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Analysis and modeling of transient earthquake patterns and their dependence on local stress regimes
(2015)
Investigations in the field of earthquake triggering and associated interactions, which includes aftershock triggering as well as induced seismicity, is important for seismic hazard assessment due to earthquakes destructive power. One of the approaches to study earthquake triggering and their interactions is the use of statistical earthquake models, which are based on knowledge of the basic seismicity properties, in particular, the magnitude distribution and spatiotemporal properties of the triggered events.
In my PhD thesis I focus on some specific aspects of aftershock properties, namely, the relative seismic moment release of the aftershocks with respect to the mainshocks; the spatial correlation between aftershock occurrence and fault deformation; and on the influence of aseismic transients on the aftershock parameter estimation. For the analysis of aftershock sequences I choose a statistical approach, in particular, the well known Epidemic Type Aftershock Sequence (ETAS) model, which accounts for the input of background and triggered seismicity. For my specific purposes, I develop two ETAS model modifications in collaboration with Sebastian Hainzl. By means of this approach, I estimate the statistical aftershock parameters and performed simulations of aftershock sequences as well.
In the case of seismic moment release of aftershocks, I focus on the ratio of cumulative seismic moment release with respect to the mainshocks. Specifically, I investigate the ratio with respect to the focal mechanism of the mainshock and estimate an effective magnitude, which represents the cumulative aftershock energy (similar to Bath's law, which defines the average difference between mainshock and the largest aftershock magnitudes). Furthermore, I compare the observed seismic moment ratios with the results of the ETAS simulations. In particular, I test a restricted ETAS (RETAS) model which is based on results of a clock advanced model and static stress triggering.
To analyze spatial variations of triggering parameters I focus in my second approach on the aftershock occurrence triggered by large mainshocks and the study of the aftershock parameter distribution and their spatial correlation with the coseismic/postseismic slip and interseismic locking. To invert the aftershock parameters I improve the modified ETAS (m-ETAS) model, which is able to take the extension of the mainshock rupture into account. I compare the results obtained by the classical approach with the output of the m-ETAS model.
My third approach is concerned with the temporal clustering of seismicity, which might not only be related to earthquake-earthquake interactions, but also to a time-dependent background rate, potentially biasing the parameter estimations. Thus, my coauthors and I also applied a modification of the ETAS model, which is able to take into account time-dependent background activity. It can be applicable for two different cases: when an aftershock catalog has a temporal incompleteness or when the background seismicity rate changes with time, due to presence of aseismic forces.
An essential part of any research is the testing of the developed models using observational data sets, which are appropriate for the particular study case. Therefore, in the case of seismic moment release I use the global seismicity catalog. For the spatial distribution of triggering parameters I exploit two aftershock sequences of the Mw8.8 2010 Maule (Chile) and Mw 9.0 2011 Tohoku (Japan) mainshocks. In addition, I use published geodetic slip models of different authors. To test our ability to detect aseismic transients my coauthors and I use the data sets from Western Bohemia (Central Europe) and California.
Our results indicate that:
(1) the seismic moment of aftershocks with respect to mainshocks depends on the static stress changes and is maximal for the normal, intermediate for thrust and minimal for strike-slip stress regimes, where the RETAS model shows a good correspondence with the results;
(2) The spatial distribution of aftershock parameters, obtained by the m-ETAS model, shows anomalous values in areas of reactivated crustal fault systems. In addition, the aftershock density is found to be correlated with coseismic slip gradient, afterslip, interseismic coupling and b-values. Aftershock seismic moment is positively correlated with the areas of maximum coseismic slip and interseismically locked areas. These correlations might be related to the stress level or to material properties variations in space;
(3) Ignoring aseismic transient forcing or temporal catalog incompleteness can lead to the significant under- or overestimation of the underlying trigger parameters. In the case when a catalog is complete, this method helps to identify aseismic sources.
