Master_Thesis_Tsipianitis

UNIVERSITY OF PATRAS
SCHOOL OF NATURAL SCIENCES
DEPARTMENT OF GEOLOGY
SEISMOLOGICAL LABORATORY
Master Thesis in Engineering Seismology
IMPROVEMENT OF REGIONAL SEISMIC HAZARD
ASSESSMENT CONSIDERING ACTIVE FAULTS
By
ALEXANDROS D. TSIPIANITIS
Environmental Engineer, Technical University of Crete, 2013
Submitted in partial fulfillment of the requirements for the degree of
Master of Science in Applied, Environmental Geology & Geophysics
Supervisor: Dr. Efthimios Sokos
Referee: Dr. Akis Tselentis
Referee: Dr. Ioannis Koukouvelas
Patras, 2015

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AUTHOR’S DECLARATION
I hereby declare that the work presented in this dissertation has been my independent work
and has been performed during the course of my Master of Science studies at the
Seismological Laboratory, University of Patras. All contributions drawn from external
sources have been acknowledged with the reference to the literature.
Alexandros D. Tsipianitis

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ACKNOWLEDGEMENTS
First and foremost, I would like to express my deepest gratitude to my supervisor, Dr.
Efthimios Sokos, for his continuous support of my M.Sc. study and research, for his patience,
motivation and immense knowledge. He helped me significantly to develop my background in
the interesting field of Engineering Seismology.
Besides my supervisor, I would like to thank the co-advisor of my master thesis, Dr.
Laurentiu Danciu, Post-Doctoral researcher of ETH, Zurich, for his excellent guidance and
support of my overall research progress. I would also like to thank the members of the
examination committee, Dr. Akis Tselentis and Dr. Ioannis Koukouvelas, for their
suggestions, remarks and insightful comments.
My sincere thanks goes to the staff of the Seismological Laboratory of University of Patras,
Dr. Paraskevas Paraskevopoulos and the Ph.D. candidate, Mr. Dimitrios Giannopoulos, for
their assistance and cooperation. They provided me an excellent atmosphere for doing
research. I am also grateful to Dr. Konstantinos Nikolakopoulos for his assistance
considering the GIS part of my dissertation.
Last but not the least, I would like to thank my family and my friends for their continuous
support throughout my studies.
Alexandros D. Tsipianitis
Patras, April 2015

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ABSTRACT
Seismic hazard assessment is a required procedure to assist effective designing of structures
located in seismically active regions. Traditionally, in a seismically active region as Greece,
the seismic hazard evaluation was based primarily on the historical seismicity, and to lesser
extent based on the consideration of the geological information. The importance of the
geological information in seismic hazard assessment is significant, for the reason that
earthquakes occur on faults. This approach also covers areas with few instrumental
recordings. Mapping, analyzing and modeling are needed for faults investigation. In the
present dissertation, we examined the seismic hazard for the cities of Patras, Aigion and
Korinthos, considering the seismically active faults. The active faults considered in this
investigation consists of 148 active faults, for which a minimum amount of information was
available (i.e. length, maximum magnitude, slip rate, etc.). For some critical parameters, e.g.
slip rate, if an estimate could not be found in the literature it was calculated based on
empirical laws. Specifically, the slip rate for each fault was resulted from the division of total
displacement with the stratigraphic age. Two different approaches (historical seismicity,
length of faults) were followed for the estimation of total displacement for each fault. A
distribution of slip rates was made because uncertainties are considered. The resulted slip
rates were converted into seismic activity. Thus, we were able to construct a complete
database for our research. Epistemic uncertainties were accounted at both seismic source
models as well as at the ground motion via a logic tree framework resulted in two different
calculation procedures (including or not the b value uncertainty). The seismic hazard model
was implemented following the OpenQuake open standards – NRML, and the seismic hazard
computation was performed for the region of interest. The seismic hazard was quantified in
terms of seismic hazard maps, hazard curves and uniform hazard spectra for the region of
interest. Different intensity measure types were considered, Peak Ground Acceleration,
Spectral Acceleration at two fundamental periods 0.1 and 1.0 sec. Finally, the results of this
thesis were compared with the Greek Seismic Code and other seismic hazard estimations for
the investigation region.

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THESIS ORGANIZATION
First chapter depicts an overview of the seismic hazard methodology, with a focus on the
description of the general framework and highlights of the main features. Further, the region
of investigation is introduced and an overview of the existing studies considering seismic
hazard assessments in the regions of Europe, Greece and Patras is provided.
Second chapter describes in greater details the probabilistic framework for ground
motion evaluation. The theoretical aspects are illustrated together with the key elements (e.g.
uncertainty, hazard curves, earthquake models, empirical relations) with a focus on their
mathematical definition.
Chapter three provides an overview of the software used: the OpenQuake hazard
engine. Herein, the focus is the theory, the main concepts, the structure and critical
parameters, e.g. logic tree types, GMPEs, hazard calculators.
Fourth chapter describes the procedures adopted for building the seismic hazard
model. All active faults database used in the present dissertation is described. Approaches and
empirical relations are presented for the estimation of total displacement. The definition and
evaluation of slip rates are also provided. Additionally, the conversion of slip rates into
activity and an implementation of magnitude-frequency distribution are presented. The
seismic sources and GMPE logic trees are provided.
Chapter five contains the output of the seismic hazard evaluation. Hazard maps,
hazard curves and uniform hazard spectra for the region of Corinth Gulf and the cities of
Patras, Aigion and Korinthos are illustrated and commented.
Finally, in chapter six comparisons with previous ground motion estimates are
presented. Additionally, a comparison with the Greek Seismic Code is provided. Also, the
summary, conclusions and remarks are presented herein.

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Contents
Acknowledgements.................................................................................................................................iii
Abstract ...................................................................................................................................................iv
Thesis organization...................................................................................................................................v
Contents .............................................................................................................................................. … vi
1. Introduction.......................................................................................................................................1
1.1 The importance of seismic hazard analysis ...................................................................................1
1.2 Seismic hazard ...............................................................................................................................1
1.3 The importance of geology and neotectonics ...............................................................................3
1.4 The study area ...............................................................................................................................4
1.5 Previous researches.......................................................................................................................5
1.5.1 Europe .................................................................................................................................5
1.5.2 Greece .................................................................................................................................7
1.5.3 Patras................................................................................................................................ 11
2. Probabilistic Seismic Hazard Assessment (PSHA) .......................................................................... 12
2.1 Introduction ............................................................................................................................... 12
2.2 Difference between DSHA & PSHA............................................................................................. 13
2.3 Characterization of seismic sources ........................................................................................... 13
2.3.1 Source types..................................................................................................................... 13
2.3.1.1 Area sources................................................................................................................. 13
2.3.1.2 Fault sources ................................................................................................................ 13
2.3.2 Estimation of rupture dimensios...................................................................................... 14
2.4 Spatial uncertainty...................................................................................................................... 14
2.5 Relations of magnitude recurrence ............................................................................................ 16
2.5.1 Distribution of magnitude................................................................................................ 17
2.5.1.1 Truncated exponential model...................................................................................... 17
2.5.1.2 Characteristic earthquake models ............................................................................... 18
2.5.1.3 Composite model ......................................................................................................... 19
2.6 Relations of empirical scaling of magnitude vs. fault area......................................................... 20
2.7 Activity rates............................................................................................................................... 20
2.8 Earthquake occurrences with time............................................................................................. 23
2.8.1 Memory-less model.......................................................................................................... 23
2.8.2 Models with memory ....................................................................................................... 24
2.8.2.1 Renewal models ........................................................................................................... 24
2.8.2.2 Markov & semi-Markov models................................................................................... 28
2.8.2.3 Slip predictable model.................................................................................................. 29
2.8.2.4 Time predictable model ............................................................................................... 30
2.9 Ground motion estimation ......................................................................................................... 30
2.9.1 Parameters of ground motion.......................................................................................... 31
2.9.1.1 Amplitude..................................................................................................................... 31
2.9.1.2 Frequency content ....................................................................................................... 31
2.9.1.3 Duration........................................................................................................................ 32

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2.9.2 Empirical ground motion relations................................................................................... 32
2.9.2.1 Factors affecting attenuation....................................................................................... 36
2.10 Hazard curves........................................................................................................................... 38
2.10.1 Hazard disaggregation...................................................................................................... 39
2.11 Uncertainty............................................................................................................................... 40
2.11.1 Epistemic uncertainty....................................................................................................... 40
2.11.2 Logic trees ........................................................................................................................ 40
2.11.3 Aleatory variability ........................................................................................................... 40
3. OpenQuake..................................................................................................................................... 41
3.1 Introduction................................................................................................................................ 41
3.2 OpenQuake-Hazard .................................................................................................................... 42
3.2.1 Main concepts.................................................................................................................. 43
3.3 Workflows of calculation............................................................................................................ 43
3.3.1 Classical Probabilistic Seismic Hazard Analysis (cPSHA) .................................................. 44
3.4 Description of input.................................................................................................................... 44
3.5 Typologies of seismic sources..................................................................................................... 45
3.5.1 Description of seismic sources typologies........................................................................ 45
3.5.1.1 Simple fault sources ..................................................................................................... 46
3.6 Description of logic trees............................................................................................................ 46
3.7 The PSHA Input Model (PSHAim) ............................................................................................... 48
3.7.1 The seismic sources system.............................................................................................. 48
3.7.1.1 Logic tree of seismic sources........................................................................................ 48
3.7.1.2 Supported branch set typologies ................................................................................. 49
3.7.2 The system of ground motion.......................................................................................... 49
3.7.2.1 The logic tree of ground motion .................................................................................. 50
3.8 Calculation settings..................................................................................................................... 50
3.9 The Logic Tree Processor (LTP) .................................................................................................. 51
3.9.1 The logic tree Monte Carlo sampler................................................................................. 51
3.9.1.1 The sampling of seismic source logic tree.................................................................... 51
3.9.1.2 The sampling of ground motion logic tree................................................................... 51
3.10 The earthquake rupture forecast calculator............................................................................ 52
3.10.1 ERF creation-fault sources case........................................................................................ 52
3.11 Calculators of seismic hazard analysis ..................................................................................... 52
3.11.1 cPSHA calculator............................................................................................................... 53
3.11.1.1 Calculation of PSHA - Considering a negligible contribution from a sequence of
ruptures in occurrence t............................................................................................... 53
3.11.1.2 Calculation of PSHA – Accounting for contributions from a sequence of ruptures in
occurrence t ................................................................................................................. 54
4. Description of methodology........................................................................................................... 55
4.1 Introduction................................................................................................................................ 55
4.2 The Greek Database of Seismogenic Sources (GreDaSS) ........................................................... 56
4.2.1 Introduction...................................................................................................................... 56
4.2.2 Types of seismogenic sources .......................................................................................... 57

