Earthquake statistics is a growing field of research with direct application to probabilistic seismic hazard evaluation. The earthquake process is a complex spatio-temporal phenomenon, and has been thought to be an example of the self-organised criticality (SOC) paradigm, in which events occur as cascades on a wide range of sizes, each determined by fine details of the rupture process. As a consequence, deterministic prediction of specific event sizes, locations, and times may well continue to remain elusive. However, probabilistic forecasting, based on statistical patterns of occurrence, is a much more realistic goal at present, and is being actively explored and tested in global initiatives. This thesis focuses on the temporal statistics of earthquake populations, exploring the uncertainties in various commonly-used procedures for characterising seismicity and explaining the origins of these uncertainties. Unlike many other SOC systems, earthquakes cluster in time and space through aftershock triggering. A key point in the thesis is to show that the earthquake inter-event time distribution is fundamentally bimodal: it is a superposition of a gamma component from correlated (co-triggered) events and an exponential component from independent events. Volcano-tectonic earthquakes at Italian and Hawaiian volcanoes exhibit a similar bimodality, which in this case, may arise as the sum of contributions from accelerating and decelerating rates of events preceding and succeeding volcanic activity. Many authors, motivated by universality in the scaling laws of critical point systems, have sought to demonstrate a universal data collapse in the form of a gamma distribution, but I show how this gamma form is instead an emergent property of the crossover between the two components. The relative size of these two components depends on how the data is selected, so there is no universal form. The mean earthquake rate—or, equivalently, inter-event time—for a given region takes time to converge to an accurate value, and it is important to characterise this sampling uncertainty. As a result of temporal clustering and non-independence of events, the convergence is found to be much slower than the Gaussian rate of the central limit theorem. The rate of this convergence varies systematically with the spatial extent of the region under consideration: the larger the region, the closer to Gaussian convergence. This can be understood in terms of the increasing independence of the inter-event times with increasing region size as aftershock sequences overlap in time to a greater extent. On the other hand, within this high-overlap regime, a maximum likelihood inversion of parameters for an epidemic-type statistical model suffers from lower accuracy and a systematic bias; specifically, the background rate is overestimated. This is because the effect of temporal overlapping is to mask the correlations and make the time series look more like a Poisson process of independent events. This is an important result with practical relevance to studies using inversions, for example, to infer temporal variations in background rate for time-dependent hazard estimation.

Large earthquakes often exhibit complex slip distributions and occur along non-planar faults, resulting in variable stress changes throughout the fault region. To better discern the role of stress changes and fluid flow on aftershock sequences, we examine areas of enhanced and reduced mean stress along the structurally complex strike-slip faults that hosted the 1992 Landers, 2010 El-Mayor Cucapah, and 2016 Kumamoto earthquakes. We characterize the behavior of aftershock sequences with the Epidemic Type Aftershock-Sequence Model and use the Maximum Log Likelihood method to determine the optimal set of ETAS parameter values along each fault. This study indicates that extensional areas experience greater secondary aftershock triggering and a higher density of aftershocks directly following the mainshock, which could be attributed to fluid influx. However, our results also highlight some shortcomings of the ETAS model, including high parameter correlation, and influence of catalog size and magnitude cutoff on parameter estimations.

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Thesis advisor: John E. Ebel / Power-law scaling relationships concerning the earthquake frequency-magnitude distribution and the fractal geometry of spatial seismicity patterns may provide applications to earthquake forecasting and earthquake hazard studies. Past studies on the fractal characteristics of seismic phenomena have observed spatial and temporal differences in earthquake clustering and b value in relation to fractal dimension value. In this thesis, an investigation of the spatiotemporal seismicity patterns in southern California for the years 1982 to 2020 was conducted. The range and temporospatial distribution of b and D2 values for earthquake hypocenters contained in the Southern California Earthquake Data Center catalogue were calculated and shown in time series and spatial distribution maps. b values were calculated using both the Least SquaresMethod and the Maximum Likelihood Method while D2 values were calculated for length scales between 1 km to 10 km. A set of b and D2 values were calculated after declustering for foreshocks and aftershocks using Gardner and Knopoff’s declustering algorithm. b values decreased while D2 values increased on the dates of M > 6.0 earthquakes, whereas b values increased and D2 values decreased on the dates after M > 6.0 earthquakes. Declustering results suggest an influence of earthquake aftershocks to increase D2 values while decreasing b values. The role for b values and D2 values to delineate both the temporal and spatial extent of aftershock sequences for large earthquakes may prove to have an application in earthquake hazard studies. / Thesis (MS) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.