Optical frequency combs (OFC) constitute an array of phase-correlated equidistant spectral lines with nearly equal intensities over a broad spectral range. The adaptations of combs generated in mode-locked lasers proved to be highly efficient for the calibration of high-resolution (resolving power > 50000) astronomical spectrographs. The observation of different galaxy structures or the studies of the Milky Way are done using instruments in the low- and medium resolution range. To such instruments belong, for instance, the Multi Unit Spectroscopic Explorer (MUSE) being developed for the Very Large Telescope (VLT) of the European Southern Observatory (ESO) and the 4-metre Multi-Object Spectroscopic Telescope (4MOST) being in development for the ESO VISTA 4.1 m Telescope. The existing adaptations of OFC from mode-locked lasers are not resolvable by these instruments.
Within this work, a fibre-based approach for generation of OFC specifically in the low- and medium resolution range is studied numerically. This approach consists of three optical fibres that are fed by two equally intense continuous-wave (CW) lasers. The first fibre is a conventional single-mode fibre, the second one is a suitably pumped amplifying Erbium-doped fibre with anomalous dispersion, and the third one is a low-dispersion highly nonlinear optical fibre. The evolution of a frequency comb in this system is governed by the following processes: as the two initial CW-laser waves with different frequencies propagate through the first fibre, they generate an initial comb via a cascade of four-wave mixing processes. The frequency components of the comb are phase-correlated with the original laser lines and have a frequency spacing that is equal to the initial laser frequency separation (LFS), i.e. the difference in the laser frequencies. In the time domain, a train of pre-compressed pulses with widths of a few pico-seconds arises out of the initial bichromatic deeply-modulated cosine-wave. These pulses undergo strong compression in the subsequent amplifying Erbium-doped fibre: sub-100 fs pulses with broad OFC spectra are formed. In the following low-dispersion highly nonlinear fibre, the OFC experience a further broadening and the intensity of the comb lines are fairly equalised. This approach was mathematically modelled by means of a Generalised Nonlinear Schrödinger Equation (GNLS) that contains terms describing the nonlinear optical Kerr effect, the delayed Raman response, the pulse self-steepening, and the linear optical losses as well as the wavelength-dependent Erbium gain profile for the second fibre. The initial condition equation being a deeply-modulated cosine-wave mimics the radiation of the two initial CW lasers. The numerical studies are performed with the help of Matlab scripts that were specifically developed for the integration of the GNLS and the initial condition according to the proposed approach for the OFC generation. The scripts are based on the Fourth-Order Runge-Kutta in the Interaction Picture Method (RK4IP) in combination with the local error method.
This work includes the studies and results on the length optimisation of the first and the second fibre depending on different values of the group-velocity dispersion of the first fibre. Such length optimisation studies are necessary because the OFC have the biggest possible broadband and exhibit a low level of noise exactly at the optimum lengths. Further, the optical pulse build-up in the first and the second fibre was studied by means of the numerical technique called Soliton Radiation Beat Analysis (SRBA). It was shown that a common soliton crystal state is formed in the first fibre for low laser input powers. The soliton crystal continuously dissolves into separated optical solitons as the input power increases. The pulse formation in the second fibre is critically dependent on the features of the pulses formed in the first fibre. I showed that, for low input powers, an adiabatic soliton compression delivering low-noise OFC occurs in the second fibre. At high input powers, the pulses in the first fibre have more complicated structures which leads to the pulse break-up in the second fibre with a subsequent degradation of the OFC noise performance. The pulse intensity noise studies that were performed within the framework of this thesis allow making statements about the noise performance of an OFC. They showed that the intensity noise of the whole system decreases with the increasing value of LFS.
