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Detection and Kirchhoff-type migration of seismic events by use of a new characteristic function
(2017)

The classical method of seismic event localization is based on the picking of body wave arrivals, ray tracing and inversion of travel time data. Travel time picks with small uncertainties are required to produce reliable and accurate results with this kind of source localization. Hence recordings, with a low Signal-to-Noise Ratio (SNR) cannot be used in a travel time based inversion. Low SNR can be related with weak signals from distant and/or low magnitude sources as well as with a high level of ambient noise. Diffraction stacking is considered as an alternative seismic event localization method that enables also the processing of low SNR recordings by mean of stacking the amplitudes of seismograms along a travel time function. The location of seismic event and its origin time are determined based on the highest stacked amplitudes (coherency) of the image function. The method promotes an automatic processing since it does not need travel time picks as input data.
However, applying diffraction stacking may require longer computation times if only limited computer resources are used. Furthermore, a simple diffraction stacking of recorded amplitudes could possibly fail to locate the seismic sources if the focal mechanism leads to complex radiation patterns which typically holds for both natural and induced seismicity.
In my PhD project, I have developed a new work flow for the localization of seismic events which is based on a diffraction stacking approach. A parallelized code was implemented for the calculation of travel time tables and for the determination of an image function to reduce computation time. In order to address the effects from complex source radiation patterns, I also suggest to compute diffraction stacking from a characteristic function (CF) instead of stacking the original wave form data. A new CF, which is called in the following mAIC (modified from Akaike Information Criterion) is proposed. I demonstrate that, the performance of the mAIC does not depend on the chosen length of the analyzed time window and that both P- and S-wave onsets can be detected accurately. To avoid cross-talk between P- and S-waves due to inaccurate velocity models, I separate the P- and S-waves from the mAIC function by making use of polarization attributes. Then, eventually the final image function is represented by the largest eigenvalue as a result of the covariance analysis between P- and S-image functions. Before applying diffraction stacking, I also apply seismogram denoising by using Otsu thresholding in the time-frequency domain.
Results from synthetic experiments show that the proposed diffraction stacking provides reliable results even from seismograms with low SNR=1. Tests with different presentations of the synthetic seismograms (displacement, velocity, and acceleration) shown that, acceleration seismograms deliver better results in case of high SNR, whereas displacement seismograms provide more accurate results in case of low SNR recordings. In another test, different measures (maximum amplitude, other statistical parameters) were used to determine the source location in the final image function. I found that the statistical approach is the preferred method particularly for low SNR.
The work flow of my diffraction stacking method was finally applied to local earthquake data from Sumatra, Indonesia. Recordings from a temporary network of 42 stations deployed for 9 months around the Tarutung pull-apart Basin were analyzed. The seismic event locations resulting from the diffraction stacking method align along a segment of the Sumatran Fault. A more complex distribution of seismicity is imaged within and around the Tarutung Basin. Two lineaments striking N-S were found in the middle of the Tarutung Basin which support independent results from structural geology. These features are interpreted as opening fractures due to local extension. A cluster of seismic events repeatedly occurred in short time which might be related to fluid drainage since two hot springs are observed at the surface near to this cluster.

Im Graduiertenkolleg NatRiskChange der Universität Potsdam und anderen Forschungseinrichtungen werden beobachtete sowie zukünftig mögliche Veränderungen von Naturgefahren untersucht. Teil des strukturierten Doktorandenprogramms sind sogenannte Task-Force-Einsätze, bei denen die Promovierende zeitlich begrenzt ein aktuelles Ereignis auswerten. Im Zuge dieser Aktivität wurde die Sturzflut vom 29.05.2016 in Braunsbach (Baden-Württemberg) untersucht.
In diesem Bericht werden erste Auswertungen zur Einordnung der Niederschläge, zu den hydrologischen und geomorphologischen Prozessen im Einzugsgebiet des Orlacher Bachs sowie zu den verursachten Schäden beleuchtet.
