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Numerical simulations of sequences of earthquakes and aseismic slip (SEAS) have made great progress over past decades to address important questions in earthquake physics. However, significant challenges in SEAS modeling remain in resolving multiscale interactions between earthquake nucleation, dynamic rupture, and aseismic slip, and understanding physical factors controlling observables such as seismicity and ground deformation. The increasing complexity of SEAS modeling calls for extensive efforts to verify codes and advance these simulations with rigor, reproducibility, and broadened impact. In 2018, we initiated a community code‐verification exercise for SEAS simulations, supported by the Southern California Earthquake Center. Here, we report the findings from our first two benchmark problems (BP1 and BP2), designed to verify different computational methods in solving a mathematically well‐defined, basic faulting problem. We consider a 2D antiplane problem, with a 1D planar vertical strike‐slip fault obeying rate‐and‐state friction, embedded in a 2D homogeneous, linear elastic half‐space. Sequences of quasi‐dynamic earthquakes with periodic occurrences (BP1) or bimodal sizes (BP2) and their interactions with aseismic slip are simulated. The comparison of results from 11 groups using different numerical methods show excellent agreements in long‐term and coseismic fault behavior. In BP1, we found that truncated domain boundaries influence interseismic stressing, earthquake recurrence, and coseismic rupture, and that model agreement is only achieved with sufficiently large domain sizes. In BP2, we found that complexity of fault behavior depends on how well physical length scales related to spontaneous nucleation and rupture propagation are resolved. Poor numerical resolution can result in artificial complexity, impacting simulation results that are of potential interest for characterizing seismic hazard such as earthquake size distributions, moment release, and recurrence times. These results inform the development of more advanced SEAS models, contributing to our further understanding of earthquake system dynamics.

While power-law distributions in seismic moment and interevent times are ubiquitous in regional catalogs, the statistics of individual faults remains controversial. Continuum fault models typically produce characteristic earthquakes or a narrow range of sizes, leading to the view that the regional statistics originates from interaction of multiple faults. I present theoretical arguments and numerical simulations demonstrating that seismicity on homogeneous planar faults can span several orders of magnitude in rupture dimensions and interevent times, if the fault dimension W is sufficiently large compared to a characteristic length Lcrit, related to the nucleation dimension. Large faults are increasingly less characteristic, with the fraction of system-size ruptures proportional to (Lcrit/W)^1/2. Earthquake statistics for large W/Lcrit is remarkably close to nature, exhibiting Omori decay and power-law distributed rupture lengths. Simple crack models are consistent with a Gutenberg-Richter distribution with b=3/4, and provide a physical basis for these distributions on individual faults.

