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Sub-μm taenite and tetrataenite grains observed in a number of (stony-)iron meteorite groups are promising sources of paleomagnetic records in meteorites. While slowly-cooled meteorites form tetrataenite—an extremely good recorder—, fast-cooled meteorites may contain fine-grained taenite, which was considered unsuitable for paleomagnetic studies. In this work, however, we show that nm-sized taenite grains are stable over billion-year timescales, indicating that taenite-bearing meteorites are reliable sources of paleomagnetic information. We find a range of sizes for which taenite forms stable single-domain structures, which coincides with the grain sizes observed in the cloudy zone of most fast cooled IVA meteorites. These meteorites, therefore, can provide reliable paleomagnetic information recorded as a stable crystallization remanent magnetization as taenite grains grown. Vortex states observed in larger (>50 nm) grain sizes are also highly stable, indicating that coarse-grained taenite observed in meteoritic microstructures can also provide reliable records of paleomagnetic fields.

The thermal demagnetization of pseudo‐single‐domain (PSD) magnetite (Fe3O4) particles, which govern the magnetic signal in many igneous rocks, is examined using off‐axis electron holography. Visualization of a vortex structure held by an individual Fe3O4 particle (~250 nm in diameter) during in situ heating is achieved through the construction and examination of magnetic‐induction maps. Stepwise demagnetization of the remanence‐induced Fe3O4 particle upon heating to above the Curie temperature, performed in a similar fashion to bulk thermal demagnetization measurements, revealed that its vortex state remains stable under heating close to its unblocking temperature and is recovered upon cooling with the same or reversed vorticity. Hence, the PSD Fe3O4 particle exhibits thermomagnetic behavior comparable to a single‐domain carrier, and thus, vortex states are considered reliable magnetic recorders for paleomagnetic investigations., Key Points Thermal demagnetization of nonideal magnetite particlesVisualized magnetization of vortex state with temperatureVortex structures are reliable paleomagnetic signal recorders

The study of the paleomagnetic signal recorded by rocks allows scientists to understand Earth’s past magnetic field and the formation of the geodynamo. The magnetic recording fidelity of this signal is dependent on the magnetic domain state it adopts. The most prevalent example found in nature is the pseudo–single-domain (PSD) structure, yet its recording fidelity is poorly understood. Here, the thermoremanent behavior of PSD magnetite (Fe3O4) particles, which dominate the magnetic signatures of many rock lithologies, is investigated using electron holography. This study provides spatially resolved magnetic information from individual Fe3O4 grains as a function of temperature, which has been previously inaccessible. A small exemplar Fe3O4 grain (~150 nm) exhibits dynamic movement of its magnetic vortex structure above 400°C, recovering its original state upon cooling, whereas a larger exemplar Fe3O4 grain (~250 nm) is shown to retain its vortex state on heating to 550°C, close to the Curie temperature of 580°C. Hence, we demonstrate that Fe3O4 grains containing vortex structures are indeed reliable recorders of paleodirectional and paleointensity information, and the presence of PSD magnetic signals does not preclude the successful recovery of paleomagnetic signals.

In situ electron microscopy is used to visualize the thermomagnetic behavior of vortex domain states within magnetic minerals., The study of the paleomagnetic signal recorded by rocks allows scientists to understand Earth’s past magnetic field and the formation of the geodynamo. The magnetic recording fidelity of this signal is dependent on the magnetic domain state it adopts. The most prevalent example found in nature is the pseudo–single-domain (PSD) structure, yet its recording fidelity is poorly understood. Here, the thermoremanent behavior of PSD magnetite (Fe3O4) particles, which dominate the magnetic signatures of many rock lithologies, is investigated using electron holography. This study provides spatially resolved magnetic information from individual Fe3O4 grains as a function of temperature, which has been previously inaccessible. A small exemplar Fe3O4 grain (~150 nm) exhibits dynamic movement of its magnetic vortex structure above 400°C, recovering its original state upon cooling, whereas a larger exemplar Fe3O4 grain (~250 nm) is shown to retain its vortex state on heating to 550°C, close to the Curie temperature of 580°C. Hence, we demonstrate that Fe3O4 grains containing vortex structures are indeed reliable recorders of paleodirectional and paleointensity information, and the presence of PSD magnetic signals does not preclude the successful recovery of paleomagnetic signals.