Die Region war Zentrum extremer Regenfälle in der Größenordnung von 100 mm innerhalb von 2 Stunden. Das 6 km² kleine Einzugsgebiet hat eine sehr schnelle Reaktionszeit, zumal bei vorgesättigtem Boden. Im steilen Bachtal haben mehrere kleinere und größere Hangrutschungen über 8000 m³ Geröll, Schutt und Schwemmholz in das Gewässer eingetragen und möglicherweise kurzzeitige Aufstauungen und Durchbrüche verursacht. Neben den großen Wassermengen mit einer Abflussspitze in einer Größenordnung von 100 m³/s hat gerade die Geschiebefracht zu großen Schäden an den Gebäuden entlang des Bachlaufs in Braunsbach geführt.

Model-Based attribution of high-resolution streamflow trends in two alpine basins of Western Austria
(2017)

Several trend studies have shown that hydrological conditions are changing considerably in the Alpine region. However, the reasons for these changes are only partially understood and trend analyses alone are not able to shed much light. Hydrological modelling is one possible way to identify the trend drivers, i.e., to attribute the detected streamflow trends, given that the model captures all important processes causing the trends. We modelled the hydrological conditions for two alpine catchments in western Austria (a large, mostly lower-altitude catchment with wide valley plains and a nested high-altitude, glaciated headwater catchment) with the distributed, physically-oriented WaSiM-ETH model, which includes a dynamical glacier module. The model was calibrated in a transient mode, i.e., not only on several standard goodness measures and glacier extents, but also in such a way that the simulated streamflow trends fit with the observed ones during the investigation period 1980 to 2007. With this approach, it was possible to separate streamflow components, identify the trends of flow components, and study their relation to trends in atmospheric variables. In addition to trends in annual averages, highly resolved trends for each Julian day were derived, since they proved powerful in an earlier, data-based attribution study. We were able to show that annual and highly resolved trends can be modelled sufficiently well. The results provide a holistic, year-round picture of the drivers of alpine streamflow changes: Higher-altitude catchments are strongly affected by earlier firn melt and snowmelt in spring and increased ice melt throughout the ablation season. Changes in lower-altitude areas are mostly caused by earlier and lower snowmelt volumes. All highly resolved trends in streamflow and its components show an explicit similarity to the local temperature trends. Finally, results indicate that evapotranspiration has been increasing in the lower altitudes during the study period.

Meteorological extreme events have great potential for damaging railway infrastructure and posing risks to the safety of train passengers. In the future, climate change will presumably have serious implications on meteorological hazards in the Alpine region. Hence, attaining insights on future frequencies of meteorological extremes with relevance for the railway operation in Austria is required in the context of a comprehensive and sustainable natural hazard management plan of the railway operator. In this study, possible impacts of climate change on the frequencies of so-called critical meteorological conditions (CMCs) between the periods 1961-1990 and 2011-2040 are analyzed. Thresholds for such CMCs have been defined by the railway operator and used in its weather monitoring and early warning system. First, the seasonal climate change signals for air temperature and precipitation in Austria are described on the basis of an ensemble of high-resolution Regional Climate Model (RCM) simulations for Europe. Subsequently, the RCM-ensemble was used to investigate changes in the frequency of CMCs. Finally, the sensitivity of results is analyzed with varying threshold values for the CMCs. Results give robust indications for an all-season air temperature rise, but show no clear tendency in average precipitation. The frequency analyses reveal an increase in intense rainfall events and heat waves, whereas heavy snowfall and cold days are likely to decrease. Furthermore, results indicate that frequencies of CMCs are rather sensitive to changes of thresholds. It thus emphasizes the importance to carefully define, validate, andif neededto adapt the thresholds that are used in the weather monitoring and warning system of the railway operator. For this, continuous and standardized documentation of damaging events and near-misses is a pre-requisite.

Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms, and urban growth is one of the most eminent transformative processes. We analyze global land cover data and extract cities as defined by maximally connected urban clusters. The analysis of the city size distribution for all cities on the globe confirms Zipf’s law. Moreover, by investigating the percolation properties of the clustering of urban areas we assess the closeness to criticality for various countries. At the critical thresholds, the urban land cover of the countries undergoes a transition from separated clusters to a gigantic component on the country scale. We study the Zipf-exponents as a function of the closeness to percolation and find a systematic dependence, which could be the reason for deviating exponents reported in the literature. Moreover, we investigate the average size of the clusters as a function of the proximity to percolation and find country specific behavior. By relating the standard deviation and the average of cluster sizes—analogous to Taylor’s law—we suggest an alternative way to identify the percolation transition. We calculate spatial correlations of the urban land cover and find long-range correlations. Finally, by relating the areas of cities with population figures we address the global aspect of the allometry of cities, finding an exponent δ ≈ 0.85, i.e., large cities have lower densities.

In der vorliegenden Arbeit wird die planetare Grenzschicht in Ny-Ålesund, Spitzbergen, sowohl bezüglich kleinskaliger („mikrometeorologischer“) Effekte als auch in ihrer Kopplung mit der Synoptik untersucht. Dazu werden verschiedene Beobachtungsdaten aus der Säule und in Bodennähe zusammengezogen und bewertet. Die so gewonnenen Datensätze werden dann zur Validierung eines nicht-hydrostatischen, regionalen Klimamodells genutzt. Weiterhin werden orographisch bedingte Einflüsse, die Untergrundbeschaffenheit und die lokale Heterogenität der Unterlage untersucht. Hierzu werden meteorologische Größen, wie die Variabilität der Temperatur und insbesondere die jährliche Windverteilung in Bodennähe untersucht und es erfolgt ein Vergleich von in-situ gemessenen turbulenten Flüssen von den Eddy-Kovarianz-Messkomplexen bei Ny-Ålesund und im Bayelva-Tal unter demselben Aspekt. Es zeigt sich, dass der Eddy-Kovarianz-Messkomplex im Bayelva-Tal sehr stark durch eine orographisch bedingte Kanalisierung der Strömung beeinflusst ist und sich nicht für Vergleiche mit regionalen Klimamodellen mit horizontalen Auflösungen von <1km eignet. Die hohe Bodenfeuchte im Bayelva-Tal führt zudem zu einem deutlich kleineren Bowen-Verhältnis, als es für diese Region zu erwarten ist. Der Eddy-Kovarianz-Messkomplex bei Ny-Ålesund erweist sich hingegen als geeigneter für solche Modellvergleiche, aufgrund der typischen, küstennahen Windverteilung und des repräsentativen Footprints. Letzteres wird durch die Bestimmung der Footprint-Klimatologie des Jahres 2013 mit einem aktuellen Footprint-Modell erarbeitet.
Weiterhin wird die Auswirkung von (Anti-) Zyklonen über den Archipel auf die zeitliche Variabilität der lokalen Grenzschichteigenschaften untersucht und bewertet. Dazu wird ein Zyklonen-Detektions-Algorithmus auf ERA-Interim-Reanalysedatensätze angewendet, wodurch die Häufigkeit von nahezu ideal konzentrischen Hoch- und die Tiefdruckgebieten für drei Jahre bestimmt wird. Aus dieser Verteilung werden insgesamt drei interessante Zeiträume zu verschiedenen Jahreszeiten ausgewählt und im Rahmen von Prozessstudien die lokalen bodennahen meteorologischen Messungen, der turbulente Austausch an der Oberfläche und die Grenzschichtdynamik in der Säule untersucht. Die zeitliche Variabilität der dynamischen Grenzschichtstabilität in der Säule wird anhand von zeitlich hoch aufgelösten vertikalen Profilen der Bulk-Richardson-Zahl aus Kompositprofilen aus Fernerkundungsinstrumenten (Radiometer, Wind-LIDAR) sowie Mastdaten (BSRN-Mast) untersucht und die Grenzschichthöhe ermittelt. Aus diesen Analysen ergibt sich eine deutliche Abhängigkeit der thermischen Stabilität beim Durchzug von Fronten, eine damit einhergehende erhebliche Abhängigkeit der Grenzschichtdynamik und der Grenzschichthöhe sowie des turbulenten Austauschs von der zeitlichen Variabilität der Windgeschwindigkeit in der Säule.
Auf Grundlage der Standortanalysen und Prozessstudien erfolgt ein Vergleich der bodennahen Messungen und den Beobachtungen aus der Säule, sowohl von den genannten Fernerkundungsinstrumenten als auch von In-situ-Messungen (Radiosonden) für den Zeitraum einer Radiosondierungskampagne mit dem nicht-hydrostatischen, regionalen Klimamodel WRF (ARW). Auf Grundlage der Fragestellung, inwieweit aktuelle Schemata die Grenzschichtcharakteristika in orographisch stark gegliedertem Gelände in der Arktis reproduzieren können, werden zwei Grenzschichtparametrisierungsschemata mit verschiedenen Ordnungen der Schließung validiert. Hierzu wird die zeitliche Variabilität der Temperatur, der Feuchte und des Windfeldes in der Säule bis 2000m in den Simulationen mit den Beobachtungsdaten vergleichen. Es wird gezeigt, dass durch Modifikation der Initialwertfelder eine sehr gute Übereinstimmung zwischen den Simulationen und den Beobachtungen bereits bei einer horizontalen Auflösung von 1km erreicht werden kann und die Wahl des Grenzschichtschemas nur untergeordneten Einfluss hat. Hieraus werden Ansätze der Weiterentwicklung der Parametrisierungen, aber auch Empfehlungen bezüglich der Initialwertfelder, wie der Landmaske und der Orographie, vorgeschlagen.

Borehole instabilities are frequently encountered when drilling through finely laminated, organic rich shales (Økland and Cook, 1998; Ottesen, 2010; etc.); such instabilities should be avoided to assure a successful exploitation and safe production of the contained unconventional hydrocarbons. Borehole instabilities, such as borehole breakouts or drilling induced tensile fractures, may lead to poor cementing of the borehole annulus, difficulties with recording and interpretation of geophysical logs, low directional control and in the worst case the loss of the well. If these problems are not recognized and expertly remedied, pollution of the groundwater or the emission of gases into the atmosphere can occur since the migration paths of the hydrocarbons in the subsurface are not yet fully understood (e.g., Davies et al., 2014; Zoback et al., 2010). In addition, it is often mentioned that the drilling problems encountered and the resulting downtimes of the wellbore system in finely laminated shales significantly increase drilling costs (Fjaer et al., 2008; Aadnoy and Ong, 2003).
In order to understand and reduce the borehole instabilities during drilling in unconventional shales, we investigate stress-induced irregular extensions of the borehole diameter, which are also referred to as borehole breakouts. For this purpose, experiments with different borehole diameters, bedding plane angles and stress boundary conditions were performed on finely laminated Posidonia shales. The Lower Jurassic Posidonia shale is one of the most productive source rocks for conventional reservoirs in Europe and has the greatest potential for unconventional oil and gas in Europe (Littke et al., 2011).
In this work, Posidonia shale specimens from the North (PN) and South (PS) German basins were selected and characterized petrophysically and mechanically. The composition of the two shales is dominated by calcite (47-56%) followed by clays (23-28%) and quartz (16-17%). The remaining components are mainly pyrite and organic matter. The porosity of the shales varies considerably and is up to 10% for PS and 1% for PN, which is due to a larger deposition depth of PN. Both shales show marked elasticity and strength anisotropy, which can be attributed to a macroscopic distribution and orientation of soft and hard minerals. Under load the hard minerals form a load-bearing, supporting structure, while the soft minerals compensate the deformation. Therefore, if loaded parallel to the bedding, the Posidonia shale is more brittle than loaded normal to the bedding. The resulting elastic anisotropy, which can be defined by the ratio of the modulus of elasticity parallel and normal to the bedding, is about 50%, while the strength anisotropy (i.e., the ratio of uniaxial compressive strength normal and parallel to the bedding) is up to 66%. Based on the petrophysical characterization of the two rocks, a transverse isotropy (TVI) was derived. In general, PS is softer and weaker than PN, which is due to the stronger compaction of the material due to the higher burial depth.
Conventional triaxial borehole breakout experiments on specimens with different borehole diameters showed that, when the diameter of the borehole is increased, the stress required to initiate borehole breakout decreases to a constant value. This value can be expressed as the ratio of the tangential stress and the uniaxial compressive strength of the rock. The ratio increases exponentially with decreasing borehole diameter from about 2.5 for a 10 mm diameter hole to ~ 7 for a 1 mm borehole (increase of initiation stress by 280%) and can be described by a fracture mechanic based criterion. The reduction in borehole diameter is therefore a considerable aspect in reducing the risk of breakouts. New drilling techniques with significantly reduced borehole diameters, such as "fish-bone" holes, are already underway and are currently being tested (e.g., Xing et al., 2012).
The observed strength anisotropy and the TVI material behavior are also reflected in the observed breakout processes at the borehole wall. Drill holes normal to the bedding develop breakouts in a plane of isotropy and are not affected by the strength or elasticity anisotropy. The observed breakouts are point-symmetric and form compressive shear failure planes, which can be predicted by a Mohr-Coulomb failure approach. If the shear failure planes intersect, conjugate breakouts can be described as "dog-eared” breakouts.
While the initiation of breakouts for wells oriented normal to the stratification has been triggered by random local defects, reduced strengths parallel to bedding planes are the starting point for breakouts for wells parallel to the bedding. In the case of a deflected borehole trajectory, therefore, the observed failure type changes from shear-induced failure surfaces to buckling failure of individual layer packages. In addition, the breakout depths and widths increased, resulting in a stress-induced enlargement of the borehole cross-section and an increased output of rock material into the borehole. With the transition from shear to buckling failure and changing bedding plane angle with respect to the borehole axis, the stress required for inducing wellbore breakouts drops by 65%.
These observations under conventional triaxial stress boundary conditions could also be confirmed under true triaxial stress conditions. Here breakouts grew into the rock as a result of buckling failure, too. In this process, the broken layer packs rotate into the pressure-free drill hole and detach themselves from the surrounding rock by tensile cracking. The final breakout shape in Posidonia shale can be described as trapezoidal when the bedding planes are parallel to the greatest horizontal stress and to the borehole axis. In the event that the largest horizontal stress is normal to the stratification, breakouts were formed entirely by shear fractures between the stratification and required higher stresses to initiate similar to breakouts in conventional triaxial experiments with boreholes oriented normal to the bedding.
In the content of this work, a fracture mechanics-based failure criterion for conventional triaxial loading conditions in isotropic rocks (Dresen et al., 2010) has been successfully extended to true triaxial loading conditions in the transverse isotropic rock to predict the initiation of borehole breakouts. The criterion was successfully verified on the experiments carried out.
The extended failure criterion and the conclusions from the laboratory and numerical work may help to reduce the risk of borehole breakouts in unconventional shales.

Quantitative thermodynamic and geochemical modeling is today applied in a variety of geological environments from the petrogenesis of igneous rocks to the oceanic realm. Thermodynamic calculations are used, for example, to get better insight into lithosphere dynamics, to constrain melting processes in crust and mantle as well as to study fluid-rock interaction. The development of thermodynamic databases and computer programs to calculate equilibrium phase diagrams have greatly advanced our ability to model geodynamic processes from subduction to orogenesis. However, a well-known problem is that despite its broad application the use and interpretation of thermodynamic models applied to natural rocks is far from straightforward. For example, chemical disequilibrium and/or unknown rock properties, such as fluid activities, complicate the application of equilibrium thermodynamics.
