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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
____________________
Co-Director: Jean Baptiste Tary
____________________
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.
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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.
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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)
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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
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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
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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.
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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.
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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 𝑐𝑚/𝑦𝑟 with an azimuth of 𝑁 80.2 𝑊. 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 𝑐𝑚/𝑦𝑟 with an azimuth of 𝑁 58.4 𝐸 (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).
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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° 𝑁) 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° 𝑁, 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° 𝑁. 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° 𝑁, 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
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(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 𝑘𝑚 at latitude 5.6° 𝑁. It separates a zone of shallow
(20°– 30°), southeastward subduction to the north that extends up to 11° 𝑁
with a WBZ located at > 300 𝑘𝑚 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
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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
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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).
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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
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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
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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
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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
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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
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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.
- 24 -
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
- 25 -
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 N40W 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
- 26 -
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° 𝑁 and
longitude: 75.4° − 77.8°𝑊), 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°𝑁 and longitude: 74.5° − 72.5°𝑊), 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
- 27 -
(120°), with a dip ~35° and a thickness of 35 km, the northern Bucaramanga
segment (NBS) (latitude: 8° − 9.5° 𝑁) 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° 𝑁) 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)).
- 28 -
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°𝑁 , 73.1 𝑊° (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 𝑘𝑚 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
- 29 -
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.
- 30 -
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
- 31 -
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
- 32 -
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.
- 33 -
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.
- 34 -
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 (𝜙), dip (𝛿) and rake (𝜆). 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).
- 35 -
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 𝑓(𝑥) that shows two characteristics: (1) randomness in the form of
irregularity and unpredictable variations from point to point and (2)
- 36 -
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).
- 37 -
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
𝑋(𝜔), its numerical outcome can be quantified however the user desires and
is denoted with a lower case letter 𝜔 , therefore, the set of possible
outcomes, Ω , are denoted by {𝜔(1), … , 𝜔(𝑛)}, where 𝑛 corresponds to the number
of possible values the variable can take. The observed outcomes (in order)
are denoted with 𝜔1, 𝜔2, 𝜔3, …. . Additionally, to fully define a random
variable X, it must be noted that it has a corresponding set of probabilities
{𝑝1, … , 𝑝𝑛} , where ∑ 𝑝𝑚 = 1𝑚=𝑛𝑚=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, 𝑍(𝑥, 𝜔), indexed by 𝑥, a value that
corresponds to points within the domain, in order to simplify it can also be
denoted with 𝑍(𝑥) and its realization (the regionalized variable) as 𝑧(𝑥).
A stochastic process is a random function for which 𝑥 varies in one dimension
only, this dimension is usually interpreted as time, therefore it is a random
function indexed by time (Chilès & Delfiner, 1999).
- 38 -
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 𝑍(𝑥) it must comply with
(Chilès & Delfiner, 1999):
(1) Constant mean: 𝐸𝑍(𝑥) = 𝑚. (m corresponds to the mean)
(2) Covariance that depends only on the separation, ℎ , between the
two points being considered: 𝜎(𝑥, 𝑥 + ℎ) = 𝐶(ℎ) = 𝐸[𝑍(𝑥) − 𝑚][𝑍(𝑥 + ℎ) −
𝑚].
Intrinsic Random Functions
This is a milder hypothesis, where it is assumed that for every vector ℎ
the increment defined as 𝑌ℎ(𝑥) = 𝑍(𝑥 + ℎ) − 𝑍(𝑥) is a stationary random
function itself, 𝑍(𝑥) is said to be an intrinsic random function and must
comply with (Chilès & Delfiner, 1999):
(1) Linear drift: 𝐸[𝑍(𝑥 + ℎ) − 𝑍(𝑥)] = ⟨𝑎, ℎ⟩
- 39 -
(2) Variogram: 𝑉𝑎𝑟 [𝑍(𝑥 + ℎ) − 𝑍(𝑥)] = 2𝛾(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:
- 40 -
𝛾(ℎ) =1
2𝑉𝑎𝑟 [𝑍(𝑥 + ℎ) − 𝑍(𝑥)]
This quantification is a means to measure the differences between 𝑍(𝑥)
and 𝑍(𝑥 + ℎ) as ℎ varies. Another way to define it, by decomposing the
definition of variance, is:
𝛾(ℎ) =1
2𝑁ℎ∑[𝑍(𝑥𝑖 + ℎ) − 𝑍(𝑥𝑖)]2
𝑁ℎ
𝑖=1
In this case 𝑥𝑖 are the different positions that 𝑍 can take and 𝑁ℎ 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 (𝑥 = 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 (𝑦 = 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
- 41 -
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
- 42 -
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 𝑛 data points in a d-dimensional space, 𝑅𝑑 ,and
with a given number of clusters, 𝑘 , the methodology will aim to determine a
𝑘 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 𝑛 number of observations
to a predetermined number of clusters, 𝑘, 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 𝑉(𝑧) containing all the data points associated to one
of the centers, 𝑧, for each stage 𝑧 is moved so that it becomes the centroid
of 𝑉(𝑧) and then 𝑉(𝑧) 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
𝑛 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, 𝑘 initial cluster centers, or seeds, 𝐶𝑘 , are chosen, each one
of them is a d–dimensional vector. This can be done randomly or by
using a default initialization mechanism.