Dusty olivine (olivine containing multiple sub-micrometer inclusions of metallic iron) in chondritic meteorites is considered an ideal carrier of paleomagnetic remanence, capable of maintaining a faithful record of pre-accretionary magnetization acquired during chondrule formation. Here we show how the magnetic architecture of a single dusty olivine grain from the Semarkona LL3.0 ordinary chondrite meteorite can be fully characterised in three dimensions, using a combination of Focussed-Ion-Beam nanotomography (FIB-nT), electron tomography and finite-element micromagnetic modelling. We present a three-dimensional (3D) volume reconstruction of a dusty olivine grain, obtained by selective milling through a region of interest in a series of sequential 20 nm slices, which are then imaged using scanning electron microscopy. The data provide a quantitative description of the iron particle ensemble, including the distribution of particle sizes, shapes, interparticle spacings and orientations. Iron particles are predominantly oblate ellipsoids with average radii 242 ± 94 nm by 199 ± 80 nm by 123 ± 58 nm. Using analytical TEM we observe that the particles nucleate on sub-grain boundaries and are loosely arranged in a series of sheets parallel to (001) of the olivine host. This is in agreement with the orientation data collected using the FIB-nT, and highlights how the underlying texture of the dusty olivine is crystallographically constrained by the olivine host. The shortest dimension of the particles is oriented normal to the sheets and their longest dimension is preferentially aligned within the sheets. Individual particle geometries are converted to a finite-element mesh and used to perform micromagnetic simulations. The majority of particles adopt a single vortex state, with ‘bulk’ spins that rotate around a central vortex core. We observed no particles, which are in a true single domain state. The results of the micromagnetic simulations challenge some pre-conceived ideas about the remanence carrying properties of vortex states. There is often not a simple predictive relationship between the major, intermediate and minor axes of the particles and the remanence vector imparted in different fields. Although the orientation of the vortex core is determined largely by the ellipsoidal geometry (i.e., parallel to the major axis for prolate ellipsoids and parallel to the minor axis for oblate ellipsoids), the core and remanence vectors can sometimes lie at very large (tens of degree) angles to the principal axes. The subtle details of the morphology can control the overall remanence state, leading in some cases to a dominant contribution from the bulk spins to the net remanence, with profound implications for predicting the anisotropy of the sample. The particles have very high switching fields (several hundred mT), demonstrating their high stability and suitability for paleointensity studies.

The thermal demagnetization of pseudo-single-domain (PSD) magnetite (Fe3O4) particles, which govern the magnetic signal in many igneous rocks, is examined using off-axis electron holography. Visualization of a vortex structure held by an individual Fe3O4 particle (~250nm in diameter) during in situ heating is achieved through the construction and examination of magnetic-induction maps. Stepwise demagnetization of the remanence-induced Fe3O4 particle upon heating to above the Curie temperature, performed in a similar fashion to bulk thermal demagnetization measurements, revealed that its vortex state remains stable under heating close to its unblocking temperature and is recovered upon cooling with the same or reversed vorticity. Hence, the PSD Fe3O4 particle exhibits thermomagnetic behavior comparable to a single-domain carrier, and thus, vortex states are considered reliable magnetic recorders for paleomagnetic investigations.

Magnetite (Fe3O4) is an important magnetic mineral to Earth scientists, as it carries the dominant magnetic signature in rocks, and the understanding of its magnetic recording fidelity provides a critical tool in the field of palaeomagnetism. However, reliable interpretation of the recording fidelity of Fe3O4 particles is greatly diminished over time by progressive oxidation to less magnetic iron oxides, such as maghemite (g-Fe2O3), with consequent alteration of remanent magnetization potentially having important geological significance. Here we use the complementary techniques of environmental transmission electron microscopy and off-axis electron holography to induce and visualize the effects of oxidation on the magnetization of individual nanoscale Fe3O4 particles as they transform towards g-Fe2O3. Magnetic induction maps demonstrate a change in both strength and direction of remanent magnetization within Fe3O4 particles in the size range dominant in rocks, confirming that oxidation can modify the original stored magnetic information.

