School of Sciences

Faculty of Geosciences

Undergraduate Thesis:

Seismotectonic Characterization of the Colombian Pacific Region: Identification of Tectonic Patterns Through Geostatistical Analysis

María Daniela Gracia

201222439

Director: Fabio Iwashita

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Co-Director: Jean Baptiste Tary

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November 24/2017

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I wish to thank my mother Pilar, father Daniel and sisters Manuela and Sara for being a constant source of help and encouragement. Special thanks to my lovely boyfriend Jesse for supporting me and helping me believe in myself and to friends who have supported me throughout the process. And finally, I wish to thank the faculty of geosciences and my professors Fabio Iwashita and Jean Baptiste Tary for their motivation, disposition to help and great knowledge.

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Abstract

Earthquake occurrence is a consequence of many processes within the Earth such as tectonic stress loading, fluid diffusion or static stress triggering. As a result of this, patterns of spatial and temporal distribution, that earthquakes have historically displayed, keep the footprint of the mechanisms that give them origin. Quantifying these patterns and the extent of the causality and correlation between seismic events is then an interesting and useful subject of study. It is useful because it opens the doors to more accurate estimations of the behavior of earthquakes, which inherently decreases the risk of catastrophes. The Colombian Pacific region is a zone that presents a high degree of geological complexity, it lies parallel to a trench where the Nazca plate subducts below the South American Plate, which inherently results in increased seismic activity and rupture. In this study a sequence of 134 events that happened in this zone in a period of 68 months is studied. These earthquakes are organized in complex spatial structures that were separated trough clustering analysis and then subjected to geostatistical analysis. The geostatistical analysis consisted of: an evaluation of the distribution of events as a function of time and a semivariogram analysis, by which the degree of correlation between events was studied. The interaction within these events is highly complex but, to some extent, some system wide correlations are observed. As opposed to what was initially expected, the semivariogram analysis did not manage to measure the degree of correlation for this particular sequence. What this means is that all semivariograms lie within a zone that denotes no-correlation and present a generalized uncorrelated form.

- 3 - Resumen

La ocurrencia de terremotos es la consecuencia de los múltiples procesos que ocurren en el interior de la Tierra como lo son la carga tectónica por esfuerzo, la difusión de fluidos o el desencadenamiento por esfuerzo estático. Como resultado de esto, los patrones de distribución espacial y temporal que los terremotos han mostrado históricamente guardan la huella de los mecanismos que los originan. Cuantificar dichos patrones y la extensión de la causalidad y correlación entre eventos sísmicos es por lo tanto una materia de estudio útil e interesante. Es útil ya que abre las puertas a un área de estudio donde las estimaciones del comportamiento de los terremotos adquieren mayor precisión, lo cual inherentemente reduce el riesgo de catástrofes. La región Pacífica de Colombia es una zona que presenta un alto grado de complejidad en su geología, yace paralela a una trinchera donde la placa Nazca subduce por debajo de la placa Sur Americana, lo que automáticamente resulta en una mayor actividad sísmica y en ruptura. En este estudio se considera una secuencia de 134 eventos que ocurrieron en esta zona en un periodo de 68 meses. Estos terremotos se organizan en estructuras espaciales complejas, dichas estructuras fueron separadas por medio de análisis de clusters y luego analizadas usando métodos geoestadísticos. El análisis geoestadístico consistió de: La evaluación de la distribución de los eventos como función del tiempo y un análisis de semivariogramas, por medio del cual el grado de correlación entre los eventos fue estudiado. La interacción entre los eventos estudiados es de alta complejidad, sin embargo, hasta cierto punto es posible observar correlaciones a lo largo de todo el sistema. A diferencia de lo que se esperaba, el análisis por medio de semivariogramas no logró medir el grado de correlación para esta secuencia particular. Lo que esto significa es que todos los semivariogramas experimentales obtenidos se encuentran dentro de una zona que denota ausencia de correlación y en general presentan una forma que no muestra relación entre la causalidad de los eventos.

- 4 - Table of Contents

1. Chapter 1. Introduction (6)

2. Chapter 2. Geology of the Colombian Western Margin (8)

2.1 Geological Setting (8) 2.2 Tectonic Setting (10) 2.2.1 Tectonic Background (14) 2.3 Main fault systems (17) 2.4 Seismicity (21) 2.4.1 Colombian National Seismic Network (Red Sismológica Nacional de Colombia) (21) 2.4.2 Historical seismicity (21) 2.4.3 General Characteristics of Seismicity (24)

3. Chapter 3: Theoretical Framework (31)

3.1 Seismology Framework (31) 3.1.1 Focal Mechanisms (31) 3.2 Geostatistical Framework (34) 3.2.1 Geostatistics (34) 3.2.2 Preliminary Definitions (36) 3.2.3 Semivariogram Analysis (38) 3.2.4 Cluster Analysis: K-Means (40)

4. Chapter 4. Data Selection, Processing and Methodology (42)

4.1 Data Selection, Variable Overview and Exploratory Analysis (42) 4.2 Spatial and Temporal Classification of Earthquakes: Clustering of the Data (44) 4.2.1 Spatial Clustering Results (49) 4.2.2 Temporal Clustering Results (51) 4.3 Distribution of Earthquakes as a Function of Time (52)

- 5 - 4.4 Semivariogram Analysis of the Data (53) 4.4.1 Correlation of Earthquakes on Individual Features (55) 4.4.2 Correlation of Earthquakes in the System (57) 4.5 Focal Mechanisms (58)

5. Chapter 5. Results, Discussion and Conclusions (58)

5.1 Clustering of the Data (58) 5.2 Fault Interaction - Earthquakes as a Function of Time (60) 5.3 Correlation of Earthquakes on individual Faults and in the System: Evaluation of Semivariogram Functions (62) 5.4 Conclusions (63)

6. Appendix A. Spatial Clustering Characteristics (66)

7. Bibliography (69)

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1. Chapter 1. Introduction.

Subduction zones have four main types of associated events: (1) shallow events occurring in the crust, (2) intraplate events due to bending of the subducting slab ahead of the trench, (3) large intraplate events and (4) deep events associated to the Wadati-Benioff zone (Scawthorn & Chen, 2002). The seismicity of the Western Colombian Margin (WCM), where the Nazca Plate subducts below the South American Plate, has been predominantly studied in terms of the associated Wadati-Benioff zones, large intraplate events, seismic nests (Cauca and Bucaramanga),current state of stress, seismic hazard and slab geometry (Barazangi & Issacks, 1976; Suárez, Molnar & Burchfiel, 1983; Wysession, Okal & Miller, 1991; Taboada,2000; Chen, Bina & Okal, 2001; Rietbrock & Waldhauser, 2004; Pedraza Garcia, Vargas & Monsalve, 2007; Pararas-Carayannis, 2012; Castilla & Sánchez, 2014; Salcedo-Hurtado & Pérez, 2016, Wagner et al, 2017.) Although it is known that seismicity in the region surrounding the trench (type 1 and 2 events) is mostly associated to active tectonic features, a more in depth study, that properly groups the events, associates them to different structures and quantifies their characteristics, is yet to be developed.

It is well known that earthquake occurrence is not randomly distributed, instead it is a phenomenon that when observed over long temporal and spatial scales behaves in a coherent and structured manner (Walsh and Watterson, 1991; Nicol et al., 2006.). As a realization of this, historical seismicity has shown evidence of both spatial and temporal clustering (Plafker & Savage, 1970; Stein et al, 1997). This behavior is directly linked to the conduct of

- 7 - the mechanisms triggering the seismic events (tectonic static stress triggering, fluid migration and extraction, etc.). Therefore, given that seismic behavior does not occur randomly, geostatistics becomes a great tool in order to quantify its characteristics.

Geostatistics have been developed in order to model and evaluate natural resources and phenomena, its main assumption is that spatial auto correlation exists (Olea, 2006). It is a useful approach at quantifying seismic information, given that it helps measure the extent and behavior of spatial correlation through tools such as the semivariogram. Some authors have applied this methodology to different areas of seismic study; Şen (1998) used semivariograms in order to identify heterogeneities in regional seismicity of Turkey and Shaefer et al. (2014) used clustering algorithms in order to separate background seismicity form triggered seismicity. Mouslopoulou & Hristopulos (2011) analyzed an entire earthquake sequence through semivariogram analysis and manage d to identify and measure system wide correlations. The latter study is particularly interesting given that it can lead to the quantification of interesting and useful spatio-temporal variables in a broad variety of scenarios. For this reason, the methodology proposed by Mouslopoulou & Hristopulos (2011) is the one that guides this project.

In the present study the goal is to identify and explore the existence of spatiotemporal patterns in seismic data from the Colombian Western Margin and based on this answer questions pertaining: the (1) structure of earthquake activity in space and time; (2) earthquake interaction along individual tectonic features; (3) system wide earthquake interaction; (4) interaction between different tectonically active structures. This will be

- 8 - achieved through: (a) spatio-temporal evaluation, (b) clustering procedures and (c) semivariogram analysis. Additionally, some focal mechanism solutions will be considered when performing the evaluation of the results. The paper is structured as follows: (I) geological, tectonic and seismic characterization of the region, (II) theoretical framework and (III) data selection, processing and analysis.

2. Chapter 2. Geology of the Colombian Western Margin.

2.1 Geological Setting.

The Colombian territory (Figure 1) is located on the northwestern part of South America and consists of two main regions; The eastern portion, which is mainly a plain terrain covered by savannah, fragmented forests at the north and tropical forests at the south and the western portion dominated by the Andes mountain ranges and also the subject of this study. The Colombian Andes consist of 3 mountain ranges; the Western Cordillera, Central Cordillera and Eastern Cordillera. The Western and Central Cordillera are separated by the Cauca-Patía Valley and are trending in a SW-NE direction, following the Pacific coastline. The Central and Eastern Cordillera are separated by the Magdalena Valley, at this point the Eastern Cordillera turns towards the east. Additionally, the Romeral Fault System located between the Cauca- Patía Valley and the Central Cordillera provides an additional division for the Colombian Andes resulting in the Western and Eastern Andes, respectively.