- 43 -
2. Distances between each point to each centroid are calculated and saved
in a 𝑛 by 𝑘 matrix 𝐷.
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 𝑘 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
- 44 -
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 𝐾𝑚 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.
- 45 -
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:
- 46 -
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 �� and standard deviation 𝑆 the z-score, 𝑧, of a data point 𝑥 is:
- 47 -
𝑧 =(𝑥 − ��)
𝑆
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
- 48 -
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 𝑘 values
ranging from 5 to 10 (this range of values was found through trial and error)
and the mean value was evaluated for each 𝑘, 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 𝑘 values ranging from 2 to 5 and the mean value
was evaluated for each 𝑘, 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 ™
- 49 -
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.
Silhouette Value
0 0.5 1
Clu
ste
r1
2
3
4
5
Silhouette plot (kmeans, k = 5)
Silhouette Value
0 0.5 1
Clu
ste
r
1
2
3
4
5
6
Silhouette plot (kmeans, k = 6)
Silhouette Value
0 0.5 1
Clu
ste
r
1
2
3
4
5
6
7
SIlhouette plot (kmeans, k = 7)
Silhouette Value
0 0.5 1
Clu
ste
r
1
2
3
4
5
6
78
Silhouette plot (kmeans, k = 8)
Silhouette Value
0 0.5 1
Clu
ste
r
1
2
3
45678
9
Silhouette plot (kmeans, k = 9)
Silhouette Value
0 0.5 1
Clu
ste
r
1
2
3
456
78
9
10
Silhouette plot (kmeans, k = 10)
avg =
0.287
avg =
0.384
avg =
0.321
avg =
0.337
avg =
0.341
avg =
0.342
- 50 -
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 𝑘 = 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
Silhouette Value
0 0.2 0.4 0.6 0.8 1
Clu
ste
r
1
2
Silhouette plot (kmeans, k = 2)
Silhouette Value
0 0.2 0.4 0.6 0.8 1
Clu
ste
r
1
2
3
Silhouette plot (kmeans, k = 3)
Silhouette Value
0 0.2 0.4 0.6 0.8 1
Clu
ste
r
1
2
3
4
Silhouette plot (kmeans, k = 4)
Silhouette Value
0 0.2 0.4 0.6 0.8 1
Clu
ste
r
1
2
3
4
5
Silhouette plot (kmeans, k = 5)
avg = 0.8093 avg = 0.7502
avg = 0.7535 avg = 0.7439
- 51 -
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.
- 52 -
Figure 14. b) Event distribution in depth. Color scale for both images indicates clusters.
Cluster Total Number
of Events
Centroid
Longitude
Centroid
Latitude
Centroid
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 𝑘 = 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.
-75
-76
Distribution of Earthquake Depth with Latitude and Longitude
Longitude (deg)
-77
-78
-79
Latitude (deg)2
4
6
180
140
120
100
80
160
60
40
20
0
Dep
th (
Km
)
C1C2C3C4C5C6
- 53 -
Cluster Total Number
of Events Date Range
1 64 02/11/12 - 10/26/14
2 70 02/18/15 – 10/13/17
Table 5. Basic characteristics for time clusters.
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
Time (days)
0 500 1000 1500 2000 2500
Magnitude
(M
w)
1
2
3
4
5
6
7
8Distribution of Earthquake Sizes with Time
1
2
Phase A Phase B
- 54 -
be done by plotting the time for each event as a function of: (1) horizontal
distance, 𝑥, (2) vertical distance, 𝑦, and (3) depth, 𝑧.