Breaking down complexity
(2015)
The unbounded expressive capacity of human language cannot boil down to an infinite list of sentences stored in a finite brain. Our linguistic knowledge is rather grounded around a rule-based universal syntactic computation—called Merge—which takes categorized units in input (e.g. this and ship), and generates structures by binding words recursively into more complex hierarchies of any length (e.g. this ship; this ship sinks…). Here we present data from different fMRI datasets probing the cortical implementation of this fundamental process. We first pushed complexity down to a three-word level, to explore how Merge creates minimally hierarchical phrases and sentences. We then moved to the most fundamental two-word level, to directly assess the universal invariant nature of Merge, when no additive mechanisms are involved. Our most general finding is that Merge as the basic syntactic operation is primarily performed by confined area, namely BA 44 in the IFG. Activity reduces to its most ventral-anterior portion at the most fundamental level, following fine-grained sub-anatomical parcellation proposed for the region. The deep frontal operculum/anterior-dorsal insula (FOP/adINS), a phylogenetically older and less specialized region, rather appears to support word-accumulation processing in which the categorical information of the word is first accessed based on its lexical status, and then maintained on hold before further processing takes place. The present data confirm the general notion of BA 44 being activated as a function of complex structural hierarchy, but they go beyond this view by proposing that structural sensitivity in BA 44 is already appreciated at the lowest levels of complexity during which minimal phrase-structures are build up, and syntactic Merge is assessed. Further, they call for a redefinition of BA 44 from multimodal area to a macro-region with internal localizable functional profiles
The origin of cosmic rays was the subject of several studies for over a century. The investigations done within this dissertation are one small step to shed some more light on this mystery.
Locating the sources of cosmic rays is not trivial due to the interstellar magnetic field. However, the Hillas criterion allows us to arrive at the conclusion that supernova remnants are our main suspect for the origin of galactic cosmic rays. The mechanism by which they are accelerating particles is found within the field of shock physics as diffusive shock acceleration. To allow particles to enter this process also known as Fermi acceleration pre-acceleration processes like shock surfing acceleration and shock drift acceleration are necessary. Investigating the processes happening in the plasma shocks of supernova remnants is possible by utilising a simplified model which can be simulated on a computer using Particle-in-Cell simulations.
We developed a new and clean setup to simulate the formation of a double shock, i.e., consisting of a forward and a reverse shock and a contact discontinuity, by the collision of two counter-streaming plasmas, in which a magnetic field can be woven into. In a previous work, we investigated the processes at unmagnetised and at magnetised parallel shocks, whereas in the current work, we move our investigation on to magnetised perpendicular shocks.
Due to a much stronger confinement of the particles to the collision region the perpendicular shock develops much faster than the parallel shock. On the other hand, this leads to much weaker turbulence. We are able to find indications for shock surfing acceleration and shock drift acceleration happening at the two shocks leading to populations of pre-accelerated particles that are suitable as a seed population to be injected into further diffusive shock acceleration to be accelerated to even higher energies. We observe the development of filamentary structures in the shock ramp of the forward shock, but not at the reverse shock. This leads to the conclusion that the development of such structures in the shock ramp of quasi-perpendicular collisionless shocks might not necessarily be determined by the existence of a critical sonic Mach number but by a critical shock speed.
The results of the investigations done within this dissertation might be useful for further studies of oblique shocks and for studies using hybrid or magnetohydrodynamic simulations. Together with more sophisticated observational methods, these studies will help to bring us closer to an answer as to how particles can be accelerated in supernova remnants and eventually become cosmic rays that can be detected on Earth.
Electron transfer (ET) reactions play a crucial role in the metabolic pathways of all organisms. In biotechnological approaches, the redox properties of the protein cytochrome c (cyt c), which acts as an electron shuttle in the respiratory chain, was utilized to engineer ET chains on electrode surfaces. With the help of the biopolymer DNA, the redox protein assembles into electro active multilayer (ML) systems, providing a biocompatible matrix for the entrapment of proteins.
In this study the characteristics of the cyt c and DNA interaction were defined on the molecular level for the first time and the binding sites of DNA on cyt c were identified. Persistent cyt c/DNA complexes were formed in solution under the assembly conditions of ML architectures, i.e. pH 5.0 and low ionic strength. At pH 7.0, no agglomerates were formed, permitting the characterization of the NMR spectroscopy. Using transverse relaxation-optimized spectroscopy (TROSY)-heteronuclear single quantum coherence (HSQC) experiments, DNAs’ binding sites on the protein were identified. In particular, negatively charged AA residues, which are known interaction sites in cyt c/protein binding were identified as the main contact points of cyt c and DNA.
