SEISMICITY ANALYSIS THROUGH MULTITYPE STRAUSS PROCESS MODELING: A CASE STUDY OF THE 1975 MAGNITUDE 6.1

Transcription

1 SEISMICITY ANALYSIS THROUGH MULTITYPE STRAUSS PROCESS MODELING: A CASE STUDY OF THE 1975 MAGNITUDE 6.1 EARTHQUAKE AND ITS AFTERSHOCKS, YELLOWSTONE NATIONAL PARK Jiefan Yu A Thesis Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE May, 2012 Committee: Xinyue Ye, Advisor Charles M. Onasch Peter V. Gorsevski

2 2012 Jiefan Yu All Rights Reserved

3 iii ABSTRACT Xinyue Ye, Advisor Point process modeling has been implemented to study interaction among seismic patterns for the past several decades. However, integration of geologic variables into point process models has not been fully explored in previous studies. In this study, the magnitude 6.1 earthquake on Jun 30, 1975 and its aftershocks in Yellowstone National Park were studied with point process analysis to identify a suitable model towards revealing the pair-wise point interaction and its correlation with geologic variables. A Multitype Strauss Process Model was adopted due to its flexibility of incorporating geologic variables into interpoint pattern simulation in quantitative seismology. The results firstly showed that the Multitype Strauss Process Model can successfully capture the distribution pattern of epicenters under the effect of interaction radii among different types of earthquakes. Secondly, two geologic variables, the distance to faults and earthquake focal depths, can explain the seismic pattern, which are also consistent with the physical mechanisms suggested in previous studies. However, the location of hydrothermal system was found to have little correlation with the earthquake distribution.

4 iv If You Were the Only Girl in the World Sometimes when I feel bad And things look blue I wish a pal I had Say one like you Someone within my heart To build a throne Someone who d never part To call my own If you were the only girl in the world And I were the only boy Nothing else would matter in the world today We could go on loving in the same old way A garden of Eden just made for two With nothing to mar our joy I would say such wonderful things to you There would be such wonderful things to do If you were the only girl in the world And I were the only boy Nat D. Ayer and Clifford Grey, 1916

5 v I dedicate this paper to my loving parents to thank for their selfless love and support to me. Also thanks for this precious opportunity to be a master student in Bowling Green State University, and all the wonderful people I have met.

6 vi ACKNOWLEDGMENTS These past two years have been a wonderful time in my life. I finally met the major, geology, to be my passion for the rest of my life. Throughout my growing path, I have to thank all the people who guided me, helped me, and watched me to make this transition. First of all, I must give my greatest appreciation to Dr. Charles M. Onasch, who led me into geology and gave me generous support and guidance as a mentor. I cannot make all the way through without the confidence he has been giving me. Also, it is impossible for me to make my day without Dr. Xinyue Ye, who mentored me throughout all my research assistant work and thesis edition. Also, I will give my genuine gratitude to Dr. Peter V. Gorsevski for his insightful opinions and critical thinking which guided me rethink my thesis and complete my work. I also would like to thank for Dr. James E. Evans, Dr. Kurt S. Panter, Dr. Margaret M. Yacobucci, and Dr. Jeffrey Snyder who taught me so many things in class and during the field camp. I will never forget that great time. I will especially thank Dr. James E. Evans to be my career epitome for his broad knowledge and neat organization. Dr. John R. Farver and Dr. Robert K. Vincent also greatly inspired me by their great passion and love toward their careers and students. Being one member of this geology family, I could not express my love enough to those outstanding professors and my dear colleagues. Special thanks for Shiva Basnet and his wife to take care of me in life, and thanks for Ina M Terry and her husband driving all the way to school just to help me revise my thesis. Finally, I give my dearest love to my family, my boyfriend, and my best pals back in China. I could have never done this without you.

7 vii TABLE OF CONTENTS INTRODUCTION... 1 Page CHAPTER I. OVERVIEW... 2 Earthquakes... 2 Previous Studies... 2 Research Objective... 6 CHAPTER II. STUDY AREA... 7 Geologic Setting of the Yellowstone Park Area... 8 Monitoring Seismic Activity in the Yellowstone Park Area Summary of Seismic Research in Yellowstone Park Region Earthquake Swarm, Volcanic and Geothermal Activity Fault Systems Remote Triggers CHAPTER III. METHODLOGY Point Process Modeling Exploratory Data Analysis CHAPTER IV. RESULTS CHAPTER V. DISCUSSION... 56

8 viii CHAPTER VI. CONCLUSIONS REFERENCES APPENDIX A. THERMINOLOGY IN SEISMOLOGY AND STATISTICS APPENDIX B. R SCRIPT... 68

9 ix LIST OF FIGURES Figure Page 1. The distribution of all the earthquakes from 1972 to The Intermountain Seismic Belt The distribution of earthquakes from 1972 to 2011 marked by the difference of depth The distribution of the three lasting earthquake swarms in Yellowstone National Park area The aftershocks of magnitude 6.1 earthquake near Norris Geyser Basin from June 30, 1975 to July 13, The distribution of earthquakes from Jun 30, 1975 to Jul 13, 1975 in meters The distribution of each category of earthquakes from Jun 30 to Jul 13, 1975 in meters Distribution of earthquake magnitudes without the two outliers Distribution of earthquake focal depth without the two outliers The density contrast of earthquakes on Jun 30, 1975 and its aftershocks The result of the accumulative distribution of nearest neighborhood (Gross test in R) from small to large earthquakes The result of the accumulative distribution of nearest neighborhood (Gross test in R) from small to small earthquakes...37