- 9 - The Western Andes region is characterized by oceanic rocks that were accreted to the continent during the Mesozoic and Cenozoic periods; The Western Cordillera is composed of turbiditic deposits and ophiolites whilst the Serranía del Baudó, a smaller mountain range located near the northern tip of the Western Cordillera, presents island arc composition (Taboada et al, 2000).The Eastern Andes (Central and Eastern Cordillera) are characterized by rock formations that have experienced several phases of deformation (Mégard, 1987); The Central Cordillera consists of a polymetamorphic (medium to low pressure metamorphism) basement (oceanic and continental) of Paleozoic age intruded by a series of plutons of Mesozoic and Cenozoic age, as well as active volcanism along its crest. The Eastern Cordillera also consists of a polymetamorphic basement (Precambrian and Paleozoic) that experienced deformation in multiple pre-Mesozoic orogenic events (Taboada et al, 2000), above the basement there is a Mesozoic and Cenozoic sedimentary sequence that was highly deformed in the Neogene (Irving, 1971).

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Figure 1. Topographic map of Colombia showing the Colombian Andes and political boundaries. (Source IGAC1)

2.2 Tectonic Setting.

Colombia is bounded by active tectonic margins in all of its coastal regions; In the north coast the Caribbean plate is moving in a E - SE trend with respect to South America creating an accretionary wedge and in the western coast (Pacific) the Nazca plate is subducing in a W-E trend forming a trench that extends for 500 to 1000 km (Norabuena et al, 1998). The rate of convergence of the Nazca and Caribbean plates (relative to South America plate) at a given location can be calculated by using the UNAVCO Plate Motion

1Geographical Institute Agustin Codazzi; Colombian entity in charge of the country’s cartography.

- 11 - Calculator2 where the different models of relative plate motions are

available. At a latitude of 4.5° north and longitude of 79° west the rate of convergence for Nazca is of 5.29 푐푚/푦푟 with an azimuth of 푁 80.2 푊. As for the Caribbean plate, at a latitude of 10.7° north and longitude of 76° west it is moving at a rate of 2.60 푐푚/푦푟 with an azimuth of 푁 58.4 퐸 (Kremmer, Blewitt and Klein, 2014).

In the Early Miocene the Farallon Plate underwent a rupture process that divided the plate into Cocos and Nazca. The splitting of the Farallon plate began in the Eocene and Oligocene (Atwater, 1989), when the Vancouver and Monterey plates detached due to pull of the California subduction zone. As for the bigger detachment (Cocos- Nazca), it was a result of: (1) An increasingly divergent slab pull at the Central and South American subduction zones below the South American plate, (2) previous detachments and (3) weakening of older portions of the plate associated to the Galapagos hotspot in the Late Oligocene (Lonsdale, 2005). After the rupture a spreading center rapidly evolved, later acquiring a direction parallel to the divergence of Cocos and Nazca plates (N-S).

The resulting Nazca plate contains evidence of stress-induced processes that occurred pre and post rupture, they manifest themselves as ridges and tears (Figure 2 (a)); although the correlation within the mechanisms is still under interpretation, Lonsdale (2005) provides a reasonable explanation. Bordering the Malpelo Island is the Malpelo Rift, now a fossil spreading

2This facility is supported by the National Science Foundation and NASA and it allows for the calculation of plate convergence rates and azimuths at a given magnitude. It can be used with different plate motion models, in this case the rates given correspond to the GSRM v2.1 (Kremmer, Blewitt and Klein, 2014).

- 12 - center, that remained active until about 8.5 Ma, linked to this structure is the Sandra Ridge (Late Miocene), an equally abandoned spreading center. The

Sandra Ridge (~ 5° 푁) presents active seismicity with focal mechanisms suggesting both strike–slip and normal faulting, the latter being less common, which has led to believe that it is undergoing reactivation (Lonsdale, 2005) as a spreading center that will eventually tear the Nazca plate (Boer et al 1998; Vargas & Mann, 2013). Lonsdale (2005) suggests that the Sandra Rift was a Cocos-Nazca spreading axis that translated west from 12 to 9 Ma, it eventually overlapped with the eastern segment of the Malpelo Rift which caused the spreading to slow down.

The geometry of the slab subducing below the Colombian Pacific trench is a matter of debate, the main observations are (1) an E-W discontinuity that marks an abrupt change in the angle of subduction near latitude 5° 푁, bounded by low angle subduction northward and normal, or more steep, subduction southward and (2) intermediate depth seismicity in the Bucaramanga Seismic

Nest (BSN) near latitude 6° 푁. Different models suggest different processes of interaction at depth and have been developed from tectonic evidence and tomographic and earthquake relocation techniques.

Taboada et al (2000) suggests that the region is experiencing an overlap of slabs at depth where the northern portion corresponds to the Paleo- Caribbean Plateau (PCP) and the southern portion to normal Nazca subduction. Both separated by a massive EW transform shear zone located at latitude

5.2° 푁, additionally the author explains the BSN as an inflexion zone in the PCP (Figure 2 (b)). Ojeda & Havskov (2001) don’t find evidence of a tear, based on observed geometry they describe two contingent subduction zones, the Cauca Subduction Zone (south) (CSZ) and the Bucaramanga Subduction Zone

- 13 - (north) (BSZ) that interact at depth. The CSZ is associated to Nazca subduction and has an angle of 35°, and the BSZ has an unclear origin with an angle of 40° in its southern portion and 27° in its northern portion, both areas are linked by a gradual change in geometry.

Other authors do suggest that the discontinuity is a tear within Nazca, Vargas & Mann (2013) describe it as a tear, or Caldas Tear as they name it, that extends for ∼ 240 푘푚 at latitude 5.6° 푁. It separates a zone of shallow (20°– 30°), southeastward subduction to the north that extends up to 11° 푁 with a WBZ located at > 300 푘푚 form the trench from a zone of steeper (30°– 40°) subduction, associated with an active NS chain of active arc volcanoes to the south which directly underlies the active Andean arc (Figure 2 (c)) (Vargas & Mann, 2013; Jaramillo et al, 2017). The proposed Caldas Tear penetrates the upper crust acting as a fault zone and is aligned with the inactive Sandra ridge (Figure 2 (a)), for this reason it has been suggested that a portion of this ridge subduced, weakened and evolved into a tear.

Chiaraba et al (2015) rephrases the issue as an abrupt offset of the Wadatti-Benioff zone at 5.8 N and suggests that the Nazca plate is segmented by an EW slab tear. The BSN is presented as an increase in the angle of subduction below the Eastern Cordillera where massive dehydration and eclogitization processes take place. Additionally, for this author it is important evidence that the tear is aligned with the Coiba Transform Fault (Figure 2 (a)), suggesting that the same structure evolved into a slab tear. Finally, Jaramillo et al (2017) have managed to better characterize history of the Pacific Margin by compiling volcanic ages and locations, they find

- 14 - that: (a) Between 14 and 9 Ma there was a continuous arc along the entire Pacific Margin directly attributed to Nazca subduction, (b) by 6 Ma a fully formed flat slab was already developed, it initially extended further to the south than it does today and (c) the current geometry has been present since

~4 Ma, therefore the Nazca Plate must comprise at least part of the northern flat slab.

Figure 2. a) Revised interpretation of the pattern of crustal isochrons and abandoned plate boundaries in the eastern Panama basin as well as main geological structures of the Nazca plate including the Malpelo and Sandra rifts. (Source: Lonsdale, 2005). b) Schematic tectonic cross section of the Northern Andes and Caribbean illustrating the geodynamic pattern after collision of the Baudó Panama island arc. (Source: Taboada et al, 2000). c) Schematic 3D model suggesting flat subduction on the northern side of the weakness zone formed by the Sandra rift and the Caldas tear. (Source: Vargas & Mann, 2013)

2.2.1 Tectonic Background.

In a geological context this region (western Colombia and surroundings) is identified as the Northern Andean Block. The Northern Andean Block can be

- 15 - separated in four lithotectonic3 realms, these realms are non-homogeneous structures that are grouped due to their genetic history (From Mesozoic- Cenozoic4 to present) and development (Cediel, Shaw and Cáceres, 2003). The ones relevant to this study are the Guiana Shield Realm, Central Continental Sub-Plate Realm and, most importantly, the Western Tectonic Realm. (Figure 3)

Guiana Shield Realm This terrain is made up of the Precambrian and autochthonous Guiana Shield, including northeastern Colombia, the eastern foreland front of the Eastern Cordillera and the Amazon basin. In this area have been identified collision, collision, penetrative deformation and high grade metamorphism during the Grenville orogeny (Pre-Andean) (Cediel, Shaw & Cáceres, 2003).

Central Continental Sub-Plate Realm (CCSP) This realm is made up of the central territory of the northern Andes including the Central and Eastern Cordilleras as well as the Magdalena Valley; The terrains of Precambrian and Paleozoic age are considered to be mostly allochtonous whilst Mesozoic to recent portions are considered to be autochthonous. This territory contains evidence of multiple pre-Andean geological events including a middle Ordovician-Silurian Cordillera type orogeny as well as deep crustal rifting during the Late Jurassic to Cretaceous

3 Lithotectonic Unit refers to a geological region or domain that has been formed and/or deformed by a distinctive tectonic environment.