Magnetite (Fe3O4) is an important magnetic mineral to Earth scientists, as it carries the dominant magnetic signature in rocks, and the understanding of its magnetic recording fidelity provides a critical tool in the field of palaeomagnetism. However, reliable interpretation of the recording fidelity of Fe3O4 particles is greatly diminished over time by progressive oxidation to less magnetic iron oxides, such as maghemite (γ-Fe2O3), with consequent alteration of remanent magnetization potentially having important geological significance. Here we use the complementary techniques of environmental transmission electron microscopy and off-axis electron holography to induce and visualize the effects of oxidation on the magnetization of individual nanoscale Fe3O4 particles as they transform towards γ-Fe2O3. Magnetic induction maps demonstrate a change in both strength and direction of remanent magnetization within Fe3O4 particles in the size range dominant in rocks, confirming that oxidation can modify the original stored magnetic information., Magnetite provides a valuable record of the Earth's geomagnetic history. Here, Almeida et al. combine electron microscopy and energy-loss spectroscopy to study the effects of in situ oxidation on the magnetization fidelity and crystalline phase of pseudo-single domain magnetite grains.

A suite of near-identical magnetite nanodot samples produced by electron-beam lithography have been used to test the thermomagnetic recording fidelity of particles in the 74–333 nm size range; the grain size range most commonly found in rocks. In addition to controlled grain size, the samples had identical particle spacings, meaning that intergrain magnetostatic interactions could be controlled. Their magnetic hysteresis parameters were indicative of particles thought not to be ideal magnetic recorders; however, the samples were found to be excellent thermomagnetic recorders of the magnetic field direction. They were also found to be relatively good recorders of the field intensity in a standard paleointensity experiment. The samples' intensities were all within ∼15% of the expected answer and the mean of the samples within 3% of the actual field. These nonideal magnetic systems have been shown to be reliable records of the geomagnetic field in terms of both direction and intensity even though their magnetic hysteresis characteristics indicate less than ideal magnetic grains. Key Points Nonideal magnetic systems accurately record field direction Weak-field remanences more stable than strong-field remanences

The thermomagnetic behavior of remanence-induced magnetite (Fe3O4) particles in the pseudo-single-domain (PSD) size range (similar to 0.1-10 mu m), which dominate the magnetic signature of many rock lithologies, is investigated using off-axis electron holography. Construction of magnetic induction maps allowed for the visualization of the vortex domain state in an individual Fe3O4 grain (similar to 200nm in diameter) as a function of temperature. Acquisition of a series of electron holograms at 100 degrees C intervals during in situ heating up to 700 degrees C demonstrates the vortex state of the Fe3O4 grain, in this instance, remains thermally stable close to its unblocking temperature and exhibits a similar in-plane remanent state upon cooling; i.e., the particle is effectively behaving like a uniaxial single-domain particle to temperatures near T-C. Such particles are thought to be robust magnetic recorders. It is suggested that evidence for PSD behavior should therefore not preclude paleomagnetic investigation.

Magnetotactic bacteria contain chains of magnetically interacting crystals (magnetosomes), which aid navigation (magnetotaxis). To improve the efficiency of magnetotaxis, magnetosome crystals (which can consist of magnetite or greigite) should be magnetically stable single domain (SD) particles. Larger particles subdivide into non-uniform multi-domain (MD) magnetic structures that produce weaker magnetic signals, while small SD particles become magnetically unstable due to thermal fluctuations and exhibit superparamagnetic (SP) behavior. In this study, we determined the stable SD range as a function of grain elongation and inter-particle separation for chains of identical greigite grains using fundamental parameters recently determined for greigite. Interactions significantly increase the stable SD range. For example, for cube-shaped greigite grains the upper stable SD threshold ze is increased from 107 nm for isolated grains to 204 nm for touching grains arranged in chains. The larger critical SD grain size for greigite means that, compared to magnetite magnetosomes, greigite magnetosomes can produce larger magnetic signals without the need for inter-grain interactions.