10 x 13. The result of the accumulative distribution of nearest neighborhood (Gross test in R) from large to large earthquakes The result of the accumulative distribution of nearest neighborhood (Gross test in R) from large to small earthquakes Fitted trend from Multitype Strauss Modeling of the probability of occurrence among small and large magnitude earthquakes The result of K and G test envelope function in meters The distance-to fault covariate in research extent in meters The location of hydrothermal area in research extent The contour map of fitted focal depth in research extent The smooth surface of potential focal depth in research region The fitted model with distance-to-fault covariate and with the probability of occurrence The fitted model with hydrothermal system covariate and with the probability of occurrence The fitted model with earthquake focal depth covariate and the probability of occurrence The fitted model with earthquake focal depth and distance-to-fault covariate and the probability of occurrence The simulated envelop of final model D visualization of earthquake hypocenters...59

11 xi LIST OF TABLES 1. The summary table of earthquake point pattern...30 Page 2. The interaction radii among each type of earthquake...35

12 1 INTRODUCTION Quantitative seismology is one of the essential fields in earthquake hazard estimation and seismic pattern prediction. There have been several attempts of statistically analysis in seismology which advanced the physical understanding of earthquake mechanism. With the advance of modern computation technology, point process modeling, as one type of seismic activity statistical method, has been implementing into more and more applications of seismic pattern recognition and physical modeling hypothesis calibration (Rundle, et al., 1999). In point processing modeling, each earthquake can be treated as a point event with attached spatial information, temporal character, and possible geologic variables (Baddeley and Turner, 2005). Potential geologic variables derived from physics-based earthquake modeling can be validated by the statistical modeling process, especially when the relationship between subsurface earthquake mechanism information is incomplete or unclear (Ogata, 1998). In this thesis, earthquakes in Yellowstone National Park, clustered from both volcanic and tectonic influences, are studied using point processing modeling to provide further insight of significant seismic triggers in that area. The results are then compared with the physics-based model.

13 2 OVERVIEW Earthquakes An earthquake is a trembling of the earth due to a sudden release of strain built up over a long period of time (Jackson, 1997). It can cause catastrophic destruction and devastating consequences making it one of the most damaging natural disasters. According to the report of United States Geological Survey (USGS), there are approximately 500,000 earthquakes detected in the world each year (USGS, 2010), and substantial number of them are significant. For example, the magnitude 8.0 earthquake in May 12, 2008 in Sichuan, China caused 69,197 deaths, 374,176 injuries, and 18,222 missing people (Cui, et al., 2011). The magnitude 9.0 Tōhoku earthquake in 2011 was the most recorded earthquake in Japan has resulted in 10,804 deaths, 2,777 injuries and 16,244 missing people (Hoshiba and Iwakiri, 2011). Throughout human history, earthquakes have contributed to tremendous environmental damage, tragic loss of life, emotional suffering, and financial crisis. Within the Unites States, the annual long-term loss due to earthquakes is estimated about $4.4 billion each year (USGS, 2010). All these impacts provide great motivation for the humans to learn about earthquakes. Earthquakes may not be avoided, but a better understanding of their nature and mechanism will contribute to minimize the loss through better predictions and preparation. Previous Studies In principle, two main approaches are used to predict earthquakes: physical modeling and mathematical modeling (Kagan, 1999). For the physical method, the detection of physical precursors of fault failure is the most essential way for earthquake prediction according to

14 3 observation data. Common strategies include detection of P-wave velocity changes, ground deformation, ground water fluctuation, and decrease in electrical resistivity of rocks, which are all more suitable for short term prediction. Moreover, the mechanism of frictional failure on a pre-existing fault is usually simulated to reveal the hidden physical reason of ground shaking. Several friction models are used to illustrate these simulations, such as Burridge-Knopoff model and Haskell dislocation model (Haskell, 1964; Burridge and Knopoff, 1967). Pore fluid pressure has been shown to play a critical role in triggering most earthquakes (Beeler, et al., 2000). Based on these theories, long term prediction might be accomplished by measuring related physical variables. For instance, if the amount of strain to promote an earthquake can be estimated, the next seismic activity could be predicted by estimating when sufficient strain can be accumulated. The measurements needed for prediction include the strain accumulation along a fault segment each year, the amount of strain was released in the last earthquake, and the time since last motion along the fault. On the other hand, mathematics-based methods have gradually been recognized in seismology studies of earthquake hazard estimation, earthquake locations or magnitudes quantification, and prediction model assessment over the last two decades (Ogata, 1998). The Gutenberg-Richter law and Omori law are two representative examples of mathematics-based methods. Gutenberg-Richter law describes the systematic relationship between total number of earthquakes and the magnitude in a worldwide extent, which means that larger earthquakes tend to be less frequent than smaller ones (Gutenberg and Richter, 1954). Omori s law claims that aftershock activity decays with increasing time after the main shock (Omori, 1894). Point process modeling is one of the new spatial analysis tools which specifically aim to

15 4 determine possible dependence or interaction among points with spatial and temporal characteristics, and sometimes the effect of covariates (Anwar, 2009). This approach has been widely applied to variety of scientific fields, including epidemiology (Gatrell, 1966), ecology (Mateu, 1988), and environmental science (Walter, 2005). In the recent decades, the application of point process modeling has received increased attention in seismic hazard estimation. A series of questions regarding earthquakes can be addressed by point process modeling, such as whether the distribution of earthquakes is total random or clustered, and whether it is possible to predict this pattern by statistical analysis which would allow one to generate a hazard assessment map. Vere-Jones (1978) investigated the relationship between volcanic eruptions and earthquakes in 1978 by the point process modeling and maximum likelihood computation. Yosihiko Ogata s (1998) research examined space-time cluster of earthquake pattern with goodness-of-fit of point process modeling. In last five years, there are also scholars, such as Bogdan Enescu and Salma Anwar, who proposed point process modeling to show correlations between seismic patterns and geologic data, like surface heat flow data and distance to the plate boundary in southern California area and northern Pakistan (Anwar, 2009; Enescu et al., 2009). Earthquake s hypocenter is a point with spatial information, time of occurrence, and magnitude. Based on that, a seismic pattern can be studied with point process modeling. Point process modeling consists of exploratory test of the point data distribution pattern, and model fitting to different distributions, such as Poisson Point Process for random distributed patterns and Strauss Point Process for correlated pair points (Baddeley and Turner, 2005). The point pattern also can be classified by the type of point, such as the type of tree, or the magnitude of