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4.2.3 Properties of seismogenic sources................................................................................... 58
4.2.4 Parameters of seismogenic sources................................................................................. 61
4.2.4.1 Individual Seismogenic Sources (ISSs) ......................................................................... 61
4.2.4.2 Composite Seismogenic Sources (CSSs) ...................................................................... 62
4.3 Application of GIS ....................................................................................................................... 62
4.4 Earthquake scaling laws.............................................................................................................. 65
4.4.1 Wells & Coppersmith (1994) ........................................................................................... 65
4.4.1.1 Displacement per event (MD) Vs. Magnitude (M) ...................................................... 65
4.4.1.2 Maximum displacement (MD) Vs. Rupture length (SRL) ............................................. 66
4.4.1.3 Rupture width (RW) Vs. Magnitude (M) ...................................................................... 66
4.4.2 Pavlides & Caputo (2004) ................................................................................................ 66
4.5 Estimation of slip rate - Approaches........................................................................................... 66
4.5.1 Approach 1 – Historical seismicity ................................................................................... 67
4.5.2 Approach 2 – Length of faults .......................................................................................... 68
4.6 Estimation of minimum & maximum fault depth....................................................................... 69
4.7 Fault characterization................................................................................................................. 69
4.7.1 Slip rate evaluation........................................................................................................... 69
4.7.2 Conversion of slip rates into seismic activity ................................................................... 70
4.7.3 Magnitude-Frequency Distribution (MFD)....................................................................... 71
4.8 Model implementation............................................................................................................... 72
4.9 Configuration.............................................................................................................................. 74
5. Results............................................................................................................................................. 75
5.1 Model A: mean b-value (no-uncertainty)................................................................................... 75
5.1.1 Hazard maps of Corinth Gulf............................................................................................ 75
5.1.2 Hazard curves of Patras.................................................................................................... 77
5.1.3 Hazard curves of Aigion.................................................................................................... 78
5.1.4 Hazard curves of Korinthos .............................................................................................. 79
5.1.5 Uniform hazard spectra.................................................................................................... 80
5.2 Model B: including b-value uncertainty...................................................................................... 82
5.2.1 Hazard maps of Corinth Gulf............................................................................................ 82
5.2.2 Hazard curves of Patras.................................................................................................... 84
5.2.3 Hazard curves of Aigion.................................................................................................... 85
5.2.4 Hazard curves of Korinthos .............................................................................................. 86
5.2.5 Uniform hazard spectra.................................................................................................... 87
5.3 Comparison................................................................................................................................. 88
5.3.1 Difference between 10% probability of exceedance for mean PGA values between Run
#1 And Run #2 .................................................................................................................. 88
5.3.2 Difference between 2% probability of exceedance for mean PGA values between Run #1
And Run #2 ....................................................................................................................... 88
5.4 Comparisons with the Greek Seismic Code ............................................................................... 89
5.5 Comparisons with previous studies ........................................................................................... 91
6. Summary and conclusions .............................................................................................................. 95
6.1 Summary..................................................................................................................................... 95

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6.2 Results......................................................................................................................................... 96
Appendix................................................................................................................................................ 97
References........................................................................................................................................... 111

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CHAPTER 1
INTRODUCTION
1.1 The importance of seismic hazard analysis
Many regions around the globe are prone to be affected by earthquakes. The threat to human
activities is something that cannot be omitted, so this triggers a more careful structure design
(Kramer 1996; Koukouvelas et al., 2010). Therefore, an earthquake-resistant building design
has the aim to produce a structure which can sustain a sufficient level of ground motion,
without presenting excessive damages (Kramer, 1996; Stein & Wysession, 2003; Baker,
2008). Generally, the construction of fully earthquake-resistant structures is generally
impossible (Komodromos, 2012).
For the reasons mentioned above, the seismic hazard analysis (SHA) plays a critical
role to the quantitative estimation of the design seismic load, which is related with the
seismicity of the study area, the level of structure‟s vulnerability and the danger that incurs to
humans, which are mainly exposed to the seismic events (Pavlides, 2003; Pitilakis, 2010).
The application of seismic hazard analysis is separated in two categories, which are
mostly implemented for the description of earthquake ground motions (Kramer, 1996; Gupta,
2002; Pavlides, 2003; Orhan et al., 2007). The first category, defined as “deterministic
method” or DSHA (Deterministic Seismic Hazard Analysis), is applied by using a historical
seismic event that occurred in the past or a specific seismic fault that is seismically active and
it has completely identified spatial and geometric parameters. The second category, defined as
“probabilistic method” or PSHA (Probabilistic Seismic Hazard Analysis), takes into account
the direct uncertainties relevant to the seismic magnitude and the time that of occurrence,
using a strict mathematical way (Kramer, 1996; Koukouvelas et al., 2010; Pitilakis, 2010).
1.2 Seismic hazard
The estimation of hazard caused by seismic events is one of the main purposes of earthquake
prediction, especially referred to the realm of long-term prediction (Scholz, 1990). Generally,

CHAPTER 1 – INTRODUCTION
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macro or microzoning maps of a site are some relative applications (Gupta, 2002). Seismic
hazard is defined as “the probability of a certain ground motion parameter to exceed a given
value, for a specific period of time” (Tselentis, 1997; Papazachos et al., 2005; Godinho, 2007;
Tsompanakis et al., 2008; Koukouvelas et al., 2010; Pitilakis, 2010; Koutromanos &
Spyrakos, 2010). The ground motion parameter can be expressed through the seismic strain or
the logarithm of ground acceleration and the time period can be considered as a year or the
lifetime of a conventional building (i.e. 50 years) (Papazachos et al., 2005).
Figure 1.1: Example of seismic hazard plot – PGA (Peak Ground Acceleration) vs. Annual frequency
(Koutromanos & Spyrakos, 2010).
Generally, seismic hazard depends on:
 the seismicity of the study area,
 the source-target distance,
 the local site conditions.
The local site conditions (Fig. 1.2) can affect in significant extent the surface ground
motion considering the following ways (Sanchez-Sesma, 1986; Papazachos et al., 2005;
Psarropoulos & Tsompanakis, 2011):
1. The amplification (or the de-amplification, for the case of soft soils and earthquakes of
large magnitude) of ground motion.
2. The extension of seismic duration.
3. The change of frequency spectrum.
4. The spatial variability of the ground response.

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Figure 1.2: Main seismic actions (Tsompanakis & Psarropoulos, 2012).
The arguments mentioned above cannot be neglected for cases such as the seismic
design of high-risk structures (e.g. hospitals, nuclear power plants, dams), seismic risk
assessment and microzonation studies (Esteva, 1977; Ruiz, 1977; Gupta, 2002; Klugel, 2008;
Koutromanos & Spyrakos, 2010).
1.3 The importance of geology and neotectonics
The estimation of seismic hazard for an area demands the specification and mapping of all the
possible seismic sources, and the active faults that can trigger capable seismic tremors (Green
et al., 1994; Pitilakis, 2010). The seismic source definition and the history of the seismicity of
a region are very important parameters. The identification, the definition and the mapping of
the seismic sources is based on the synthesis and analysis of a database, whose main
characteristics are the following (Pitilakis, 2010):
 the historical seismicity of the study area,
 the information of instrumental recordings,
 the geological study of the area,
 the information related to neotectonics,
 the information from paleoseismological investigations (Fig. 1.3).

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Figure 1.3: Paleoseismological investigation of the Eliki fault, Gulf of Corinth, Greece (Koukouvelas
et al., 2000).
1.4 The study area
The study area of this dissertation is the Corinth Gulf (CG) which contains the city of Patras,
Aigion & Korinthos (Fig. 1.4). All of them are located in the north part of Peloponnese coast.
Corinth Gulf is a very seismic prone area characterized by a high rate of deformation rates
(Pantosti et al., 2004). The CG‟s length is approximately 115 km and its width ranges from 10
to 30 km (Stefatos et al., 2002). This region includes many normal onshore & offshore active
faults that have played an important role to the geomorphological changes of the shorelines
and landscapes (Koukouvelas et al., 2005). The most recent damaging seismic events were the
1981 earthquake sequence of Corinth and the 1995 earthquake of Aigion (Pantosti et al.,
2004).
Figure 1.4: The Corinth Gulf including the active faults from the database.