One major aspect of the publications presented in this Habilitationsschrift are new approaches to unravel dynamic and chemical histories of rocks that include applications to chemically open system behaviour. This approach is especially important in rocks that are affected by element fractionation due to fractional crystallisation and fluid loss during dehydration reactions. Furthermore, chemically open system behaviour has also to be considered for studying fluid-rock interaction processes and for extracting information from compositionally zoned metamorphic minerals. In this Habilitationsschrift several publications are presented where I incorporate such open system behaviour in the forward models by incrementing the calculations and considering changing reacting rock compositions during metamorphism. I apply thermodynamic forward modelling incorporating the effects of element fractionation in a variety of geodynamic and geochemical applications in order to better understand lithosphere dynamics and mass transfer in solid rocks.
In three of the presented publications I combine thermodynamic forward models with trace element calculations in order to enlarge the application of geochemical numerical forward modeling. In these publications a combination of thermodynamic and trace element forward modeling is used to study and quantify processes in metamorphic petrology at spatial scales from µm to km. In the thermodynamic forward models I utilize Gibbs energy minimization to quantify mineralogical changes along a reaction path of a chemically open fluid/rock system. These results are combined with mass balanced trace element calculations to determine the trace element distribution between rock and melt/fluid during the metamorphic evolution. Thus, effects of mineral reactions, fluid-rock interaction and element transport in metamorphic rocks on the trace element and isotopic composition of minerals, rocks and percolating fluids or melts can be predicted.
One of the included publications shows that trace element growth zonations in metamorphic garnet porphyroblasts can be used to get crucial information about the reaction path of the investigated sample. In order to interpret the major and trace element distribution and zoning patterns in terms of the reaction history of the samples, we combined thermodynamic forward models with mass-balance rare earth element calculations. Such combined thermodynamic and mass-balance calculations of the rare earth element distribution among the modelled stable phases yielded characteristic zonation patterns in garnet that closely resemble those in the natural samples. We can show in that paper that garnet growth and trace element incorporation occurred in near thermodynamic equilibrium with matrix phases during subduction and that the rare earth element patterns in garnet exhibit distinct enrichment zones that fingerprint the minerals involved in the garnet-forming reactions.
In two of the presented publications I illustrate the capacities of combined thermodynamic-geochemical modeling based on examples relevant to mass transfer in subduction zones. The first example focuses on fluid-rock interaction in and around a blueschist-facies shear zone in felsic gneisses, where fluid-induced mineral reactions and their effects on boron (B) concentrations and isotopic compositions in white mica are modeled. In the second example, fluid release from a subducted slab and associated transport of B and variations in B concentrations and isotopic compositions in liberated fluids and residual rocks are modeled. I show that, combined with experimental data on elemental partitioning and isotopic fractionation, thermodynamic forward modeling unfolds enormous capacities that are far from exhausted.
In my publications presented in this Habilitationsschrift I compare the modeled results to geochemical data of natural minerals and rocks and demonstrate that the combination of thermodynamic and geochemical models enables quantification of metamorphic processes and insights into element cycling that would have been unattainable so far.
Thus, the contributions to the science community presented in this Habilitatonsschrift concern the fields of petrology, geochemistry, geochronology but also ore geology that all use thermodynamic and geochemical models to solve various problems related to geo-materials.

The timing and location of the two largest earthquakes of the 21st century (Sumatra, 2004 and Tohoku 2011, events) greatly surprised the scientific community, indicating that the deformation processes that precede and follow great megathrust earthquakes remain enigmatic. During these phases before and after the earthquake a combination of multi-scale complex processes are acting simultaneously: Stresses built up by long-term tectonic motions are modified by sudden jerky deformations during earthquakes, before being restored by multiple ensuing relaxation processes.