4 The Mesozoic- Cenozoic period of the Northern Andean Block is characterized by accretions, deformations, uplift, and magmatism (Cediel, Shaw and Cáceres, 2003).

- 16 - in the inverted sedimentary basin of the Eastern Cordillera. (Cediel, Shaw & Cáceres, 2003).

Western Tectonic Realm (WTR) The WTR is the most relevant to this study, it is a result of the convergence of the Nazca and South America plates in the western margin of Colombia, it is made up of the region that encloses the Western Cordillera and is considered to be allochtonous. It consists of fragments of the Pacific oceanic plateau, aseismic ridges, ophiolites and island arcs that have been organized in three main terrains: Pacific Asemblage Terrain (PAT), Caribbean Terranes (CAT) to the north and the Choco Arc Terrain (CHO) in the northwest.

The PAT includes Romeral, Dagua-Piñon and Gorgona terrains, they consist of a variety of oceanic complexes including mafic and ultramafic sequences, ophiolites, oceanic sediments, basalts, pillow lavas and gabbros and are dated from the Late Jurassic to Late Cretaceous. The CAT contains the San Jacinto and Sinú terrains; The first one presents northeast structural trend while the latter has a strike and slip structural pattern within a magnetic basement, the oldest structures in the territories are from the Paleocene and Oligocene respectively. The CHO contains Cañas Gordas and Baudó and a northeast oriented vergence. Both terrains are characterized by the alternation of oceanic sediments and volcanic rocks (basalts), however, Cañas Gordas contains a few intrusions dated in the Late Cretaceous and more recently in the Eocene, the intrusions occurred prior to the accretion of the terrain to the continental land (Cediel, Shaw & Cáceres, 2003).

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Figure 3. Lithotectonic and morphostructural map of northwestern South America; (Source: Cediel, Shaw, & Cáceres, 2003)

2.3 Main Fault Systems.

Given that the Northern Andean Block is made up of a conjunction of autochthonous and allochtonous terrains of different origins and ages an

- 18 - important fault system must be present to account for this. The Colombian fault system is large and highly complex and it must be noted that strike- slip faulting is the dominant faulting mechanism; the following are the most important fault systems relevant to this study as detailed by Cediel, Shaw & Cáceres, 2003. (Figure 4).

Figure 4. a) Main fault system distribution in Colombia. (Source: Ojeda & Havskok). b) West-east transect across the Colombian Andes. Principal sutures: 1 = Grenville (Orinoco) Santa Marta–Bucaramanga–Suaza faults; 2 = Ordovician-Silurian Palestina fault system; 3 = Aptian Romeral-Peltetec fault system; 4 = Oligocene-Miocene Garrapatas-Dabeiba fault system; 5 = late Miocene Atrato fault system. (Source: Cediel, Shaw, & Cáceres, 2003)

Bucaramanga – Santa Marta Fault System Active during the Grenville Orogeny, later reactivated in the Aptian- Albian and currently active and associated to the Bucaramanga Seismic Nest. This fault system is a paleosuture that links a portion of the CCSP to the Guiana Shield, it displays a dominant left lateral displacement, with a total lateral displacement in the order of 40 km (Toro, 1990) and a total

- 19 - displacement of over 100 km (Rodríguez, 1985). Given that it is a paleosuture it presents deep crustal penetration as well as some magmatism located at the south of the seismic nest of Pliocene-Pleistocene age (Cediel and Cáceres, 2000).

Suaza Fault System It corresponds to the paleosuture that links the southern portion of the CCSP to the Guiana Shield and is connected to the Bucaramanga fault in the subsurface of the Eastern Cordillera. This fault system reactivated in the Neogene, which resulted in series of associated right-lateral oblique thrust faults (Velandia et al, 2001).

Llanos Fault System This term refers to the group of faults that formed a thrust front and allowed the Eastern Cordillera to position itself over the foreland sequences of the Llanos basin. It consists of at least three main thrust fronts one below the other in a NS direction with a predominant NE strike (Cediel, Shaw and Cáceres, 2003).

Palestina Fault System This system includes multiple faults including the Chapetón- Pericos, Ibague and Cucuana faults; it is a paleosuture for the Cajamarca and Valdivia terranes. The faults associated to this system present right lateral strike- slip displacement, evidence of shearing and merge into the Romeral fault system towards the south (Cediel, Shaw and Cáceres, 2003).

Romeral – Peltetec Fault System As it was previously mentioned, this system separates the western and eastern Andes in Colombia. It is an important suture (paleo-continent margin) where the oceanic Cretaceous territory of the Western Tectonic Realm meets

- 20 - the CCSP and Guiana Shield, it has an extension of over 1000 km and its activity began in the Triassic and Late Jurassic and reached a peak of activity during the Upper Cretaceous (Vinasco & Cordani, 2012). This system is complex and has a series of associated geological processes, which result in an assortment of geological formations (Jurassic to Late Cretaceous) that include: High degree metamorphic rocks such as eclogite and blueschist, ophiolites, volcanic rocks, marine sediments and meta sediments and mafic and ultramafic rocks. This fault system presents right lateral strike-slip displacementin some of the associated faults and a dominantly NS strike (Cediel, Shaw & Cáceres, 2003).

San Jacinto Fault System (Romeral North) This is the northern extension of the Romeral Fault System, with the distinction of absent subduction associated magmatism. It is the evidence of the accretion of the Caribbean San Jacinto and Sinú terrains to the continental margin (Cediel, Shaw & Cáceres, 2003).

Cauca Fault System This fault system corresponds to the suture where the Romeral terrain meets the oceanic terrains of Dagua-Piñón and outcrops in a large area. It is dominantly of right-lateral strike-slip motion and presents west verging thrust displacement in the sub surface (Cediel, Shaw & Cáceres, 2003).

Garrapatas-Dabeiba Fault System It corresponds to the fault that separates the PAT from the CHO terrains (Western Tectonic Realm), both oceanic, it’s origin has been suggested to be an ancient transform fault from the Farallon plate during the Late Mesozoic and Cenozoic (Barrero, 1997). It has also been linked to an already extinct ridge within the Nazca plate and has facilitated the obduction of the Cañas

- 21 - Gordas Terrain (CHO) (Cediel, Shaw & Cáceres, 2003).

Atrato Fault System This suture system occurs within the Baudó terrain (CHO) and is responsible for the obduction of the Baudó terrain above Cañas Gordas western margin. It consists mainly of east verging echelon thrust faults (Cediel, Shaw and Cáceres, 2003).

2.4 Seismicity.

2.4.1 Colombian National Seismic Network (Red Sismológica Nacional de Colombia).

The National Seismologic Network of Colombia (RSNC) belongs to the Colombian Geological Service, an important entity of the National Plan for Disaster Attention and Prevention. It began proper activities in 1993 and has grown ever since with the support of the Colombian and Canadian governments as well as the United Nations. It has a total of 50 seismic stations distributed in the Colombian territory and provides information on all registered events, this is the agency that provided the data used in this study

2.4.2 Historical Seismicity.

The history of seismicity in the Americas has its first records in the mid late XV century, this records come from the Aztecs and the Colombian and Venezuelan Indians, respectively (Ramirez, 1975). As for more concrete

- 22 - documentation, the historical background goes back to the XVIII and XIX centuries and consists of colonial documents containing personal annotations, records and some early scientific studies from historians and scientists (Espinosa, 2001). In the XX century more systematic studies began to take place, the first seismic station was installed in Bogotá in the year 1923, followed by a more modern station installed in 1941 and three more in 1948. This was also the century in which the first Colombian historic seismic catalogue was developed, it was published in 1975 by Jesús Emilio Ramírez and is a compilation of sources including: international seismic catalogues, scientific magazines, history books, newspapers, information provided by peers, verbal data from witnesses and seismographic recordings.

Figure 5. Map showing the location of some historical seismic events in the Colombian Pacific region. The events are labeled with their year of occurrence. Size indicates magnitude.

- 23 - The most significant seismic events that have taken place in the Colombian Pacific can be seen in figure 5 and include (RSNC; Kanamori & McNally, 1962; Ramirez, 1975; Herd et al., 1981; Espinosa, 2001; Espinoza, Gómez & Salcedo, 2004;)):

1906, January 1st, 10:36 am (local time, UTC-5): This event, considered as a great earthquake, occurred along the Colombian Pacific coast and is a thrust event associated to the subduction zone. Its moment magnitude is estimated to be of 8.8 and it ruptured approximately 500 km of the earth in a NE direction. It is notable for the tsunami it generated, whose magnitude has been calculated to be of 8.7, bearing heights between 2 and 5 meters. The tsunami and earthquake altogether resulted in a number of casualties between 1000 and 1500, multiple towns were destroyed and effects in nature such as cracks, soil liquefaction and landslides were noted.

1970, September 26th, 07:02 am, 09:57 am, 10:38 pm (local time, UTC-5): This series of three consecutive events did not cause any deaths, however they destroyed Bahia Solano (a town in the Colombian Chocó region) almost completely. Their respective moment magnitudes are 6.6, 5.4 and 6.5

1974, July 12th, 08:18 pm (local time, UTC-5): This event occurred in the Darien province in the Pacific coastal region of Panamá near the Colombian border in the Sambú fault. The main damage due to this event occurred in the Chocó region of Colombia and Darién region in Panama. It’s moment magnitude has been calculated to be of 7.1 at 10 km depth.

1976, July 11th, 11:56 am, 03:41 pm (local time, UTC-5): This events, both superficial, occurred close to the Pacific coast of Panamá. The first one only affected the Panamanian region and presented a smaller moment magnitude of 6.8. The second one presented a moment magnitude of 7.3 and was felt

- 24 - throughout Colombia, particularly in the Choco region, generating a small Tsunami.