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1.5 Previous researches
1.5.1 Europe
In this subchapter, some case studies on seismic hazard estimation are presented. Generally,
many seismic hazard assessments have been carried out for the continent of Europe (Chung-
Han, 2011). It is worth mentioning the most important investigations:
 In the framework of Global Seismic Hazard Assessment Program (GSHAP, Fig. 1.5), a
study was done for Europe and the Mediterranean region (Grunthal et al., 1999a,b; Chung-
Han, 2011).
Figure 1.5: PGA (horizontal) seismic hazard map for an occurrence rate of 10% within 50 years-
GSHAP for the Mediterranean region (Grunthal et al., 1999b).
 Project SESAME (Seismotectonic & Seismic Hazard Assessment of the Mediterranean
basin, Fig. 1.6), extended for entire Europe (Jimenez et al., 2003; Chung-Han, 2011).

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Figure 1.6: ESC-SESAME hazard map for the European & Mediterranean region (Jimenez et al.,
2003, www.ija.csic.es).
 Project SHARE (Seismic Hazard Harmonization in Europe, Fig. 1.7), which is the most
updated assessment until now. A probabilistic approach was used and three interpretations
of earthquake rates have been applied in the current project (Giardini et al., 2013):
1. The historical seismicity of moderate to large seismic events. A SHARE
European Earthquake Catalog (SHEEC) was compiled, which contains a
combination of 30377 seismic events in the period 1000-2007, with Mw 3.5.
2. The European Database of Seismogenic Faults (EDSF) includes an amount of
1128 active faults with a total length of 64000 km and models related to three
subduction zones.
3. The deformation rates of earth‟s crust, as studied by GPSs (Global Positioning
Systems.

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Figure 1.7: European seismic hazard map for PGA expected to be exceeded with a 10% probability in
50 years-Application of OpenQuake (Giardini et al., 2013, www.share-eu.org).
1.5.2 Greece
Greece presents an extremely high level of seismicity, thus a lot of scientific reports dedicated
to the seismic hazard analysis of this territory and the surrounding regions exist. The main
studies concerning the SHA of Greece are presented below.
 The Greek Seismic Code (EAK 2003).
Figure 1.8: The unified seismic hazard zonation of Greece, return period of 475 years (EAK, 2003).

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 Tsapanos et al. (2004).
All seismological observations and historical instrumental recordings have been considered
for this SHA. For the reason that the attenuation law was related to shallow seismic events,
only the shallow shocks were taken into account in this case.
Figure 1.9: Probabilistic seismic hazard map of Greece and surrounding regions for PGA values.
Return period of 475 years (10% probability in 50 years) (Tsapanos et al., 2004).
 Danciu et al. (2007).
This hazard map (Fig. 1.10) has been generated by applying well known engineering
parameters. The ground motion parameters investigated in this report have been applied
through the use of the attenuation equations of Danciu & Tselentis (2007). These relationships
are mainly based on strong ground motion data of Greek seismic events.
Figure 1.10: Seismic hazard map of Greece for PGA values and probability of 10% in 50 years. Case
of ideal bedrock soil condition (Danciu et al., 2007).

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 Tselentis & Danciu (2010).
In this study, a PSHA for Greece has been implemented including some significant
engineering parameters (PGA, PGV, Arias intensity, cumulative absolute velocity) for a lower
acceleration value of 0.05g. The hazard map (Fig. 1.11) has been estimated for a return period
of 475 years.
Figure 1.11: Probabilistic seismic hazard map (PGA), according to Tselentis & Danciu (2010).
 Vamvakaris (2010).
The computation of the maximum expected PGA values was achieved by making various
comparisons related to the choice of the suitable attenuation relationships. For each type of
hypocental depth (low, intermediate, high) different equations have been applied.
Figure 1.12: Values of maximum expected PGA for seven return periods (Vamvakaris, 2010).

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 Segkou (2010).
The methodology followed in this dissertation for the PSHA of Greece (Fig. 1.13) is based on
the survey and appraisal of the respective previously generated hazard maps in global scale.
The PSHA is based on the evaluation of different seismic source models identified by
seismological, geological and geophysical observations, in order to be suitable to the
requirements of Greek region.
Specifically, different processes were applied for the estimation of total expected
ground motion:
- The linear seismic source model, which is based on the identification of active faults
through geographical, seismological and geological criteria (Papazachos et al., 2001)
and associated to the seismic hazard due to shallow earthquakes.
- The random seismicity model, based on the analysis of shallow earthquakes seismicity
catalogue. This model corresponds to the estimation of seismic hazard related to
earthquakes with magnitude of 5 to 6.5 R.
- A seismic source model aiming to describe seismicity associated with the subduction
zone (this seismic source model is called by Segkou as “uniform basement zone”).
Figure 1.13: Seismic hazard map (PGA) for rock basement. Average return period of 475 years
(Segkou, 2010).
 Koravos (2011).
A SHA for shallow earthquakes of the Greek territory was made by applying the Ebel-Kafka
method (Fig. 1.14). This method uses synthetic catalogues computed with the Monte Carlo
simulation. For the estimation of seismic hazard, the Ebel-Kafka code was modified for the
purposes of the attenuation relationship suitable to the Greek area. The attenuation equation

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used for the PGA computation of shallow shocks was taken from Skarlatoudis et al. (2003),
because it contains seismicity data from Greece.
Figure 1.14: Illustration of the maximum PGA estimation considering shallow earthquakes for 1000
years seismicity data. The probability of exceedance is 10% (Koravos, 2011).
1.5.3 Patras
 Sokos (1998)
The seismic hazard estimation for the city of Patras (Fig. 1.15) was carried out using the
SEISRISK III software. This program has the ability to estimate the maximum level of
ground motion depended on the attenuation relationship considering a certain probability of
exceedance for a specific time period.
The seismic sources that were used in this application were these proposed by
Papazachos (1990), Papazachos & Papaioannou (1997) and for the seismic hazard assessment
of Rio-Antirio Bridge. Three different definitions for the seismic sources were made for the
research of seismic hazard dependency on the seismic sources.
Figure 1.15: Acceleration curves for the city of Patras with 90% probability of exceedance for the
next 50 years (Sokos, 1998)

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CHAPTER 2
PROBABILISTIC SEISMIC HAZARD
ASSESSMENT (PSHA)
2.1 Introduction
As inferred by Cornell (1968) and Baker (2008), the Probabilistic Seismic Hazard Analysis
(PSHA) contains two representative features, the event (how, where, when) and the resulting
ground motion (frequency, amplitude, duration). These characteristics provide a methodology
relative to the quantitative representation of the relationship associated with the probabilities
of occurrence, the potential seismogenic sources and ground motion parameters. “PSHA
computes how often a specified level of ground motion will be exceeded at the site of
interest” (Godinho, 2007; Ross, 2011).
The resulting information is presented by the form of return period or annual rate of
exceedance. Thus, seismic hazard computations provided by PSHA that can be implemented
for seismic risk assessment. Therefore, engineers possess an extremely useful tool concerning
the seismic resistance of a building (Godinho, 2007; Ross, 2011). According to Reiter (1990),
PSHA can be divided into four steps:
1. The first step is referred to the identification and characterization of seismic sources.
This step is similar to the first step of DSHA (Deterministic Seismic Hazard
Assessment), with the difference that there should be a characterization of the
probability distribution of the potential rupture locations within the source.
2. Secondly, there should be a characterization of the seismicity or the distribution of
earthquake occurrence. The aim of a recurrence relationship is the specification of an
average rate, at which a seismic event of some size will occur. Its use is related to the
characterization of the seismicity of each seismogenic source.

CHAPTER 2 – PROBABILISTIC SEISMIC HAZARD ASSESSMENT (PSHA)
13
3. In this step, the use of predictive equations should be linked with the produced ground
motion at the area by seismic events of any possible size that occurred at any potential
point in each seismic zone.
4. Finally, a combination between the uncertainties in earthquake size, location and
ground motion parameter prediction is made, in order to obtain the probability of
exceedance of ground motion parameter during a specific period of time.
2.2 Difference between DSHA & PSHA
Before the development of PSHA, the compilation of many seismic hazard assessments was
under the perspective of a deterministic view, using scenarios of location and magnitude for
each source in order to evaluate the ground motion design (Abrahamson, 2006; Baker, 2008).
It can be stated that PSHA is an assessment which is composed of an infinite number of
DSHAs, taking into account all possible seismogenic sources and scenarios of distance and
magnitude (Godinho, 2007; Koukouvelas et al., 2010).
2.3 Characterization of seismic sources
In this section, there is a description of the rate at which earthquakes of given dimensions and
magnitudes take place in a specific location. First of all, the potential sources are identified
and their dimension parameters are modeled. This requires the definition of source type and
the estimation of source dimensions (Godinho, 2007; Baker, 2008; Koutromanos & Spyrakos,
2010).
2.3.1 Source types
2.3.1.1 Area sources
Some seismic faults which have inadequate geological data can be modeled as area sources,
based on data related to their historical seismicity. Therefore, an assumption was made that
seismic zones have unique source properties in time and space. Additionally, the use of area
sources is preferred at the modeling of “background zones” of seismic areas, for the purpose
of the occurrence of seismic events away from known mapped active faults (Abrahamson,
2006; Baker, 2008).
2.3.1.2 Fault sources
The identification and definition of the location of seismic faults is feasible, when adequate
geological data is available. Despite their linear source modeling, many fault source models
have multi-planar characteristics and there is an assumption for the ruptures, which implies
that they are distributed over the entire fault plane (Abrahamson, 2006).