16 5 earthquake in this case (Baddeley, 2010). Traditionally, point pattern simulation and prediction is purely based on the distribution of data. More recently, covariate or variable has been used in point process modeling. For instance, geologic information can be utilized as a covariate of a hidden mechanism process and distribution pattern, such as the distance to plate boundary or fault, ground deformation, or migration of pore fluids to provide a better estimation of hazard s location, time, frequency, and magnitude to increase the accuracy of model-fitting of earthquakes. The function of point process modeling is to test the geologic relationships with a statistical analysis, which also enhances the understanding of physical mechanism of earthquake. The advantage of point process modeling over other statistical analysis methods of earthquake prediction has grown with the development of modern computation technology. For example, open source statistical software such as R and its computation packages, assist the progress of point process modeling (Baddeley, 2010). In the history of seismic analysis, physics-based modeling describes the physical relationship between earthquakes and the nearby environment under well defined assumptions, such as how the pore fluid pressure impacts on fault failure. By contrast, mathematical modeling creates an empirical model to recognize the seismic pattern and simulate the potential distribution, especially with incomplete information to quantify the uncertainty about further potential seismic events. However, these two approaches do not function alone and both can be used to compliment the other.

17 6 Research Objective The main objective of the study is to implement a point process model to study the interaction between earthquakes of different magnitude and background volcanic and tectonic factors in Yellowstone National Park area. The magnitude 6.1 earthquake on Jun 30, 1975 was the largest earthquake within Yellowstone National Park in recent history. It created two new hydrothermal systems near the Norris Geyser Basin leading to speculation that this event was related with hydrothermal fluid fluctuation associated with volcanic activity. To evaluate this hypothesis, a point process model with geologic covariates, earthquake pattern from this event is categorized into two groups by magnitude and analyzed with a Multitype Strauss Model to test the correlation between the main shock and its aftershocks in the Yellowstone area. The best model will be chosen based on maximum likelihood approach in the seismic pattern recognition, and the simulation and prediction results could contribute to the understanding of hidden physical earthquake mechanisms, estimation of further potential seismic hazard, and exploration of the possible application of point process modeling in seismic studies.

18 7 STUDY AREA As one of the most seismically active regions, the Yellowstone National Park area has long been the focus of earthquake studies (Rubeis, 2006). From the earliest earthquake report in 1872, there have been over 32,000 earthquakes recorded in the Yellowstone National Park area (Chang et al., 2010). Most of them are small magnitude (less than 3), and occur as earthquake swarms, which happen in shallow crust and sometimes last several days or longer. Those swarms are located both within the Yellowstone calderas, between the calderas, and from the rupture zone of the 1956 Hebgen Lake earthquake to the northwest. The largest earthquake swarm happened in 1985 with over 3,000 earthquakes that lasted for three months. Another large earthquake swarm in Yellowstone National Park occurred during the two weeks from December 27, 2008 to January 7, 2009 and included more than 1,000 earthquakes. Although most earthquakes are small magnitude, serious earthquakes with large magnitude and causing significant damage also happened in the region throughout its history. The largest one was magnitude 7.5 Hebgen Lake earthquake that occurred on August 18, 1959, resulting in 28 deaths, $11 billion in damage, and 6.7 m subsidence of the local area (USGS, 2004). The location was about 24 km northwest of the Yellowstone caldera. The most recent and only large earthquake within the caldera happened on Jun 30, 1975 (Chang, 2010). This magnitude 6.1 earthquake and its aftershocks generated two new hydrothermal areas near Norris Geyser Basin. In addition, there were a total of 17 earthquakes that happened with magnitude greater than 3 that closed a 12 mi section of a road between Norris Junction and Madison Junction for almost one day due to the landslide hazard (Pitt, 1979). Based on

19 8 the previous studies, all these large and small earthquakes appear to be highly correlated with Yellowstone volcanic activity and fault systems as described below. Geologic Setting of the Yellowstone Park Area As the most volcanically and seismically active region in the United States, Yellowstone National Park covers an area of 8,983 km 2 (Rubeis, 2006). It is mostly located in Wyoming, with a small portion in Montana and Idaho. There are several unique geologic features in and around the national park area, including Yellowstone caldera, hydrothermal areas like the famous Old Faithful Geyser, and unique ecological systems. Yellowstone National Park is also a classic case for studying the relationship between seismic activity, volcanic activity, and fault system. The Yellowstone National Park is one of the most geological valued regions in United States (Figure 1). The park lies on the 2 km-high Yellowstone Plateau and intersects with a 1,300 km-long Intermountain Seismic Belt, which extends from northern Montana south to northern Arizona (Smith and Arabasz, 1991). A hotspot in the upper mantle of earth s crust, which currently exists beneath the Yellowstone National Park, is thought to be responsible for the abundant volcanic and seismic activity in this area (Yuan, 2010). Unlike most hotspots, which occur beneath the ocean, Yellowstone s hotspot lies under the North America continent with a mantle plume between a depth of km according to tomographic research (Smith, 2009). Tremendous heat and magma are generated from the mantle plume, which propagates to the surface of tectonic plate, and melts the surrounding rocks (Chang et al., 2010). At the same time, the

20 9 North American plate is moving at a rate of 4.6 cm/yr toward the southwest, leaving behind a track of major volcanic activity and accompanying earthquakes as landmarks. Over the last several million years, three large volcanic eruptions happened at 2.1, 1.3, and 0.64 Ma (Chang et al., 2010). The Yellowstone caldera, an 80 x 64 km depression, is the result of the most recent massive volcanic eruption, which occurred 630 Ka ago. This collapsed basin is filled with younger sediments and rhyolite flows, the youngest of which occurred 70 Ka years ago on the southern rim of the caldera (USGS, 2004). Smaller basaltic eruptions are also found around the margin of the caldera. Two 500 m high resurgent domes lie on the southwest and northeast side of the caldera, indicating the continuing intrusion of hot magma into the upper crust. Being an active volcanic area, thousands of earthquakes, geysers, hot springs, other unique geologic features, and ecologic environments together contribute to this unique park.

21 10 Figure 1. The distribution of all the earthquakes from 1972 to 2011, divided into two categories by magnitude. The larger dots represent earthquakes over 3 magnitude, and the smaller dots are the earthquake under 3 magnitude. Note the spatial relationship between the earthquakes and the caldera and faults.

22 11 The Intermountain Seismic Belt is a zone of normal faulting extending across southern Nevada/northern Arizona, Utah, Idaho, Wyoming to the northwest Montana (Figure 1). It lies across the boundary of Basin and Range province and intersects with the Rocky Mountains, Yellowstone National Park, and nearby Teton National Park and has a SE-NW trend (Sbar, 1972). Subduction of the Pacific plate under the North American plate generated this seismically active zone with most of the earthquakes occurring at a shallow depths of less than 20 km. The magnitude 7.5 Hebgen Lake earthquake was the largest historic earthquake in both Intermountain Seismic Belt and Yellowstone National Park (White, 2009). In addition to the Intermountain Seismic Belt, volcanic movement also creates a ring of normal faults along the rim of the caldera (Figure 2). Monitoring Seismic Activity in the Yellowstone Park Area Yellowstone National Park has long been monitored and studied since the first earthquake reported by Hayden in 1871 (Hayden, 1873). As a wonderful area to study the seismic activity, volcanic activity, fault systems, and other geologic triggers, Yellowstone National Park has been the site of various monitoring and research studies from early 1950s to the present. Several Global Positioning System (GPS) stations are installed around this area to detect the real-time ground deformation in and around the caldera. Interferometric Synthetic Aperture Radar (InSAR) is also utilized to investigate the motion of the caldera. The United States Geological Survey (USGS) plays an important role in collecting seismic data and conducting real-time monitoring data. The Earthquake Information Center at University of Utah contributes seismic data, earth structure analysis, and interpretation. The

23 12 Figure 2. Map of the Intermountain Seismic Belt. The square highlights the location of Yellowstone National Park.

24 13 Yellowstone Volcano Observatory (YVO) also maintains a cooperative partnership between the U.S. Geological Survey (USGS), Yellowstone National Park, and University of Utah to strengthen the long-term monitoring of volcanic and seismic activity in the Yellowstone National Park region. Summary of Seismic Research in the Yellowstone Park Region In general, seismic activity in the Yellowstone area is intimately related to the Yellowstone volcanic system, hydrothermal features, and the Intermountain Seismic Belt. Under the effect of these geologic controls, the seismic activity in Yellowstone National Park falls into several time, space, or magnitude clusters. The most intense activity occurs in the northwest part of the Yellowstone caldera near the 1956 Hebgen Lake earthquake (Figure 1), which is also the location of several large, long lasting earthquake swarms (Waite and Smith, 2002). This zone extends from the Hebgen Lake to the northern rim of caldera with the highest cumulative seismic motions. The focal depth of those earthquakes varies from 3 to a maximum of 12 km near Hebgen Lake area. The focal depth of earthquakes varies dramatically within and outside the caldera. Most of the seismic activity within the caldera occurred at less than 5 km depth, whereas that outside the caldera to the northwest and southeast is more than 10 km deep (Figure 3), especially ones with maximum depth of 15 km in the Hebgen Lake region. This clear transition is believed to be related to the movement of magma, which is at a depth of 6-15 km melts the surround rocks beneath the caldera surface and uplifts the contact layer between brittle and ductile rocks to no more than 5 km (Smith and Arabasz, 1991; Miller and Smith,

25 ). The accumulated pressure triggers the shallower earthquakes in the upper and surrounding brittle layers within the caldera. Being a seismically active area with clear spatial clusters of earthquakes, distinctive focal depth variation and other associated geologic features, Yellowstone National Park area is chosen as a study case to simulate and modeling the pattern of seismic activity. To better understand the geologic factors related to seismic activity, previous studies are summarized below. Earthquake Swarm, Volcanic and Geothermal Activity An earthquake swarm is a group of small magnitude (less than 3) earthquakes that lasts for days or even months. In the history of Yellowstone seismic activity, the swarm is one of the most important categories of earthquakes, which has been found mostly within the extent of each caldera, between the three calderas, and along the zone from the calderas to Hebgen Lake (Figure 4). For instance, over 1,000 earthquakes occurred during the time period between December 27, 2008 and January 7, 2009 in Yellowstone Lake area. The occurrence of shallow focus earthquake swarms has been shown to be highly associated with the presence of geothermal features (Waite and Smith, 2002). For instance, there was a close relationship in both number and location of earthquake swarms and geothermal temperatures and flow rates near Norris Geyser Basin in the caldera, between the three calderas, and near the northwest zone of Hebgen Lake earthquake (Figure 4). For instance, over 1,000 earthquakes occurred during the time period between December 27, 2008 and January 7, 2009 in Yellowstone Lake area. The occurrence of shallow focus

