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.

http://www.ija.csic.es/


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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).

http://www.share-eu.org/


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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


11

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)

12

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

( )

Wells & Coppersmith (1994) Strike-slip

( )

Wells & Coppersmith (1994) 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).

http://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):

http://www.openquake.org/

http://www.github.com/gem

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



52

3.10 The earthquake rupture forecast calculator

The Earthquake Rupture Forecast (ERF) is a basic concept used in the OpenSHA framework

(Field et al., 2003) and OpenQuake‟s hazard component (Crowley et al., 2011). The initial

procedure of ERF‟s calculation includes a seismic source model, which is created by the LTP


In the case of epistemic uncertainty‟s absence in the seismic source system, there is a

one-to-one correspondence between the initial seismic source and the seismic source model

applied in the hazard calculation (Crowley et al., 2011). Then, the LTP copies the data of

seismic source model contained in the initial seismic source model and, finally, sources that

produce seismicity in accordance with Poisson temporal occurrence model are supported by

OpenQuake (Crowley et al., 2011).

3.10.1 ERF creation-fault sources case

Two categories of fault sources are mainly supported by OpenQuake. Their differences are

mostly associated to the dimensions of the fault surface. Shallow sources are modeled by fault

sources with a simple geometry. On the contrary, subduction interface sources are modeled by

fault sources which present a more complex geometry (Crowley et al., 2011).

3.11 Calculators of seismic hazard analysis

Probabilistic seismic hazard computed by OpenQuake uses two methodologies: the classical

method (cPSHA) and a method which is based on the generation of a stochastic event set


The cPSHA methodology, which is used in OpenQuake, is the one mentioned by Field

et al. (2003) and applied in the OpenSHA software. The specific structure mentioned above

and also presented by Chiang et al. (1984), has the considerable feature of using probabilities

during the calculation procedure instead of working with rates of occurrence (Bender &

Perkins, 1987). The decoupling of the probability seismicity occurrence model creation is one

benefit of the OpenSHA methodology (Crowley et al., 2011). The demonstration of Field et

al. (2003) shows that this methodology is very stable by assuming negligible contributions to

hazard derived from multiple occurrences.

On the other hand, the method of stochastic event generation follows recent

approaches in PSHA calculation (Musson, 2000). The basic benefits of the above mentioned

approach are the following (Crowley et al., 2011):


53

1. Hazard can be associated to an earthquake sequence.

2. The elements of ground motion remained on each studied area can be taken

into account by considering the ground motion spatial correlation.

3.11.1 cPSHA calculator

This way of calculation is the one considered as the most effective for the PSHA calculation

results (hazard curves, hazard maps, hazard spectra), taking as input the elements presented

below (Crowley et al., 2011):

a ground motion model,

an Earthquake Rupture Forecast (ERF).

3.11.1.1 Calculation of PSHA - Considering a negligible contribution from a sequence of

ruptures in occurrence

The PSHA calculation method which is available in OpenQuake is mainly applied in

OpenSHA (Crowley et al., 2011). It is similar to the classical method considering the

hypothesis of the negligibility of the hazard contribution derived from multiple ruptures (Field

et al., 2003).

The hazard estimation for a unique site ( ) and a single parameter of ground

motion ( ) is performed through a repetitive process (Crowley et al., 2011). Then, the

contributions are integrated. These are derived from the ruptures contained in the ERF and

located at a distance from the site parameter, shorter than a minimum value of 200-300 km

(Crowley et al., 2011). During each repetition procedure, a calculation of the probability of

exceedance ( ) in time ( ) is made, by taking a rupture ( ) within source ( ). All these

are described through the Equation 3.1, taken from Crowley et al. (2011):

( ) ( ) ( ) ( )

On the one hand, the product between the conditional probability of exceedance ( ) at

site and the probability of occurrence in a time t, corresponds to the probability

( ). On the other hand the probability of occurrence linked to

during the creation of ERF is defined by the symbol ( ). The next relationship

(Equation 4.2, taken from Crowley et al., 2011) can be written in an alternative way by

changing the corresponding magnitude and node within source ( ) to each rupture.