Moreover, the sophisticated task of arranging proteins on electrode surfaces to create functional ET chains was addressed. Therefore, two different enzyme types, the flavin dependent fructose dehydrogenase (FDH) and the pyrroloquinoline quinone dependent glucose dehydrogenase (PQQ-GDH), were tested as reaction partners of freely diffusing cyt c and cyt c immobilized on electrodes in mono- and MLs. The characterisation of the ET processes was performed by means of electrochemistry and the protein deposition was monitored by microgravimetric measurements. FDH and PQQ-GDH were found to be generally suitable for combination with the cyt c/DNA ML system, since both enzymes interact with cyt c in solution and in the immobilized state. The immobilization of FDH and cyt c was achieved with the enzyme on top of a cyt c monolayer electrode without the help of a polyelectrolyte. Combining FDH with the cyt c/DNA ML system did not succeed, yet. However, the basic conditions for this protein-protein interaction were defined. PQQ-GDH was successfully coupled with the ML system, demonstrating that that the cyt c/DNA ML system provides a suitable interface for enzymes and that the creation of signal chains, based on the idea of co-immobilized proteins is feasible.
Future work may be directed to the investigation of cyt c/DNA interaction under the precise conditions of ML assembly. Therefore, solid state NMR or X-ray crystallography may be required. Based on the results of this study, the combination of FDH with the ML system should be addressed. Moreover, alternative types of enzymes may be tested as catalytic component of the ML assembly, aiming on the development of innovative biosensor applications.
By perturbing the differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse mathematical disciplines, such as functional analysis, differential geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will be developed. From the very beginning we will consider quasicomplexes with curvature in an ideal class. We introduce the Euler characteristic, the cone of a quasiendomorphism and the Lefschetz number. In particular, we generalise Euler's identity, which will allow us to develop the Lefschetz theory on nonseparable Hilbert spaces. Finally, in the third chapter the abstract theory will be applied to elliptic quasicomplexes with pseudodifferential operators of arbitrary order. We will show that the Atiyah-Singer index formula holds true for those objects and, as an example, we will compute the Euler characteristic of the connection quasicomplex. In addition to this we introduce geometric quasiendomorphisms and prove a generalisation of the Lefschetz fixed point theorem of Atiyah and Bott.
Methicillin resistant Staphylococcus aureus (MRSA) is one of the most important antibiotic-resistant pathogens in hospitals and the community. Recently, a new generation of MRSA, the so called livestock associated (LA) MRSA, has emerged occupying food producing animals as a new niche. LA-MRSA can be regularly isolated from economically important live-stock species including corresponding meats. The present thesis takes a methodological approach to confirm the hypothesis that LA-MRSA are transmitted along the pork, poultry and beef production chain from animals at farm to meat on consumers` table. Therefore two new concepts were developed, adapted to differing data sets.
A mathematical model of the pig slaughter process was developed which simulates the change in MRSA carcass prevalence during slaughter with special emphasis on identifying critical process steps for MRSA transmission. Based on prevalences as sole input variables the model framework is able to estimate the average value range of both the MRSA elimination and contamination rate of each of the slaughter steps. These rates are then used to set up a Monte Carlo simulation of the slaughter process chain. The model concludes that regardless of the initial extent of MRSA contamination low outcome prevalences ranging between 0.15 and 1.15 % can be achieved among carcasses at the end of slaughter. Thus, the model demonstrates that the standard procedure of pig slaughtering in principle includes process steps with the capacity to limit MRSA cross contamination. Scalding and singeing were identified as critical process steps for a significant reduction of superficial MRSA contamination.
In the course of the German national monitoring program for zoonotic agents MRSA prevalence and typing data are regularly collected covering the key steps of different food production chains. A new statistical approach has been proposed for analyzing this cross sectional set of MRSA data with regard to show potential farm to fork transmission. For this purpose, chi squared statistics was combined with the calculation of the Czekanowski similarity index to compare the distributions of strain specific characteristics between the samples from farm, carcasses after slaughter and meat at retail. The method was implemented on the turkey and veal production chains and the consistently high degrees of similarity which have been revealed between all sample pairs indicate MRSA transmission along the chain.