26 Figure 3. The distribution of earthquakes from 1972 to 2011 color coded by depth. 15

27 16 earthquake swarms has been shown to be highly associated with the appearance of geothermal features (Waite and Smith, 2002). The subsidence of Old Faithful Geyser caused by fluid migration is also correlated with nearby earthquake swarms in the recent decades (Waite and Smith, 2002). The Yellowstone hydrothermal system is mostly located near the two resurgent domes in the most recent caldera, and follows the fault system to the northern Norris Geyser Basin (Waite and Smith, 2002). For some geothermal areas, there is a correlation between the hydrothermal features and earthquakes swarms clusters both in time and space, such as Upper Geyser Basin and central part of Yellowstone Lake area; on the other hand, some swarms occur away from the areas of hydrothermal activity, like West Thumb Geyser Basin and Lower Geyser Basin (Figure 4). This correlation has been explained by the movement of hydrothermal fluids. The hydrothermal system is derived from the heated fluids around the magma bodies at km depth. Hot meteoric and magmatic fluids migrate out from rhyolitic layer or magma chamber, and are transported along the ductile permeable rocks and fracture system within the shallow crust into the brittle area outside the caldera (Waite and Smith, 2002). Increased pore fluid pressure decreases the shear stress needed for slipping on faults and fractures, and triggers small magnitude earthquakes in the shallower crust. The movement of hot fluids not only explains the correlation between earthquake swarms and hydrothermal areas, but also limits the focal depth difference of earthquake within and outside the Yellowstone caldera. The ground deformation also is related to the migration of hot fluids and fluctuation of geothermal system shown by GPS and InSAR data (Waite and Smith. 2002).

28 17 Figure 4. The distribution of the three largest earthquake swarms in Yellowstone National Park area in the relation to the calderas, faults, and geothermal areas.

29 18 Besides clustering with the hydrothermal areas, the earthquake swarms are also impacted by the magma generated from the hotspot. As discussed above, the Yellowstone volcano is still active. Migration and accumulation of magma depresses or raises up the entire caldera as indicated by the subsidence or uplift of the ground surface (Waite and Smith, 2002). This subsidence or uplift sometimes lasts a long time, but can reverse within a short period of time. The earthquake swarms appear to be correlated to this sudden shift of caldera ground deformation in both location and time as shown by station measurements (Waite and Smith, 2002). The earliest ground deformation measurements were done in 1923 by the first-order leveling method (Pelton and Smith, 1982), and indicated the caldera uplifted up to 1 m from 1923 to1984. The maximum uplifted area is around the central of the caldera with a rate of 22 mm/yr from 1976 to A sudden shift from uplift to subsidence happened in 1985 accompanied by the first large earthquake swarm (Waite and Smith, 2002). This shift was accomplished within one year and the earthquake swarms concentrated along the northwest direction and moved away from the caldera nearly 150 m/d. After this, the caldera continued to subsidence from 1985 to 1995 with a rate of 19 mm/yr and a total amount of nearly 190 mm in one decade (Dzurisin, 1990). Another shift occurred in Norris Geyser basin in 1995 transferring from a decade of subsidence to local uplift, also was accompanied by another large earthquake swarms in June 1995 around the same area. This uplift lasted until 2000 and was also detected by InSAR monitoring.

30 19 Fault Systems Besides the effect of volcanic activity on the seismic patterns, the northwest-trending Cenozoic Intermountain Seismic Belt and local fault system also influenced the earthquake activity (Smith and Sbar, 1974). In the Yellowstone National Park area, the fault system starts from east of West Yellowstone Basin to the east end of Hebgen Lake fault (Figure 2). The east part of fault system contains Norris Geyser Basin, northwest-trending faults, and Gallatin Range. The west portion of fault system is mainly Hebgen Lake fault zone. Moreover, normal faults in the Basin and Range area have the capability to contribute to the large magnitude earthquakes near the boundary of the Yellowstone Plateau and east in the Snake River Plain (Waite and Smith, 2004). As shown by the fault plate solution of the 364 double-couple focal mechanism, the fault system in Yellowstone National Park is accommodating a general crustal extension (Hamilton and Myers, 1966), which is consistent with the deformation in the Intermountain Seismic Belt intersecting the Yellowstone National Park, and the Hebgen Lake fault zone, which is under the north south extension (Puskas, 2007). The normal fault system is not only responsible for the transport of hydrothermal fluids and earthquake swarms, but also contributes to some of the large earthquakes. The most representative one is the magnitude 7.5 Hebgen Lake earthquake along the Hebgen Lake fault (Trimble and Smith, 1975). Remote Triggers Other than the influence of volcanic activity, and faults, and hydrothermal activity, the earthquakes in Yellowstone National Park area can also be affected by remote large

31 20 magnitude earthquakes. For instance, a large magnitude earthquake in Alaska earthquake in 2002 triggered more than 250 earthquakes throughout the Yellowstone caldera within the following 24 hours, especially around the geothermal areas in and around the caldera (Husen, et al., 2004). Activity in the Intermountain Seismic Belt in nearby Teton National Park also has the capability to trigger small earthquakes in Yellowstone National Park area (White, 2009).