Palaeomagnetic observations are being used in increasingly sophisticated geological and geophysical interpretations. It is therefore important to test the theories behind palaeomagnetic recording by rocks, and this can only be achieved using samples containing precisely controlled magnetic mineralogy, grain size and interparticle spacing, the last of which controls the degree of magnetostatic interactions within the samples. Here we report the room-and low temperature magnetic behaviour of a set of samples produced by the nano-scale patterning technique electron beam lithography. The samples consist of 2-D arrays of near-identical magnetite dots of various sizes, geometries and spatial configurations, with dot sizes from ranging from near the single domain threshold of 74-333 nm. We have made a series of magnetic measurements including hysteresis, first-order-reversal curve measurements and remanence acquisition, many as a function of temperature between 20 and 300 K, to quantify the samples' behaviour to routine palaeomagnetic measurement procedures. We have also examined the behaviour of saturation isothermal remanences (SIRM) to cooling and warming cycling of the sample below room temperature. In addition, we investigated the samples' responses to alternating-field demagnetization of room temperature induced SIRM, anhysteretic remanent magnetization (ARM) and partial ARM. ARM was used as a non-heating analogue for natural thermoremanence. Given the 2-D spatial distribution of the samples, in all the experiments we conducted both in-plane and out-of-plane measurements. Generally, the samples were found to display pseudo-single-domain hysteresis characteristics, but were found to be reliable recorders of weak-field remanences like ARM. For the closely packed samples, the samples' magnetic response was highly dependent on measurement orientation.

Micromagnetic calculations relevant to paleomagnetism have generally focused on ideal shapes such as spheres and cubes. However, oxide grains that occur naturally in rocks often have irregular morphologies, highly skeletal dendritic forms being particularly common. To investigate the potential effects of complex grain morphology on magnetic stability, we have carried out two parallel sets of calculations. The first is based on randomly distorted 30-120 nm magnetite spheres. We use a three-dimensional finite element/boundary integral micromagnetic model able to generate suitable morphologies unrestricted by the regular cell structure required by finite difference models. The second model consists of a 300 nm magnetite octahedron from which most of the material has been removed to leave a small octahedral crystallite at each of the six apices connected by an orthogonal framework of thin rods. The results obtained imply that micromagnetic models currently provide no unambiguous evidence that morphological complexities endow magnetite nanoparticles with enhanced coercivity.

In classical domain theory, single-domain (SD) grains change their magnetization by coherent rotation, where the energy barrier to domain reversal is provided by the magnetocrystalline anisotropy or by shape anisotropy for elongated grains. However, numerical micromagnetic models have shown that domain structure in SD grains is rarely perfectly uniform. For example, magnetite has significant “flowering” of its magnetization even in grains that approach the room temperature superparamagnetic (SP) size of ∼30 nm. The flowering deforms slightly to accommodate the grain shape and thereby produces anisotropy independent of magnetocrystalline effects but dependent on magnetization direction within the grain. This can be similar in magnitude to that of magnetocrystalline anisotropy, even for equidimensional grains (where distance from the centroid to the grain faces is equal). The interaction of the domain structure and grain geometry is termed configurational anisotropy and has been studied mainly in relation to man-made isotropic magnetic media but received little attention in rock magnetism. In this paper we examine configurational anisotropy in SD to pseudo-single-domain (PSD) grains of magnetite using a three-dimensional finite element/boundary integral (FEBI) micromagnetic model. Equidimensional grains of magnetite of three different shapes are considered: a cube, an octahedron, and a regular tetrahedron, and in each case the effects magnetocrystalline anisotropy were removed in order to isolate the configurational anisotropy. The numerical models predict that very large coercivities are possible even for SD equidimensional grains. For tetrahedral grains coercivities of ∼120 mT were obtained, which otherwise would require a grain elongation of ∼1:1.75. Depending on the orientation of the principle crystalline axis to the grain shape, the configurational anisotropy may increase or decrease the overall energy barrier to domain reversal.

Viscous magnetization (VM) and viscous remanent magnetization (VRM) have been measured, as a function of temperature, between room temperature and the Curie temperature using a suite of well-characterized synthetic and natural multidomain (MD) magnetite samples. Particular attention was given to possible diffusion aftereffects such as dislocation creep (stress relaxation) and disaccommodation (vacancy and ionic reordering) and their contribution to viscous behavior in what has been commonly thought of as a purely thermal fluctuation process. Dislocation creep was examined by measuring viscosity before and after annealing. Annealing was found to reduce the non-log(t) behavior, where t is time. Non-log(t) behavior has been associated with diffusion aftereffects, suggesting that these are a major contributor to viscosity and (de)magnetization processes in MD samples. The positive curvature of the non-log(t) acquisition processes indicates that dislocation creep dominates over disaccommodation. This does not imply that VM and VRM are due solely to dislocation creep, but rather that VRM and VM reflect a number of unrelated temperature-dependent processes, primarily thermal fluctuations and dislocation creep. This is the first time that dislocation creep has been directly identified as contributing to viscosity at temperature. These findings will have particular implications for paleointensity determinations, as on heating a sample, its dislocation structure may relax, giving rise to demagnetizations not associated with thermal fluctuations. This will lead to incorrect intensity estimates. If no heating is performed on a geological specimen, then it is very likely that laboratory timescale stress relaxation processes will have already occurred in situ.