( ) ( ) ( ) ( )


54

The product between the probability of exceedance and probability of magnitude

occurrence on node ( ) corresponds to the probability of exceedance of in

(Crowley et al., 2011). This is the interpretation of the above mentioned equation. Finally, the

final hazard value located at a site ( ) will be acquired by merging the contributions

derived from all of seismic sources taken into account during the process of ERF creation


( ) ∏ ( ( )

( )

3.11.1.2 Calculation of PSHA - Accounting for contributions from a sequence of

ruptures in occurrence

In some cases, the hypothesis of negligible contributions to the final hazard value derived

from a sequence of ruptures is not valid. Therefore, in order to conduct more accurate hazard

estimations, it is indispensable to consider any potential contribution, which is a product of

ERF‟s sources (Crowley et al., 2011). Equation 3.4 is presented in order to account for

repeated ruptures (Crowley et al., 2011):

( ) ∑( ( )

)

( ) ( )

where:

( ): the definition of the probability of a least one exceedance of given

one or more ruptures occurring within source ( ). Then, Equation 3.5 has the

following form (Crowley et al., 2011):

( )

∑ (∑( ( ) )

( ))

( )

55

CHAPTER 4

DESCRIPTION OF METHODOLOGY

4.1 Introduction

Before the main part of this master thesis, i.e. the estimation of seismic hazard using the

Openquake software, it is necessary to describe the methodology followed for the collection

of the data related to active seismic faults of Greece.

The identification of active faults is the first step of any seismic hazard assessment

(Tselentis, 1997; Mohammadioun & Serva, 2001). The data which are used in this thesis are

taken from two databases, the GreDaSS (Greek Database of Seismogenic Sources,

www.gredass.unife.it) and fault database of the Institute of Geodynamics (National

Observatory of Athens, www.gein.noa.gr) (IG-NOA) (Ganas et al., 2013). Additional

information was taken from bibliographic sources, such as published papers and scientific

books.

The collected data refer to the active faults around the city of Patras (north

Peloponnese, Greece) in a radius of approximately 200 km. It consist of some basic

parameters, such as the code of each seismic fault (i.e. GR0785), the name, the minimum and

maximum depth of the fault‟s surface, the strike, dip and rake, the slip rate, the maximum

recorded magnitude, the location and, finally, the length and width. Pavlides et al. (2007)

separated the faults into five categories, depending on their degree of activity:

1. Holocene active faults (confirmed displacement during the last 10,000 years & high

values of slip rate).

2. Late Quaternary active faults (confirmed displacement during the last 40,000 years).

3. Quaternary active faults (confirmed displacement during the Quaternary & low to

medium values of slip rate).

4. Capable faults of uncertain age, that can be possibly activated in the future.

5. Faults of uncertain activity, which are possibly inactive.

http://www.gredass.unife.it/

http://www.gein.noa.gr/

CHAPTER 4 – DESCRIPTION OF METHODOLOGY

56

Figure 4.1: Map of capable faults (Pavlides et al., 2007).

4.2 The Greek Database of Seismogenic Sources (GreDaSS)

4.2.1 Introduction

In this chapter the database of GreDaSS is presented (Fig. 4.2). According to Sboras et al.

(2014), the construction of this database is based on geological information and investigation

techniques. As stated by Sboras et al. (2014), GreDaSS is a project which goals are:

1. The systematic collection of all available information related to neotectonics, active,

capable faults and generally the seismogenic volumes.

2. The critical analysis of the collected data and the quantification of the basic

seismogenic features of several sources including a related degree of uncertainty.

3. Provide a complete view of probable damaging active faults for a better effectiveness

of SHA in Greece.


57

Figure 4.2: The form of GreDaSS showing the ISSs & CSSs layers (www.gredass.unife.it).

