988 research outputs found

    Improved modeling of segmented earthquake rupture informed by enhanced signal analysis of seismic and geodetic observations

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    Earthquake source modeling has emerged from the need to be able to describe and quantifythe mechanism and physical properties of earthquakes. Investigations of earthquake ruptureand fault geometry requires the testing of a large number of such potential sets of earthquakesources models. Earthquakes often rupture across more than one fault segment. If such rupturesegmentation occurs on a significant scale, a simple model may not represent the rupture processwell. This thesis focuses on the data-driven inclusion of earthquake rupture segmentation intoearthquake source modeling. The developed tools and the modeling are based on the jointuse of seismological waveform far-field and geodetic Interferometric Synthetic Aperture Radarnear-field surface displacement maps to characterise earthquake sources robustly with rigorousconsideration of data and modeling errors.A strategy based on information theory is developed to determine the appropriate modelcomplexity to represent the available observations in a data-driven way. This is done inconsideration of the uncertainties in the determined source mechanisms by investigating theinferences of the full Bayesian model ensemble. Application on the datasets of four earthquakesindicated that the inferred source parameters are systematically biased by the choice of modelcomplexity. This might have effects on follow-up analyses, e. g. regional stress field inversionsand seismic hazard assessments.Further, two methods were developed to provide data-driven model-independent constraints toinform a kinematic earthquake source optimization about earthquake source parameter priorestimates. The first method is a time-domain multi-array backprojection of teleseismic datawith empirical traveltime corrections to infer the spatio-temporal evolution of the rupture. Thisenables detection of potential rupture segmentation based on the occurrence of coherent high-frequency sources during the rupture process. The second developed method uses image analysismethods on satellite radar measured surface displacement maps to infer modeling constraints onrupture characteristics (e.g. strike and length) and the number of potential segments. These twomethods provide model-independent constraints on fault location, dimension, orientation andrupture timing. The inferred source parameter constraints are used to constrain an inversion forthe source mechanism of the 2016 Muji Mw 6.6 earthquake, a segmented and bilateral strike-slipearthquake.As a case study to further investigate a depth-segmented fault system and occurrence of co-seismic rupture segmentation in such a system the 2008-2009 Qaidam sequence with co-seismicand post-seismic displacements is investigated. The Qaidam 2008-2009 earthquake sequence innortheast Tibet involved two reverse-thrust earthquakes and a postseismic signal of the 2008earthquake. The 2008 Qaidam earthquake is modeled as a deep shallow dipping earthquakewith no indication of rupture segmentation. The 2009 Qaidam earthquake is modeled on threedistinct south-dipping high-angle thrusts, with a bilateral and segmented rupture process. Agood agreement between co-seismic surface displacement measurements and coherent seismicenergy emission in the backprojection results is determined.Finally, a combined framework is proposed which applies all the developed methods and tools inan informed parallel modeling of several earthquake source model complexities. This frameworkallows for improved routine determination of earthquake source modeling under considerationof rupture segmentation. This thesis provides overall an improvement for earthquake sourceanalyses and the development of modeling standards for robust determination of second-orderearthquake source parameters

    Probabilistic waveform inversion: Quest for the law

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    Full-waveform inversion (FWI) is an algorithm (and a part of the measuring procedure in a wide sense) with the aim to find the governing law of a physical system using the partially measured physical fields with limited computational resources. A law is a forward theory equipped with the model parameters and the data parameters. The main characteristic of the law is the realizability assumption: the law explains all subsets of the measured data parameters and predicts all subsets of the unmeasured (in the given experiment) data parameters. To find the law, we have to guess a law (a forward theory and parametrization), measure some data parameters and check the realizability assumption. To put it more precisely, I formulate a new probabilistic setting for inverse problems and full-waveform inversion. Instead of using the Bayes\u27 theorem, the Tarantola-Valette conjunction or the principle of maximum entropy based on the prior information for the averaged quantities, I propose a principle of minimum relative information using the prior information for the non-averaged quantities. The Tarantola-Valette formula is obtained as a special case under the assumption that the theoretical and prior measures exist. Using the realizability assumption as a prior information, the principle of minimum relative information provides the parametric probabilistic solution with the arbitrary misfit functions. Maximization of the parametric probabilistic solution leads to a multiobjective minimization problem. All global Pareto optima are the sample points of the probabilistic solution with the highest values of the volumetric measure. Unfortunately, even a local multiobjective minimization problem is computationally intractable for FWI with many millions of model parameters. To make it computationally attractive for large-scale FWI and to find at least a few local solutions of the multiobjective minimization problem, I implement the bilevel multiobjective waveform inversion (BMWI) using a single randomly chosen shot gather at each iteration. BMWI is a stochastic, nested algorithm with an adaptive parabolic line search and multiscale strategy. The computational cost per iteration is five forward modellings only. BMWI can worsen some of the single-shot misfit functions and the different random runs of BMWI converge to different points in the model manifold. I interpret these inverted models as the sample points of the probabilistic solution. I estimate the solution, uncertainty and sensitivity using the sample estimates of the mean, standard deviation and initial deviation of the sample points, respectively. Using the numerical examples with the Marmousi-2 model, I illustrate the potential of BMWI for automatic uncertainty and sensitivity analysis with just two-three sample points. To test the idea with real-world data, I apply stochastic single-shot BMWI in a 2D acoustic finite-difference approximation to a 2D line of pressure data acquired in a shallow-water river delta with ocean bottom cables. I use minimal data preprocessing (only a new 3D-to-2D transform which is strictly valid in a linear-gradient medium), the linear gradient starting models and the diagonal preconditioners with a negligible regularization. I estimate the theoretical uncertainties due to the neglected 3D effects using the 3D-to-2D transforms. The uncertainties estimated by the random sequences of BMWI are higher than the uncertainties related to the 3D-to-2D transforms. I provide the estimates of the solution, uncertainty and sensitivity using up to fourteen sample points inverted with the different linear-gradient starting models, the differently 3D-to-2D-transformed real data sets and the different random sequences of descent directions. The uncertainty of sound velocities is the lowest in the central semicircle with the radius 3 km equal to half the length of the ocean bottom cable. The uncertainty of mass densities is the highest in the central semicircle. The sensitivity of the measuring procedure with respect to sound velocity and mass density is the highest in the central semicircle representing a footprint of the acquisition geometry. Outside the central semicircle the parameters are not falsifiable in the specified setting. Full-waveform inversion is the quest for the unique governing law of the physical system under study. If the governing law is deterministic and the sample mean, standard deviation and initial deviation of the sample points represent the insufficient description of the solution, uncertainty and sensitivity, then the measuring procedure in a wide sense has to be improved