1979, December 12th, 02:59 am (local time, UTC-5): This massive earthquake occurred in the Pacific coast and was felt in most of the Colombian territory with particular focus in the Pacific region. It had an 8.1 moment magnitude and occurred 80 km southwest of Tumaco at a depth of around 28 km. It had a thrust mechanism and ruptured a 280 by 130 km zone, covering some of the area already ruptured by the 1906 earthquake, in a N40W direction which resulted in subsidence of 1.2 to 1.6 m along the segment. Additionally, a tsunami that affected the entire coast all the way from Tumaco to Buenaventura (200 km) occurred as a result of this event, it’s magnitude was calculated to be 8.2 and the highest reported waves were of 2.5 m.

2004, November 15th, 04:06 am (local time, UTC-5): This event occurred near Bajo Baudó in the Chocó region, damage extended all the way to Buenaventura, Valle del Cauca and Cauca areas. It’s moment magnitude has been calculated to be of 7.2 at depth of 16 km.

2.4.3 General Characteristics of Seismicity.

Colombian seismicity is complex and abundant, most of it occurs in the Andean region and Pacific coast and is mainly linked to the subduction of the Nazca plate. Some seismicity occurs in the Caribbean region and although less studied, it is linked to the interaction between the Caribbean and South American plates. Within a time lapse of 24 years (01/06/1993 to 01/06/2017) a total of 164,868 seismic events have been recorded in the Colombian territory and its close surroundings by the Red Sismológica Nacional de

- 25 - Colombia (RSNC). As for the distribution in depth for these events 25.9 % occur between 0 and 30 km (shallow), 4.9 % between 30 and 70 km, (shallow), 10.3 % between 70 and 120 km (intermediate), 58.7 % between 120 and 180 km (intermediate) and less than 1 % for depths below 180 km (Figure 6).

Seismicity, as described by Ojeda & Havskov (2000), can be analyzed in terms of shallow and deep seismicity in order to separate different features and can be seen in Figure 6. Shallow seismicity (< 30 km) delineates the main fault systems and tectonic boundaries in the crust. In the west most seismic events are associated to the subduction of Nazca in the Colombian Pacific trench, with most of the activity concentrated towards the south. In the center of the country the seismicity is linked to the main fault systems including Romeral and Cauca, where the major part of the seismic activity takes place. High levels of shallow seismicity are observed in the eastern portion of the Eastern Cordillera in the Salinas fault system (Figure 4. (a)) and some is present in the northern portion of the Santa Marta- Bucaramanga system. In the East, the Frontal fault system (Llanos Fault system) (Figure 4. (a)) is the boundary between the Northern Andean block and the South American Plate, additionally shallow seismicity fails to delimit the boundary with the Caribbean territory (Ojeda & Havskov, 2000).

Deep seismicity (80 km – 200 km), on the other hand, is clustered in two main spots: (1) in the Cauca Segment at the west (latitude: 3.2° − 5.6° 푁 and longitude: 75.4° − 77.8°푊), linked to the subduction process between the Nazca and South American plates and in the (2) Bucaramanga Segment at the northeast (latitude: 5.0° − 9.5°푁 and longitude: 74.5° − 72.5°푊), that might be related mostly to the to the subduction process of the Caribbean under the South American plate. The Cauca segment strikes in a SE direction

- 26 - (120°), with a dip ~35° and a thickness of 35 km, the northern Bucaramanga segment (NBS) (latitude: 8° − 9.5° 푁) has a SE strike (103°), a dip of ~27° and thickness less than 40 km, and the southern Bucaramanga segment (SBS)

(latitude: 6.7° − 6.85° 푁) includes the Bucaramanga Nest, strikes towards the SE (115°) has a dip of 40° and thickness of 20 km (Ojeda & Havskov, 2000).

It must be noted that within these segments there are two important clusters of seismic activity, including the Bucaramanga nest. Seismic nests are defined by a high stationary activity relative to their surroundings and can be related to tectonic processes in subduction zones or located on down going slabs and related to volcanic activity (Zarifi et al, 2007). Therefore, in addition to the proposed Caldas Tear, or discontinuity within the Wadatti- Benioff Zone, that separates the Cauca and Bucaramanga Segments there are two additional structures, or discontinuities, defined by increased seismic activity known as the Bucaramanga seismic nest and Cauca seismic cluster (Figure5(b)).

- 27 -

Figure 6. a) Tectonic map of northwestern South America and Panama showing the distribution of hypocentral solutions of ∼30;000 earthquakes extracted from the entire catalog of the RSNC during 1993–2012. Color scale indicates depth of earthquakes. (Source: Vargas & Mann, 2013). b) Map showing the seismicity allocated in the Cauca and Bucaramanga (South and North) segments, which have been delineated (Source: Ojeda & Havskov, 2001).

2.4.3.1 Bucaramanga Seismic Nest.

This cluster is centered at 6.8°푁 , 73.1 푊° (Zarifi et al, 2007), its uniqueness relies on the fact that it has a very high rate of activity concentrated in a relatively small volume. According to Zarifi et al (2007) the cluster is elliptical and located ~160 푘푚 deep with an angle of ~29°, it elongates in a NE direction and presents an average thickness of 25 km. Most of the events, according to the Harvard CMT solution, have a non-double couple Compensated Linear Vector Dipole (CLVD) solution and nearly a quarter of the total number of events are double-couple solutions.

This information brings insight with regards to the mechanism producing

- 28 - the seismic activity, CLVD’s are usually associated with zones that present either fluid movements, such as volcanic areas (Stein & Wysession, 2003), or very complex tectonics. For this reason, Schneider et al. (1987) and Shih et al. (1991) propose that the BSN is the result of magma intrusion, migration and eventually volcanism, however there is no volcanic activity in the surroundings of the BSN. Cortes & Angelier (2005) suggest that the BSN corresponds to down dip extension and possibly tearing of the Caribbean slab that is subducing at an angle of ~50°, which corresponds to the value of σ3 from the stress inversion they carried out. Van der Hilst & Mann (1994), from seismic relocation and tomographic analyses, propose that it is the result of the interaction between the Nazca and Caribbean plate slabs and Taboada et al (2000) claims that it is specifically due to their overlapping. Cortés & Angelier (2005) associate the BSN to extreme bending of the Nazca slab and Chiarabba et al (2016) attribute it on massive dehydration and eclogitization of a thickened oceanic crust of Nazca. Finally, Zarifi et al. (2007) propose the scenario of both subduction and collision between two slabs (Figure 7), which leads to the conclusion that there are multiple models all built from similar information and therefore the only affirmation that can be made is that there is a complex mechanism producing the earthquakes.

- 29 -

Figure 7. Model of the boundary conditions separating northern and southern Bucaramanga segments and showing the BSN. (Source: Zarifi et al, 2007)

2.4.3.2 Cauca Seismic Cluster.

This seismic cluster is located in the previously delimited Cauca Segment, ∼400 km southwest of the Bucaramanga nest near the Romeral Fault System and along the proposed line for the Caldas Tear (Yarce et al, 2014). It has a NS trend with events distributed in depths from 70 to 150 km, two distinct regions have been observed: (1) in the northern portion it presents events with focal mechanism solutions that show pure gravitational collapse and (2) in the southern portion it presents strike-slip events parallel to the Caldas tear fault.(Vargas, Mann & Borrero, 2011).

The geometry of the subducing slab at the Cauca Cluster is unclear, Cortes & Angelier (2005) propose that this region corresponds to an overlap, where the Caribbean plate lies on top of the Nazca plate, and therefore it is the result of slab tearing. Vargas, Mann & Borrero (2011) suggest, in the same line of ideas, that it will probably result as an extension of the Caldas

- 30 - tear. In addition, it has also been noted that this structure, as well as the Bucaramanga nest, lie in a portion of the slab where maximum bending is taking place (Cortes & Angelier, 2005)but that doesn’t seem to be the case.

2.4.3.3 Pacific Seismicity.

The abundant seismicity associated to the Colombian Pacific (CP), and main focus of this study, is an essential subject of study. Its importance lies on the fact that the events generated in this zone:(1) have sometimes large magnitudes and the active potential of being tsunami generators and (2) give insight into the formation and development of the Nazca plate. This is a zone of moderate to high seismic activity that lies in a very complex tectonic environment (Castilla & Sanchez, 2014), impacted mainly by the interaction of four tectonic plates; the Nazca, Caribbean, South American and Cocos plates to be exact. The Nazca and Caribbean plates are moving eastward with respect to the South American plate and are converging with it, whilst the Cocos and Nazca plates are moving away from each other and are responsible from the formation of the Panama Basin, the region where the CP lies. The Panama Basin is enclosed by the continental shelves of Colombia and Panama and the Cocos and Carnegie ridges (Pennington, 1981) (Figure 2 (a)).

Pennington (1981) finds that focal mechanisms in the region are of normal and reverse nature, typical for trench and near trench environments. The thrust events possibly lie at the plate boundary and within the deeper portions of the oceanic plate near the trench, where it is being compressed due to bending, whilst the normal events occur in the upper portion of the bending slab, where extensional stresses dominate (Stauder, 1968). Within

- 31 - the Nazca plate seismicity is associated to well-known bathymetric features, more specifically, 90 % of the events recorded in the region lie on or near seamounts, hotspot traces, islands and former plate boundaries (fracture zones and extinct ridges) (Wysession et al, 1991). Therefore, the zones that present high seismic activity in the CP, as determined by Castilla & Sanchez (2014), are: (a) The zone of interaction between the Nazca, Cocos and South American plate, (b) the Colombo-Ecuadorian subduction zone and the (c) Yaquina grabben. Additionally, the Carnegie, Cocos, Sandra, Regina and Malpelo ridges lie in the area and can be linked to some of the seismic activity (Figure 2 (a)).