The critical size for stable single-domain (SD) behavior has been calculated as a function of grain elongation for magnetite grains using a numerical micromagnetic algorithm. Importantly, for the first time, we consider the contribution of intergrain magnetostatic interactions on the SD/multidomain (MD) critical size (d0). For individual grains our numerical estimates for d0 for elongated grains are lower than that determined by previous analytical and numerical calculations. Nevertheless, the inclusion of magnetostatic interactions into the model was found to increase d0 to values significantly higher than any previously published estimates of d0 for individual grains. Therefore the model calculations show that there is a relatively wide range of grain sizes within which depending on the degree of magnetostatic interactions and elongation, a grain can be either SD or MD. The model results are compared to observations of magnetosomes found in magnetotactic bacteria. The newly calculated upper d0 limit for the interacting grains now accommodates the largest magnetosomes reported in the literature. These large magnetosomes were previously thought to be MD, suggesting that evolutionary processes are highly efficient at optimizing magnetosome grain size and spatial distribution.

Extraction of primaries-only reflection data from full surface reflection data by a combina- tion of Marchenko redatuming and convolutional interferometry, incorporates artefacts, and noise following the constructed primaries. I have shown that the only true information recov- ered are primaries travel times, any dynamic information is artificial. I develop two extended versions of the original workflow, one of which processes seismic data throughout, avoids noise following the primary, and mitigates artefacts typical of this type of primaries construc- tion workflow. The other one uses travel time information as input and output, avoids noise following the primary, and also avoids artefacts by applying a quality control criterion dur- ing the convolutional interferometry step. It is cheaper and faster than the first version, and the resulting 2D primaries travel times matrices need less storage than seismograms. For complex data, it is difficult to extract a sufficient amount of kinematic information to gain an advantage over the full reflection data during velocity analysis and velocity model build- ing. The mechanics of the primaries construction workflow introduce a new class of artificial arrivals, which are indistinguishable from true arrivals. I have used imaging with the true model here to identify them. In addition, the bottom of a thin layer can be omitted in the final data, even if the primary reflection is present in the input data. I have used a horizon- tally layered subsurface model to show that mathematical convergence of the Marchenko redatuming scheme, as measured by the behaviour of convergence energy, is no guarantee for physical convergence towards the correct solution. Inverting for redatuming parameters using the trend of the convergence energy, or related measures applied to the same wave fields, can produce reliable looking results, but these are misleading and mostly false. Since the approach fails for a specific model, it is to be considered unreliable in general.

In paleomagnetism, practical measurements are rarely made using perfect, isolated, single-phase, ferromagnetic crystals. Experimental observations are typically made using magnetic materials formed by a variety of natural processes. In this thesis, we will look at bridging the gap between current numerical modelling capability and experimental observations. First, we work towards micromagnetic modelling of multi-phase magnetic materials, including magnetostriction, embedded in a rocky matrix, along with crystal defects. We present a derivation of the Boundary Element Method formulation used by the micromagnetics package, MERRILL, and provide an extension of this from single-phase materials to multi-phase. After discussing issues with previous approaches to modelling magnetostriction, we derive and present a more robust and flexible approach. This model of magnetostriction is suitable for non-uniformmagnetizations, for multi-phase materials, and for arbitrary boundary conditions, and can be incorporated into MERRILL.We then outline a method for extending our model to materials embedded in an infinite elastic matrix of arbitrary elasticity. Finally, we present a method for modelling the magnetic response of a material due to crystal defects, along with a concrete example of a magneto-dislocation coupling energy at a magnetite-ilmenite boundary where stress due to lattice misfit is eased by regular edge dislocations. Second, we work towards being able to verify micromagnetic models against nano-scale experimental data. To do this, we present two techniques for simulating electron holograms from micromagnetic modelling results, a technique capable of imaging magnetic structures at the nano-scale. We also present example electron holograms of commonly occurring magnetic structures in nano-scale rock and mineral magnetism, and highlight some distinguishing features, which may be useful for interpreting experimental electron holography data.

