A vital component in the management of seismic hazard is the study of past seismic events. Classically, this has been the domain of seismology, which studies the dynamic manifestations of the event to infer properties such as epicenter and moment magnitude. More recently it has become possible to perform similar analyses on the basis of the static consequences of a seismic event, as satellite borne Synthetic Aperture Radar (SAR) data allows us to compare the local surface geometries before and aftera seismic event. The locality of the deformation data promises reconstructions with greater detail and subject to fewer model uncertainties. With current technology, it is not possible to use SAR to their full potential. The non-linearity of the static dislocation problem that links faulting mechanisms to observed deformations causes any inverse method to require many evaluations of the forward model. This poses limits on the permissible cost of solving the dislocation problem, restricting most approaches to simplified model assumptions such as material homogeneity and absence of topography. In situations where more accurate information is available, this presents a clear opportunity for improvement by accelerating the computational methods instead. This thesis presents the Weakly-enforced Slip Method (WSM), a modification of the Finite Element Method (FEM), as a fast approach for solving static dislocation problems. While the computational cost of the WSM is similar to that of the FEM for single dislocations, the WSM is significantly faster when many different dislocation geometries are considered, owing to the reuse of computationally expensive components such as matrix factors. This property makes the method ideally suited for inverse settings, opening the way to incorporating all available in situ data in a forward model that is simultaneously flexible and cheaply evaluable. Moreover, we prove that the WSM retains the essential convergence properties of the FEM. A limitation of the WSM is that it produces continuous displacement fields, which implies a large error local to the dislocation. We show that this error decreases rapidly with distance, and that in a typical scenario the majority of deformation data has a discretization error that is smaller than observational noise, particularly when a fault is buried. In the case of shallow or rupturing faults, neighbouring data needs to be discarded from the analysis to avoid disruption. With this measure in place, we show via Bayesian inference of synthesized datasets that the discretization errors of the WSM do not significantly affect the inverse problem.@en

Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what affects particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM can accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 1 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 10 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that is often forced to impose model restrictions in a concession to computability.

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As part of the Terrafirma Validation Experiment a comparison of Persistent Scatterer Interferometry (PSI) with in-situ measurements is performed. The experiment purports to validate the processing chains of partners participating in the Terrafirma project, in order to obtain a better understanding of the performance of the techniques. Two test sites are chosen in the Netherlands: (i) the trajectory of a subway line in the centre of Amsterdam, still to be constructed, and (ii) the area around the city of Alkmaar, affected by subsidence due to gas extraction. The Amsterdam site is monitored using Envisat-ASAR data, whereas for the Alkmaar area both ERS1/2-AMI and Envisat-ASAR data sets are used. Due to the difference in deformation phenomena, available ground truth and surface characteristics, different validation procedures are applied to the two test sites. Here we describe these validation methodologies and the validation results.

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