4.2.2 Types of seismogenic sources

Some fundamental elements of GreDaSS database are also presented, as inferred by Basili et

al. (2008); Sboras et al. (2009). There are two basic categories of seismogenic sources, the

“Individual Seismogenic Sources” (ISS) and the “Composite Seismogenic Sources” (CSS)

(Fig. 4.2 & 4.3).

“Individual Seismogenic Sources” (ISS) are derived from the synthesis of geological

and geophysical data. These types of seismogenic sources include a complete set of

geometric characteristics, such as strike, dip, length, width and depth, kinematic

parameters (rake) and seismological-palaeoseismological features, such as the average

displacement per event, the magnitude, the slip rate and the return period. Their use is

referred to the deterministic seismic hazard assessment (DSHA), the calculation of

earthquake scenarios and geodynamic research.

“Composite Seismogenic Sources” (CSS) have the same initial features concerning the

geometric and kinematic parameters, but the difference is about the looser definition

and the combination of two or more individual sources. This type of seismogenic

sources is not necessarily capable of a specific earthquake, but their possible activity

can be detected from the existing data. Instead of the previous category, the CSSs have

http://www.gredass.unife.it/


58

a complete record of potential earthquake sources and accurate description. In

conclusion, the CSS can be used for the preparation of regional PSHA and the study of

geodynamic procedures.

Figure 4.3: Schematic representation of an ISS (a) & CSS (b) seismogenic source (Sboras, 2011). The

description is presented below, according to Basili et al. (2009).

The depiction of the ISSs is associated with a rectangular (polygon) and a vector

placed at the central part (Fig. 4.3a). The purpose of the rectangular is the representation of

the vertical projection of fault plane on the ground surface. The top edge is associated with

the fault trace, in the case that the fault is characterized as emergent. When the fault is blind,

the section between the hypothetical continuation of ground surface and fault plane appears as

a line parallel to the top edge. Finally, the slip vector of fault‟s motion is represented by a

vector located in the rectangular.

The CSSs (Fig. 4.3b) have a looser shape because of their capability of containing

several fault segments (ISSs) and their incomplete data. The polygon includes two roughly

parallel long sides (such as the ISSs), which correspond to the top and bottom edges of fault

plane and two short lines parallel to the width. The top edge is represented with a thicker line

and in the case of the fault reaches the surface, the scarps or fault traces are followed by the

top edge.

4.2.3 Properties of seismogenic sources

Further and useful information about a seismogenic source can be obtained by clicking on it.

Then, a new web browser window will open, containing the information needed, separated


59

into four categories. This form is similar for both CSSs and ISSs. The information window

contains the following metadata pages:

i. “Source Info Summary”: the basic parameters are contained in this metadata page.

These are the “General Information” (Code, Name, Compilers, Contributors, Latest

update date), the “Parametric Information” (kinematic, geometric, seismotectonic

information) and finally the “Associated Earthquake”, which is referred only to the

ISSs (latest events, associated with a specific source).

ii. “Commentary”: three sections are included: the “Comments” (contains helpful

comments for a better description of the source, more details about the extra data,

etc.), the “Open Questions” (contains whichever parameter remains doubtful) and the

“Summary” (includes the information related to the source, which can be extracted

from the available bibliography).

iii. “Pictures”: pictures, figures, maps and images are enclosed in this metadata page.

iv. “References”: this is the last page, which contains all the literature linked with the

hosted source.

Figure 4.4: Source Info Summary, example of Palaeochori ISS fault (Sboras, 2011).


60

Figure 4.5: Commentary, example of Palaeochori ISS fault (Sboras, 2011).

Figure 4.6: Pictures, example of Palaeochori ISS fault (Sboras, 2011).

Figure 4.7: References, example of Palaeochori ISS fault (Sboras, 2011).


61

4.2.4 Parameters of seismogenic sources

For a better understanding of GreDaSS‟s environment, a definition and a qualitative

description of the parametric fields is made starting with the ISSs and CSSs. We take into

consideration the necessary precision and completeness. After Sboras (2011).