The field of paleomagnetism attempts to understand in detail the the processes of the Earth by studying naturally occurring magnetic samples. These samples are quite unlike those fabricated in the laboratory. They have irregular shapes; they have been squeezed and stretched, heated and cooled and subjected to oxidation. However micromagnetic modelling allows us to simulate such samples and gain some understanding of how a paleomagnetic signal is acquired and how it is retained. Micromagnetics provides a theory for understanding how the domain structure of a magnetic sample alters subject to what it is made from and the environment that it is in. It furnishes the mathematics that describe the energy of a given domain structure and how that domain structure evolves in time. Combining micromagnetics and ever increasing computer power, it has been possible to produce simulations of small to medium size grains within the so-called single to pseudo single domain state range. However processors are no longer built with increasing speed but with increasing parallelism and it is this that must be exploited to model larger and larger paleomagnetic samples. The purpose of the work presented here is twofold. Firstly a micromagnetics code that is parallel and scalable is presented. This code is based on FEniCS, an existing finite element framework, and is shown to run on ARCHER the UK’s national supercomputing service. The strategy of using existing libraries and frameworks allow future extension and inclusion of new science in the code base. In order to achieve scalability, a spatial mapping technique is used to calculate the demagnetising field - the most computationally intensive part of micromagnetic calculations. This allows grain geometries to be partitioned in such a way that no global communication is required between parallel processes - the source of favourable scaling behaviour. The second part of the theses presents an exploration of domain state evolution in increasing sizes of magnetite grains. This simulation, whilst a first approximation that excludes magneto-elastic effects, is the first attempt to map out the transition from pseudo-single domain states to multi domain states using a full micromagnetic simulation.

Radioactive waste repositories, designed in accordance with the current UK concept, would be required to provide containment for thousands of years beneath hundreds of metres of rock. The physical processes, both geological and other processes, that might lead to migration of radionuclides are slow in comparison to human timescales — it is impractical to make an experiment of the whole system and so these systems are typically investigated through the use of numerical models. Predictive models are based on combinations of: assumptions, mathematical formulations and parameter values derived from experimental observations. The Ventilation Experiment in the Opalinus Clay at Mont Terri, Switzerland, was designed to involve geological and other physical processes that would be active during the excavation and construction phases of a repository, and with consequences for the repository performance during the operational phase. The experiment consisted of a 10m long tunnel of 1:3m diameter through which air of known relative humidity was circulated in order to force drying and re-saturation through the tunnel wall. Two such cycles over four years have been observed via installed instrumentation. Several numerical models have been constructed of the ventilation experiment by different international teams under the decovalex project using different approaches for cross-validation. Through participation in this project, a 1D model using Richards’ Equation was developed that effectively reproduces the hydrodynamic, mechanical and conservative mass transport results. During the course of developing that model, many other domains, meshes, formulations and software versions were investigated. Now that the field scale Ventilation Experiment can be reproduced with numerical models, the findings (assumptions, formulations, parameter values, computational methods and software) would be transferable to other argillaceous formations to enable predictive modelling of similar scenarios and contribute to the safe disposal of nuclear waste and other problems involving similar geological processes. Work of this type fills the gap between laboratory scale experiments and regional scale modelling of geological systems. The gap is especially wide for low-permeability formations because the size and time-scale limitations effect the ability to make direct observations and measurements. Two particular problems were also addressed in this work: that of the use relative permeability functions and also the computational treatment of the physical interface between the tunnel domain and the rock domain. A sensitive component in many models of unsaturated flow through porous media and covering a wide variety of applications, including reservoir engineering, is the representation of permeability at an unsaturated point (kx) as a scaling of the saturated permeability (ksat) by introducing some function of the pressure head, or saturation as the relative permeability (krel) in the relation kx = ksatkrel. The choice of the particular function and its parameter values adds little to our understanding of the physical parameters. A solution is proposed to the second problem, of how to computationally represent, implement and manage the interface between two physical (i.e. spatial) domains. The scheme maps every part of the boundary of one domain onto the corresponding part of the boundary of the other domain, storing the state variables in shared memory and converting between physical components.