3. Chapter 3: Theoretical Framework.

3.1 Seismology Framework.

3.1.1 Focal Mechanisms.

Focal mechanism solutions (FMS) are the result of analysis of waveforms generated by an earthquake and recorded by a number of seismographs (Corin, 2004), they are represented with a symbol displaying the planar projection of the lower hemisphere surrounding the source. Given that earthquakes are essentially modelled as slip on a fault surface, FMS are a representation of stress orientation and, as a result of this, of the geometry surrounding the source. This representation comes from the notion of the way the forces are distributed, more specifically, force distribution for seismic events is usually considered as a double couple source since it is able to produce a displacement field that is equivalent to slip on a fault surface.

- 32 -

The double couple model is extended in three dimensions by the seismic moment tensor, a symmetrical matrix made up of 9 components. The double- couple source is represented by three orthogonal axes as well: The pressure (P), tension (T) and null (N) axes (Figure 8 (b)). The P and T axes point in the directions of maximum and minimum compression, respectively, and are represented in the FMS as the two axes that bisect the dilatational and compressional lobes (Scholz, 2002)

The determination of FMS is usually done by analyzing first motions of the P-wave in multiple locations surrounding the event, which in addition must be located in the most accurate way. For each arrival it is determined if the first motions are of “up” or “down” motion at the time of the event (Figure 8 (a)), meaning compression and tension respectively, posteriorly these arrivals are plotted on the stereonet projection as black and white dots for example. Two orthogonal great circle arcs are then drawn on the stereonet, separating black and white dots and then colored following the convention (black: tension axis, white: pressure axis) (Figure 8 (c)), these are the nodal planes. Therefore, the FMS itself consists of four quadrants, two compressional and two dilatational, that are divided by two orthogonal planes known as nodal planes. At first sight there is an ambiguity in the diagram since there is no distinction between the two nodal planes, therefore additional geological observations must be used in order to determine which one represents the orientation of the fault plane and which one corresponds to the auxiliary plane with no structural significance.

- 33 -

Figure 8. a) First motion interpretation. (Source: Cronin, 2004). b) Geometry of the double- couple earthquake fault plane solution. Compressional and dilatational first motions of P waves are indicated by positive and negative signs respectively. Fault slip is right-lateral in this example. (Source: Scholz, 2002). c) Plotting a focal a FMS. (Source: Cronin, 2004)

The geometry of each FMS, as the geometry of a fault, can be described with three parameters: strike (휙), dip (훿) and rake (휆). The strike and dip define the orientation of the fault plane and the rake measures the angular distance between the slip vector, defined by the movement of the hanging wall relative to the foot wall, and the strike of the fault plane (Shearer,

2009). The rake ranges from 180° to −180°, has a positive value when measured anticlockwise from the reference strike and a negative value otherwise. The significance of this is that for negative values the movement will always have a normal component and for positive values the movement will always have an inverse component in the slip motion. Therefore, whenever the fault plane can be positively identified the FMS provide the orientation of the fault plane as well as the type of fault involved in the earthquake, so from a large amount of FMS reliable statements regarding stress orientation and earthquake dynamics can be drawn (Angelier, 1984; Gephardt & Forsyth, 1984).

- 34 - Some examples for FMS are shown in Figure 9 to show the main faulting mechanisms.

Figure 9. Plotting a focal a FMS. (Source: Cronin, 2004) Examples of focal spheres and their corresponding fault geometries. (Source: Shearer, 2009)

3.2 Geostatistical Framework.

3.2.1 Geostatistics.

Matheron (1971) defines geostatistics as the application of the theory of regionalized variables to the estimation of mineral deposits, this theory aims to: (1) express the structural properties of the data and to (2) estimate the distribution of regionalized variables from fragmented data. The term regionalized variable, again as described by Matheron (1971), refers to a function 푓(푥) that shows two characteristics: (1) randomness in the form of irregularity and unpredictable variations from point to point and (2)

- 35 - structure, as it reflects the characteristics of a regionalized phenomenon. The current definition of geostatistics is no longer restricted to mineral deposits, it is now the study, more specifically the quantitative description (or application of probabilistic methods), of values that are associated with regionalized variables in the form of natural phenomena that distribute in space, time or both. These variables include mineral deposits, depth and thickness of geological layers, contamination of pollutants, crime distribution, density and distribution of species, seismic event distribution, etc.

In order to properly comply with the aim of geostatistics the numerical techniques applied usually imply the use of: (a) probabilistic models and (b) pattern recognition techniques (Olea, 2009). Considering the previous statement, the importance of geostatistics lies on the fact that it manages to provide mechanisms that are able to quantify the spatial, and in a few cases temporal, uncertainty that is associated to the regionalized variable. In order to do this the regionalized variable is regarded as random by considering it as one realization, amongst many possible realizations, of a random function, in order to pursue this a stochastic model must be used. The selection of the model, regardless of the method, will always be guided by simplicity, where the simplest approach will always be chosen to explain and quantify a particular behavior. On this note it is very importance to establish that geostatistics are focused on modeling the behavior of regionalized variables (phenomena) not their interpolating surfaces, therefore, they are of descriptive nature, as opposed to the usual interpretative nature of statistics (Chilès & Delfiner, 1999).

- 36 - 3.2.2 Preliminary Definitions.

Random Variable Random variables are not variables in the traditional sense of the word, a good way to describe them is by considering them to be functions by which random processes are quantified, meaning that the values assigned to it are randomly generated by a probabilistic mechanism (Isaaks & Srivastava, 1989). For notation a random variable is denoted with an upper case letter, say

푋(휔), its numerical outcome can be quantified however the user desires and is denoted with a lower case letter 휔 , therefore, the set of possible outcomes, Ω , are denoted by {휔(1), … , 휔(푛)}, where 푛 corresponds to the number of possible values the variable can take. The observed outcomes (in order) are denoted with 휔1, 휔2, 휔3, …. . Additionally, to fully define a random variable X, it must be noted that it has a corresponding set of probabilities

푚=푛 {푝1, … , 푝푛} , where ∑푚=1 푝푚 = 1 (Chilès & Delfiner, 1999).

Random Functions and Stochastic Process Random functions can be considered as an infinite families of random variables all belonging to the same probabilistic space, in other words, they are a collection of random variables. For notation a random function is denoted as a function of two variables, 푍(푥, 휔), indexed by 푥, a value that corresponds to points within the domain, in order to simplify it can also be denoted with 푍(푥) and its realization (the regionalized variable) as 푧(푥). A stochastic process is a random function for which 푥 varies in one dimension only, this dimension is usually interpreted as time, therefore it is a random function indexed by time (Chilès & Delfiner, 1999).

- 37 - Stationarity in Random Functions A random function can have the quality of being stationary, meaning that it behaves homogeneously in space, and therefore, its defining properties do not vary. For instance, a strictly stationary random function contains random variables that have the same mean and probability distribution functions (Chilès & Delfiner, 1999). Since strict stationarity is usually hard to achieve there are two terms that describe stationarity more broadly: (1) second order stationarity and the (2) intrinsic property.

Second Order Stationarity Second order stationarity, as it was previously mentioned, refers to a function that is stationary in a wider sense, so 푍(푥) it must comply with (Chilès & Delfiner, 1999):

(1) Constant mean: 퐸푍(푥) = 푚. (m corresponds to the mean)

(2) Covariance that depends only on the separation, ℎ , between the two points being considered: 휎(푥, 푥 + ℎ) = 퐶(ℎ) = 퐸[푍(푥) − 푚][푍(푥 + ℎ) − 푚].

Intrinsic Random Functions

This is a milder hypothesis, where it is assumed that for every vector ℎ the increment defined as 푌ℎ(푥) = 푍(푥 + ℎ) − 푍(푥) is a stationary random function itself, 푍(푥) is said to be an intrinsic random function and must comply with (Chilès & Delfiner, 1999):

(1) Linear drift: 퐸[푍(푥 + ℎ) − 푍(푥)] = 〈푎, ℎ〉

- 38 - (2) Variogram: 푉푎푟 [푍(푥 + ℎ) − 푍(푥)] = 2훾(ℎ)

Ergodicity This quality makes statistical interference possible, it states that one realization is enough to make reliable assessments, meaning that one sample is enough. In other words, a stationary random function is ergodic if its spatial average over a given domain converges to the mean as the space tends to infinity. This quality allows the mean to be determined from a single realization of the stationary random function, additionally it must be noted that not all stationary random functions are ergodic (Chilès & Delfiner, 1999).

3.2.3 Semivariogram Analysis.

The semivariogram is a function by which spatial correlation is quantified, it is used to perform structural analysis of regionalized variables, which is the main target of geostatistics. Since the definition of semivariogram itself implies the use of intrinsic random functions (IRF), which naturally include stationary random functions (SRF), it is a great tool that serves in a very generalized way since it manages to include a variety of functions, additionally it does not require prior knowledge of the mean (Chilès & Delfiner, 1999).