32 21 METHODLOGY Point Process Model Point process refers to how existing point pattern localize in space or time. As a spatial statistical method, point process modeling aims to explore, simulate, and predict point patterns by parametric model-fitting (Baddeley, 2010). The point can be unmarked or marked with specific characteristics attached, such as the type of trees, the size of the area, or the magnitude of the earthquakes. This point pattern could be totally random or highly clustered when evaluated by certain statistical tests. The modeling process could be assisted with or without continuous explanatory covariates, which are assumed to explain the behavior of the point pattern (Baddeley and Turner, 2005). Point process modeling has long been an essential strategy to explore the point patterns in areas including neuroscience, forestry and plant ecology, astronomy, and seismology (Baddeley, 2010). Point process modeling consists of determining first and second order effects in order to understand their statistical significance. The first order effect shows the average point number in each unit, which can be indicated by intensity and density test (Baddeley, 2010) The point pattern could be homogeneous or clustered in specific units to tell the distribution trend of point process modeling. The second order effect represents variation of point number in each unit, illustrating the interaction relationship between different types of point or inter-point in the expression of distance (Baddeley, 2010). Point pair tests in second order effects include Ripley s K, F, G, and L-function, which are also called as nearest neighborhood distribution functions. Based on differences in the properties of point patterns indicated by first and second order

33 22 effects, several point process models fitted by ppm (point pattern model) object in R are suggested to simulate the point pattern in point process modeling. For instance, in the Complete Spatial Randomness (CSR) situation with uniform intensity λ, homogeneous Poisson Point Process can be fitted into the point pattern, which is also called as null model in statistical meaning (Baddeley, 2010). The extent of all the points is defined as a window, W; and any location within this extent is defined as u; so the point pattern x under homogeneous Poisson Point Process and conditional intensity λ>0 can be expressed as: λ (u, x) = β (1) The inhomogeneous Poisson process is a model with intensity function β (u): λ (u, x) = β (u) (2) For clustered point patterns, the distribution depends on the interaction parameter, interaction distance between each point pair, and distribution density. Strauss point process is one of the models used to investigate these clustered relationships as proposed by Strauss (1975). The Strauss Point Process is a pair-wise interaction model with interaction constant γ, and the distance radius less than r. The t (u, x) represent how many points from X are located within the r radius (Baddeley and Turner, 2005). λ (u, x) = t( u, x) ( u, v) (3) Since a point can be marked as different types, the Multitype Strauss Process is one Strauss Point Model which pair-wise interaction depends on not only the interaction among points, but also the type of the points, or mark. (Baddeley and Turner, 2005): 1 if c( u, v) if u v u v r r (4)

34 23 The evaluation of parameters can be judged by the Maximum Likelihood Estimation, a way to decide which pair of index is able to make the probability distribution to the maximum compared to the observation data (Akaike, 1973). The information derived from the exploration portion of the analysis indicates the modeling parameter choice with the Akaike Information Criterion (AIC) in which npar represents number of parameter, and k = 2 for usual AIC (Akaike, 1973; Baddeley and Turner, 2005). The lower value of AIC indicates a better parameter. AIC=-2*log-likelihood + k*npar (5) The goodness-of-fit of simulated model also can be judged by the simulation envelope. Certain statistical method, like Nearest Neighborhood Distance Estimation, is used to evaluate the ability of the model to summarize the statistical significance of the observation data. Random number of points can be generated based on the simulation model. The result generates an upper and lower boundary of distribution, in other word, an envelope. If the observation data all fall into the envelope, we say the simulation model captures the variability of the observation data well (Baddeley and Turner, 2005). Earthquakes can be treated as a series of point data with attributes of location, time, magnitude, and depth. The large number of earthquakes that happen in one specific area over time can be equivalent to a seismic pattern with first and second order effect and other mathematic indications behind it. The study of this seismic pattern can contribute to the understanding of the earthquake activity and exploration of its relationship with geologic features. In this paper, different point process models will be applied to earthquakes of Yellowstone National Park area to simulate the seismic pattern so as to test the role of

35 24 different geologic variables in the earthquake mechanisms and evaluate the potential application of point process modeling to study seismic events. Exploratory Data Analysis The seismic dataset used in this study was obtained from the Earthquake Information Center, University of Utah. All available earthquakes are from November 8, 1972 to December 21, 2011 were used. This includes a total number of 38,582, with 3,332 greater than or equal to magnitude 3 and 38,250 less than magnitude 3. Associated geologic information consisting of the location of faults, hydrothermal features, and caldera-related data are from Montana s Official State Website. From the total dataset, this study will focus on the magnitude 6.1 earthquake on Jun 30, 1975 and its aftershocks (Figure 5). Point process modeling was implemented to simulate the earthquake distribution and test the hypothesis of captured geologic variables for further seismic hazard assessment and prediction. The software utilized in the research are ARCGIS 10.0, open source software R and its statistical packages including point process package SpatStat, sp, and related point process functions and models for spatial statistical analysis, like G-test, K-test, Poisson models, and Strauss model (Baddeley and Turner, 2005). To prepare for the point process modeling, a total 115 earthquakes, including the magnitude 6.1 main shock on Jun 30, 1975 and its aftershocks until July 13, are divided into two categories: magnitude greater than or equal to 3, and magnitude less than 3. The reason to categorize earthquakes in this way is based on the statistical feature of historic seismic activity. Most of the earthquakes in Yellowstone National Park are smaller than magnitude 3, especially numerous earthquake swarms. Besides,

36 25 Figure 5. The aftershocks of magnitude 6.1 earthquake near Norris Geyer Basin from June 30, 1975 to July 13, 1975.