The Neoproterozoic is one of the most enigmatic periods in Earth history. In the juxtaposition of glacial and tropical deposits the sedimentary record provides evidence for extreme climate change. Various models have tried to explain these apparent contradictions. One of the most popular models is the Snowball Earth Hypothesis which envisages periods of global glaciations. All climatic models are dependent on palaeogeography which as yet remains poorly constrained for the Neoproterozoic. This thesis presents a multidisciplinary study of two Neoproterozoic sedimentary basins on the Congo and West Africa cratons including radiometric dating of glacial deposits themselves. In the West Congo Belt, western Congo Craton, a new U-Pb baddeleyite age for the Lower Diamictite provides the first high quality direct age for the older of two glacial intervals. This age is significantly different from previously dated glaciogenic deposits on the Congo Craton. This result strongly suggests that the mid-Cryogenian was a period during which several local glaciations occurred, none of which were global. While the palaeomagnetic results from carbonates around the younger glacial interval are probably remagnetised, detrital zircon and chemostratigraphic results allow correlation with numerous late-Cryogenian glaciogenic deposits worldwide and a Snowball Earth scenario is favoured here. In the Adrar Sub-Basin of the vast Taoudéni Basin, West Africa, the terrigenous Jbeliat glacial horizon has been studied in great detail. Detrital zircon geochronology reveals large changes in provenance through this glacial unit with implications for sedimentological approaches and techniques for provenance characterisations based on one sample alone. Together with recently published U-Pb data these results constrain the age of the Jbeliat Group to a narrow window providing vital geochronological information for this younger glacial event. Combining provenance geochemistry, chemostratigraphy and U-Pb dating has greatly improved our understanding of two of the largest Neoproterozoic sedimentary basins. The dominance of Mesoproterozoic detrital material, for which no source has been reported near either of the field areas, has consequences for the proximity of other cratons at the time of deposition, prior to the final amalgamation of Gondwana.

NE/D0020366/1 Magnetic minerals are abundant within our Earth's crust and can retain, through one of a number of processes, a remanent magnetisation induced by the Earth's magnetic field. Analyses of palaeomagnetic samples have been used for the past fifty years to improve our understanding of many of the Earth's major processes. Recent studies utilising newly developed imaging techniques, namely holographic transmission electron microscopy, have for the first time allowed direct observations of the magnetic structure in palaeomagnetic samples on a nanoscale. It is commonly observed that igneous rocks contain closely packed magnetic lamellae with a non-magnetic matrix, a result of the chemical process of exsolution. However, the results of current micromagnetic models, generated to predict the magnetic structure within such samples, are not in agreement with these direct observations. The results do, however, show strong similarities to the direct observations. The discrepancies between the direct observations and micromagnetic models indicate a lack of understanding of the magnetic interactions within such samples. To examine this two distinct hypotheses have been tested. Firstly, the geometry of the system has been altered to examine the effect of this on the magnetic structure of the grains. Secondly, a multiphase model has been produced. This multiphase model allows the simulation of more complicated systems that include more than one magnetic material in direct contact. This multiphase model has allowed us to examine the effect of varying the exchange in these multiphase structures and its effect on the modelled magnetic structure. Further, this multiphase model has allowed us to examine theoretical systems involving combinations of magnetic materials commonly found in palaeomagnetic samples.