The current study examined the psychological effects of recurring earthquake aftershocks in the city of Christchurch, New Zealand, which began in September 2010. Although it has been identified that exposure to ongoing adverse events such as continuing terrorist attacks generally leads to the development of increasing symptomology over time, differences in perceived controllability and blame between man-made and natural adverse events may contribute to differences in symptom trajectories. Residents of two Christchurch suburbs differentially affected by the earthquakes (N = 128) were assessed on measures of acute stress disorder, generalised anxiety, and depression, at two time points approximately 4-5 months apart, in order to determine whether symptoms intensified or declined over time in the face of ongoing aftershocks. At time 1, clinically significant levels of acute stress were identified in both suburbs, whereas clinical elevations in depression and anxiety were only evident in the most affected suburb. By time 2, both suburbs had fallen below the clinical range on all three symptom types, identifying a pattern of habituation to the aftershocks. Acute stress symptoms at time 2 were the most highly associated with the aftershocks, compared to symptoms of generalised anxiety and depression which were identified by participant reports to be more likely associated with other earthquake-related factors, such as insurance troubles and less frequent socialisation. The finding that exposure to ongoing earthquake aftershocks leads to a decline in symptoms over time may have important implications for the assessment of traumatic stress-related disorders, and provision of services following natural, as compared to man-made, adverse events.

Thesis advisor: John E. Ebel / Thesis advisor: Mark D. Behn / On January 12, 2015, a magnitude 3.1 mainshock occurred in Plainfield, Connecticut near Wauregan Tilcon Quarry, causing modified Mercalli II-IV intensities. Shortly after the event, a team from Weston Observatory installed portable seismographs in the epicentral area. The portable array detected hundreds of small earthquakes from around the quarry, with 26 events that were accurately located. P-wave first motion directions obtained from readings of the mainshock suggest a thrusting focal mechanism on a NNE-SSW trending fault. In this research, we collected 113 gravity measurements in the proximity of the quarry to verify and correct local fault geometry proposed by historic aeromagnetic and geologic mapping. Interpretations of the computed simple Bouguer anomaly are consistent with historic mapping, with a few exceptions. The gravity survey constrains a NNE-SSW trending fault that dips west underneath the quarry, inferred to be the Lake Char-Honey Hill Fault, and reduces ambiguity in the position of an undefined ESE-WNW trending fault, which appears to be on strike to intersect the quarry. A 3D boundary element program (3D~Def) is used to simulate quarry-induced stress changes on these faults in order to analyze the possibility of inducing seismicity through crustal unloading in the region. Quarry operations resulted in the removal of mass from the crust, which decreased lithostatic load. In a setting confined by a maximum horizontal compressional stress, decreasing the lithostatic load, orminimum principal stress (σ3), shifts a Mohr-Coulomb diagram toward failure. The boundary element model shows that following the excavation of materials at the quarry, positive Coulomb failure stress changes occur on the west dipping Lake Char-Honey Hill Fault. In agreement with past studies, our results suggest that quarrying operations can trigger seismic activity in specific settings with stress regime, fault orientations, and rock characteristics such as those that exist in the northeastern U.S. In order to mitigate the risk for future earthquakes related to quarrying operations, these factors must be considered before operations begin. / Thesis (MS) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.

To better understand the ground motion and associated seismic hazard of earthquakes in the central and eastern United States (CEUS), this dissertation focuses on the source parameters and wave propagation characteristics of both tectonic earthquakes and induced earthquakes in the CEUS. The infrequent occurrence of significant earthquakes in the CEUS limits the necessary observations needed to understand earthquake processes and to reduce uncertainty in seismic-hazard maps. The well-recored aftershock sequence of the 2011 Mineral, Virginia, earthquake offers a rare opportunity to improve our understanding of earthquake processes and earthquake hazard in this populous region of the United States. Moreover, the rapid increase of seismicity in the CEUS since 2009 that has been linked to wastewater injection has raised concern regarding the potential hazard. In this dissertation, I first present a detailed study of the aftershock sequence of the 2011 Mw 5.7 Mineral, Virginia earthquake. It involves the hypocenter locations of ~3000 earthquakes, ~400 focal mechanism solutions, statistics of the aftershock sequence, and the Coulomb stress modeling that explains the triggering mechnanism of those aftershocks. Second, I examine the S-wave attenuation at critical short hypocentral distances (< 60 km) using the aftershock data. The observed S-wave amplitudes decay as a function of hypocenter distance R according to R^-1.3 - R^-1.5, which is substantially steeper than R^-1 for a homogeneous whole space. Finally, I propose and apply a stable multi-window coda spectral ratio method to estimate corner frequencies and Brune-type stress drops for the 2011 Mineral, Virginia mainshock and aftershocks, as well as induced earthquakes in Oklahoma. The goal of this comparative study is to find out whether or not there are systematical differences in source parameters between tectonic earthquakes and induced earthquakes in the CEUS. I found generally much higher stress drops for the Mineral, Virginia sequence. However, the stress drops for those induced earthquakes in Oklahoma exhibit large varation among individual earthquake sequences, with the large mainshocks having high stress drops (20-30 MPa, Brune-type) except for the 2011 Mw 5.6 Prague, Oklahoma earthquake. And spatially varying stress drops indicates strong fault heterogeneity, which in the case of induced earthquakes may be influenced by the injection of fluids into the subsurface. / Ph. D.