14
2.3.2 Estimation of rupture dimensions
The fault rupture dimensions can be estimated through the following two ways (Wells &
Coppersmith, 1994; Henry & Das, 2001):
 based on the size of fault rupture plane,
 or based on the size of the aftershock zone.
The measurement of length of fault expression on the free surface and the estimation
of the seismogenic zone, are some actions required for the estimation of fault rupture. The
distinction between primary and secondary source rupture is very important for the estimation
of fault rupture length. The primary source is mainly associated with the tectonic rupture,
which is the fault rupture plane that intersects the ground surface. On the other hand, the
secondary rupture is related to fractures caused by initial rupture effects, such as landslides,
ground shaking or ruptures from earthquakes which were triggered on nearby active faults
(Wells & Coppersmith, 1994; Godinho, 2007). The corner frequency fc of source spectra for
large events (obtained from ground motion recordings) plays an important role concerning the
estimation of rupture dimensions (Molnar et al., 1973; Beresnev, 2002).
The determination of the subsurface rupture length, as indicated by the spatial pattern of
aftershocks, is the second method associated with the estimation of fault‟s dimensions. The
determination of rupture width can also be done through this way. Studies have shown the
reliability of this method, but it is known that there are factors which contribute to its
uncertainty (Godinho, 2007). According to Henry & Das (2001), in the case that time period
after the main seismic event is small, the aftershock territory provides reliable estimates of
rupture dimensions.
2.4 Spatial uncertainty
The tectonic processes play a significant role concerning the dimensions of earthquake
sources (Fig. 2.1). Earthquakes generated in zones that are too small (i.e. seismic events
caused by the activity of volcanoes) are characterized as point sources. The consideration of
two-dimensional (2-D) areal sources can be taken into account in the case that earthquakes
can occur at several different locations and a good definition of the fault planes exists. Three-
dimensional (3-D) volumetric sources can be considered when there are areas where (Kramer,
1996):
 there is an obvious extension of the faulting, so the separation of individual fault is not
possible,

15
 there is a poor definition of earthquake mechanisms.
In order to compile a seismic hazard assessment, the source zones should present a
similarity to the real seismogenic source. This depends on the dimensions of the source, the
study area and the completeness of source data (Kramer, 1996).
It is assumed that the distribution of earthquakes usually takes place within a specific
source area. Ground motion parameters are expressed by some predictive relationships in
terms of some measure of source-to-site distance, so the description of spatial uncertainty
should be with respect to the suitable parameter of distance. A probability density function
can describe this uncertainty (Kramer, 1996).
Considering the point source (Fig. 2.1a), the distance, , is presented as . Therefore,
there is an assumption that the probability that is to be 1 and the probability that
is to be zero. In the case of linear source (Fig. 2.1b), the probability that occurs
between and is similar to the probability that an occurrence of a seismic
event takes place on a small section of the fault between and , so (Kramer,
1996):
( ) ( ) ( )
where:
( ), ( ) probability density functions for the variables and .
Figure 2.1: Geometries of source zones: (a) short fault – point source, (b) shallow fault – linear
source, (c) 3-D source zone (Kramer, 1996).

16
Figure 2.2: Source-to-site distance variations for different source zone dimensions (Kramer,
1996).
( ) ( ) ( )
For the assumption of the uniform distribution of the earthquakes over the length of the fault,
( ) . Since the probability density function of has the following
form (Kramer, 1996):
( )
√
( )
The evaluation of ( ) by numerical rather than analytical processes is a more
straightforward way for the case of having source zones with complex geometries.
2.5 Relations of magnitude recurrence
The expression of the seismicity of a source is associated with a magnitude recurrence
relation, with the premise that the dimensions of the source are well-defined and a suitable
magnitude scale selected. The characterization of magnitude occurrence equations is referred
to the activity rate of seismogenic sources and a function which describes the magnitude
distribution. The integration of magnitude distribution density function and the scale
considering the activity rate are the principal elements for the computation of a recurrence
relation, as the following (Godinho, 2007):
∫ ( ) ( )

17
where:
: the average rate of earthquakes with magnitude greater than or equal to a magnitude M,
: a specified magnitude,
: source‟s activity rate,
( ): magnitude distribution density function.
2.5.1 Distribution of magnitude
The definition of randomness in the number of relative number of large, intermediate and
small sized seismic events occurring in a given source, can be done through a probability
density function. There are two model types used for the representation of magnitude
distributions (Godinho, 2007):
1. The truncated exponential model.
2. The characteristic earthquake model.
Studied by Youngs & Coppersmith (1985), the characteristic model is more suitable for
the characterization of individual active faults. There are seismicity models that use a hybrid
approach, i.e. truncated exponential model for small-to-moderate seismicity and characteristic
model for large magnitudes. The resulting difference in seismic hazard between the two
models depends of fault-to-site distance and acceleration level, thus, on the SHA also
(Godinho, 2007).
2.5.1.1 Truncated exponential model
This model, based on Gutenberg-Richter magnitude recurrence relation (Gutenberg-Richter,
1956), is described through the following equation:
( )
where:
: the a-value, which represents the source activity rate,
: the b-value, which represents the relative likehood of earthquakes with different
magnitudes (values between 0.8-1.0).
In addition, there is an alternative form of the truncated exponential model:
( )
( )

18
where:
and ( )
It is obvious that earthquake magnitudes present an exponential distribution. So, the
mean recurrence rate of small magnitude earthquakes is a lot larger than that of large-sized
earthquakes (Godinho, 2007).
Despite the fact that the application of standard Gutenberg-Richter recurrence relation
has to do with an infinite range of magnitudes, the application of bounds at minimum and
maximum values of magnitude is very common because there is a connection between
seismic sources and the capacity for producing maximum magnitude Mmax (Godinho, 2007).
From the viewpoint of engineers, earthquakes of very small magnitudes, which do not cause
some type of damage to buildings, are not being taken into account (Abrahamson, 2006). The
following probability density function, which uses the minimum (Mmin) and maximum (Mmax)
values, is presented through an equation and a graph:
( )
( )
( )
( )
Figure 2.3: Magnitude probability distribution function – truncated exponential model (Godinho,
2007).
2.5.1.2 Characteristic earthquake models
These types of models are based on the hypothesis that individual faults have the tendency to
generate same size, or representative earthquakes (Schwarz & Coppersmith, 1985). According
to Godinho (2007), prior to 1980‟s the magnitude associated with the characteristic
earthquake was based on the assumption that some fraction of total fault length would rupture
(i.e. ¼ of total fault‟s length) (Abrahamson, 2006). Nowadays, the prevailing theory states the

19
separation of active fault into segments, which can be used as boundaries of rupture geometry
(Abrahamson, 2006).
The characteristic earthquake model includes a type named as model of “maximum
magnitude” (Godinho, 2007). This form is not applicable to smaller-to-intermediate events.
The basic idea refers to the assumption of Abrahamson (2006), which supports that all
seismic energy is derived from characteristic earthquakes. According to Figure 2.4, this model
can be used only for a narrow range of magnitudes.
Figure 2.4: Magnitude probability density function – truncated normal model (Godinho, 2007).
2.5.1.3 Composite model
Previous investigations have applied a combination of the characteristic and truncated
exponential model, for the accommodation of distribution related to large magnitude
earthquakes (Youngs & Coppersmith, 1985). Therefore, the modeling of characteristic
earthquake behavior is allowed, without other magnitude events being excluded. The
magnitude density function concerning this model (Fig. 2.5) presents an exponential
distribution with some magnitude, M, and a uniform distribution of given width, which is
centered on the mean characteristic magnitude. Additionally, an extra constraint in order to
define the relative amplitudes of two distributions is required (Godinho, 2007). As noted by
Youngs & Coppersmith (1985), the relative amount of the released seismic moment through
small magnitude events and characteristic earthquakes are represented by this constraint. This
model is based on empirical data.

20
Figure 2.5: Magnitude probability density function – composite characteristic & exponential
model (Godinho, 2007).
2.6 Relations of empirical scaling of magnitude vs. fault area
Models of magnitude distribution, like those presented in the previous subchapter, have some
limits between minimum and maximum magnitude values. The minimum level of energy
release expected to cause damage to buildings is represented by the minimum magnitudes
(Abrahamson, 2006). On the other hand, maximum magnitudes refer to stress drop and fault
geometry. Specifically, the stress drop is a parameter which describes the distribution of
seismic moment release in time and space (Godinho, 2007). Below, there is a table (Table
2.1) that presents some scaling relations between rupture dimension and magnitude (Godinho,
2006):
Wells & Coppersmith (1994)
All fault types
( )
Strike-slip
( )
Reverse
( )
Ellsworth (2001)
Strike-slip for A>500km2 ( )
Somerville et al. (1999)
All fault types
( )
Table 2.1: Magnitude (M)-area (A) scaling equations (Godinho, 2007).
2.7 Activity rates
While relative earthquake rate at several magnitudes is provided by magnitude distribution
models for the complete representation of source seismicity through a recurrence relation,
there is a requirement of activity rate (Godinho, 2007). According to Godinho (2007), activity
rate is the rate of earthquakes above a minimum magnitude. The activity rate of a seismic
source can be defined through the following two approaches:

21
1. Seismicity
There is a possibility of estimating the activity rates which are based on recordings from
earthquake catalogues. This is applicable to seismically active areas where there is availability
of significant historical data. When the exponential distribution is fitted to the historical data,
the computation of seismicity parameters (b-value in Gutenberg-Richter‟s relation, activity
rate) can be retrieved by using a regression analysis (maximum likelihood method) (Godinho,
2007).
In the case of being based on earthquake catalogues, in order to provide data related to
earthquake occurrence, it must be noted that there is a dependence of the accuracy of the
estimated activity rate with catalogues‟ reliability. Thus, there must be a completeness and
adequacy study of the earthquake data but also an exclusion of the aftershocks and foreshocks
from the study (dependent events) (Abrahamson, 2006; Godinho, 2007).
2. Geological information-slip rate
Slip rate can be useful to the estimation of activity rates for other earthquake models
(characteristic earthquake model). This is feasible when there is adequacy of historical data
for the estimation of activity rates (Youngs & Coppersmith, 1985). The advantage of this
method is its application, because it covers seismic areas with few recordings related to
earthquake occurrence (Godinho, 2007). It also provides further information concerning the
recurrence that allows an improved computation of mean earthquake frequency (Youngs &
Coppersmith, 1985).
A reliable estimate of slip rate must be based both on historical and geological data
(Godinho, 2007). Youngs & Coppersmith (1985) have made some hypotheses concerning the
estimations of these parameters:
 The consideration of all observed slip as seismic slip, which can be assumed as an
effect of creep.
 Short term fluctuations are not considered, because slip rate represents an average
value.
 Slip rates at seismogenic depths and along the entire fault length are assumed to be
represented by all surface measurements.
The computation of activity rate is achieved by balancing the long term accumulation of
seismic moment with is long term release (Godinho, 2007). According to Aki (1979), the rate
of moment build up is expressed through this relation:

22
̅
̅̇ ( )
where:
̅̇: the slip rate (cm/year),
: the fault rupture area,
: the shear modulus.
If a scaling relation is used for the definition of fault‟s characteristic magnitude,
( ) ( )
The amount of moment released by an individual characteristic earthquake can be expressed
by using a moment-magnitude relation.
( ) ( )
( ) ( )
The product of the moment release per characteristic earthquake and earthquake occurrence
rate ( ) equals the total rate of moment release.
̇ ( )
If the rate of moment release is equated with the rate of moment build-up, the direct
estimation of activity rate is the next step.
̇ ̇ ( )
̇ ( )
⁄
̇
⁄
( )

23
2.8 Earthquake occurrences with time
When the computation of recurrence rate of a given magnitude seismic event has been made,
the next step is the conversion of this rate into a probability of earthquake occurrence
(Godinho, 2007). A hypothesis concerning the earthquake occurrence with time is required,
especially if a “memory” or “memory-less” pattern is followed by a process of earthquake
occurrence (Godinho, 2007).
For a better understanding of the physical process of earthquake occurrence, the
theory of elastic rebound will be described. First introduced by Reid (1911) and also
presented by Kramer (1996), the theory refers that “the occurrence of earthquakes is a product
of the successive build-up and release of strain energy in the rock adjacent to faults”. The
setup of strain energy is an outcome of the movement of earth‟s tectonic plates. This
movement causes shear stresses increased on fault planes, which are considered as plates‟
boundaries (Godinho, 2007). In the case that shear stresses reach the maximum shear strength
of rock, there is failure and release of the accumulated strain energy. A strong rock will
rupture rapidly and the cause will be the sudden release of energy in the form of earthquake
(Kramer, 1996).
2.8.1 Memory-less model
The assumption that earthquake process is memory-less is a basic feature of many PSHAs.
This means that no memory of time, location and size of former events exists. It can be said
that there is no dependence between the probability of an earthquake occurring in a given year
and the elapsed time since the previous seismic event (Godinho, 2007).
Therefore, an exponential distribution of earthquake recurrence intervals is
characteristic of the Poisson process, which defines the occurrence of earthquakes (Godinho,
2007).
( ) ( )
( ) ∫ ( ) ∫ ( )
where:
: the recurrence rate,
: time between events.

24
Figure 2.6: Probability density function of earthquake occurrence - exponential distribution model
(Godinho, 2007).
By using the probability theorem of Bayes, the expression of probability of an
earthquake occurrence within years from former events is the following:
[ ]
[ ]
[ ]
∫ ( )
∫ ( )
( ) ( )
( )
( )
where:
: the elapsed time since the former seismic event,
: the intermit time between events.
The equation changes its form when there is evaluation of the probability expression
using the cumulative distribution function, which is related to the assumption of Poisson:
[ ]
( )
( )
( )
It can be noticed that the time which remains since the last earthquake ( ) does not
exist anymore in the probability expression. This demonstrates the nature of “memory-less”
model (Godinho, 2007). The hazard function of exponential distribution can be represented:
( )
( )
( )
( )
2.8.2 Models with memory
2.8.2.1 Renewal models
A conventional way for the representation of earthquake occurrence with time is to assume it
presents some periodicity (Godinho, 2007). In contrast with Poisson model, which supports
the hypothesis that earthquake occurrence intervals are exponentially distributed, different

25
distributions are applied by renewal models that allow the increase of the probability of
occurrence ( ) with elapsed time since the former earthquake (Cornell & Winterstein, 1988).
Four types of typical distributions concerning the earthquake occurrence are examined:
 Lognormal,
 Brownian Time Passage,
 Weibull,
 Gamma.
The main characteristics of most renewal model distributions are two statistical
parameters, the covariance and the mean (Godinho, 2007). The first parameter is related to the
measure of periodicity of earthquake recurrence intervals. The second parameter is associated
with the average elapsed time between events (Cornel & Winterstein, 1988; Godinho, 2007).
(a) Lognormal
This distribution is one of the most ordinary distributions practically used:
( )
√
(
( )
) ( )
Figure 2.7: Probability density function of earthquake occurrence - lognormal distribution model
(Godinho, 2007).
It is worth to state that this type of mathematic distribution has some important
parameters, such as the median ( ) and the standard deviation ( ). The relations which
describe these parameters are the following (Godinho, 2007):

26
̅
( )
( )
√ ( ) ( )
(b) Brownian Passage Time
This category of distribution is also known as the Wald or Gaussian distribution. The basic
parameters of Brownian Passage Time (BPT) are the mean recurrence interval (̅) and
parameter, which represents the aperiodicity (Godinho, 2007).
( ) √
̅
*
( ̅)
̅
+ ( )
Figure 2.8: Probability density function of earthquake occurrence - BPT distribution model (Godinho,
2007).
Examined by Matthews et al. (2002), the BPT distribution model is applied in the
characterization of earthquake occurrence using a Brownian relaxation oscillator, which is
represented by the state variable ( ).
( ) ( ) ( )

27
Figure 2.9: Example of load state paths - Brownian relaxation oscillator (Matthews et al., 2002).
(c) Weibull & Gamma
These distributions have some similarities related to their general form and relation to the
exponential density distribution. The constants and are associated with the variation and
the mean distribution (Godinho, 2007):
( ) ( )
( )
( )
( )
( ) ( )
( )
( )
Figure 2.10: Probability density function of earthquake occurrence - Weibull distribution model
(Godinho, 2007).

28
Figure 2.11: Probability density function of earthquake occurrence - Gamma distribution model
(Godinho, 2007).
2.8.2.2 Markov & semi-Markov models
Markov property is a main characteristic of many earthquake occurrence models, which are
based on stochastic processes. Therefore, this transitional probability is conditional only on
the present state. It is also independent of the process‟s state in the past (Patwardhan et al.,
1980; Godinho, 2007).
( ) ( ) ( )
Figure 2.12: Schematic representation – semi Markov process (Patwardhan et al., 1980).
Developed by Patwardhan et al. (1980) and also noted by Votsi et al. (2010), these
models of earthquake occurrence apply this primary Markov property of one-step memory.
The modeling of waiting time and size of successive earthquakes is allowed from the
application of semi-Markov properties in earthquake occurrence models (Godinho, 2007).

29
2.8.2.3 Slip predictable model
The dependence of future events on time of the last appearance is one conventional property
of most earthquake occurrence memory models (Godinho, 2007). The magnitude of a
successive earthquake, which is reflected by the amount of the released stress, consists of a
function only of the time elapsed since the last earthquake. This is based on the hypothesis
that stress accumulates at a stable rate for some time period and is independent of the former
seismic event‟s magnitude (Kiremidjian & Anagnos, 1984). This shows the representation of
a positive “forward” correlation between successive magnitudes and inter-arrival times, which
are considered to be distributed in a random way (Godinho, 2007). Developed by Kiremidjian
& Anagnos (1984), a schematic representation of the model is shown in Figure 2.13:
Figure 2.13: Slip-predictable model: (a) time history of stress release and accumulation (b)
relationship between time between seismic events and coseismic slip (c) sample path for the Markov
renewal process (Kiremidjian & Anagnos, 1984).
Below there is an illustration of the comparison between the Poisson and the slip-
predictable model.
Figure 2.14: Comparison between Poisson and slip-predictable model (Kiremidjian & Anagnos,
1984).

30
2.8.2.4 Time predictable model
Based on the hypothesis of time-predictable behavior, an alternative model has been
developed while slip-predictable models use the time between events for the estimation of
earthquake‟s magnitude (Godinho, 2007). In time-predictable models the information is
provided by the magnitude of last earthquake. This means a correlation between earthquake
size and intermit times (Godinho, 2007). Presenting many similarities to the slip-predictable
model, Figure 2.15 is a schematic illustration of the corresponding time-predictable model:
Figure 2.15: Time-predictable model: (a) time history of stress release and accumulation (b)
relationship between time between seismic events and coseismic slip (c) sample path for the Markov
renewal process (Kiremidjian & Anagnos, 1984).
2.9 Ground motion estimation
As studied by Boore (2003), the application of ground motion estimation takes place in
structure‟s design. This is feasible by using the existing building codes or the site-specific
structures‟ design. Despite the efforts related to the gathering of more ground motion data in
seismically active regions, it can be said that there are insufficient amount of data considering
the empirical computation of design ground motions (Godinho, 2007). Therefore, many
scientific projects have been devoted to the development of the estimation of ground motion
parameters, which will be practical for structures‟ design based on the features of seismic
sources, such as distance or magnitude (Godinho, 2007).