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,
Time (days)
0 500 1000 1500 2000 2500
x (
km
)
0
200
400Feature 2
Time (days)
0 500 1000 1500 2000 2500
y (
km
)
400
600
800Feature 2
Time (days)
0 500 1000 1500 2000 2500
z (
km
)
0
50
100Feature 2
Time (days)
0 500 1000 1500 2000 2500
x (
km
)
0
200
400Feature 3
Time (days)
0 500 1000 1500 2000 2500
y (
km
)
200
400
600
800Feature 3
Time (days)
0 500 1000 1500 2000 2500
z (
km
)
0
50
100
150Feature 3
Time (days)
0 500 1000 1500 2000 2500
x (
km
)
100
200
300
400Feature 6
Time (days)
0 500 1000 1500 2000 2500
y (
km
)
200
400
600
800Feature 6
Time (days)
0 500 1000 1500 2000 2500
z (
km
)
0
50
100
150Feature 6
Time (days)
0 500 1000 1500 2000 2500
x (
km
)
-200
0
200
400System
Time (days)
0 500 1000 1500 2000 2500
y (
km
)
0
500
1000System
Time (days)
0 500 1000 1500 2000 2500
z (
km
)
0
100
200System
- 55 -
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.
- 56 -
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, 𝑥𝑠(𝑡) ,(2) distance
along y, 𝑦𝑠(𝑡) and (3) vertical distance 𝑧𝑠(𝑡). For each one of this distances
a semivariogram, 𝛾𝑥, 𝛾𝑦 and 𝛾𝑧 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.
- 57 -
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.
- 58 -
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, 𝑋𝑠(𝑡) ,(2) distance along y, 𝑌𝑠(𝑡) and (3) vertical distance
𝑍𝑠(𝑡). For each one of this distances a semivariogram, 𝛾𝑋, 𝛾𝑌 and 𝛾𝑍
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.
- 59 -
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
- 60 -
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.
- 61 -
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
Time (days)
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
Fea
ture
1
2
3
4
5
6
Time Range for Each Feature
Phase BPhase A
- 62 -
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
- 63 -
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
- 64 -
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
- 65 -
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.
- 66 -
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.
- 67 -
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
Cluster
1
Total Number of Events 3
Initial Date - Final Date 09/30/12 - 12/28/16
Duration of Activity
(days) 1549.52
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)
Cluster
2
Total Number of Events 39
Initial Date - Final Date 08/21/12 - 10/11/17
Duration of Activity
(days) 1877.85
Magnitude Range (Mw) 2.9 - 5.3
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)
Cluster
3
Total Number of Events 36
Initial Date - Final Date 02/11/12 - 08/05/15
Duration of Activity
(days) 1271.06
Magnitude Range (Mw) 2.2 - 4.8
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)
- 68 -
Attributes Value
Cluster
4
Total Number of Events 18
Initial Date - Final Date 08/03/14 - 04/03/17
Duration of Activity
(days) 974.06
Magnitude Range (Mw) 3.0 - 5.2
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))
Cluster
5
Total Number of Events 13
Initial Date - Final Date 06/10/12 - 09/17/17
Duration of Activity
(days) 1925.81
Magnitude Range (Mw) 2.8 - 4.2
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)
Cluster
6
Total Number of Events 25
Initial Date - Final Date 06/02/14 - 10/13/2017
Duration of Activity
(days) 1228.51
Magnitude Range (Mw) 1.6 - 4.3
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.
- 69 -
Figure A.1: 3D scatter plots for each one of the clusters, the centroid location for each
cluster is indicated with red.
-75
Longitude (deg)
-76-77
-78
C1
-792
Latitude (deg)
46
0
50
150
100
De
pth
(K
m)
-79
Longitude (deg)
-78-77
-76-75
C2
6
Latitude (deg)
42
0
100
Dep
th (
Km
)
Longitude (deg)
-76
-782
C3
Latitude (deg)
46
100
150
50
0
De
pth
(K
m)
-75
Longitude (deg)
-76-77
-78-79
C4
2Latitude (deg)
46
100
0
50
150De
pth
(K
m)
-75
Longitude (deg)
-76-77
-78-79
C5
2Latitude (deg)
46
0
150
100
50
Dep
th (
Km
)
-75-76
Longitude (deg)
-77-78
C6
-792
4
Latitude (deg)
6
100
0
150
50D
ep
th (
Km
)
- 70 -
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