NER/S/A/2006/14230 The Moon displays weak magnetic fields resulting from areas of the lunar crust that are remanently magnetised. The origins of the magnetic fields that produced this remanent magnetisation are still under discussion, and theories include among several, an ancient lunar dynamo, or processes occurring on the Moon as a result of impacts. Lunar crustal fields have been mapped globally by the Magnetometer (MAG) and Electron Reflectometer (ER) on the satellite Lunar Prospector, providing vector magnetic field measurements at an average altitude of 30 km, and estimates of the total surface field. This thesis presents global and regional models of the magnitude and direction of lunar magnetisation within a layer, produced from both the MAG and ER data independently and jointly using several inversion methods. The inverse modelling techniques are based on those developed for terrestrial and Martian data sets, employing equivalent source dipoles as basis functions, and Green’s functions relating a magnetic field observation to a spatially continuous magnetisation distribution. A unique magnetisation solution is selected having the smallest rootmean- square (RMS) magnetisation for a given fit to the data, controlled by a damping parameter. The non-uniqueness in magnetisation distributions and the determination of source parameters is discussed with the use of forward models to assist the interpretation of the crustal magnetisation models. Suites of magnetisation models for layers with thicknesses between 10 and 50 km, and with different dipole depths, are able to reproduce both the ER and MAG data well. Inverse models utilising the scalar ER data have been developed successfully, resulting in a joint inversion of the ER and MAG data for one of the strongest magnetic anomalies on the Moon, Reiner Gamma. The largest concentrations of strongly magnetised crust are, like the crustal fields themselves, located antipodal to the youngest large impact basins, and in some isolated areas associated with the strongest crustal fields. The magnetisation distributions show robust magnitudes with different data sets and modelling techniques showing the extent of magnetised sources, but can not be used to infer the direction of the magnetising fields. Average magnetisation values in magnetised regions of 30-40 mA/m are similar to the measured magnetisations of the Apollo samples and significantly weaker than crustal magnetisations for Mars and the Earth. A global preference for a 30 km thick magnetised layer suggests that a dynamo field may be more consistent with these magnetisation models. The magnetisation models in this thesis are the first global magnetisation models for the Moon, and the first to combine the vector MAG and the scalar ER data. These magnetisation models can be used to predict the crustal contribution to the lunar magnetic field environment at a particular location, and in the absence of reliable sample returns, provide valuable information on the magnitude of lunar crustal magnetisation.

Energy released from the Earth’s crust in the form of earthquakes commonly follows a powerlaw gamma type probability distribution. This spontaneous organisation is in apparent contradiction to the second law of thermodynamics that states that a system should naturally evolve to a state of maximum disorder or entropy. However, developments in the field of modern thermodynamics suggest that some systems can undergo organisation locally, at the expense of increasing disorganisation (or entropy) globally through a process of entropy production. The primary aim of this thesis is to investigate self-organisation in the Earth’s seismogenic lithosphere as a driven, far-from-equilibrium, self-organising ‘dissipative structure’ in a very near critical steady-state and the underlying general mechanisms involved. The secondary aim is to test in more detail the applicability of the Bak, Tang and Wiesenfeld (BTW) model of Self-Organised Criticality (SOC) in describing Earth’s seismicity. This is done by: 1. Mathematical derivation of analytical solutions for system energy and entropy using the tools of equilibrium statistical mechanics; 2. The study of conservative and non-conservative versions of the BTW numerical model and 3. Analysis of temporal and spatial properties of earthquake data from the Harvard Centroid Moment Tensor catalogue and the Global Heat Flow Database. The modified gamma distribution predicts analytically that entropy S is related to the energy probability distribution scaling exponent B and the expectation of the logarithm of seismic energy hlnEi in the form of the gamma entropy equation S » BhlnEi. This solution is con- firmed for both numerical model results and real earthquake data. Phase diagrams of B vs. hlnEi suggest that the universality in B need not be maintained for a system to remain critical provided there is a corresponding change in hlnEi and S. The power-law systems examined are different from equilibrium systems since the critical points do not occur at global maximum entropy. For the dissipative BTW model at a steady-state, the externally radiated energy follows out-of-equilibrium power-law gamma type statistics, but, the internal energy has two icharacteristics that are indicative of equilibrium systems; a Gaussian type energy probability distribution and a Brownian noise power-spectrum for the internal energy fluctuations. This suggests an observer dependency in assessing criticality. The internal and external entropies calculated for the model are negatively correlated suggesting that driven systems self-organise at the expense of increasing entropy globally through a process of dissipation. A power-law dependency of mean radiated energy hEi on dissipation 1¡® is confirmed for a locally driven dissipative system in the form hEi » (1¡®)¡0:975. The BTW model shows spatial heterogeneity whilst maintaining universality in contradiction to previous assumptions. The quantitative analysis of real data reveals that earthquakes are more predictable spatially then temporally. Regionalisation using the Flinn-Engdahl classification shows that mid-ocean ridges are more organised (lower entropy) than subduction zones. A regional study of three different scaling exponents suggests that universality in earthquake scaling is violated, in contradiction to the original model of SOC. A model of self-organised sub-criticality (SOSC) is proposed as an alternative model for Earth seismicity. Overall, the results suggest that the tools of equilibrium thermodynamics can be applied to a steady-state far-from-equilibrium system such as the Earth’s seismogenic lithosphere, and that the resulting self-organisation occurs at the expense of maximising dissipation and hence entropy production.