As the proposed methods are not specific to process chains or pathogens they offer a broad field of application and extend the spectrum of methods for bacterial transmission assessment.
Synchronization of large ensembles of oscillators is an omnipresent phenomenon observed in different fields of science like physics, engineering, life sciences, etc. The most simple setup is that of globally coupled phase oscillators, where all the oscillators contribute to a global field which acts on all oscillators. This formulation of the problem was pioneered by Winfree and Kuramoto. Such a setup gives a possibility for the analysis of these systems in terms of global variables. In this work we describe nontrivial collective dynamics in oscillator populations coupled via mean fields in terms of global variables. We consider problems which cannot be directly reduced to standard Kuramoto and Winfree models.
In the first part of the thesis we adopt a method introduced by Watanabe and Strogatz. The main idea is that the system of identical oscillators of particular type can be described by a low-dimensional system of global equations. This approach enables us to perform a complete analytical analysis for a special but vast set of initial conditions. Furthermore, we show how the approach can be expanded for some nonidentical systems. We apply the Watanabe-Strogatz approach to arrays of Josephson junctions and systems of identical phase oscillators with leader-type coupling.
In the next parts of the thesis we consider the self-consistent mean-field theory method that can be applied to general nonidentical globally coupled systems of oscillators both with or without noise. For considered systems a regime, where the global field rotates uniformly, is the most important one. With the help of this approach such solutions of the self-consistency equation for an arbitrary distribution of frequencies and coupling parameters can be found analytically in the parametric form, both for noise-free and noisy cases.
We apply this method to deterministic Kuramoto-type model with generic coupling and an ensemble of spatially distributed oscillators with leader-type coupling. Furthermore, with the proposed self-consistent approach we fully characterize rotating wave solutions of noisy Kuramoto-type model with generic coupling and an ensemble of noisy oscillators with bi-harmonic coupling.
Whenever possible, a complete analysis of global dynamics is performed and compared with direct numerical simulations of large populations.
Stream water and groundwater are important fresh water resources but their water quality is deteriorated by harmful solutes introduced by human activities. The interface between stream water and the subsurface water is an important zone for retention, transformation and attenuation of these solutes. Streambed structures enhance these processes by increased water and solute exchange across this interface, denoted as hyporheic exchange.
This thesis investigates the influence of hydrological and morphological factors on hyporheic water and solute exchange as well as redox-reactions in fluvial streambed structures on the intermediate scale (10–30m). For this purpose, a three-dimensional numerical modeling approach for coupling stream water flow with porous media flow is used. Multiple steady state stream water flow scenarios over different generic pool-riffle morphologies and a natural in-stream gravel bar are simulated by a computational fluid dynamics code that provides the hydraulic head distribution at the streambed. These heads are subsequently used as the top boundary condition of a reactive transport groundwater model of the subsurface beneath the streambed. Ambient groundwater that naturally interacts with the stream water is considered in scenarios of different magnitudes of downwelling stream water (losing case) and upwelling groundwater (gaining case). Also, the neutral case, where stream stage and groundwater levels are balanced is considered. Transport of oxygen, nitrate and dissolved organic carbon and their reaction by aerobic respiration and denitrification are modeled.
The results show that stream stage and discharge primarily induce hyporheic exchange flux and solute transport with implications for specific residence times and reactions at both the fully and partially submerged structures. Gaining and losing conditions significantly diminish the extent of the hyporheic zone, the water exchange flux, and shorten residence times for both the fully and partially submerged structures. With increasing magnitude of gaining or losing conditions, these metrics exponentially decrease.
Stream water solutes are transported mainly advectively into the hyporheic zone and hence their influx corresponds directly to the infiltrating water flux. Aerobic respiration takes place in the shallow streambed sediments, coinciding to large parts with the extent of the hyporheic exchange flow. Denitrification occurs mainly as a “reactive fringe” surrounding the aerobic zone, where oxygen concentration is low and still a sufficient amount of stream water carbon source is available. The solute consumption rates and the efficiency of the aerobic and anaerobic reactions depend primarily on the available reactive areas and the residence times, which are both controlled by the interplay between hydraulic head distribution at the streambed and the gradients between stream stage and ambient groundwater. Highest solute consumption rates can be expected under neutral conditions, where highest solute flux, longest residence times and largest extent of the hyporheic exchange occur. The results of this thesis show that streambed structures on the intermediate scale have a significant potential to contribute to a net solute turnover that can support a healthy status of the aquatic ecosystem.
