Our knowledge of Earth's structure and dynamics is owed, in large part, to techniques that allow us to infer the physical properties of rocks based on observations made near the surface. In particular, passive seismic imaging relies on natural sources of elastic wave energy (typically earthquakes) to illuminate Earth's interior. The frequency-dependent dispersive characteristics of surface waves from earthquakes provides a valuable constraint on the depth heterogeneity beneath the surface, which can be used to infer structure of the lithosphere (i.e., tectonics). The first part of this thesis develops novel tools for passive seismic imaging considering surface-wave dispersion. Specifically, Bayesian (probabilistic) methods are developed that provide rigorous uncertainty quantification. The ability to estimate the directional dependence of surface-wave speeds (i.e., seismic anisotropy) is demonstrated. Furthermore, a general approach for considering circular (wrapped) data, such as surface-wave phase measurements, is developed and applied to estimate the average dispersion between pairs of seismic stations. These ideas are applied to data recorded at seismic stations over British Columbia, Canada, to produce a large volume of data products that will help improve our understanding of the tectonics throughout the region. The second part of this thesis investigates the structural and mechanical conditions in subduction zones, where tectonic plates collide and one plate is thrust beneath the other. Specifically, a type of passive seismic imaging based on recordings of body waves from distant earthquakes (known as receiver functions) is used to infer subduction zone structure in relation to the coupling between tectonic plates. Receiver function data calculated for stations over the Cascadia subduction zone (southwestern Canada) suggest that episodes of slow slip on the plate interface occur in tandem with changes in mechanical conditions. Receiver function data calculated for stations over the Hikurangi subduction zone (New Zealand) suggest that stress and deformation along the margin are spatially linked to plate coupling. These results improve our understanding of the dynamics of these tectonic systems, including the seismic hazards that they pose.

New Insights on the Uncertainties in Finite-Fault Earthquake Source Inversion Hoby Njara Tendrisoa Razafindrakoto Earthquake source inversion is a non-linear problem that leads to non-unique solutions. The aim of this dissertation is to understand the uncertainty and reliability in earthquake source inversion, as well as to quantify variability in earthquake rupture models. The source inversion is performed using a Bayesian inference. This technique augments optimization approaches through its ability to image the entire solution space which is consistent with the data and prior information. In this study, the uncertainty related to the choice of source-time function and crustal structure is investigated. Three predefined analytical source-time functions are analyzed; isosceles triangle, Yoffe with acceleration time of 0.1 and 0.3 s. The use of the isosceles triangle as source-time function is found to bias the finite-fault source inversion results. It accelerates the rupture to propagate faster compared to that of the Yoffe function. Moreover, it generates an artificial linear correlation between parameters that does not exist for the Yoffe source-time functions. The effect of inadequate knowledge of Earth’s crustal structure in earthquake rupture models is subsequently investigated. The results show that one-dimensional structure variability leads to parameters resolution changes, with a broadening of the posterior 5 PDFs and shifts in the peak location. These changes in the PDFs of kinematic parameters are associated with the blurring effect of using incorrect Earth structure. As an application to real earthquake, finite-fault source models for the 2009 L’Aquila earthquake are examined using one- and three-dimensional crustal structures. One- dimensional structure is found to degrade the data fitting. However, there is no significant effect on the rupture parameters aside from differences in the spatial slip extension. Stable features are maintained for both structures. In the last part of this work, a multidimensional scaling method is presented to compare and classify earthquake slip distributions. A similarity scale to rank them are thus formulated. Dissimilarities among slip models (from various parameterizations) are computed using two different distance metrics, normalized squared and gray-scale metrics. Multidimensional scaling is then used to visualize the differences among the models. The analyzes are done for 2 case studies; one based on artificial scenarios with a known answer and another one based on the published rupture models of the 2011 Tohoku earthquake.