First we must define the semivariogram function, in order to do this the second part of the definition for intrinsic random functions must be remembered and solved for the semivariogram function, resulting in:

- 39 - 1 훾(ℎ) = 푉푎푟 [푍(푥 + ℎ) − 푍(푥)] 2

This quantification is a means to measure the differences between 푍(푥) and 푍(푥 + ℎ) as ℎ varies. Another way to define it, by decomposing the definition of variance, is:

푁ℎ 1 2 훾(ℎ) = ∑[푍(푥𝑖 + ℎ) − 푍(푥𝑖)] 2푁ℎ 𝑖=1

In this case 푥𝑖 are the different positions that 푍 can take and 푁ℎ is the number of samples for a particular distance ℎ. Using the semivariogram function a semivariogram is built, this is a plot in which different distances, known as lag, are plotted on the x axis against the semivariogram function on the y axis. The three parameters that define a semivariogram are: range, sill and nugget. The range is the horizontal distance measured from the origin (푥 = 0) to the point where the semivariogram reaches a plateau, meaning that at this point there are no more vertical increments. The sill is the vertical distance measured at the plateau that the semivariogram reaches at the value of the range, it can be interpreted as the mean of the regionalized variable. The nugget, although not always present, is the vertical discontinuity at the origin of the plot, it is a jump from the origin (푦 = 0) to the lowest value that the variogram takes and cannot be explained, it corresponds to pure randomness (Figure 10). After the experimental (observed) semivariogram is plotted an empirical (mathematical) model is usually fit to it in order to further analyze the spatial distribution of the variable, the selected theoretical model and its fitting is fundamental since the prediction of the variable in unsampled

- 40 - locations is defined by it (Mc Bratney & Webster, 1986), the most significant theoretical models are the spherical, exponential and gaussian.

Figure 10. Semivariogram and its main components. (Source: Biswas & Si, 2013)

3.2.4 Cluster Analysis: K-Means.

Cluster analysis is a great tool when dealing with multidimensional data, it can be defined as the partitioning of a data set into a set of clusters of ‘similar’ characteristics, without any previous knowledge about the subsets (Van Hulle, 2012). The most common definition implies that for the process to be optimal the distances within clusters should be minimized and the distances between clusters maximized, therefore, the data being analyzed can either belong exactly in one cluster or have a degree of membership in each one of the clusters of the system. Regardless, the definition of a good cluster depends on the application itself, so depending on the desired criteria and application a proper methodology can be selected. It should be noted that cluster analysis has many applications including data mining, data re-dimension and vector quantization and pattern recognition and classification. Methodologies include splitting and merging, randomized approaches, methods based on neural nets and formulations based on minimizing

- 41 - an objective function, which is the case of k-means clustering (Kanungo et al, 2002).

Different approaches to solve the k-means problem have been proposed, one of the most popular ones and the one that will be used is the generalized Lloyd’s algorithm, which is based on the idea that the optimal location for a center is the centroid of its associated cluster. Therefore, in this algorithm given a set of 푛 data points in a d-dimensional space, 푅푑 ,and with a given number of clusters, 푘 , the methodology will aim to determine a 푘 number of points, which will be treated as centers, so that the mean squared distance of each data point to its nearest center is minimized

(Kanungo et al, 2002). In other words, it assigns an 푛 number of observations to a predetermined number of clusters, 푘, partitioning the data into exclusive groups where the distance between objects is minimized and the distance between groups maximized. This method works in an iterative way, therefore given a set 푉(푧) containing all the data points associated to one of the centers, 푧, for each stage 푧 is moved so that it becomes the centroid of 푉(푧) and then 푉(푧) is updated by computing the distances between each point to its nearest center. After running the algorithm for a desired number of iterations, or until the convergence criteria is met, a vector of

푛 elements is obtained, in this vector the class associated to each data point is noted. A more detailed explanation of the algorithm, as described in the MATLAB platform is:

1. First, 푘 initial cluster centers, or seeds, 퐶푘 , are chosen, each one of them is a d–dimensional vector. This can be done randomly or by using a default initialization mechanism.

- 42 - 2. Distances between each point to each centroid are calculated and saved

in a 푛 by 푘 matrix 퐷.

3. There are two ways to proceed at this point:

a. Batch update: Each data point is assigned to the cluster with the closest centroid.

b. Online update: If a data point decreases the sum of the within- cluster distances then it is individually assigned to a cluster.

4. Calculate 푘 new centroid locations

5. Repeat steps 2 to 4 until the convergence criteria or the maximum number of iterations is met.

4. Chapter 4. Data Selection, Processing and Methodology.

This section will focus on the gathering of the data and on the procedures that will take place in the data processing, mainly: (1) data Selection, (2) spatial and temporal clustering of the dataset and (2) semivariogram analysis.

4.1 Data Selection, Variable Overview and Exploratory Analysis.

The data set used for this study was collected from the RSNC, the main goal was to select events located in the surroundings of the Colombian Pacific subduction margin, therefore this includes some interplate and some

- 43 - intraplate events. Although the events are associated to a subduction zone, most of them do not correspond to Wadatti Benioff zone activity or to other intraplate seismic nests and lie in the vicinity of the trench. Most are located in the associated accretionary prism, in the South American plate and in the Nazca plate. In order to select data that would fit the above criteria an area of study was carefully delimited, within this area only

events with a superficial error below 25 퐾푚 and a depth error below 25 % were selected.

A total of 134 events were retrieved, each event contains information on: (1) date, (2) time, (3) latitude, (4) longitude, (5) depth, (6) moment magnitude, (7) recurrence interval5, (8) total time6 and 9) X,Y coordinates7; and for 32 of the events the focal mechanism solutions are known, for this reason some events, additionally, have an associated (10) strike, (11)dip and (12) rake.(Table 1 and Figure 12)

Attributes Value Total Number Of Events 134 Initial Date - Final Date 02/11/2012 - 10/13/2017 Duration Of Activity (days) 2070 Magnitude Range (Mw) 1.6 - 7.1 Average Magnitude (Mw) 3.59 Depth Range (Km) 15.2 - 172 Average Depth (Km) 53.61 Recurrence Interval Range (days) 0 - 116 Average Recurrence Interval (days) 15 Latitude Range 1.45 N - 7.15 N Longitude Range 76.50 W - 79.79 W Table 1. Main statistics for the dataset.

5 Time between two adjacent events. 6 Measured with base on the first event. 7 UTM zone 18 N projection.

- 44 -

Figure 11. Map of the Colombian Pacific region, showing distribution of the 134 events extracted from the RSNC catalogue. Color scale indicates depth of earthquakes.

4.2 Spatial and Temporal Classification of Earthquakes: Clustering of the Data.

The first step in order to process the data is the identification of clusters within its different dimensions, this procedure has two main purposes: (a) identification of spatial and temporal patterns and (b) categorization of the data for further analysis. Particularly, two clustering procedures will be run in this study:

- 45 - 1. Spatial Clustering: This procedure will take into account six observations: (1) total time, (2) recurrence interval, (3) moment magnitude, (4) depth, (5) X and (6) Y coordinates. The reasoning behind the inclusion of temporal variables in a clustering procedure that will be analyzed spatially is due to the fact that it has been shown that there is a strong correlation between the temporal behavior of seismic events and their location (Mouslopoulou & Hristopulos, 2011). Given that faulting structures are complex and don’t present a linear behavior or easily defined surfaces a higher amount of variables leads to a better definition of groups of associated events.

2. Temporal Clustering: This procedure will be performed considering only one variable: (1) total time. It will be done this way in order to identify solely the linear time distribution of events.

In order to perform this step two functions, from the MATLAB™ software, are used: kmeans and zscore.

Z - score (zscore)

This function is used in this study in order to scale the data so that all dimensions, or attributes, are in the same scale when the clustering procedure is performed. This is important in order to compare variables with very different range of values and to avoid introducing biases within the clustering. It transforms data through standardization, therefore, the resulting dataset has a mean of 0 and standard deviation of 1 and the same skewness and kurtosis (shape properties) as the original set. For a dataset with mean 푋̅ and standard deviation 푆 the z-score, 푧, of a data point 푥 is:

- 46 -

(푥 − 푋̅) 푧 = 푆

K – means (kmeans)

This MATLAB™ function is guided by a modified Lloyd’s algorithm, k-means ++, which improves the running time and the quality of the solution, it uses a heuristic approach in order to choose the centroid seeds (David & Vassilvitskii, 2007. When running this function it is fundamental to make a thorough evaluation in order to determine the optimal number of clusters.

Optimal Number of Clusters: Defining k

In order to define the optimal number of clusters it is important to have in mind the application for which the clustering mechanism is being used. In this case, for the spatial clustering analysis, for every fit cluster a semivariogram analysis will be performed, therefore, a manageable number of clusters with enough assigned data for each cluster is necessary. For the case of temporal clustering, although a manageable number of clusters is preferred, a particular number of clusters is not required since this procedure will be performed mostly for visualization purposes.

MATLAB™ provides the evalclusters™ function which contains different criteria by which the ideal number of clusters for a data set can be evaluated. The silhouette criteria is particularly useful, it is a function that measures how similar a point is to points in its own cluster when compared to points from other clusters. It takes values ranging from -1 to

- 47 - 1, where 1 denotes high similarity with values in the same cluster and high dissimilarity with values form different clusters and -1 denotes the opposite. If many points have low or negative values, the clustering solution is not the most appropriate8, therefore, in order to quantify the results of this function the average silhouette value can be calculated, higher values indicate better solutions whereas lower or negative values indicate less ideal solutions.

This function was applied to the spatial clustering data set for 푘 values ranging from 5 to 10 (this range of values was found through trial and error)

and the mean value was evaluated for each 푘, the results can be observed in figure 12 and table 2. Although the silhouette values were not particularly high for any solution, for the purpose of this study the solution with the highest value, k = 6, will be used. In the case of temporal clustering the

function was evaluated for 푘 values ranging from 2 to 5 and the mean value was evaluated for each 푘, the results can be observed in figure 13 and table 3. The silhouette values for this test were higher in general, with the highest for k = 2, which will be the value used for the k-means clustering procedure.