In seismology, an important goal is to attain a better understanding of the earthquake process. In this study of the physics of aftershock generation, I couple statistical analysis with modelling of physical processes in the postseismic period. I present a theoretical formulation for the distribution of interevent times for aftershock sequences obeying the empirically well established Omori law. As opposed to claims by other authors, this work demonstrates that the duration of the time interval between two successive earthquakes cannot be used to identify whether or not they belong to the same aftershock sequence or occur as a result of the same underlying process. This implies that a proper understanding of earthquake interevent time distributions is necessary before conclusions regarding the physics of the earthquake process are drawn. In a discussion of self-organised criticality (SOC) in relation to empirical laws in seismology, I find that Omori's law for aftershocks cannot be used as evidence for the theory of SOC. Instead, I consider that the occurrence of aftershocks in accordance with Omori's law is a result of a physical process that can be modelled and understood. I analyse characteristic features in the spatiotemporal distribution of aftershocks in the south Iceland seismic zone, following the two M6.5 June 2000 earthquakes and a M4.5 earthquake in September, 1999. These features include an initially constant aftershock rate, whose duration is larger following a larger main shock, and a subsequent power law decay that is interrupted by distinct and temporary deviations in terms of rate increases and decreases. Based on pore pressure diffusion modelling, I interpret these features in terms of main shock initiated diffusion processes. I conclude that thorough data analysis and physics-based modelling are essential components in attempts to improve our understanding of processes governing the occurrence of earthquakes.

It is well known that direct surface waves of large earthquakes are capable of triggering shallow earthquakes and deep tremor at long-range distances. Recent studies have shown that multiple surface waves circling the earth could also remotely trigger microearthquakes. However, it is still not clear whether multiple surface waves returning back to the main shock epicenters could also trigger/modulate aftershock behavior. Here we conduct a study to search for evidence of such triggering by systematically examining aftershock patterns of earthquakes with magnitude ≥ 8 since 1990 that produce observable surface waves circling the globe repeatedly. We specifically examine the 2011 M9 Tohoku-Oki event using a composite catalog of JMA, HiNet and newly detected events obtained by waveform cross correlation. We compute the magnitude of completeness for each sequence, and stack all the sequences together to compute the seismicity and moment rates by sliding data windows. The sequences are also shuffled randomly and these rates are compared to the actual data as well as synthetic aftershock sequences to estimate the statistical significance of the results. Our results suggest that there is some moderate increase of early aftershock activity after a few hours when the surface waves return to the epicentral region. However, we could not completely rule out the possibility that such an increase is purely due to random fluctuations of aftershocks or caused by missing aftershocks in the first few hours after the mainshock.