This thesis details a cross-scale thermomechanical model developed with the aim of simulating the entire subduction process from earthquake (1 minute) to million years’ time scale, excluding only rupture propagation. The model employs elasticity, non-linear transient viscous rheology, and rate-and-state friction. It generates spontaneous earthquake sequences, and, by using an adaptive time-step algorithm, recreates the deformation process as observed naturally over single and multiple seismic cycles. The model is thoroughly tested by comparing results to those from known high- resolution solutions of generic modeling setups widely used in modeling of rupture propagation. It is demonstrated, that while not modeling rupture propagation explicitly, the modeling procedure correctly recognizes the appearance of instability (earthquake) and correctly simulates the cumulative slip at a fault during great earthquake by means of a quasi-dynamic approximation.
A set of 2D models is used to study the effects of non-linear transient rheology on the postseismic processes following great earthquakes. Our models predict that the viscosity in the mantle wedge drops by 3 to 4 orders of magnitude during a great earthquake with magnitude above 9. This drop in viscosity results in spatial scales and timings of the relaxation processes following the earthquakes that are significantly different to previous estimates. These models replicate centuries long seismic cycles exhibited by the greatest earthquakes (like the Great Chile 1960 Earthquake) and are consistent with the major features of postseismic surface displacements recorded after the Great Tohoku Earthquake.
The 2D models are also applied to study key factors controlling maximum magnitudes of earthquakes in subduction zones. Even though methods of instrumentally observing earthquakes at subduction zones have rapidly improved in recent decades, the characteristic recurrence interval of giant earthquakes (Mw>8.5) is much larger than the currently available observational record and therefore the necessary conditions for giant earthquakes are not clear. Statistical studies have recognized the importance of the slab shape and its surface roughness, state of the strain of the upper plate and thickness of sediments filling the trenches. In this thesis we attempt to explain these observations and to identify key controlling parameters. We test a set of 2D models representing great earthquake seismic cycles at known subduction zones with various known geometries, megathrust friction coefficients, and convergence rates implemented. We found that low-angle subduction (large effect) and thick sediments in the subduction channel (smaller effect) are the fundamental necessary conditions for generating giant earthquakes, while the change of subduction velocity from 10 to 3.5 cm/yr has a lower effect. Modeling results also suggest that having thick sediments in the subduction channel causes low static friction, resulting in neutral or slightly compressive deformation in the overriding plate for low-angle subduction zones. These modeling results agree well with observations for the largest earthquakes. The model predicts the largest possible earthquakes for subduction zones of given dipping angles. The predicted maximum magnitudes exactly threshold magnitudes of all known giant earthquakes of 20th and 21st centuries.
The clear limitation of most of the models developed in the thesis is their 2D nature. Development of 3D models with comparable resolution and complexity will require significant advances in numerical techniques. Nevertheless, we conducted a series of low-resolution 3D models to study the interaction between two large asperities at a subduction interface separated by an aseismic gap of varying width. The novelty of the model is that it considers behavior of the asperities during multiple seismic cycles. As expected, models show that an aseismic gap with a narrow width could not prevent rupture propagation from one asperity to another, and that rupture always crosses the entire model. When the gap becomes too wide, asperities do not interact anymore and rupture independently. However, an interesting mode of interaction was observed in the model with an intermediate width of the aseismic gap: In this model the asperities began to stably rupture in anti-phase following multiple seismic cycles. These 3D modeling results, while insightful, must be considered preliminary because of the limitations in resolution.
The technique developed in this thesis for cross-scale modeling of seismic cycles can be used to study the effects of multiple seismic cycles on the long-term deformation of the upper plate. The technique can be also extended to the case of continental transform faults and for the advanced 3D modeling of specific subduction zones. This will require further development of numerical techniques and adaptation of the existing advanced highly scalable parallel codes like LAMEM and ASPECT.