8 Mathworks ™

- 48 - Silhouette plot (kmeans, k = 5) Silhouette plot (kmeans, k = 6) SIlhouette plot (kmeans, k = 7) 1 1 1 avg = avg = avg = 0.321

2 0.287 2 0.384 2

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C C 4 C 4 4 5 5 6 5 6 7 0 0.5 1 0 0.5 1 0 0.5 1 Silhouette Value Silhouette Value Silhouette Value Silhouette plot (kmeans, k = 8) Silhouette plot (kmeans, k = 9) Silhouette plot (kmeans, k = 10) 1 1 avg = 1 avg = avg = 0.337 0.341 2 0.342 2 2

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C C 4 C 6 5 6 7 7 6 8 8 7 9 9 8 10 0 0.5 1 0 0.5 1 0 0.5 1 Silhouette Value Silhouette Value Silhouette Value

Figure 12. Silhouette plots to evaluate the ideal number of spatial clusters using k-means clustering. The dotted line represents the average silhouette value for each cluster.

k Average Silhouette Value 5 0.287 6 0.384 7 0.321 8 0.337 9 0.341 10 0.342

Table 2. Average silhouette values for the possible spatial clustering solutions. The highest value, for k = 6, is chosen as the most ideal for the spatial clustering procedure.

- 49 - Silhouette plot (kmeans, k = 2) Silhouette plot (kmeans, k = 3)

avg = 0.8093 avg = 0.7502 1

1

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0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Silhouette Value Silhouette Value Silhouette plot (kmeans, k = 4) Silhouette plot (kmeans, k = 5)

avg = 0.7439 1 avg = 0.7535 1

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0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Silhouette Value Silhouette Value

Figure 13. Silhouette plots to evaluate the ideal number of time clusters using k-means clustering. The dotted line represents the average silhouette value for each cluster.

k Average Silhouette Value 2 0.809 3 0.750 4 0.753 5 0.743

Table 3. Average silhouette values for the possible temporal clustering solutions. The highest value, for k = 2, is chosen as the most ideal for the temporal clustering procedure.

4.2.1 Spatial Clustering Results.

This procedure resulted in 푘 = 6 clusters, their distribution and properties can be observed in figure 14 a and b and in table 4, additionally, in Appendix A each one of the clusters is described in more detail. Given

- 50 - that only clusters 2, 3 and 6 contain a number of elements around 30, which is a minimal recommended value to perform a semivariogram analysis, they are the ones that will be studied in more detail. After performing this procedure the rest of this study will be based under the assumption that clusters 2, 3 and 6 are three individual structures, meaning that each one of them will now be associated to an active tectonic feature. In further sections they will be referred to as Feature 2, Feature 3 and Feature 6.

Figure 14. a) Map of the Colombian Pacific region, showing distribution of the 134 events.

- 51 - Distribution of Earthquake Depth with Latitude and Longitude C1 C2 C3 C4 0 C5 C6 20 40

60 )

m 80

K

(

h

t 100

p e

D 120 140 160 180

6 -75 -76 4 -77 Latitude (deg)2 -78 -79 Longitude (deg)

Figure 14. b) Event distribution in depth. Color scale for both images indicates clusters.

Total Number Centroid Centroid Centroid Cluster of Events Longitude Latitude Depth (Km)

1 3 -76.721 2.192 153.567 2 39 -77.551 5.882 27.818 3 36 -76.954 4.074 54.297 4 18 -78.996 2.620 50.089 5 13 -77.083 4.318 57.115 6 25 -76.839 3.881 82.436

Table 4. Basic characteristics for spatial clusters and their respective centroids.

4.2.2 Temporal Clustering Results.

This procedure resulted in 푘 = 2 clusters that will be referred to as phase A and phase B, their distribution in time with respect to magnitude and properties can be observed in figure 15 and table 5.

- 52 -

Total Number Cluster Date Range of Events 1 64 02/11/12 - 10/26/14 2 70 02/18/15 – 10/13/17

Table 5. Basic characteristics for time clusters.

Distribution of Earthquake Sizes with Time 8 1 2

7

6 )

w 5

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(

e

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i n

g 4

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2 Phase A Phase B

1 0 500 1000 1500 2000 2500 Time (days)

Figure 15. Distribution of earthquake size with time. Color scale indicates phase (cluster).

4.3 Distribution of Earthquakes as a Function of Time.

In order to investigate the characteristics of the region in terms of the development of active tectonic features and rupture, the interaction of mechanisms that may cause seismic migration will now be studied. This will

- 53 - be done by plotting the time for each event as a function of: (1) horizontal distance, 푥, (2) vertical distance, 푦, and (3) depth, 푧.

Feature 2 Feature 2 Feature 2

400 800 100

)

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Figure 16. Spatial distribution of earthquake hypocenters along each feature and along the entire system as a function of time. Positive or negative correlation of earthquake hypocenters with time suggests progressive failure. Directions x, y and z correspond to East-West, North-South and depth, respectively.

4.4 Semivariogram Analysis of the Data.

In order to further explore if correlation between events exists, experimental semivariogram plots of the hypocenter locations as a function of time will be calculated, this will be done for: (1) earthquakes within individual features and (2) earthquakes in the whole system. The semivariograms will be calculated using Schwanghart’s (2010) experimental semivariogram function for Matlab™. For these, the lag spacing will be a value close to the average sampling distance and the maximum lag distance will be close to one third of the total temporal extent of the data (Olea,

- 54 - 2006). The mechanism by which the extent of the correlation will be evaluated is the “no-correlation zone” as proposed by Mouslopoulou & Hristopulos (2011).

No-Correlation Zone

This zone tests the existence of correlation and is determined as follows:

(1) For each plot 1000 random permutations of the locations are performed, this destroys their temporal ordering, this was done using the MATLAB™ toolbox.

(2) For each permutation the semivariogram function is calculated (using the same number of lags as in plot being evaluated), as a result for each lag there are now 1000 associated semivariogram values.

(3) The maximum and minimum semivariogram values for each lag are extracted, with the maximum values the upper boundary of the no- correlation zone is built and with the minimum values the lower boundary is constructed.

As a result, a shaded are is obtained for each plot. The semivariograms that lie completely inside indicate uncorrelated migration of epicenters whilst semivariograms that lie partially outside indicate some correlation.

- 55 - 4.4.1 Correlation of Earthquakes on Individual Features.

For each feature (F2, F3 and F6) and all associated events we will use the center of each cluster (Appendix A) as a spatial reference point and based on it we will calculate the: (1) distance along x, 푥푠(푡) ,(2) distance along y, 푦푠(푡) and (3) vertical distance 푧푠(푡). For each one of this distances a semivariogram, 훾푥, 훾푦 and 훾푧 respectively, will be calculated as a function of time and it will be plotted along with its respective no-correlation zone.

Figure 17. a) Experimental semivariograms for F2 along x, y and z. The shaded area indicates no correlation.

- 56 -

F3 – along x

Figure 17. b) Experimental semivariograms for F3 along x, y and z. The shaded area indicates no correlation.

F6 – along x

Figure 17. c) Experimental semivariograms for F6 along x, y and z. The shaded area indicates no correlation.

- 57 - 4.4.2 Correlation of Earthquakes in the System.

Similarly, for the entire earthquake sequence and all associated events, the average cluster location (283.21, 423.47, 70.88) in three dimensions will be used as a spatial reference point, based on it we will calculate the: (1) distance along x, 푋푠(푡) ,(2) distance along y, 푌푠(푡) and (3) vertical distance

푍푠(푡). For each one of this distances a semivariogram, 훾푋, 훾푌 and 훾푍 respectively, will be calculated as a function of time and it will be plotted along with its respective no-correlation zone.

Figure 18. Experimental semivariogram for the system along x, y and z. The shaded area indicates no correlation.

- 58 - 4.5 Focal Mechanisms.

Initially it was planned that some FMS would be a part of the clustering analysis, however when performing this procedure, it did not lead to improved solutions. Instead they acted as noise and when evaluated with the silhouette criteria the results showed to be poor. The reason for this occurrence was that there were very few solutions available, it would be interesting to perform the same procedure with a more complete database since it would probably lead to improved solutions.

5. Chapter 5. Results, Discussion and Conclusions.

5.1 Clustering of the Data.

Spatial earthquake clustering is evident in figures 13 a and b. This implies that certain groups of events are generated on specific tectonically active features or by specific processes. Given that the location of the events is not of high precision it is difficult to associate the given groups of events to singular faults or failure planes, however, a clustering mechanism that minimizes intracluster distance and maximize intercluster distance (k-means) was used in order to investigate groups of similar events and subsequently separate them. This resulted in six groups of data, it would be over-interpretation to associate each one of this groups to a particular faulting structure so they are simply referred to as features. The silhouette criteria, used to determine the ideal number of clusters, is also a useful tool at evaluating a clustering solution. These criteria suggest that features one, two, three, four and six are the most contingent for this given

- 59 - clustering solution because most of their values lie within the positive spectra and they are the ones that contain the majority of the information. On the other hand, a big portion of cluster five lies in the negative spectra which suggests that the similarity for events that have been associated to it in comparison to events associated to other clusters is rather low.

Rupture occurred in two main temporal phases, that were also differentiated using kmeans, their characteristics can be observed in table 5 and figure 15. Their silhouette evaluation turned out only positive values with good event distribution which suggests that this is a reliable separation. When evaluating the way in which the temporal and spatial clustering fall together (figure 19) the first thing to note is that all features present rupture during both phases. For some features it is clear that to some degree they can be separated based on time, this is the case of features three, four and six. Feature number three is the one that initiates rupture and takes place during phase A and the initial quarter of phase B. Features five, two and one, respectively, initiate rupture in the first quarter of phase A and terminate in the last portion of phase B. Finally features four and six start acting in the last quarter of phase A and end their activity in the last portion of phase B, therefore dominating in the latter. Therefore, feature three can be associated to phase A and features six and four to phase B.