Continental rifts are excellent regions where the interplay between extension, the build-up of topography, erosion and sedimentation can be evaluated in the context of landscape evolution. Rift basins also constitute important archives that potentially record the evolution and migration of species and the change of sedimentary conditions as a result of climatic change. Finally, rifts have increasingly become targets of resource exploration, such as hydrocarbons or geothermal systems. The study of extensional processes and the factors that further modify the mainly climate-driven surface process regime helps to identify changes in past and present tectonic and geomorphic processes that are ultimately recorded in rift landscapes.
The Cenozoic East African Rift System (EARS) is an exemplary continental rift system and ideal natural laboratory to observe such interactions. The eastern and western branches of the EARS constitute first-order tectonic and topographic features in East Africa, which exert a profound influence on the evolution of topography, the distribution and amount of rainfall, and thus the efficiency of surface processes. The Kenya Rift is an integral part of the eastern branch of the EARS and is characterized by high-relief rift escarpments bounded by normal faults, gently tilted rift shoulders, and volcanic centers along the rift axis.
Considering the Cenozoic tectonic processes in the Kenya Rift, the tectonically controlled cooling history of rift shoulders, the subsidence history of rift basins, and the sedimentation along and across the rift, may help to elucidate the morphotectonic evolution of this extensional province. While tectonic forcing of surface processes may play a minor role in the low-strain rift on centennial to millennial timescales, it may be hypothesized that erosion and sedimentation processes impacted by climate shifts associated with pronounced changes in the availability in moisture may have left important imprints in the landscape.
In this thesis I combined thermochronological, geomorphic field observations, and morphometry of digital elevation models to reconstruct exhumation processes and erosion rates, as well as the effects of climate on the erosion processes in different sectors of the rift. I present three sets of results: (1) new thermochronological data from the northern and central parts of the rift to quantitatively constrain the Tertiary exhumation and thermal evolution of the Kenya Rift. (2) 10Be-derived catchment-wide mean denudation rates from the northern, central and southern rift that characterize erosional processes on millennial to present-day timescales; and (3) paleo-denudation rates in the northern rift to constrain climatically controlled shifts in paleoenvironmental conditions during the early Holocene (African Humid Period).
Taken together, my studies show that time-temperature histories derived from apatite fission track (AFT) analysis, zircon (U-Th)/He dating, and thermal modeling bracket the onset of rifting in the Kenya Rift between 65-50 Ma and about 15 Ma to the present. These two episodes are marked by rapid exhumation and, uplift of the rift shoulders. Between 45 and 15 Ma the margins of the rift experienced very slow erosion/exhumation, with the accommodation of sediments in the rift basin.
In addition, I determined that present-day denudation rates in sparsely vegetated parts of the Kenya Rift amount to 0.13 mm/yr, whereas denudation rates in humid and more densely vegetated sectors of the rift flanks reach a maximum of 0.08 mm/yr, despite steeper hillslopes. I inferred that hillslope gradient and vegetation cover control most of the variation in denudation rates across the Kenya Rift today. Importantly, my results support the notion that vegetation cover plays a fundamental role in determining the voracity of erosion of hillslopes through its stabilizing effects on the land surface.
Finally, in a pilot study I highlighted how paleo-denudation rates in climatic threshold areas changed significantly during times of transient hydrologic conditions and involved a sixfold increase in erosion rates during increased humidity. This assessment is based on cosmogenic nuclide (10Be) dating of quartzitic deltaic sands that were deposited in the northern Kenya Rift during a highstand of Lake Suguta, which was associated with the Holocene African Humid Period. Taken together, my new results document the role of climate variability in erosion processes that impact climatic threshold environments, which may provide a template for potential future impacts of climate-driven changes in surface processes in the course of Global Change.