37 26 earthquakes less than 3 magnitude are usually imperceptible. These categories are demonstrated as marks (small and large) in the point process model to investigate the pair-wise interaction among each category of earthquake. A class of objects in R named ppp (planar point pattern) was used to handle 2D point pattern data in the spatial analysis package SpatStat, defined as ppp (x, y, xrange, yrange, marks = m). In theory, x and y represent the location (or longitude/latitude) of each point; xrange and yrange are the extent of study area (by the unit of meters in this study); m is the data type or mark of the point. In our study, x and y is the location of earthquakes under projected geographic coordinate of NAD_1983_UTM_Zone_12N. Categorized earthquake data are marked as small (less than magnitude 3) and large (greater than and equal magnitude 3) to make a Multitype Strauss point pattern. The research extent of point process modeling is defined as the maximum x and y coordinates of earthquake distribution (Figure 6). The exploratory analysis of class ppp summarizes the basic statistical variance of the earthquake pattern. For instance, Figure 6 shows the overall distribution of earthquakes from Jun 30, 1975 to Jul 13, 1975 and Figure 7 shows the distribution of each type of earthquakes. There are total 115 points in the point process modeling with marks of small or large magnitude and frequency information is summarized in Table 1. Two earthquakes are not considered in this point process modeling because they out lie of the extent. However, the physical reason for the occurrence of these two points near Hebgen Lake fault can be explained by the spatial correlation with the fault. Since the point process modeling focus is to investigate the main relationship between each mark of earthquakes and related geologic information, these two outliers are not considered in the modeling.

38 27 Figure 6. The distribution of earthquakes from Jun 30, 1975 to Jul 13, 1975 in meters. The triangles represent the small earthquakes, and the circles represent the large ones. The lower Figure shows the distribution of each type of earthquakes.

39 28 Figure 7. The distribution of each category of earthquakes from Jun 30, 1975 to Jul 13, 1975 in meters.

40 29 The histogram of earthquake magnitudes in Figure 8 shows most of the earthquakes are small and out weight the average frequency of large earthquakes for this earthquake event. The histogram of depth (Figure 9) shows that most of the other earthquakes have focal depths of less than 5 km, which is similar to most of focal depth of historic earthquakes within the caldera. The shallow focal depth near Norris Basin location also suggests a role of hydrothermal fluids and factures in this earthquake event. The first order effect of this earthquake event aims to test the Complete Spatial Randomness (CSR, henceforth) by intensity function shown in Figure 10a. All earthquakes show a distribution interest of large and small earthquake both around the main shock but under a slightly different trend of direction (Figure 10b). This inhomogeneous point distribution and marks of different magnitude of earthquakes suggest a pair inter-point process modeling, such as Strauss model or Multitype Strauss model. The second order effect of the earthquake pattern reveals the inter-point relationships among large and small earthquakes. G-test (Gross function in R) demonstrates the distance from nearest neighborhood of pair-wise inter-point. As Figure 11, 12, 13, and 14 shows, the simulated curve is significantly above the theoretical curve of Poisson process modeling, meaning the earthquakes are highly clustered among same and difference earthquake types. The pair-wise interaction radius among small and large magnitude earthquakes illustrated the statistical features between different types of seismic patterns. The cumulative distribution from small to large earthquakes indicates the maximum effect radius is 800 m, illustrating a tightly clustering distribution of small earthquakes around large ones (Figure 14). On the other hand, the maximum radius of nearest large earthquakes around small ones is within 10

41 30 Table 1. The summary table of earthquake point pattern. Marked planar point pattern: 115 points Average intensity 6.39e-08 points per square unit Multitype: frequency proportion intensity large e-09 small e-08 Window: rectangle = [497685, ]x[ , ]units Window area = square meters

42 Figure 8. Distribution of earthquake magnitudes without the two outliers. 31

43 Figure 9. Distribution of earthquake focal depth without the two outliers. 32

44 33 a. b. Figure 10. The density contrast of earthquakes on Jun 30, 1975 and its aftershocks. (a) The density contrast of all earthquakes from Jun 30, 1975 to Jul 13, 1975 in three dimensions. (b)the density contrasts of two types of earthquakes without two outliers are showed with the probability of occurrences.

45 34 km, which means a relatively loose clustering distribution of large earthquakes around small ones (Figure 11). For the nearest neighborhood from the same type of earthquakes, the maximum distance from one large earthquake to another large one is within 1500 m, demonstrating all the large earthquakes are close to each other (Figure 13). The largest interaction distance between small earthquakes is also clustered to be within 2000 m (Figure 12). The Nearest Neighborhood Algorithm (G-function in R) not only reveals the interaction radius among different interaction parameters, but also a key element for the seismic pattern to fit in the Multitype Strauss Model. Since the Multitype Strauss Model also allow the interaction radius as a symmetric matrix (Baddeley and Turner, 2005), effect radius r can only be determined by best fit from observation data (Table 2)and result of Nearest Neighborhood Algorithm (Isham, 1984).

46 35 Table 2. The Interaction Radii among each type of earthquake in the unit of meter. Interaction radii: large small large small

47 36 Figure 11. The result of the cumulative distribution of nearest neighborhood (Gross test in R) from small to large earthquakes in meters. The blue line represents the distribution summary based on completely random distribution. The black line is the observation data and the red and green lines are the correct and smoothed observation data.

48 37 Figure 12. The result of the cumulative distribution of nearest neighborhood (Gross test in R) from small to small earthquakes in meters. The blue line represents the distribution summary based on completely random distribution. The black line is the observation data and the red and green lines are the correct and smoothed observation data.

49 38 Figure 13. The result of the cumulative distribution of nearest neighborhood (Gross test in R) from large to large earthquakes in meters. The blue line represents the distribution summary based on completely random distribution. The black line is the observation data and the red and green lines are the correct and smoothed observation data.

50 39 Figure 14. The result of the cumulative distribution of nearest neighborhood (Gross test in R) from large to small earthquakes. They show the interaction distance among large and small earthquakes within different distribution radii in meters. The blue line represents the distribution summary based on completely random distribution. The black line is the observation data and the red and green lines are the correct and smoothed observation data.