Earthquake clustering has proven the most useful tool to forecast changes in seismicity rates in the short and medium term (hours to months), and efforts are currently being made to extend the scope of such models to operational earthquake forecasting. The overarching goal of the research presented in this thesis is to improve physics-based earthquake forecasts, with a focus on aftershock sequences. Physical models of triggered seismicity are based on the redistribution of stresses in the crust, coupled with the rate-and-state constitutive law proposed by Dieterich to calculate changes in seismicity rate. This type of models are known as Coulomb- rate and-state (CRS) models. In spite of the success of the Coulomb hypothesis, CRS models typically performed poorly in comparison to statistical ones, and they have been underepresented in the operational forecasting context. In this thesis, I address some of these issues, and in particular these questions: (1) How can we realistically model the uncertainties and heterogeneity of the mainshock stress field? (2) What is the effect of time dependent stresses in the postseismic phase on seismicity? I focus on two case studies from different tectonic settings: the Mw 9.0 Tohoku megathrust and the Mw 6.0 Parkfield strike slip earthquake. I study aleatoric uncertainties using a Monte Carlo method. I find that the existence of multiple receiver faults is the most important source of intrinsic stress heterogeneity, and CRS models perform better when this variability is taken into account. Epistemic uncertainties inherited from the slip models also have a significant impact on the forecast, and I find that an ensemble model based on several slip distributions outperforms most individual models. I address the role of postseismic stresses due to aseismic slip on the mainshock fault (afterslip) and to the redistribution of stresses by previous aftershocks (secondary triggering). I find that modeling secondary triggering improves model performance. The effect of afterslip is less clear, and difficult to assess for near-fault aftershocks due to the large uncertainties of the afterslip models. Off-fault events, on the other hand, are less sensitive to the details of the slip distribution: I find that following the Tohoku earthquake, afterslip promotes seismicity in the Fukushima region. To evaluate the performance of the improved CRS models in a pseudo-operational context, I submitted them for independent testing to a collaborative experiment carried out by CSEP for the 2010-2012 Canterbury sequence. Preliminary results indicate that physical models generally perform well compared to statistical ones, suggesting that CRS models may have a role to play in the future of operational forecasting. To facilitate efforts in this direction, and to enable future studies of earthquake triggering by time dependent processes, I have made the code open source. In the final part of this thesis I summarize the capabilities of the program and outline technical aspects regarding performance and parallelization strategies. Die örtliche und zeitlich Häufung von Erdbeben ist geeignet, um Änderungen in Seismizitätsraten auf kurzen bis mittleren Zeitskalen (Stunden bis Monate) zu prognostizieren. Kürzlich wurden vermehrt Anstrengungen unternommen, den Umfang solcher Modelle auf Operationelle Erdbebenvorhersage auszudehnen, welche die Veröffentlichung von Erdbebenwahrscheinlichkeiten beinhaltet mit dem Ziel, die Bevölkerung besser auf mögliche Erdbeben vorzubereiten. Das vorrangige Ziel dieser Dissertation ist die Verbesserung von kurz- und mittelfristiger Erdbebenprognose basierend auf physikalischen Modellen. Ich konzentriere mich hier auf Nachbebensequenzen. Physikalische Modelle, die getriggerte Seimizität erklären, basieren auf der Umverteilung von Spannungen in der Erdkruste. Berechnung der Coulomb Spannung können kombiniert werden mit dem konstituivem Gesetz von Dieterich, welches die Berechnung von Änderungen in der Seismizitätsrate ermöglicht. Diese Modelle sind als Coulomb-Rate-and-State (CRS) Modelle bekannt. Trotz der erfolgreichen Überprüfung der Coulomb-Hypothese, schneiden CRS-Modelle im Vergleich mit statistischen Modellen schlecht ab, und wurden deshalb bisher kaum im Kontext operationeller Erdbenbenvorhersage genutzt. In dieser Arbeit, gehe ich auf einige der auftretenden Probleme ein. Im Besonderen wende ich mich den folgenden Fragen zu: (1) Wie können wir die Unsicherheiten und die Heterogenität des Spannungsfeldes infolge des Hauptbebens realistisch modellieren? (2)Welche Auswirkungen haben zeitlich variable Spannungsänderungen in der postseismischen Phase? Ich konzentriere mich hierbei auf zwei Beispiele in unterschiedlichen tektonischen Regionen: die Aufschiebung des Mw9.0 Tohoku Erdbeben und die Blattverschiebung des Mw6.0 Parkfield Erdbeben. Ich untersuche aleotorische Unsicherheiten der Coulomb-Spannung durch Variabilität in der Orientierung der betroffenen Bruchflächen und durch Spannungsgradienten innerhalb von Modellzellen. Ich zeige, dass die Existenz der unterschiedlichen Bruchflächen die bedeutenste Quelle für intrinsiche Spannungheterogenität ist und das CRS-Modelle deutlich besser abschneiden, wenn diese Variabilität berücksichtigt wird. Die epistemischen Unsicherheiten aufgrund von unterschiedlichen Ergebnissen von Inversionen von Daten für die Verschiebung entlang der Bruchfläche haben ebenso erhebliche Auswirkungen auf die Vorhersage. Ich gehe dann auf die Rolle von postseismischen Spannung ein, insbesondere auf zwei Prozesse: aseismische Verschiebung entlang der Störungsfläche des Hauptbebens (Afterslip) und die Veränderung von Spannungen durch vorhergehende Nachbeben (sekundäres Triggern). Ich demonstriere, dass das Modellieren von sekundärem Triggern die Modellvorhersage in beiden Fallbeispielen verbessert. Die Einbeziehung von Afterslip verbessert die Qualität der Vorhersage nur für die Nachbebensequenz des Parkfield Erdbebens. Dagegen kann ich nachweisen, dass Afterslip infolge des Tohoku Bebens eine höhere Seismizität auf Abschiebungsflächen im Hangenden begünstigt. Die dargestellten Verbesserungen des CRS-Modells sind sehr vielversprechend im Kontext operationeller Erdbebenvorhersage, verlangen aber nach weiterer Überprüfung. Ich stelle die vorläufigen Ergebnisse eines gemeinschaftlichen Tests für die Erdbebenfolge von Canterbury 2010-2012 vor, welcher von CSEP durchgeführt wurde. Die physikalischen Modelle schneiden hier im Vergleich mit statistischen Modellen gut ab. Daher scheint eine Anwendung von CSR-Modellen, die Unsicherheiten und sekundäres Triggering berücksichtigen, in zukünftigen operationellen Erdbebenvorhersagen empfehlenswert. Um die Bemühungen in dieser Richtung zu unterstützen und weitere Studien zum Triggern von Erdbeben durch zeitabhängige Prozesse zu ermöglichen, habe ich meinen Open Source Code öffentlich zugänglich gemacht. Im letzen Teil dieser Arbeit fasse ich die Leistungsfähigkeit des Programms zusammen und skizziere die technischen Aspekte bezüglich der Effiziens und der Parallelisierung des Programmes.

Magmatic intrusions release extensional strain in the Earth's crust upon availability of magma. Intrusions are typically accompanied by earthquake swarms and by surface faulting that is often larger than what is expected from the magnitude of the induced earthquakes. The 2000 Miyakejima dike intrusion triggered the largest volcanic earthquake swarm monitored so far, with five Ml>6 earthquakes. We analyze the seismicity and deformation induced by the Miyakejima dike with the aim of constraining the timescale and mechanisms of slow strain release during the episode. In six earthquake bursts lasting few hours and migrating at ∼1 km h−1 we find candidates for slow earthquakes. Each burst nucleated at the tips of previous bursts, suggesting stress interaction. The variability of fault plane solutions indicates that the bursts occurred on a complex system of fractures, consistent with weakly consolidated surface layers strained by spatially inhomogneous stresses that change in time, such as those induced by a dike. Based on dislocation models, we find that deformation is best explained by aseismic slip (in addition to the seismic burst), with a moment 1.3 to 2.3 times larger than the earthquakes' seismic moment, and opening of 0.20 ± 0.07 m on the dike. The aseismic slip occurred over a few hours, with moment, duration, and migration velocity consistent with that of previously observed slow slip events. We argue that the seismic bursts are likely driven by slow slip, sharing most properties with tectonic slow slip events and swarms, but occurring on a set of nonaligned faults.