31
2.9.1 Parameters of ground motion
2.9.1.1 Amplitude
Peak horizontal acceleration is a basic parameter which is used in the characterization of
ground motion amplitude. Peak ground velocity, which is less sensitive to high frequencies, is
applicable for the computation of structures‟ ground motions, which are vulnerable to
frequencies of intermediate level (tall flexible structures) (Godinho, 2007).
2.9.1.2 Frequency content
As defined by Godinho (2007), the way that ground motion amplitude is distributed amongst
different frequencies is described by the frequency content. Its definition can be through
different types of spectra and spectral parameters.
Studied by Kramer (1996), a plot of Fourier amplitude represents a Fourier spectrum
defined as the product of performing a Fourier time series‟ transformation. Immediate
indications considering the ground motion‟s frequency content are given by the spectrum of
Fourier (Godinho, 2007).
The power spectrum is another type of spectrum which is used in the description of
frequency content. It allows the computation of some statistical parameters used in stochastic
methods for the development of ground motion estimation, with the premise that ground
motion is characterized as a random process (Godinho, 2007).
The maximum response of SDOF (Single Degree Of Freedom, Fig. 2.16) system
containing a specific level of viscous damping (e.g. 5%) as a function of natural frequency is
described by a response spectrum (Fig. 2.16, 2.17). It is commonly applicable to structural
design and engineering purposes. The illustration of response spectrum is on tripartite
logarithm scale, including in the same plot the parameters of velocity, acceleration response
and peak displacement (Godinho, 2007).
Figure 2.16: SDOF system (www.scielo.org.za).

32
Figure 2.17: Response spectrum (Godinho, 2007).
2.9.1.3 Duration
The ground motion‟s duration is an important parameter related to the prevention of damage,
which is caused by physical processes that are sensitive to the amount of load reversals (e.g.
the degradation of stiffness and strength, the development of pore water pressures-
liquefaction). There is also a correlation between the duration of ground motion and the
length of rupture. Therefore, there is a proportion related to the parameters of an event‟s
magnitude and the duration of ground motion. Specifically, when the size of an earthquake
increases, the duration of the resulting ground motion increases too (Godinho, 2007).
Through the bracketed duration, the duration can be defined as the time between the
first and last exceedance of some threshold acceleration‟s value (e.g. 0.05g) (Bolt, 1969). The
significant duration is an additional applicable parameter of duration, defined as the measure
of time in which there is dissipation of a specified energy amount (Godinho, 2007). Another
parameter, which is conventially used in determining liquefaction potential, is the equivalent
number of ground motion‟s cycles, which consists an alternative expression of duration
(Stewart et al., 2001).
2.9.2 Empirical ground motion relations
A probability distribution function of a specific ground motion parameter (e.g. response
spectra, peak acceleration) is a form that often characterizes the ground motions (Godinho,
2007). Equations named as attenuation relations or Ground Motion Prediction Equations
(GMPE), which are derived through regression analysis of empirical data, determine some
statistical moments such as standard deviation and median. These moments are based on

33
seismological parameters (source-to-site distance, magnitude). Table 2.2 presents some
models for ground motion attenuation in active seismic areas:
Magnitude
Range
Distant
Range
(km)
Distance
Measure
Site Parameters
Other
Parameters
Atkison &Boore
(1997)
5.5-7.5 0-100 rjb 30m-Vs Fault type
Campbell
(1997, 2000,
2001)
4.7-8.1 3-60 rseism
Soft rock, hard
rock, depth to
rock
Fault type,
hanging wall
Abrahamson &
Silva (1997)
>4.7 0-100 r Soil/rock
Fault type,
hanging wall
Sadigh et
al.(1997)
4.0-8.0 0-100 r Soil/rock Fault type
Idriss (1991,
1994)
4.6-7.4 1-100 r Rock only Fault type
Table 2.2: Attenuation models for horizontal spectral acceleration in active fault areas (Godinho,
2007).
The expression of the attenuation equation‟s general form is the following:
( ) ( ) ( ) ( ) ( ) ( )
where:
: parameter of ground motion amplitude,
: constants determined by regression analysis,
: moment magnitude,
: source to site distance (Fig. 2.18),
: factor accounting for local site conditions,
: factor accounting for fault type (e.g. reverse, strike-slip),
: factor accounting for hanging-wall effects.
The basis for most attenuation equations is expressed through a number of assumptions
(Stewart et al., 2001):
 Uncertainty in ground motions
The uncertainty or variability ( or ) in ground motion amplitudes and the mean ground
motion ( ) are defined by attenuation relations. It is assumed that ground motion amplitudes

34
are lognormally distributed, so ( ) and ( ) consist the representations of mean and
uncertainty.
 Magnitude dependence
Moment magnitude and other magnitude scales are derived using the logarithm of peak
ground motion parameters. Therefore, there is the hypothesis which supports that ( ) is
proportional to the magnitude of the event ( ).
 Radiation damping
The energy, which is released by a seismic fault during the occurrence of a seismic event, is
radiated out through traveling body waves. When they travel away from the seismogenic
source, there is a phenomenon called “radiation damping” which describes the reduction of
wave amplitudes at a rate of ⁄ ( : source-to-site distance).
Figure 2.18: Measures of source-to-site distance – ground motion attenuation models: (a) vertical
faults, (b) dipping faults (Godinho, 2007).

35
 Factors that affect attenuation
Various factors associated to site and source characteristics affect the attenuation of ground
motions. Therefore, a reference model is implemented in order to examine the influence on
the attenuation of ground motions.
The model introduced by Campbell & Bozorgnia (2003), consists of near-source
horizontal and vertical ground motion attenuation relations for 5% damped pseudo-
acceleration response spectra and peak ground acceleration.
( ) √ ( ) ( ) ( ) ( ) ( )
It is observable that this model has a similar form to the equation presented above
(2.27). Figure 2.19 presents two examples: M=7.5 and M=5.5 for Peak Spectral Acceleration
(PSA) of 0.1 sec and Peak Ground Acceleration (PGA).
Figure 2.19: Attenuation relations: (a) peak spectral acceleration, (b) peak ground acceleration
(Campbell & Bozorgnia, 2003).

36
2.9.2.1 Factors affecting attenuation
1. Site conditions
Many forms can represent the effects of local site conditions, starting from a simple constant
till more complex functions (Godinho, 2007). There are some models applied for a simple
soil/rock soil classification (Abrahamson & Silva, 1997; Sadigh et al., 1997), but others use
more quantitative methods of classification, such as the 30m shear wave velocity (Atkinson &
Boore, 1997). Generally, there is a hypothesis which supports that standard error in
attenuation is unaffected by site conditions (Godinho, 2007).
Figure 2.20: Peak spectral acceleration (damping=5%) using Campbell & Bozorgnia ground motion
attenuation – effects of site conditions (Mw=7.0, rseis=10km, strike-slip fault) (Campbell & Bozorgnia,
2003).
2. Near-fault effects
Many studies, such as Campbell & Bozorgnia (2003), have shown that near-fault effects on
ground motion play a very important role. These surveys have concluded that there is a
sensitivity of ground motion at near-source site to what is considered as “rupture directivity”.
The long period energy of ground motion and the duration are affected by this parameter

37
(Godinho, 2007). The phenomenon which takes place when there is fault propagation towards
the site is named “forward directivity”.
Primarily, its effects are founded in the horizontal direction normal to fault rupture.
Therefore, shock wave effects characterize the ground motion, which is associated with a
short duration and large amplitudes at intermediate to long periods. On the other hand, a
relatively low amplitude and long duration describes the ground motions, which are affected
by backward directivity (Godinho, 2007).
3. Tectonic regime
The tectonic region, in which the seismogenic sourced is located, is one of the most basic
factors that affect the features of ground motion. For each subduction, stable continental and
active region zones, there is a development of some attenuation relations. A development of a
large proportion of attenuation equations is observed too, because of the specific amount of
the available ground motion data (Godinho, 2007). There is not availability of very strong
motion data for the case of stable continental areas. Therefore, for these areas the basis of
attenuation relations refers to simulated motions instead of the available recordings (Atkinson
& Boore, 1995-1997b; Toro et al., 1997).
4. Focal mechanism-fault type
As studied by Boore (2003), ground motion parameters (frequency content, amplitude) are
influenced by faulting mechanism. Strike slip faults can be used as a reference of attenuation
relations and additional factors. A larger proportion of higher levels of frequency content for
thrust and reverse active faults and higher mean ground motion are included in some
observations of fault-type effects (Godinho, 2007).
Figure 2.21: Peak spectral acceleration (damping=5%) using Campbell & Bozorgnia ground motion
attenuation – effects of faulting mechanism (Mw=7.0, rseis=10km, firm soil) (Campbell & Bozorgnia,
2003).

