic arrays of shapes which are representative of bedforms that occur in the natural environment. We again find a strong correlation between the optimisation of both turbulence mixing and resistance to the flow. We are unable to distinguish bedform shapes that promote long runout length relative to the flat bed case. However, we are able to distinguish those bedform shapes that have large resistance to flow and large turbulence mixing compared to those that have low resistance and low turbulent mixing, with the latter case occurring for widely spaced asymmetric dunes with a long low angled slope facing the flow. Finally, we develop a model for flow and sediment transport which takes into account erosion and deposition from the bottom boundary. We first apply this model to flow over fixed dune shapes, in order to assess the influence of bedform shape on flow capacity, stratification, and the energy budget. An important result of this study is that flow capacity is optimised for the class of bedform shapes that promote low flow resistance and low turbulent mixing. We conclude by applying the model to the two-way coupled flow of a mobile dune, starting from an initially symmetric inherited dune morphology. We find that, for sufficiently large grain sizes, the dune evolves into a sequence of asymmetric dunes, rather than to a flat bed, and that the long-time evolution tends to be towards those dune shapes that promote large relative flow capacity. However, the model has a discrepancy in that it is unable to prevent the dune shape exceeding the maximum angle of repose. Hence, further work is required before these results can be regarded as reliable

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

The saline Interface of a Shallow Unconfined Aquifer, Rangitikei Delta

The coastal communities of Tangimoana and Scott's Ferry have a long history of using shallow groundwater bores. The cumulative effect of pumping over decades could influence the saline interface given the close proximity of the communities to the seashore and river estuary. It is important to quantify the effects of pumping on both the shallow groundwater system and the dynamics of the saline interface. This is necessary to protect the groundwater system against saline intrusion especially given the increasing number of high volume groundwater consents to support dairying. Resistivity soundings and traverses, coupled with chemical analyses of groundwater samples, were found to be an effective method for defining the saline interface of the shallow groundwater aquifer under the Rangitikei delta. The saline interface extends from the salt marsh to beneath the farmland north of Tangimoana. The interface is a zone of diffusion with freshwater and brackish water mixing from the estuary. The interface is currently located on the outskirts of Tangimoana, and it is likely to extend beneath the township. The infiltration of brackish surface waters into sediments of the salt marsh form a surficial mixing zone that decreases with distance from the salt marsh. There is no indication of salinity in the area to the north of the Rangitikei delta. This area is most at risk of contamination from saline intrusion because of high volume groundwater abstractions, even though these abstractions are from deeper aquifers. The shallow groundwater beneath Tangimoana showed high concentrations of Ca and HCO3 ions. This may be a result of carbonate dissolution, which can occur when saline and freshwater mix. This creates groundwater that is under-saturated with calcium. The mixing water dissolves carbonates and increases the concentrations of Ca and HCO3. The major source of sodium and chloride was likely rainwater with evaporated solutes from seawater. The saline interface near Tangimoana appears to be relatively static, but the estuary and salt marsh are areas of low relief. There are preferential flows paths across the salt marsh to the farmland. These factors make the shallow groundwater in the Rangitikei delta vulnerable to saline intrusion

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic