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Active seismic methodologies provide a non-invasive tool to remotely characterise the physical properties of fractures at a wide range of scales, and have a positive impact in helping to solve rock engineering problems in a variety of geo-industrial applications. With current advances in seismic processing tools, such as full waveform inversion (FWI), and accurate models of seismic wave interaction with fractures, seismic characterisation of fractures can be tackled by utilising the entire seismic wavefield recorded at the receiver locations. A two-step strategy, using the genetic algorithm (GA) for global optimisation and the Neighbourhood Algorithm (NA) for evaluating uncertainties, was developed to simultaneously estimate the fracture properties (both fracture specific stiffness and equivalent fracture stiffness) and the background material properties directly from seismic waveforms. The optimisation involves minimising the difference between the observed (measured) and forward-modelled full waveforms through the finite difference code WAVE3D. The development, named Genetic Algorithm Full-Waveform Fracture Inversion (GAFWFI), looks beyond conventional seismic methods which focus on characterising fracture-induced anisotropy, by reducing the need to manually condition the data (e.g. manual picking of seismic phases), and by providing a robust means to explore multiple solutions. The development also allows the gap between different representations of fracturing to be bridged within a comprehensive method which can employ both discrete fracture and effective fracture models. GA-FWFI is tested initially on synthetic ultrasonic experiments with parallel fractures. Results confirm that the method can effectively invert for physical properties such as fracture stiffness, location, background material properties, while the posterior probability density (PPD) show that inversions are very well constrained. GA-FWFI is then applied to waveforms from a laboratory experiment investigating fracture slip and again results show high degree of accuracy. GA-FWFI is then utilised to unveil the coupling between discrete fracture networks (DFNs) and their equivalent fracture zone properties. The results reveal that the transition from a medium with open cracks to one with welded interfaces leads to the equivalent media having the equivalent medium stiffness non-linearly related to the crack specific stiffness. An attribute χ is proposed which helps guide the interpretation of a cracked medium by giving a range of likely values for crack size and crack stiffness. This work paves the way for novel strategies to seismically characterise fractures.

The global interseismic strain rate map is being accomplished rapidly with measurements of the space-based geodetic technique of InSAR. High-resolution measurements of crustal deformation from InSAR can provide crucial constraints on a region's active tectonics, geodynamics, and seismic hazard. However, space-based InSAR usually only provides good constraints on horizontal displacement in the east-west direction, with the north-south component typically provided by low-resolution GNSS measurements. Sentinel-1, on the other hand, has the potential to provide measurements that are sensitive to north-south motion, through exploitation of the burst overlap areas produced by the TOPS acquisition mode. However, the significant noise contributions from decorrelation and propagation through the ionosphere make it challenging to detect surface displacements associated with interseismic deformation needing millimeters per year accuracy. The ionospheric phase advance is a significant nuisance term that can bias InSAR measurements. Although methods have been developed to mitigate the effect, they are not always routinely applied when processing C-band SAR images, for which the effect is generally expected to be small. Nevertheless, the effect can be significant, especially when analyzing low deformation gradients over large areas using time-series analysis. Here, the work in Chapter 3 presents a time-series approach to ionospheric noise mitigation, which improves on existing methods. Firstly, I estimate the ionospheric contribution for each individual acquisition from multiple interferograms, which reduces noise. Secondly, this work improved the identification of unwrapping errors, which can bias the estimation. Thirdly, I introduce a new filtering approach, which gives better results, particularly at image edges and areas with variable density of coherent measurements. Furthermore, the approach is applicable when estimating along-track motion in burst overlap areas. The results show that applying the correction improves velocity accuracy significantly for both conventional line-of-sight and burst overlap interferometry techniques. The application of measuring long-term tectonic signals that concentrate in the north-south component with millimeters per year accuracy is essential to constrain interseismic strain globally. In Chapter 4, I also demonstrate a time-series approach with the burst overlap interferometry appropriate for extracting subtle long-term displacements. The approach includes mitigation of ionospheric noise, and I investigate different filtering approaches to optimize the reduction of decorrelation noise. I present the mean ground velocity in the azimuth direction from data acquired between 2014 and 2019 along the West-Lut Fault, a north-south striking fault in eastern Iran. The chi-square statistic defines a good agreement between the results and independent GNSS measurements. Moreover, the denser coverage of the technique allows to detect the variation in strain accumulation between northern and southern segments of the fault, with our modeling indicating a variation of slip rate from 9.2±0.5 mm/yr in the south to 4.3±0.5 mm/yr in the north. With current efforts to use InSAR to constrain strain rates globally, along-track measurements can fill a crucial gap in north-south sensitivity. With the achievement of that the burst overlap InSAR technique can measure azimuth motions across a slowly deforming area where the surface displacements are concentrated in the north-south component, this results in that, in the TOPS burst overlap region, the number of observations for a ground displacement can reach 3-4 times with different observational components. Measurement redundancy allows for the decomposition of observed velocities into three-dimensional components. In Chapter 5, I apply InSAR observations to estimate a deformation across the Chaman fault in both line-of-sight and along-track components using images from ascending and descending passes. I demonstrate an inversion to estimate the decomposed velocities. The algorithm employs a sparse GNSS network across the region to transform InSAR velocities to the GNSS reference frame. The results show that constraining the long-wavelength signal across the InSAR observations using GNSS data can mitigate the long-wavelength ionospheric disturbance that remains in the observations. The variation in slip rates across the Chaman fault is depicted by two transect profiles. The mean velocity profile at latitude 31˚N, where the Chaman fault is the only tectonic structure to accommodate strain, is consistent with 10.4±0.4 mm/yr of slip rate derived from the interseismic modeling. The optimal fault slip rate to fit with the mean velocity of the southern profile at latitude 29˚N is 5.5±0.8 mm/yr across the Chaman fault and 15.5±0.9 mm/yr across the parallel fault (the Ghazaband fault). I also demonstrate the benefits of high temporal sampling of InSAR observations with TOPS acquisition mode to study time-dependent surface deformation. I present the evolution of fault creeps, including seismic and aseismic fault slip along the Chaman fault during 2014-2018.

This thesis examines the development of shear-zone localisation in the continental lithosphere. I use non-Newtonian, viscous models to examine the controls on strain localisation with depth and on the development of horizontal shear-zones in regions away from strength contrasts. I show how the vertical extent of strain localisation is principally controlled by lithology and geothermal gradient, and how the horizontal extent of localisation is a consequence of strain-weakening and the geometry of strength contrasts. I explore how strain localisation develops from an initial isolated weak inclusion. The progress of strain localisation follows a power-law growth that is strongly non-linear. When applied to the rheological laws for common lithospheric minerals, the temperature and stress-dependence provide a direct means of predicting the depth below which localisation does not occur. I apply the calculations to four major continental strike-slip zones and find observations from seismic data agree with the calculations. Localisation to the base of the lithosphere is not supported by the calculations or the geophysical data. I use a model configured to resemble the India-Asia convergence that includes an isolated weak region within the Tibetan Plateau area and, in selected experiments,strong regions representing the Tarim and Sichuan Basins. I rotate a strong India region into a weaker Asia and observe the evolving strain. Shear zones develop adjacent and propagate outwards from the weak region. Where the Basins are present then high strain- rate zones develop adjacent to them and the overall distribution of strain within the model is altered. A high strain-weakening component enables shear-zones to localise. Micro-plate models assume the pre-existence of such high strain regions but I show how a continuum model can initiate and grow localised deformation within a region of generally diffuse deformation.

A diverse set of hazards are posed by the world's 1500 subaerial volcanoes, yet the majority of them remain unmonitored. Measurements of deformation provide a way to monitor volcanoes, and synthetic aperture RaDAR (SAR) provides a powerful tool to measure deformation at the majority of the world's subaerial volcanoes. This is due to recent changes in how regularly SAR data are acquired, how they are distributed to the scientific community, and how quickly they can be processed to create time series of interferograms. However, for interferometric SAR (InSAR) to be used to monitor the world's volcanoes, an algorithm is required to automatically detect signs of deformation-generating volcanic unrest in a time series of interferograms, as the volume of new interferograms produced each week precludes this task being achieved by human interpreters. In this thesis, I introduce two complementary methods that can be used to detect signs of volcanic unrest. The first method centres on the use of blind signal separation (BSS) methods to isolate signals of geophysical interest from nuisance signals, such as those due to changes in the refractive index of the atmosphere between two SAR acquisitions. This is achieved through first comparing which of non-negative matrix factorisation (NMF), principal component analysis (PCA), and independent component analysis (ICA) are best suited for solving BSS problems involving time series of InSAR data, and how InSAR data should best be arranged for its use with these methods. I find that NMF can be used with InSAR data, providing the time series is formatted in a novel way that reduces the likelihood of any pixels having negative values. However, when NMF, PCA, and ICA are applied to a set of synthetic data, I find that the most accurate recovery of signals of interest is achieved when ICA is set to recover spatially independent sources (termed sICA). I find that the best results are produced by sICA when interferograms are ordered as a simple ``daisy chain'' of short temporal baselines, and when sICA is set to recover around 1-3 more sources than were thought to have contributed to the time series. However, I also show that in cases such as deformation centred under a stratovolcano, the overlapping nature of a topographically correlated atmospheric phase screen (APS) signal and a deformation signal produces a pair of signals that are no longer spatially statistically independent, and so cannot be recovered accurately by sICA. To validate these results, I apply sICA to a time series of Sentinel-1 interferograms that span the 2015 eruption of Wolf volcano (Galapagos archipelago, Ecuador) and automatically isolate three signals of geophysical interest, which I validate by comparing with the results of other studies. I also apply the sICA algorithm to a time series of interferograms that image Mt Etna, and through isolating signals that are likely to be due to instability of the east flank of the volcano, show that the method can be applied to stratovolcanoes to recover useful signals. Utilising the ability of sICA to isolate signals of interest, I introduce a prototype detection algorithm that tracks changes in the behaviour of a subaerial volcano, and show that it could have been used to detect the onset of the 2015 eruption of Wolf. However, for use in an detection algorithm that is to be applied globally, the signals recovered by sICA cannot be manually validated through comparison with other studies. Therefore, I seek to incorporate a module into my detection algorithm that is able to quantify the significance of the sources recovered by sICA. I achieve this through extensively modernising the ICASO algorithm to create a new algorithm, ICASAR, that is optimised for use with InSAR time series. This algorithm allows me to assess the significance of signals recovered by sICA at a given volcano, and to then prioritise the tracking of any changes they exhibit when they are used in my detection algorithm. To further develop the detection algorithm, I create two synthetic time series that characterise the different types of unrest that could occur at a volcanic centre. The first features the introduction of a new signal, and my algorithm is able to detect when this signal enters the time series by tracking how well the baseline sources are able to fit new interferograms. The second features the change in rate of a signal that was present during the baseline stage, and my algorithm is able to detect when this change in rate occurs by tracking how sources recovered from the baseline data are used through time. To further test the algorithm, I extended the Sentinel-1 time series I used to study the 2015 eruption of Wolf to include the 2018 eruption of Sierra Negra, and I find that my algorithm is able to detect the increase in inflation that precedes the eruption, and the eruption itself. I also perform a small study into the pre-eruptive inflation seen at Sierra Negra using the deformation signal and its time history that are outputted by ICASAR. A Bayesian inversion is performed using the GBIS software package, in which the inflation signal is modelled as a horizontal rectangular dislocation with variable opening and uniform overpressure. Coupled with the time history of the inflation signal provided by ICASAR, this allows me to determine the temporal evolution of the pre-eruptive overpressure since the beginning of the Sentinel-1 time series in 2014. To extend this back to the end of the previous eruption in 2005, I use GPS data that spans the entire interruptive period. I find that the total interruptive pressure change is ~13.5 MPa, which is significantly larger than the values required for tensile failure of an elastic medium overlying an inflating body. I conclude that it is likely that one or more processes occurred to reduce the overpressure within the sill, and that the change in rate of inflation prior to the final failure of the sill is unlikely to be coincidental. The second method I develop to detect volcanic deformation in a time series of interferograms uses a convolutional neural network (CNN) to classify and locate deformation signals as each new interferogram is added to the time series. I achieve this through building a model that uses the five convolutional blocks of a previously state-of-the-art classification and localisation model, VGG16, but incorporates a classification output/head, and a localisation output/head. In order to train the model, I perform transfer learning and utilise the weights made freely available for the convolutional blocks of a version of VGG16 that was trained to classify natural images. I then synthesise a set of training data, but find that better performance is achieved on a testing set of Sentinel-1 interferograms when the model is trained with a mixture of both synthetic and real data. I conclude that CNNs can be built that are able to differentiate between different styles of volcanic deformation, and that they can perform localisation by globally reasoning with a 224 x 224 pixel interferogram without the need for a sliding window approach. The results I present in this thesis show that many machine learning methods can be applied to both time series of interferograms, and individual interferograms. sICA provides a powerful tool to separate some geophysical signals from atmospheric ones, and the ICASAR algorithm that I develop allows a user to evaluate the significance of the results provided by sICA. I incorporate these methods into an deformation detection algorithm, and show that this could be used to detect several types of volcanic unrest using data produced by the latest generation of SAR satellites. Additionally, the CNN I develop is able to differentiate between deformation signals in a single interferogram, and provides a complementary way to monitor volcanoes using InSAR.

Moving towards detecting and understanding volcanic unrest prior to eruptions, there has been significant improvements in understanding the structure and dynamics of magma plumbing systems. However, deciphering subsurface processes during inter-eruptive periods often remains challenging, and whether magma is involved or not is an essential question to be able to assess the degree of activity of a volcano. In this thesis, I explore the integration of surface deformation and temporal gravity, using the Askja volcano (Iceland) as a case study. Magmatic processes are usually closely linked to pressurization-depressurization mechanisms, which can translate into subsurface volume changes and lead to surface deformation responses. Because magmatic processes are diverse, integrating temporal gravity can help narrowing down the list of possible on-going processes. Indeed, temporal gravity is related to subsurface mass change, and for example, a surface uplift associated with a gravity increase could be caused by a magma intrusion, whereas an uplift with no mass change could be caused by gas pressurization resulting from temperature increase. Additionally, comparing both signals can help evaluating the contributions of external processes, such as of hydrothermal or tectonic origin. The Askja volcano, which is one of the most active volcanoes in Iceland, has erupted at least 40 times in the last 1,100 years. Some events were very powerful, such as the 1875 VEI-5 caldera-forming Plinian event and the most recent event was a basaltic fissure eruption, which occurred in 1961. Since at least 1983, the main caldera has been subsiding and all the previous studies that applied analytical modelling to surface deformation records at Askja agree that the subsidence can be best explained over periods of 10 years or less, by a deflating source, located at 3-3.5 km depth beneath the caldera centre. The constrained linear volume changes have diminished from about -0.002 km^3 yr^{-1} near 2000 to about -0.001 km^3 yr^{-1} near 2010. In parallel, gravity measurements, which were recorded between 1988 and 2010, highlighted a gradual gravity decrease of about 140 microgal up to 2007, centred on the main caldera, and a gravity increase of about 60 microgal was observed between 2007 and 2009, while the subsidence continued. Due to the lack of spatial coverage, no analytical model could be performed using the gravity results, hence there were no constraints on the depth and magnitude of mass changes. Due to the correlation in locations, previous studies assumed that mass and volume changes were related to the same process, occurring at 3-3.5 km depth. Based on this assumption it was suggested that the main process causing the subsidence was a magma drainage down to deeper levels with possible additional effects from magma crystallisation. A magma intrusion at the shallow reservoir and/or mass variations in the hydrothermal system were proposed to explain the temporary gravity increase. Finally, the likely high contribution of plate spreading as a cause of subsidence was demonstrated using finite-element modelling, considering the caldera and shallow chamber as zones of weak materials, embedded in a two-layer crust model with a visco-elastic lower crust. In this thesis, I take the analyses of both surface deformation and temporal gravity at Askja a step further, to clarify the causes of subsidence. I use the Interferometric Synthetic Aperture Radar (InSAR) technique to investigate the spatial and temporal signature of the long-term subsidence, considering a 15-year-long time period. This technique, which was used at Askja in two previous studies, can measure surface deformation at the centimetre scale over large areas with spatial resolution of tens to hundreds of meters. My results show that the caldera is steadily subsiding as a whole, and can be fitted by an exponential decay with relaxation time of about 42 years. Using the Bayesian inversion modelling approach paired with the Markov chain Monte Carlo sampling, and incorporating the exponential behaviour of the subsidence, I refine the depth of the shallow reservoir with narrower bounds compared with previous studies: when assuming a point pressure source, which can reproduce well the circular spatial deformation pattern observed in the caldera, there is 95% chance that the reservoir is located at 3+/-0.1 km beneath the caldera centre and the exponential volume decrease has total amplitude of 0.07+/-0.01 km^3. In parallel, I investigate the spatial and temporal evolution of gravity changes over 2015-2017, from a larger gravity network and using improved methodologies compared with previous studies. My results show a spatial-bowl shape signature over 2015-2016, with maximum decrease of about 100+/-30 microgal at the caldera centre. Although this annual change is spatially correlated with the synchronous subsidence, the following annual gravity change, showing negligible variations across the caldera, is not. This suggests that both signals do not relate to the same processes, and the difference in magnitude of gravity changes compared with previous studies is due to the choice of reference station. I then further investigate the link between gravity changes and deformation, by performing the first gravity inversion at Askja, and using the Bayesian inversion modelling approach paired with the Markov chain Monte Carlo sampling. Even though poorly constrained, the inversion suggests that, when assuming a spherical source, the gravity changes over 2015-2016 have 95% chance to be due to a mass decrease within 1.5x10¹²-7.5x10¹⁰ kg and located within 2.7-9.9 km. These large confidence intervals are due to the large uncertainties of the gravity results. Assuming magma drainage, the mass change derived from the volume decrease constrained from the exponential deformation is outside the 95% confidence interval of mass change constrained from gravity. The uncorrelated temporal variations and discrepancy in magnitude between both types of signals therefore suggest that magma drainage is unlikely to be responsible for the subsidence at Askja. Alternatively, the steady and gradually decaying subsidence could be driven by extension due to plate spreading, which would induce pressure decrease at the shallow reservoir, and crystallisation processes could also participate. On the other hand, the gravity changes could be due to mass fluctuations in a hydrothermal system just above the shallow magma reservoir. To precisely extract gravity changes related to magma movements and/or hydrothermal mass variations and fully integrate errors in my gravity analysis, I have developed a statistical approach that estimates the total error budget associated with temporal gravity, when using spring relative gravimeters. In this thesis, I present the method in detail, providing equations for users to estimate case-by-case error budgets, and I also provide ranges of best-to-worst case scenarios, to guide users on where to focus effort to minimizing errors, depending on the magnitude of the signal of interest. My results show that the choice of gravimeter is essential to minimize vibration noise and errors due to imprecise levelling, which can both reach hundreds of microgals. Similarly, monitoring the temporal evolution of calibration factor should be usual practice, especially when studying gravity time-series spanning several years. Finally, I demonstrate that a bulk estimate of errors due to unknown meterological effects, which can reach a few tens of microgals, can be derived from base station measurements spanning at least a few days.

To participate in the REDD+ mechanism of the UN Framework Convention on Climate Change (UNFCCC), developing countries must upgrade their national forest monitoring systems to become Measurement, Reporting and Verification (MRV) systems that can monitor changes in forest carbon stocks. However, despite support from international REDD+ Readiness programmes, most developing countries still have limited forest monitoring capacity. The sociology of remote sensing systems has been little studied until now, especially in developing countries. To evaluate the adoption of technologies proposed in these schemes, this research has devised and tested an Information Production (IP) Framework and a Technology Adoption System (TAS) Framework that enable the evaluation of more complex instances of technology adoption than current frameworks. This research found that although REDD+ Readiness schemes have been implemented in Cambodia and Indonesia, the capacity to supply forest carbon information is still limited because upgrading forest monitoring systems has been limited by self-constrained optimisation that has led to only incremental evolution. Cambodia and Indonesia have shown relatively high improvements in forest area monitoring capacity, compared to growing stock monitoring capacity, but the quality of forest area and carbon information produced by the two countries is still insufficient to meet international demand. Technology adoption has involved self-constrained optimisation because adopting new technologies was constrained by human capital, institutions and perceptions, existing technologies, financial resources, and communication between organisations. Technology adoption and information production are also influenced by other factors, such as the relationship between national and international demand for forest information, organisational substitution, and difficulties in improving the organisation of forest monitoring. Since in both countries the improvement of forest monitoring has reached a plateau due to self-constrained optimisation and path dependency, escaping from the plateau may require increasing human capital and stronger financial incentives.

In order to understand how earthquakes nucleate, propagate and terminate it is essential to understand the properties and stress conditions of the surfaces upon which earthquakes occur. Fault surfaces control frictional properties and by measuring exhumed faults we can better understand earthquake propagation and how this may be linked to fault structure. In order to forecast areas of a fault likely to be at risk from future failure it is necessary to accurately model the slip that occurs during each measured earthquake. In recent years many lines of evidence suggest that fault surfaces and earthquake slip show fractal properties. This includes high resolution scans of fault surfaces, observations of coseismic surface slip and analysis of published slip distributions. In this thesis I investigate how fault structure may affect the fractal properties of fault surface roughness, by investigating the along-strike changes in properties of the Campo Felice fault in the Italian Apennines. I then incorporate observations of fractal properties into earthquake slip inversions through a new form of regularisation, which I develop using Bayesian methods. Through this I aim to improve our understanding of the surfaces upon which earthquakes occur, how this links to fault structure and to improve our coseismic slip models, that provide the basis of stress models and hazard analysis. Fault surfaces displaying fractal properties mean that there is a power-law relationship between the topography of a fault and the wavelength of this topography: the magnitude of height fluctuations depends upon the scale at which they are observed. Whilst many studies have investigated fault roughness properties, here I present the first study of how fault roughness varies along the strike of a fault. I use terrestrial laser scans and laser profilometer scans at 14 locations along the length of the Campo Felice normal fault in the Italian Apennines, as well as a scan encompassing several hundred meters along the length of the fault. These scans show that the Campo Felice fault displays fractal properties over at least six orders of magnitude perpendicular to slip and at least three orders of magnitude parallel to slip. But, contrary to previous findings on other faults, I find that the Hurst parameter, which controls the fractal nature of the fault surface, changes considerably and unpredictably along the length of the fault, even between observations tens of metres apart. I suggest that this variability may be due to the variation of slip vector along the length of the fault, as is frequently observed in earthquakes. This variability could, additionally, be linked to fault asperities halting or impeding rupture, such that some areas of the fault experience more earthquakes, or experience different stress conditions during the same earthquake. I also find that the magnitude of topography displayed by Campo Felice fault is low compared to previous studies, suggesting it may be at risk of larger earthquakes. Observations of fractal fault surfaces suggest that earthquake slip should be fractal too. By using geodetic data taken at the surface before and after an earthquake we can perform slip inversions to give a model of how much slip occurred underground, on the fault surface. This is routinely performed for large, continental earthquakes. Due to noise and lack of data these inversions are frequently regularised to produce a stable solution, but the standard regularisation techniques have little physical basis. I incorporate fractal properties of earthquake slip into slip inversions by introducing a new regularisation technique: von Karman regularisation. I use a Bayesian method to fully explore parameter space and better understand uncertainties on the model parameters. From synthetic tests I find that this regularisation performs comparably, if not better, than other frequently used methods upon both fractal and Laplacian input slip distributions. Using InSAR (Interferometric Synthetic Aperture Radar) and GPS (Global Positioning System) data from the 2014 Mw 6.0 Napa Valley earthquake, I invert for slip using a two-segment fault model. I find that the choice of regularisation changes the location and magnitude of slip, which could have important implications for stress transfer and our understanding of the so-called shallow slip deficit. Through its incorporation of fractal properties, von Karman regularisation represents a more physical regularisation of earthquake slip along a fault plane. However, some bias can be introduced by incorrectly choosing the length and width of the fault plane. If a fault plane is too large, the regularisation can cause slip smearing, particularly at depth where the model is poorly constrained by the data, in order to improve the von Karman probability. To eliminate this bias I modify my Bayesian inversion scheme to solve for the size of the fault plane during the inversion, along with slip, rake and a hyperparameter controlling slip variance. This makes the inversion trans-dimensional, and aims to reduce the bias caused by an incorrect model. I apply it to the Mw 6.2 Central Tottori earthquake, Japan, using InSAR and GNSS (Global Navigation Satellite System) data. My model shows that the earthquake ruptured most of the seismogenic zone, in contrast to seismological studies. My results in this thesis further confirm that fault surface roughness shows fractal properties, and that fault structure may play an important role in the exact relationship between fault topography and the lengthscale of observation. Further investigation of exhumed fault surfaces can help inform earthquake models, including earthquake slip inversions, particularly if an earthquake were to occur on a fault upon which surface roughness measurements had already been taken. By incorporating observed fractal properties into earthquake slip inversions I aim to introduce less bias than other, less physical regularisations. With the European Space Agency's new satellites Sentinel-1a/b providing regular observations of the Earth's deforming regions, we are in a position to model earthquake slip better than ever before. I hope that by incorporating more realistic observations and using Bayesian methods to fully understand uncertainties, we can produce better, more realistic models. These models help our understanding of earthquakes, and, most importantly, earthquake hazard.

In order for an earthquake to become a natural disaster, it needs to be significantly large, close to vulnerable populations or both. The largest earthquakes in the world occur in subduction zones, where cool, shallowly dipping fault planes enable brittle failure over a large area. However, these earthquakes often occur far away from major cities, reducing their impact. Similar, low angle fault planes can be found in continental fold and thrust belts, where sub-horizontal decollements offer large potential rupture areas. These seismic sources are often much closer to major urban centres than off-shore subduction zone sources. It is therefore essential to understand the processes that control how strain is accommodated and released in such settings. Much of our current understanding of the earthquake cycle comes from studying strike-slip faults. Can our knowledge of strike-slip faults be transferred over to dip-slip faults, and in particular, fold and thrust belts? Previous work has suggested that there may be significant differences between strike-slip and dip-slip settings, and therefore further study of the earthquake cycle in dip-slip environments is required. The recent launch of Sentinel-1, and the extensive Synthetic Aperture Radar (SAR) archive of the European Space Agency (ESA), offer an opportunity to obtain measurements of strain in dip-slip environments that can contribute to our understanding. In this thesis, I use geodetic measurements to contribute to our understanding of the earthquake cycle. Enhanced surface deformation rates following earthquakes (so called postseismic deformation) show temporal and spatial variation. Such variation can be used to investigate the material properties of faults and the surrounding medium. I collate measurements of postseismic velocity following contintental earthquakes to examine the temporal evolution of strain following an earthquake over multiple timescales. The compilation show a simple relationship, with velocity inversely proportional to time since the earthquake. This relationship holds for all fault types, with no significant difference between dip-slip and strike-slip environments. Such lack of difference implies that, at least in terms of the temporal evolution of near field postseismic deformation, both environments behave similarly. I compare these measurements with the predictions of various models that are routinely used to explain postseismic deformation. I find that the results are best explained using either rate-strengthening afterslip or power-law creep in a shear zone with high stress exponent. Such a relationship indicates that fault zone processes dominate the near-field surface deformation field from hours after an earthquake to decades later. This implies that using such measurements to determine the strength of the bulk lithosphere should only be done with caution. I then collate geodetic measurements from throughout the earthquake cycle in the Nepal Himalaya to constrain the geometry and frictional properties of the fault system. I use InSAR to measure postseismic deformation following the 2015 Mw~7.8 Gorkha earthquake and combine this with Global Navigation Satellite System (GNSS) displacements to infer the predominance of down-dip afterslip. I then combine these measurements with coseismic and interseismic geodetic data to determine fault geometries which are capable of simultaneously explaining all three data sets. Unfortunately, the geodetic data alone cannot determine the most appropriate geometry. It is therefore necessary to combine such measurements with other relevant data, along with the expertise to understand the uncertainties in each data set. Such combined measurements ought to be understood using physically consistent models. I developed a mechanically coupled coseismic-postseismic inversion, based on rate and state friction. The model simultaneously inverts the coseismic and postseismic surface deformation field to determine the range of frictional properties and coseismic slip which can explain the data within uncertainties. I applied this model to the geodetic data compilation in Nepal and obtained a range of values for the rate-and-state 'a' parameter between 0.8 - 1.6 x 10^-3, depending on the geometry used. Whilst the Nepal Himalaya is well instrumented, many continental collision zones suffer from a severe lack of data. The Sulaiman fold and thrust belt is one such region, with very sparse GNSS data, but significant seismicity. I apply InSAR to part of the Sulaiman fold and thrust belt near Sibi to examine the evolution of strain throughout the seismic cycle. I tie together observations from ERS, Envisat and Sentinel-1 to produce a time series of displacements over 25 years long which covers an earthquake which occurred in 1997. Using this time series, I investigate the contributions of different parts of the earthquake cycle to the development of topography. I find that postseismic deformation plays a clear role in the construction of short wavelength folds, and that the combination of coseismic and postseismic deformation can reproduce the topography over a variety of lengthscales. The shape of the frontal section of the fold and thrust belt, including the gradient of the topography, is roughly reproduced in a single earthquake cycle. This suggests that fold and thrust belts can maintain their taper in a single earthquake cycle, rather than through earthquakes occurring at different points throughout the belt. I find that approximately 1000 earthquakes like the 1997 event, along with associated postseismic deformation, can reproduce the topography seen today to first order. Such a result may aid our use of topography as a long-term record of earthquake cycle deformation. I finish by drawing these various findings together and commenting on common themes. Afterslip plays an important role in the earthquake cycle, contributing to the surface deformation field in multiple locations, over multiple timescales, and generating topography. This afterslip can be explained using a rate-strengthening friction law with a*sigma between 0.2 and 1.54 MPa. Combining this rate dependence with the static coefficient of friction determined from other methods, such as critical taper analysis, would enable a more complete picture of fault friction to be determined. Fault geometry in fold and thrust belts may control the size of potential ruptures, with junctions and changes in dip angle potentially arresting ruptures. In order to fully determine the role of fault geometry and friction in controlling the earthquake cycle in dip-slip settings, I suggest a more thorough exploitation of the wealth of InSAR data which is now available. These data then need to be combined with measurements from other fields, and models produced which are consistent within the uncertainties of each data set. I suggest that measurements of topography and insights from structural geology may help with understanding the long term and short term processes governing earthquake patterns in an area. As both observations and models are developed, interdisciplinary teams may be able to better constrain the key controls on earthquake hazard in continental dip-slip settings.