My dissertation focuses primarily on the following three aspects associated with passing seismic waves in the field of earthquake seismology: temporal changes of fault zone properties, nonlinear site response, and dynamic triggering. Quantifying the temporal changes of material properties within and around active fault zones (FZ) is important for better understanding of rock rheology and estimating the strong ground motion that can be generated by large earthquakes. As high-amplitude seismic waves propagate through damaged FZ rocks and/or shallow surface layers, they may produce additional damage leading to nonlinear wave propagation effects and temporal changes of material properties (e.g., seismic velocity, attenuation). Previous studies have found several types of temporal changes in material properties with time scales of tens of seconds to several years. Here I systematically analyze temporal changes of fault zone (FZ) site response along the Karadere-Düzce branch of the North Anatolian fault that ruptured during the 1999 İzmit and Düzce earthquake sequences. The coseismic changes are on the order of 20-40%, and are followed by a logarithmic recovery over an apparent time scale of ~1 day. These results provide a bridge between the large-amplitude near-instantaneous changes and the lower-amplitude longer-duration variations observed in previous studies. The temporal changes measured from this high-resolution spectral ratio analysis also provide a refinement for the beginning of the longer more gradual process typically observed by analyzing repeating earthquakes. An improved knowledge on nonlinear site response is critical for better understanding strong ground motions and predicting shaking induced damages. I use the same sliding-window spectral ratio technique to analyze temporal changes in site response associated with the strong ground motion of the Mw6.6 2004 Mid-Niigata earthquake sequence recorded by the borehole stations in Japanese Digital Strong-Motion Seismograph Network (KiK-Net). The coseismic peak frequency drop, peak spectral ratio drop, and the postseismic recovery time roughly scale with the input ground motions when the peak ground velocity (PGV) is larger than ~5 cm/s, or the peak ground acceleration (PGA) is larger than ~100 Gal. The results suggest that at a given site the input ground motion plays an important role in controlling both the coseismic change and postseismic recovery in site response. In a follow-up study, I apply the same sliding-window spectral ratio technique to surface and borehole strong motion records at 6 KiK-Net sites, and stack results associated with different earthquakes that produce similar PGAs. In some cases I observe a weak coseismic drop in the peak frequency when the PGA is as small as ~20-30 Gal, and near instantaneous recovery after the passage of the direct S waves. The percentage of drop in the peak frequency starts to increase with increasing PGA values. A coseismic drop in the peak spectral ratio is also observed at 2 sites. When the PGA is larger than ~60 Gal to more than 100 Gal, considerably stronger coseismic drops of the peak frequencies are observed, followed by a logarithmic recovery with time. The observed weak reductions of peak frequencies with near instantaneous recovery likely reflect nonlinear response with essentially fixed level of damage, while the larger drops followed by logarithmic recovery reflect the generation (and then recovery) of additional rock damage. The results indicate clearly that nonlinear site response may occur during medium-size earthquakes, and that the PGA threshold for in situ nonlinear site response is lower than the previously thought value of ~100-200 Gal. The recent Mw9.0 off the Pacific coast of Tohoku earthquake and its aftershocks generated widespread strong shakings as large as ~3000 Gal along the east coast of Japan. I systematically analyze temporal changes of material properties and nonlinear site response in the shallow crust associated with the Tohoku main shock, using seismic data recorded by the Japanese Strong Motion Network KIK-Net. I compute the spectral ratios of windowed records from a pair of surface and borehole stations, and then use the sliding-window spectral ratios to track the temporal changes in the site response of various sites at different levels of PGA The preliminary results show clear drop of resonant frequency of up to 70% during the Tohoku main shock at 6 sites with PGA from 600 to 1300 Gal. In the site MYGH04 where two distinct groups of strong ground motions were recorded, the resonant frequency briefly recovers in between, and then followed by an apparent logarithmic recovery. I investigate the percentage drop of peak frequency and peak spectral ratio during the Tohoku main shock at different PGA levels, and find that at most sites they are correlated. The third part of my thesis mostly focuses on how seismic waves trigger additional earthquakes at long-range distance, also known as dynamic triggering. Previous studies have shown that dynamic triggering in intraplate regions is typically not as common as at plate-boundary regions. Here I perform a comprehensive analysis of dynamic triggering around the Babaoshan and Huangzhuang-Gaoliying faults southwest of Beijing, China. The triggered earthquakes are identified as impulsive seismic arrivals with clear P- and S-waves in 5 Hz high-pass-filtered three-component velocity seismograms during the passage of large amplitude body and surface waves of large teleseismic earthquakes. I find that this region was repeatedly triggered by at least four earthquakes in East Asia, including the 2001 Mw7.8 Kunlun, 2003 Mw8.3 Tokachi-oki, 2004 Mw9.2 Sumatra, and 2008 Mw7.9 Wenchuan earthquakes. In most instances, the microearthquakes coincide with the first few cycles of the Love waves, and more are triggered during the large-amplitude Rayleigh waves. Such an instantaneous triggering by both the Love and Rayleigh waves is similar to recent observations of remotely triggered 'non-volcanic' tremor along major plate-boundary faults, and can be explained by a simple Coulomb failure criterion. Five earthquakes triggered by the Kunlun and Tokachi-oki earthquakes were recorded by multiple stations and could be located. These events occurred at shallow depth (< 5 km) above the background seismicity near the boundary between NW-striking Babaoshan and Huangzhuang-Gaoliying faults and the Fangshan Pluton. These results suggest that triggered earthquakes in this region likely occur near the transition between the velocity strengthening and weakening zones in the top few kms of the crust, and are likely driven by relatively large dynamic stresses on the order of few tens of KPa.