51 40 RESULTS Based on the result of exploratory data analysis of the earthquake pattern and previous studies of relationship between the geology and seismic activity, four different Multitype Strauss Models were tested to investigate the distribution interaction among each type of earthquake mark and possible geologic variables, including the occurrence of geothermal features, distance to the faults, and focal depth of earthquakes. An object named ppm is built to fit the Multitype Strauss Model in R. X represents the dataset of the point pattern; trend represent the general distribution orientation of the point dataset, often showing as polynoms with different degrees depending on the complexity of the pattern (Baddeley and Turner, 2005). The trend could be ~1 for stationary Strauss process, or ~x + y for a non-stationary Poisson process with a loglinear intensity, or ~ polynom(x, y, 2) under 2 order polynoms in the Cartesian coordinates in which the intensity is in a log-quadratic spatial trend (Baddeley and Turner, 2005). The interaction reveals the correlation between the each data type, illustrating by the interaction radius among small and large earthquakes in this study. ppm (X, trend, interaction,...) (6) The first model is purely based on the interpoint relationship among large and small magnitude earthquakes. The radii showing interpoint correlation was determined from the second order effect as discussed above. The matrix of radius cannot totally rely on the result of G-function, because the Multitype Strauss Model limits the radius matrix only to be a symmetric equation. However, the best radius applied in the study can be determined by observation of the real seismic pattern, result indicated by G-function, and numerous attempts

52 41 for achieving a result most similar to reality (Isham, 1984). The final radius applied in this study is: r <- matrix (c (1500, 10000, 10000, 2000), nrow=2, ncol=2) (7) The most appropriate Multitype Strauss Model based on marked earthquakes and interaction radius among different marks was decided on after numerous tests as: ppm (EQP, ~ polynom (x, y, 2), MultiStrauss (c ("small", "large"), r)) (8) which achieves the best fit with AIC = The result of the Multitype Strauss Model returns estimated values of interaction parameters and fitted coefficients as follows.

53 42 Figure 15. Fitted trend from Multitype Strauss Modeling of the probability of occurrence among small and large magnitude earthquakes.

54 43 The value of interaction parameters demonstrates the clustering relationship among earthquake marks. For instance, the interaction radii between large and large earthquakes and between small and small earthquakes are both larger than 1, meaning the seismic pattern is highly correlated among same type of earthquake. Since the interaction radius between different types of earthquakes is approximately 1, there is a possibility for those interactions to be clustered more than inhibition. The fitted trends of each type of earthquake are shown in Figure 15 illustrating the possibility of earthquake events by graduated colors. The goodness-of-fit can be carried out by evaluating the fitness between observation data and simulated envelop of K, G-functions (Figure 16), in which the upper and lower boundaries are developed by randomly generating realistic data under the fitted model and calculating the distance from the nearest neighborhood (Baddeley and Turner, 2005). If the observation pattern lies between the upper and lower boundaries of generated simulation envelop, the model is considered to reflect an adequate fit. As the Figure 16 demonstrates, most of the observation data fall between the upper and lower boundaries of simulated envelopes indicating the Multitype Strauss Model and the interaction radius explain most of the variability of earthquake distribution. However, there is still some observation data that fall out of the simulated envelop, meaning some variables related to the seismic pattern are still unexplained. Multitype Strauss Model also can be utilized for the scenarios in which the seismic pattern depends on spatial covariates (Baddeley, 2010). Based on the previous studies, the presence of faults, location of hydrothermal areas, and focal depth of earthquakes are suggested to control the earthquake distribution. In this thesis, those geologic factors

55 Figure 16. The result of K and G test envelope function in meters. The envelope is created by 44

56 45 99 randomly generated points, and the black line is the observation data.are separately tested as covariates in Multitype Strauss Model to investigate and verify those geologic influences on interpoint interaction between earthquakes. To prepare for the model fitting, the covariates are integrated into a format of pixel image or data list. The distmap function in R calculated the distance to line segments by meter as the covariate of distance-to-fault (Figure 17) in which the fault system includes the Intermountain Seismic Belt and caldera ring faults. The occurrence of hydrothermal system is converted from a shapefile in ARCGIS and clipped by the extent of earthquake patterns (Figure 18). The earthquake focal depth covariate is interpolated and fitted into a trend surface by Generalized Least-squares in surf.gls function (Figure 19 and 20). All the covariates converted in to R are under projected geographic coordinate NAD_1983_UTM_Zone_12N and unit by meter. The Multitype Strauss Model with covariate of distance-to-fault is first applied to investigate the impact of fault system on seismic activity by the same radius matrix. fit <- ppm (EQP, ~ Fa + polynom (x, y, 2), covariates=list(fa=f), MultiStrauss (c ("large","small"), r)) (9) The AIC of the model is Decreased AIC value demonstrates the suitability of the model and effect of newly added fault-to-distance covariate. The value of interaction parameters and other returned results are:

57 46 Figure 17. The distance-to fault covariate in research extent in meters. Figure 18. The location of hydrothermal area in research extent.

58 47 Figure 19. The contour map of fitted focal depth in research extent in meters. Figure 20. The smooth surface of potential focal depth in research region.

59 48 The fitted trend of this model is demonstrated in Figure 21. The Multitype Strauss Model with covariate of hydrothermal system location is the second to be applied. fit <- ppm (EQP, ~ The + polynom (x, y, 2), covariates=list(the=th), MultiStrauss (c ("large","small"), r)) (10) The resulting AIC is , which is slightly larger than the first model. The increase of AIC value indicates the location of hydrothermal system does not explain the earthquake distribution in Multitype Strauss Model. The estimated values of interaction parameter of the second model are:

60 49 Figure 21. The fitted model with distance-to-fault covariate and with the probability of occurrence.