38
5. Hanging wall effect
Abrahamson & Somerville (1996) have concluded that sites which are located over the
hanging wall of dipping faults present a considerable increase in ground motions. The
experience (e.g. Northridge earthquake, 1994) has shown that this increase can be as much as
50% (Abrahamson & Silva, 1997).
2.10 Hazard curves
The determination of the final seismic hazard can be done when distribution functions
compute and characterize the ground motion estimates. The final step defines the frequency
that a significant level of ground motion (peak ground acceleration, duration, displacement)
will be exceeded at an area of interest (Godinho, 2007). The following equation describes the
individual hazard of a single seismogenic source:
( ) ( ) ∫ ∫ ( ) ( ) ( ) ( ) ( )
where:
: annual rate of events or return period,
: level of ground motion,
: specified level of ground motion to be exceeded,
: magnitude,
: distance,
: number of standard deviation.
The source-to-site distance, the ground motion and the probability density functions
for magnitude are integrated over the above relation. The contribution of a single seismogenic
source is reflected by the hazard expression mentioned above. In addition, a sum of total
hazard contributions for each individual source is necessary, for the case of multiple seismic
sources consideration (Godinho, 2007).
( ) ∑ ( ) ( )

39
Then, the value of return period or annual rate of events must be converted into a form
of probability. The likelihood that the ground motion will exceed the level at least once
during a significant time interval is reflected by this probability (Godinho, 2007).
Figure 2.22: Hazard curves for spectral period of 2 sec – individual source (McGuire, 2001).
2.10.1 Hazard disaggregation
According to Bazzuro & Cornell (1999), disaggregation of hazard is a procedure that
indicates the greatest contribution to the hazard. It is completed using a two-dimensional
disaggregation into bins of different source-to-site distances and earthquake sizes. Then,
Figure 2.23 represents the disaggregation of hazard corresponding to the total contribution for
source hazard curves, shown in the previous graph (Fig. 2.22).
Figure 2.23: Disaggregation of hazard for spectral period of 2 sec and ground motion level of 0.5g
(McGuire, 2001).

40
2.11 Uncertainty
The definition and treatment of uncertainties are some important features of PSHAs. In the
realm of structural system designing, the limitation of uncertainty is a very crucial and
considerable factor (Tsompanakis et al., 2008). Two types of uncertainties are involved:
epistemic uncertainty and aleatory variability (Godinho, 2007).
2.11.1 Epistemic uncertainty
For the reason that is a product of limited knowledge and data, epistemic uncertainty is
usually referred to as scientific uncertainty. Generally, this category of uncertainty can be
reduced as more information becomes available and the use of alternative models is one of its
characteristics (Godinho, 2007).
2.11.2 Logic trees
Logic trees are a basic characteristic of PSHAs (Fig. 2.24). They are useful for the
determination of design ground motions (Bommer & Scherbaum, 2013). The use of a logic
tree is an ordinary way for handling the epistemic uncertainty related to the inputs to PSHA
(Godinho, 2007; Bommer & Scherbaum, 2013). It provides some ways for the effective
organization and assessment of the credibility of alternative models used in this uncertainty
(Godinho, 2007).
Logic trees have the form of separated branches, in which there are different types of
uncertainties according to the choice of each researcher (Aiping & Xiaxin, 2013).
Figure 2.24: Logic tree used in PSHAs (Godinho, 2007).
2.11.3 Aleatory variability
The innate randomness in a process is the definition of aleatory variability. Generally, it is
included in the calculations, specifically through the parameter of standard deviation and,
therefore, it plays an important role considering the resulting hazard curve (Abrahamson &
Bommer, 2005; Godinho, 2007).

41
CHAPTER 3
OPENQUAKE
3.1 Introduction
OpenQuake (www.openquake.org) is a software used for the calculation of seismic hazard
and risk, developed by the Global Earthquake Model (GEM) (Monelli et al., 2012; Silva et al.,
2012; Crowley et al., 2013). Summer 2010 was the starting date of the application of
OpenQuake, which derives from several GEM‟s projects (GEM Foundation, 2010) using a
wide range of data related to hazard and risk (Danciu et al., 2010; Crowley et al., 2010a;
Crowley et al., 2010b; Pagani et al., 2010; Crowley et al., 2011).
Specifically, OpenQuake is a combination of Python and Java programming code.
Their development was achieved by applying the most usual methods of an open source
software improvement (open mailing lists, public repository, IRC channel) (Crowley et al.,
2011). The released source code can be found on a free and accessible web based repository
(www.github.com/gem). It must be mentioned that open source projects such as Celeryd,
RabbitMQ and OpenSHA played a crucial role to the development of OpenQuake (Crowley
et al., 2011). Therefore, the main characteristics of OpenQuake are the following (Monelli et
al., 2012):
 The XML (eXtensible Markup Language) data schema is a basic feature. OpenQuake
uses an alternative form of XML, defined as NRML („Natural hazard‟ Risk Markup
Language). The description of a variety of data structures required for seismic hazard
and risk assessment is feasible through this NRML formal.
 It is designed for evaluating seismic hazard models for various global areas and
updated according to the special requirements of each regional seismic hazard/risk
programs.
The figure presented below (Fig. 3.1) is a schematic illustration of OpenQuake‟s structure
and contains (Crowley et al., 2011):

CHAPTER 3 – OPENQUAKE
42
1. Purple boxes, which are the representation of the crucial modules of the hazard
component.
2. White boxes, with main products estimated by the distinct modules.
3. Orange rectangles, which illustrate the essential input data.
Figure 3.1: Openquake‟s schematic representation (Crowley et al., 2011).
3.2 OpenQuake-Hazard
The basic definition of Probabilistic Seismic Hazard Analysis (PSHA) (see §2.1) has been
rapidly developed over the years, and it has been more accurate because of the reduced degree
of uncertainty (Crowley et al., 2011). This resulted from the improvement of instrumental
seismology and the computing power of hardware. EQRISK (McGuire, 1976) and SEISRISK
(Bender & Perkins, 1982, 1987) are programming codes which played an important role
concerning the evolution of PSHA.
Nowadays, many implementations of PSHA are more complex due to the challenges
presented continuously. The location, the geographical scale and, generally, the differences of
each studied case can affect the way of application. On the one hand, PSHA for specific sites
and high-risk structures (e.g. nuclear plants) demand more detailed, complex inputs and a

43
more extensive characterization of the parameter of uncertainty (Crowley et al., 2011). On the
other hand, PSHA for urban areas does not demand such complex data and input model
(Crowley et al., 2011).
3.2.1 Main concepts
OpenQuake follows the procedure presented below for the computation of probabilistic
seismic hazard (Crowley et al., 2011):
1. The reading of the PSHA input model (e.g. the combination of the ground motion and
seismic source system) and calculation options.
The required information for the creation of one or many seismic source models can be found
in the seismic source system. The epistemic uncertainties must be considered in such a
calculation, thus the system contains the following tools (Crowley et al., 2011):
 One or many Initial Seismic Source Models.
 One logic tree, also called „seismic source logic tree‟. It describes the epistemic
uncertainties associated with features and objects that characterize the Initial
Seismic Source Models.
The required information for the use of one or many ground motion models can be found in
the ground motion system. The epistemic uncertainties must be taken into account.
2. The processing of logic tree structures in order to account for epistemic uncertainties,
which are mainly connected with the seismogenic source and ground motion. Finally,
ground motion and seismic source models are created.
The necessary information for the creation of an ERF Earthquake Rupture Forecast (e.g. the
seismicity occurrence probability model) without taking into account any epistemic
uncertainty is contained into the seismic source model. The necessary data for the hazard
computation using a seismic source model is included into a ground motion model.
3. The hazard computation, taking into account as many seismic sources and ground
motion models as needed for the adequate characterization of uncertainties.
4. The post-processing of the obtained results for distinct estimations and the calculation
of simple mathematical statistics.
3.3 Workflows of calculation
Various approaches are followed by the hazard component of OpenQuake-hazard, which
computes seismic hazard analysis (SHA). There are three basic categories of analysis
presented below (Crowley et al., 2011):

44
1. Classical Probabilistic Seismic Hazard Analysis (cPSHA). This type calculates hazard
curves and maps, considering the classical integration method (Cornell, 1968;
McGuire, 1976) as mentioned by Field et al. (2003).
2. Event-Based Probabilistic Seismic Hazard Analysis (ePSHA), which calculates ground
motion fields derived from stochastic event sets.
3. Deterministic Seismic Hazard Analysis (DSHA). It estimates ground motion fields
from a single earthquake rupture event considering ground motion aleatory variability.
For the purposes of this master dissertation, the Classical Probabilistic Seismic Hazard
Analysis (cPSHA) is analyzed extensively in the next subchapter and used for the calculation
of Corinth Gulf‟s hazard map.
3.3.1 Classical Probabilistic Seismic Hazard Analysis (cPSHA)
Input data used for the cPSHA has a PSHA input model, which is provided with a set of
calculation options. Then, the basic calculators applied for the analysis performance are (Fig.
3.1) (Crowley et al., 2011):
 Logic Tree Processor
A seismic source model is created by the Logic Tree Processor (LTP), which takes the PSHA
input model as an input data. Specifically, the seismic source model describes the activity
rates and the geometry of each seismogenic source without any epistemic uncertainty. Then, a
ground motion model is created by the LTP (Crowley et al., 2011).
 Earthquake Rupture Forecast Calculator (ERF)
The ERF, which estimates the probability of occurrence over a specified time span for each
earthquake rupture produced by the source model, uses the resulted seismic source model as
an input (Crowley et al., 2011).
 cPSHA Calculator
The ground motion model and the ERF are used by the cPSHA for the computation of hazard
curves on each area specified in the calculation options (Crowley et al., 2011).
3.4 Description of input
Two basic data blocks are discussed in this chapter, the PSHA input model and calculation
settings. The accurate meaning of a PSHA input model (PSHAim) is taken from Crowley et
al. (2011): “PSHAim defines the properties of the seismic sources of engineering interest