This thesis develops a Bayesian inversion algorithm for autonomous underwater vehicle localization, and carries out a study of several factors contributing to localization accuracy in an underwater acoustic positioning system. Specifically, a ray-based algorithm is described that estimates target position through the linearized inversion of transmission arrival time differences, and provides linearized uncertainty estimates for model parameters. Factors contributing to source localization uncertainty considered here included: (1) modelling transmission paths accounting for refraction due to a depth-varying SSP instead of using a constant sound-speed approximation and straight-line propagation, (2) inverting for a potential bias in the measured sound-speed profile, (3) accounting for errors in hydrophone position by including these positions as unknown parameters in the inversion, and (4) applying path-dependent timing correction factors to account for lateral variability in the sound-speed profile. In each case, nonlinear Monte Carlo analysis is applied in which a large number of noisy data sets are considered, to obtain statistical measures of the localization improvement that results by addressing these factors. / Graduate

Neural networks are extremely versatile tools, as evidenced by their widespread adoption into many fields in the sciences and beyond, including the geosciences. In seismology neural networks have been primarily used to automatically detect and discriminate seismic signals within time-series data, as well as provide location estimates for their sources. However, as neural network research has significantly progressed over the past three decades, so too have its applications in seismology. Such applications now include earthquake early warning systems based on smartphone data collected from large numbers of users, the prediction of peak ground acceleration from earthquake source parameters, the efficient computation of synthetic seismograms, providing probabilistic estimates of solutions to geophysical inverse problems, and many others. This thesis contains three components, each of which explore novel uses of neural networks in seismology. In the first component, a previously established earthquake detection and location method is supplemented with a neural network in order to automate the detection process. The detection procedure is then applied to a large volume of seismic data. In addition to automating the detection process, the neural network removes the need for several user-defined thresholds, subjective criteria otherwise necessary for the method. In the second component, a novel approach is developed for inverting seafloor compliance data recorded by ocean-bottom seismometers for the shallow shear-wave velocity structure of oceanic tectonic plates. The approach makes use of mixture density networks, a type of neural network designed to provide probabilistic estimates of solutions to inverse problems, something that standard neural networks are incapable of. In the final component of this thesis, the mixture density network approach to compliance inversion is applied to a group of ocean-bottom seismometers deployed along the continental shelf of the Cascadia Subduction Zone in order to investigate shelf sediment properties.

Ambient seismic noise from generation to its application for determination of sub-surface velocity structures is analyzed using continuous data recordings from the Swedish National Seismic Network (SNSN). The fundamental aim of the thesis is to investigate the applicability of precise velocity measurements from ambient noise data. In the ambient noise method, a form of interferometry, the seismic signal is constructed from long-term cross correlation of a random noise field. Anisotropy of the source distribution causes apparent time shifts (velocity bias) in the interferometric signals. The velocity bias can be important for the study area (Sweden) which has relatively small velocity variations. This work explores the entire data path, from investigating the noise-source distribution to a tomographic study of southern Sweden. A new method to invert for the azimuthal source distribution from cross-correlation envelopes is introduced. The method provides quantitative estimates of the azimuthal source distribution which can be used for detailed studies of source generation processes. An advantage of the method is that it uses few stations to constrain azimuthal source distributions. The results show that the source distribution is inhomogeneous, with sources concentrated along the western coast of Norway. This leads to an anisotropic noise field, especially for the secondary microseisms. The primary microseismic energy comes mainly from the northeast. The deduced azimuthal source distributions are used to study the level of expected bias invelocity estimates within the SNSN. The results indicate that the phase-velocity bias is less than 1% for most station pairs but can be larger for small values of the ratio of inter-station distance over wavelength. In addition, the nature of velocity bias due to a heterogeneous source field is investigated in terms of high and finite-frequency regimes. Graphical software for phase-velocity dispersion measurements based on new algorithms is presented and validated with synthetic data and by comparisons to other methods. The software is used for phase-velocity measurements, and deduced azimuthal source distributions are used for velocity-bias correction. Derived phase-velocity dispersion curves are used to construct two-dimensional velocity maps of southern Sweden at different periods based on travel-time tomography. The effect of the bias correction is investigated, and velocity maps are interpreted in comparison to previous geological and geophysical information.

A high-resolution infrared Fourier Transform Spectrometer (FTS) has been operational at the Toronto Atmospheric Observatory (TAO)since May 2002. An optimal estimation retrieval technique is used to analyse the observed spectra and provide regular total and partial column measurements of trace gases in the troposphere and stratosphere as part of the Network for the Detection of Atmospheric Composition Change. The quality of these results were assessed through two ground-based validation campaigns, comparisons with three satellite instruments, and comparison with a three-dimensional chemical transport model. The two ground-based campaigns involved two lower-resolution FTS instruments: the University of Toronto FTS and the Portable Atmospheric Research Interferometric Spectrometer for the Infrared. The first campaign took place over the course of four months and is the longest side-by-side intercomparison of ground-based FTS instruments, to date. The second campaign was more focused and involved all three instruments measuring over a two-week period. Simultaneous measurements of O3, HCl, N2O, and CH4 were recorded and average total column differences were all < 3.7% in the extended campaign, and < 4.5% in the focused campaign. Satellite-based comparisons were done with the SCanning and Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS), and the Optical Spectrograph and InfraRed Imager System (OSIRIS). Total column CO, CH4, and N2O compared with SCIAMACHY all had average differences < 10% with results from the TAO-FTS being as good as, or better, than that of other instruments. Validation with the ACE-FTS showed that average partial columns of O3, NO2, N2O, CH4, and HCl were within 10% while observations of CO and NO each had an average bias of about 25%. Comparisons of monthly average partial column O3 and NO2 with OSIRIS were highly correlated (R = 0.82-0.97) with monthly mean differences of < 3.1% for O3 and < 2.6% for NO2. Finally, comparisons with the GEOS-Chem chemical transport model revealed that the model consistently over-estimates tropospheric columns of CO and C2H6 observed at TAO. It was determined that the enhanced CO values were partially due to the North American emissions specified in the model, but more work must be done in the future if the source of this discrepancy is to be fully explained.

A high-resolution infrared Fourier Transform Spectrometer (FTS) has been operational at the Toronto Atmospheric Observatory (TAO)since May 2002. An optimal estimation retrieval technique is used to analyse the observed spectra and provide regular total and partial column measurements of trace gases in the troposphere and stratosphere as part of the Network for the Detection of Atmospheric Composition Change. The quality of these results were assessed through two ground-based validation campaigns, comparisons with three satellite instruments, and comparison with a three-dimensional chemical transport model. The two ground-based campaigns involved two lower-resolution FTS instruments: the University of Toronto FTS and the Portable Atmospheric Research Interferometric Spectrometer for the Infrared. The first campaign took place over the course of four months and is the longest side-by-side intercomparison of ground-based FTS instruments, to date. The second campaign was more focused and involved all three instruments measuring over a two-week period. Simultaneous measurements of O3, HCl, N2O, and CH4 were recorded and average total column differences were all < 3.7% in the extended campaign, and < 4.5% in the focused campaign. Satellite-based comparisons were done with the SCanning and Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS), and the Optical Spectrograph and InfraRed Imager System (OSIRIS). Total column CO, CH4, and N2O compared with SCIAMACHY all had average differences < 10% with results from the TAO-FTS being as good as, or better, than that of other instruments. Validation with the ACE-FTS showed that average partial columns of O3, NO2, N2O, CH4, and HCl were within 10% while observations of CO and NO each had an average bias of about 25%. Comparisons of monthly average partial column O3 and NO2 with OSIRIS were highly correlated (R = 0.82-0.97) with monthly mean differences of < 3.1% for O3 and < 2.6% for NO2. Finally, comparisons with the GEOS-Chem chemical transport model revealed that the model consistently over-estimates tropospheric columns of CO and C2H6 observed at TAO. It was determined that the enhanced CO values were partially due to the North American emissions specified in the model, but more work must be done in the future if the source of this discrepancy is to be fully explained.

I implemented and tested the method of Non-Linear Conjugate Gradients (NLCG) to invert magnetotelluric (MT) and radiomagnetotelluric (RMT) data in two dimensions. The forward problem and the objective function gradients were computed using finite-difference methods. The NLCG algorithm was applied to three field data sets to test the performance of the code. It was then compared to the inversion techniques of Occam and damped Occam considering the quality of the output resistivity models and the computation times. The implemented code was further investigated by testing two line search techniques to reduce the objective function along a given search direction. The first line search procedure was constrained to the first Wolfe condition, leading to a rather inexact line search. The second, more thorough line search, was additionally constrained to the second Wolfe condition. Three preconditioners were applied to the NLCG algorithm and their performance was analysed. The first preconditioner was set to the diagonal of the approximate Hessian matrix and updated every 20-th iteration. Preconditioners two and three were updated with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm using the identity matrix and the diagonal of the approximate Hessian matrix as start preconditioners, respectively. The tests showed that the method of NLCG is more efficient pertaining to computation times compared to the Gauss-Newton (GN) based techniques (Occam and damped Occam). For the two smaller data sets that were inverted, the NLCG inversion was two to four times faster than Occam and damped Occam. For the larger data set, the NLCG inversion converged more than one order of magnitude faster than the GN based inversion techniques. This is because GN methods require to evaluate the entire sensitivity matrix to update the model, whereas NLCG only needs to compute a matrix-vector product of the Jacobian. Moreover, expensive operations such as matrix products and direct inversions of linearised systems are avoided by NLCG. A limitation of the NLCG algorithm is that it is prone to converge to local minima due to the fixed Lagrange multiplier that is used in the penalty function. Occam inversion, which determines the optimal Lagrange multiplier as part of the inversion, did not show such problems. The line search tests of the NLCG algorithm showed that an inexact line search yields higher convergence per CPU time than a more exact line search. In accordance to previous studies, preconditioning accelerated the convergence of the NLCG algorithm considerably. The preconditioners updated with the BFGS algorithm achieved highest convergence. Choosing the identity matrix as a start preconditioner led to fast but unstable convergence. The reasons for that could not be determined completely. Taking the diagonal of the approximate Hessian as a start preconditioner instead of the identity matrix led to slower convergence for most of the inversion tests, but convergence could be stabilised. All the tests performed within this project led to a robust implementation of the NLCG algorithm. A default set-up pertaining to line search and preconditioning could be established. However, the NLCG set-up can be adjusted by the user to improve convergence for a specific data set. This makes the algorithm implemented in this thesis more flexible than previously introduced NLCG codes. Preconditioning can certainly still be improved with further tests. Moreover, a future project will be to extend the 2D code to 3D, where NLCG should perform especially well, because the number of model parameters is usually higher in 3D.

abstract: Aquifers host the largest accessible freshwater resource in the world. However, groundwater reserves are declining in many places. Often coincident with drought, high extraction rates and inadequate replenishment result in groundwater overdraft and permanent land subsidence. Land subsidence is the cause of aquifer storage capacity reduction, altered topographic gradients which can exacerbate floods, and differential displacement that can lead to earth fissures and infrastructure damage. Improving understanding of the sources and mechanisms driving aquifer deformation is important for resource management planning and hazard mitigation. Poroelastic theory describes the coupling of differential stress, strain, and pore pressure, which are modulated by material properties. To model these relationships, displacement time series are estimated via satellite interferometry and hydraulic head levels from observation wells provide an in-situ dataset. In combination, the deconstruction and isolation of selected time-frequency components allow for estimating aquifer parameters, including the elastic and inelastic storage coefficients, compaction time constants, and vertical hydraulic conductivity. Together these parameters describe the storage response of an aquifer system to changes in hydraulic head and surface elevation. Understanding aquifer parameters is useful for the ongoing management of groundwater resources. Case studies in Phoenix and Tucson, Arizona, focus on land subsidence from groundwater withdrawal as well as distinct responses to artificial recharge efforts. In Christchurch, New Zealand, possible changes to aquifer properties due to earthquakes are investigated. In Houston, Texas, flood severity during Hurricane Harvey is linked to subsidence, which modifies base flood elevations and topographic gradients. / Dissertation/Thesis / Doctoral Dissertation Geological Sciences 2018

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