- 60 - Time Range for Each Feature

Phase A Phase B

6

5

e

r u

t 4

a

e F

3

2

1

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 Time (days) Figure 19. Extent of rupture for each feature in comparison to the extent of rupture for each one of the phases.

Clusters one, three, five and six are mostly located inland and follow the lines of the Cauca and Romeral fault systems in the south as well as the line of the Occidental fault chain in the north. Cluster number four is located offshore and is aligned with the Carnegie ridge along the part that coincides with Colombia-Ecuador trench. Finally, cluster number two has two sections, one occurs inland and the other one offshore, the offshore section is coincident with sections of the Malpelo ridge and Sandra rift. (figures 2 and 4). They are all located in a region that reflects the deformation associated to the convergence of the Panama arc, the Nazca plate and the Colombian continental terrains.

5.2 Fault Interaction - Earthquakes as a Function of Time.

Although defining the geometry for each one of the features is not in the capacity of this study since it would require a more thorough analysis and higher location accuracy, one can study event migration in a three

- 61 - dimensional scenario in order to observe the presence of any trends. This trends can give us an idea of the migration and behavior of the mechanisms causing the events which is directly linked to geometry of the studied area. This form of analysis can additionally help identify interaction between adjacent structures through the observation of changes in the behavior of the distribution. Figure 16 summarizes the spatial distribution of features two, three, and six and for the entire system as a function of time, directions x, y and z correspond to East-West, North-South and depth, respectively. Below is the individual directional analysis for each feature as well as the collective analysis of the features.

For feature two, in the horizontal direction x, it is observed that as time goes by there is slight migration of events towards the west, additionally there is increased activity between 1000 and 2000 days (which is observed in all directions for this particular feature). In the horizontal direction y the area of rupture grows past the 500-day mark and remains active in most of its extension, the same occurs for vertical direction z. For feature three (in direction, y and z) there is a slow increase in the occurrence of events until a very noticeable peak is reached past the 500- day mark, after which the dimension of the area being ruptured is reduced. In direction x the area of rupture increases during the peak of activity and is then restricted to only present motion in its eastern portion., in direction y the area is reduced during the peak of activity and the frequency of events decreases notoriously. In the z direction there is inverse correlation, where the area of rupture slowly decreases to shallower depths as time goes by. For feature six, none of the directions presents any strong trends or migration. Finally, when reviewing the entire system, the biggest observation occurs in the x direction where the area of rupture increases at

- 62 - around 1000 days, it suddenly grows to include a bigger portion of the western territory.

As for the relationship between features, feature three and features six and two show inverse correlation in the sense that they initiate and terminate rupture respectively, therefore as activity in features six and two begins activity in feature three is ceasing. For features two and three there are some clear trends, in the x direction, when feature three migrates its activity towards the east and has a decrease in earthquake frequency, the frequency of activity in feature 2 is intensified. In the y direction, immediately after the intense activity cluster in feature 3, the range of rupture and frequency of activity in feature 2 is intensified whilst the opposite happens for feature three. Additionally, it must also be noted that lack of migration does not necessarily imply lack of interaction within features.

5.3 Correlation of Earthquakes on individual Faults and in the System – Evaluation of Semivariogram Functions.

Figures 16 a, b and c and 17 display the semivariograms for Features 2, 3 and 6 and for the entire system, respectively. As a general observation the semivariograms for all the structures that were studied present a (1) generalized complex behaviour, a (2) discontinuity or “jump” at the origin, which suggests that all of the events have a component that is fundamentally random, (3) none of them show a tendency to increase, instead they remain horizontal in average, suggesting that they don’t have a correlated component. Additionally, and very importantly, (4) all of them lie within

- 63 - the no correlation zone and therefore, in their organization, do not reveal any correlated structures. Mouslopoulou & Hristopulos (2011) describe such behaviour for most faults where there is first order, along strike migration, additionally they note that finding correlation when evaluating sequences with larger recurrence times and fewer earthquakes is rather difficult, this might be a proof of that all structures present some sort of migration and larger recurrence times. As for the evaluation of the whole system, it presents all of the characteristics that have been described for the individual features.

With regards to all of the points above, the lack of correlation agrees with recent work that suggests that seismic events include both a correlated component and an uncorrelated component (Touati et al, 2009). The reason for an absent correlated component could be that (1) the location accuracy for the studied events is not enough, (2) enough events are not located by the present network in the CP area (i.e., events are not close enough in space- time in order to detect their triggering and organization) or that (3) the sample is not big enough. Another option is that (4) this particular sequence is not correlated in nature; however further analysis would be required in order to prove this. The fact that the overall system does not display correlation is an automatic reflection of the behaviour of the individual features that make it up, since their behaviour is determinant when evaluating the system.

5.4 Conclusions.

Faults are not single continuous surfaces, instead they are composed of a series of disconnected segments or sub-faults. It has been shown that they

- 64 - form joints that are linked together, in other words, they originate at a point and rupture with progressive slip. Stress concentrates at rupture tips and slip concentrates inside, as a result of this each fault has a correspondent stress field which inevitably interacts with the stress field of nearby rupture planes. This interaction can take place in multiple ways, for instance, it can be of repulsion or coalescence, where fault planes eventually merge together (Scholz, 2002). All of the above, to illustrate the extent of interaction within seismic events, because as it can be seen it is in their nature to behave in a way that presents some degree of correlation and organization when observed under a proper scale.

Now, the main observations of this study show that the studied sequence presents both an organized and a disorganized component, in both time and space. The organized component is evident in the clustering observations, where events are grouped in very specific regions both superficially and in depth, the spatial clustering algorithm confirmed this, since it managed to automatically group the events in a way that allowed for some of their characteristics to be differentiated. In this sense it is also interesting to note that, superficially, some of the clusters overlap, which is a clear reflection of the complex depth organization of faulting structures. Meaning, that they can’t be modelled and dealt with as linear structures but are generally 3D structures such as planes, particularly, it would be too much of an assumption to do it in a region of this level of complexity. Organization is also evident when evaluating migration, where clear patterns can be observed both in individual structures and when comparing multiple structures.

- 65 - The semivariogram analysis was expected to show some degree of correlation, however contrary to this it proved the exact opposite and did not manage to measure any correlation. It is naturally difficult to prove there is an organized relationship within such complex structures, therefore, it must be noted that the fact that this test suggested that this relationship is not present does not necessarily imply that some degree of it does not exist. There is a big possibility that in the observed scale the semivariogram test does not manage to record correlation, or alternatively, that there is indeed no correlation in the given scale. However, this examination is not determinant and being open to other solutions is fundamental, therefore, running this test with higher accuracy would result in a (1) more accurate location of the events and (2) a bigger data set to work with, since a lower number of events would be dismissed due to errors. Performing the same study after improving such conditions might lead to improved clustering and to an improved semivariogram analysis. So, as a conclusion of this study it must be noted that the behaviour of seismic events is complex and difficult to quantify, nevertheless, to some degree spatiotemporal patterns were evident in this dataset. This opens the door to further studies with improved precision which could possibly lead to the quantification of seismic variables to an extent where seismic evaluation of risk areas could be improved.

- 66 - 6. Appendix A. Spatial Clustering Characteristics.

Below are in depth attributes of each one of the spatial clusters as well as 3D scatter plots for each one of them.

Attributes Value Total Number of Events 3 Initial Date - Final Date 09/30/12 - 12/28/16 Duration of Activity 1549.52 Cluster (days) 1 Magnitude Range (Mw) 4.8 - 7-1 Average Magnitude (Mw) 5.86 Depth Range (km) 138.7 -172.0 Average Depth (km) 153.56

Center [x,y,z] (km) (308.55, 242.35, 153.56) Total Number of Events 39 Initial Date - Final Date 08/21/12 - 10/11/17 Duration of Activity 1877.85 (days) Cluster Magnitude Range (Mw) 2.9 - 5.3 2 Average Magnitude (Mw) 3.69 Depth Range (km) 15.2 - 50.6 Average Depth (km) 23.25 Center [x,y,z] (km) (217.51, 650.82, 27.81) Total Number of Events 36 Initial Date - Final Date 02/11/12 - 08/05/15 Duration of Activity 1271.06 (days) Cluster Magnitude Range (Mw) 2.2 - 4.8 3 Average Magnitude (Mw) 3.27 Depth Range (km) 18.2 - 129.4 Average Depth (km) 54.29 Center [x,y,z] (km) (283.12, 450.53, 54.29)

- 67 -

Attributes Value Total Number of Events 18 Initial Date - Final Date 08/03/14 - 04/03/17 Duration of Activity 974.06 (days) Cluster Magnitude Range (Mw) 3.0 - 5.2 4 Average Magnitude (Mw) 3.77 Depth Range (km) 21.5 - 94.3 Average Depth (km) 50.08 Center [x,y,z] (km) (55.39, 290.32, 50.08)) Total Number of Events 13 Initial Date - Final Date 06/10/12 - 09/17/17 Duration of Activity 1925.81 (days) Cluster Magnitude Range (Mw) 2.8 - 4.2 5 Average Magnitude (Mw) 3.47 Depth Range (km) 18.0 - 104.9 Average Depth (km) 57.11 Center [x,y,z] (km) (268.87, 477.57, 57.11) Total Number of Events 25 Initial Date - Final Date 06/02/14 - 10/13/2017 Duration of Activity 1228.51 (days) Cluster Magnitude Range (Mw) 1.6 - 4.3 6 Average Magnitude (Mw) 3.55 Depth Range (km) 30.5 - 133.7 Average Depth (km) 82.43 Center [x,y,z] (km) (295.84, 429.24, 82.43) Table A.1: Some Attributes for each spatial cluster.

- 68 - C1 C2

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Figure A.1: 3D scatter plots for each one of the clusters, the centroid location for each cluster is indicated with red.

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