45
within the region considered in the analysis and the models capable to describe the properties
of the shaking expected at the site”.
Additionally, two main features are contained: the seismic source system and the
ground motion system. Geometry, location, seismicity occurrence properties of active faults
and probable epistemic uncertainties that affect this information are specified by the seismic
source system. The details of ground motion forecast relationships adopted in the estimation
and the associated epistemic uncertainties are described by the ground motion system
Therefore, two forms of logic trees define the OpenQuake‟s PSHA input models. The
seismic source logic tree, which describes the epistemic uncertainties related to the formation
of the ERF, and the ground motion logic tree, which considers the uncertainties connected
with the application of models able to forecast the expected ground motion at a region. When
the epistemic uncertainties are inconsiderable, the logic tree structure has one branching level
with only one branch (Crowley et al., 2011).
3.5 Typologies of seismic sources
An amount of sources that belong to a measurable set of possible typologies is included in a
usual OpenQuake input model (PSHAim). This software contains four seismic source
categories; each of them has a limited number of parameters, which are indispensable for the
specification of the geometry and seismicity occurrence. In the next subchapter a more
extensive analysis of the source typologies supported by the OpenQuake software is provided
3.5.1 Description of seismic source typologies
As mentioned above, four seismic source typologies are supported by OpenQuake (Pagani et
al., 2010; Crowley et al., 2011):
1. Area source: the type with the most frequent use in regional and national PSHA
models.
2. Grid source: for the reason that both area and grid sources model the distributed
seismicity, this type can easily replace the area source category.
3. Simple fault source: the specification of a fault source in OpenQuake program
becomes more fluent using the simple fault type, which is frequently used for the
description of shallow active fault sources. It is also adopted for the purposes of the
current master thesis.

46
4. Complex fault source: this application is mostly related to the modeling of
subduction interface sources with a complex geometry.
The main hypotheses accepted in the definition of the above presented source typologies
are the following (Suckale et al., 2005; Crowley et al., 2011):
1. The distribution of seismicity over the source is homogeneous (area & simple fault
sources).
2. A Poissonian model is followed by seismicity temporal occurrence.
3. The frequency-magnitude distribution can be estimated to an evenly discretized
distribution.
3.5.1.1 Simple fault sources
The most applied source type for the modeling of faults is the “simple fault” category. The
dimensions of the seismogenic source acquired by the projection of a trace or polyline along a
dip direction are the meaning of the word “simple” (Crowley et al., 2011). Some interesting
features of simple fault sources taken from Crowley et al. (2011) are:
 A fault trace in the form of a polyline.
 A rake angle, as specified by Aki & Richards (2002).
 A value of the dip angle, as specified by Aki & Richards (2002).
 A discrete frequency-magnitude distribution.
 A labeling which specifies if magnitude scaling equations are followed by the size of
ruptures and a homogeneous distribution over the fault surface exists, or there is the
acceptance of the assumption that the entire fault surface will always be ruptured by
ruptures within a given magnitude range.
3.6 Description of logic trees
Logic trees (Fig. 3.2 & 3.3) are a tool which purpose is to handle the epistemic uncertainties
of models and parameters contained in a hazard analysis (Crowley et al., 2011). In our case,
we used two types of logic trees. The first category contained the seismic source models with
their adjusted weights. The second type of logic tree included additionally the b value
uncertainty, which was adjusted in each seismic source model in order to attempt the
reduction of the uncertainty parameter.

47
Figure 3.2: Example of branch set-epistemic uncertainties of faults dip angle (Crowley et al., 2011).
Crowley et al. (2011) note three fundamental elements included in a logic tree:
1. Branching level.
2. Branch set (Fig. 3.3).
3. Branch.
The distance of a given element from the start of the logic tree is expressed by the
branching level. It can be said that each branching level is connected with a single type
uncertainty, so the number of branching levels is proportional to its complexity (Crowley et
al., 2011). An uncertainty model is described by a branch set, which contains various
exclusive and exhaustive settings (Bommer & Scherbaum, 2008). Finally, a specific
alternative in a set of branches is represented by a branch.
Figure 3.3: Example of OpenQuake‟s logic tree structure (Crowley et al., 2011).

48
Figure 3.4: Logic tree data structure-individual branches, branch sets & branching levels (Crowley et
al., 2011).
3.7 The PSHA Input Model (PSHAim)
PSHAim includes (a) the data required for the definition of shape, position, activity rates and
relative epistemic uncertainties of engineering importance seismogenic sources within a given
data, and (b) the use of the ground motion models and related uncertainties for the estimation
of PSHA. The seismic sources and the ground motion system are two corresponding objects
contained in the PSHAim (Crowley et al., 2011).
3.7.1 The seismic sources system
It consists of one or more initial seismic source models (list of seismic source data) and the
seismic sources logic tree (Fig. 3.5). One or several seismogenic sources that account for
distributed seismicity are usually included in a seismic source model (Crowley et al., 2011).
Epistemic uncertainties related to the parameters applied for the characterization of the
initial seismic source models are described by the seismic sources logic tree. During the
application of this type of logic tree, the epistemic uncertainties related to all the parameters
that characterize each source typology can be considered by the user (Crowley et al., 2011).
3.7.1.1 Logic tree of seismic sources
This version of OpenQuake defines the seismic sources logic tree as following (Crowley et
al., 2011):
 There is an assumption than one or more substitute initial seismic source models are
described by the first branching level.
 Source parameter uncertainties are defined by subsequent branching levels. Each
seismic source in a source model applies parameter uncertainties, which are assumed
that are uncorrelated between various seismogenic sources.

49
 Branching level can define one branch set.
3.7.1.2 Supported branch set typologies
Only two built-in typologies of branch set are included in this version of OpenQuake. The
next Figure 3.5 is the illustration of a source model logic tree, containing the settings
available in the current version of this program (Crowley et al., 2011).
Gutenberg-Richter b value uncertainties
These uncertainties are depicted in Figure 3.5 as the branch set in the second branching level
of the current seismic sources logic tree. An infinite amount of branches are contained in this
branch set (Crowley et al., 2011).
Figure 3.5: Seismic sources logic tree (Crowley et al., 2011).
Gutenberg-Richter maximum magnitude uncertainties
For this branch set, a value (positive or negative) can be specified by the user in order to be
added to the Gutenberg-Richter maximum magnitude values (Crowley et al., 2011).
3.7.2 The system of ground motion
The ground motion system is a blend of one or many logic trees, which are related with a
particular tectonic area or a source group. The alternative ground motion models available for
a specific source group are defined by each ground motion logic tree. Only hardcoded Ground
Motion Prediction Equation (GMPE) are provided by the OpenQuake program (Fig. 3.6). An
insufficiency of tools which allow the specification of new GMPEs by the user also exists

50
Figure 3.6: Ground Motion Prediction Equations (GMPEs) contained in OpenQuake and OpenSHA
3.7.2.1 The logic tree of ground motion
The epistemic uncertainties associated to the ground motion models are represented by the
ground motion logic tree (Crowley et al., 2011). The consideration of multiple GMPE logic
trees, one for each tectonic area category taken into account in the source model, are
supported by OpenQuake given that ground motion models are frequently associated to a
specific tectonic area (Crowley et al., 2011).
This version contains a GMPE logic tree permitted to have one branching level
including one branch set, where a specific GMPE is linked to each individual branch. With
these available options, epistemic uncertainties derived from different models can be
considered, but this does not apply for the case of epistemic uncertainties inside each model
3.8 Calculation settings
Calculation settings are an object that includes the data available for hazard estimation. Some
relative basic elements are mentioned below (Crowley et al., 2011):
 The geographical coordinates of the study area, where the hazard computation is
conducted and the site‟s soil condition (vs,30).
 The methodology followed for the hazard estimation (see §4.3).
- cPSHA.
- DSHA.
- ePSHA.
 The typology of the expected results computed by the current version of OpenQuake:
- Hazard maps.

51
- Hazard curves.
3.9 The Logic Tree Processor (LTP)
In this section, the logic tree processor is presented analytically. LTP‟s purpose is the data
processing in a PSHAim, which consists of a seismic source model creation derived from the
seismic source logic tree (see §3.7.1.1) and ground motion model derived from the ground
motion logic tree (see §3.7.2.1) (Crowley et al., 2011).
3.9.1 The logic tree Monte Carlo sampler
The creation of a set of seismic source and ground motion interpretations, which represent the
combinations permitted by the logic tree structure as defined by the user, is the main goal of a
logic tree Monte Carlo sampler (LTMCS) (Crowley et al., 2011). The final results will reflect
the uncertainty introduced by the lack of accurate parameter and model definition (Gupta,
2002; Crowley et al., 2011).
3.9.1.1 The sampling of seismic source logic tree
The LTMCS creates a seismic source model processing all branching levels. In the first
branching level, there is a selection of an initial seismic source model, with a probability
equal to the weight of uncertainty (Crowley et al., 2011). For each branching level that
follows, there is a start of a loop procedure over the seismogenic sources. Then, for each
source there is a random selection of an epistemic uncertainty value (Crowley et al., 2011).
3.9.1.2 The sampling of ground motion logic tree
The ground motion logic tree defines the multiple branch sets that include various ground
motions models (Crowley et al., 2011). It follows a loop procedure over the various tectonic
area categories, which are defined by the user. For each of them, there is a random selection
of a GMPE considering their weights. A ground motion model for each tectonic area
category, taken into account in the source model, will be included in the final sample set
In addition, the methodology of the inverse transform method (Martinez & Martinez,
2002) is used for the sampling of epistemic weights. The method used for both the source
model and ground motion logic trees, computes the inverse distribution of the epistemic
weights and generate a uniform random value between 0 and 1.0 (Crowley et al., 2011).Then,
an epistemic uncertainty model with a probability equal to the related weight is given

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