    A Fully Parallelized and Budgeted Multi-level Monte Carlo Framework for Partial Differential Equations: From Mathematical Theory to Automated Large-Scale Computations

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    All collected data on any physical, technical or economical process is subject to uncertainty. By incorporating this uncertainty in the model and propagating it through the system, this data error can be controlled. This makes the predictions of the system more trustworthy and reliable. The multi-level Monte Carlo (MLMC) method has proven to be an effective uncertainty quantification tool, requiring little knowledge about the problem while being highly performant. In this doctoral thesis we analyse, implement, develop and apply the MLMC method to partial differential equations (PDEs) subject to high-dimensional random input data. We set up a unified framework based on the software M++ to approximate solutions to elliptic and hyperbolic PDEs with a large selection of finite element methods. We combine this setup with a new variant of the MLMC method. In particular, we propose a budgeted MLMC (BMLMC) method which is capable to optimally invest reserved computing resources in order to minimize the model error while exhausting a given computational budget. This is achieved by developing a new parallelism based on a single distributed data structure, employing ideas of the continuation MLMC method and utilizing dynamic programming techniques. The final method is theoretically motivated, analyzed, and numerically well-tested in an automated benchmarking workflow for highly challenging problems like the approximation of wave equations in randomized media

    Proceedings of the International Workshop on Medical Ultrasound Tomography: 1.- 3. Nov. 2017, Speyer, Germany

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    Ultrasound Tomography is an emerging technology for medical imaging that is quickly approaching its clinical utility. Research groups around the globe are engaged in research spanning from theory to practical applications. The International Workshop on Medical Ultrasound Tomography (1.-3. November 2017, Speyer, Germany) brought together scientists to exchange their knowledge and discuss new ideas and results in order to boost the research in Ultrasound Tomography

    Ultrasound medical imaging using 2d viscoacoustic full-waveform inversion = Medizinische Bildgebung mit Ultraschall unter Nutzung der 2d viskoakustischen Wellenfeldinversion

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    In dieser Arbeit führe ich eine ausführliche Literaturrecherche bezüglich der Brustbildgebung mit Ultraschall durch, wobei der Schwerpunkt auf bisherigen Anwendungen der Wellenfeldinversion (WFI) in diesem Forschungsgebiet liegt, untersuche das Potential der zweidimensionalen viskoakustischen WFI mit Hilfe von Rekonstruktionstests mit einem anatomiegetreuen numerischen Brustmodell unter optimalen Bedingungen und prüfe ob sich Datensätze, welche mit dem KIT 3D USCT II, dem ersten automatisierten Brustultraschallsystem mit einer vollständig dreidimensionalen Aufnahmegeometrie, aufgenommen wurden, mit dreidimensionaler WFI ausgewertet werden können. Die synthetischen Tests zeigen, dass die Schallgeschwindigkeit und Dämpfung mit hoher Genauigkeit rekonstruiert werden können, auch wenn niedrige Frequenzen genutzt werden. Die Nutzung niedriger Frequenzen ist in zweierlei Hinsicht von Vorteil, da diese eine hohe Stabilität der Inversion gewährleistet und gleichzeitig den nötigen Rechenaufwand reduziert. Die Durchführbarkeitsstudie befasst sich mit mehreren Herausforderungen, welchen man sich bei der Anwendung der dreidimensionalen WFI stellen muss, wie zum Beispiel die Berücksichtigung der Abstrahl- und Empfangscharakteristik der verwendeten Ultraschallsonden und Bewegungen der Brust während der Messungen. Es sind viel zu wenige Empfänger installiert, weshalb der räumliche Alias-Effekt Artefakte in den Gradienten hervorruft und nur eine sehr geringe Auflösung erreicht werden kann. Ich komme zu dem Ergebnis, dass eine Anwendung der dreidimensionalen WFI auf Daten des KIT 3D USCT II den extrem hohen Rechenaufwand nicht wert ist, da bei einer so stark begrenzten Auflösung das Potenzial der WFI nicht ausgeschöpft werden würde
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