4.2.4.1 Individual Seismogenic Sources (ISSs)

Location (degrees): this parameter indicates the location of the fault on the map.

Length (km): the length of the fault plane.

Minimum depth (km): this parameter is associated with the vertical distance (depth)

of fault‟s top edge from the ground surface or the sea floor.

Maximum depth (km): the calculated depth of the bottom edge of fault plane from

the surface.

Width (km): the distance between the top and bottom edges of fault plane.

Strike (degrees): it has a similar meaning to fault‟s strike. Values which belong to the

eastern semicircle (0-180o) have a dip direction (plunge) inside the southern semicircle

(90-270o). On the contrary, values which belong to the western semicircle (181-360

o)

have a dip direction inside the northern semicircle (271-90o).

Dip (degrees): the dip-angle of fault plane.

Rake (degrees): the measured counter-clockwise angle, formed between the slip

vector and the strike. The rake‟s range is between 0o and 360

o.

Slip per event (m): the mean co-seismic displacement on the fault plane is

represented by this parameter. It is usually suggested by the database software based

on empirical laws, or it can be set directly.

Slip rate (mm/a): the ratio between the displacement and the necessary time to

produce it.

Recurrence (years): the recurrence interval time between two characteristic seismic

events.

Magnitude (Mw): this is a representation of the magnitude produced by a specific

seismic event, or the possible magnitude of the fault which is based on scaling laws. In

the realm of magnitude, there is dependence between the fault‟s dimensions and slip

per event.

Last earthquake (years): the date or the time elapsed from the last seismic event is

included in this part.


62

Penultimate earthquake (years): generally, it is a rarely available information

derived from paleoseismological studies and, sometimes, from historical references.

Elapsed time (years): the time interval between the last known seismic event and the

year 2000, which is used as a reference.

4.2.4.2 Composite Seismogenic Sources (CSSs)

Minimum depth (km): description similar to the ISSs.

Maximum depth (km): description similar to the ISSs.

Strike (degrees): it has the same meaning with the ISSs. The only difference has to do

with the requirement of a range of values.

Dip (degrees): description similar to the ISSs.

Rake (degrees): the definition is the same with the ISSs, but in this case a range of

values is required.

Slip rate (mm/a): description similar to the ISSs.

Maximum magnitude (Mw): it is the representation of the potential seismic

magnitude, or the maximum expected magnitude produced by the CSS.

Approximate location (degrees): same definitions with the ISSs. It is the center of

the source.

Total length (km): similar to the ISSs.

Total width (km): similar to the ISSs.

Typical fault length (km): it is based on the maximum magnitude field and

calculated from several scaling laws.

Typical fault width (km): this parameter is based on the maximum magnitude field,

the typical length and the dip angle range. It is derived from calculations between

analytical and scaling laws.

Typical fault slip (m): it has similar meaning to the former two parameters. Typical

fault slip is defined as the average displacement per event, based on scaling laws.

4.3 Application of GIS

The G.I.S. (Geographic Information Systems) software is used in order to create a complete

database for the case study (investigation of the active faults, 200 km away of Patras, north

Peloponnese, Greece). These data files considering the active faults are taken from the

GreDass‟ and IG-NOA‟s database.


63

The database related to active faults is classified into three layers, according to the

completeness of the data. The first layer (Fig. 4.8) includes the active faults with complete

data, the second layer (Fig. 4.9) includes the faults with an intermediate level of data

completeness (slip rate, length, max magnitude) and the last category (Fig. 4.10) includes the

seismogenic sources with poor data completeness (only length). Additionally, after the

merging of all shape files, the total faults database is illustrated by Figure 4.11. The attribute

table (Fig. 4.12) of each layer presents the values of the parameters of active faults.

Figure 4.8: 1st layer – complete level of data.

Figure 4.9: 2nd

layer – intermediate level of data


64

Figure 4.10: 3rd

layer – poor level of data.

Figure 4.11: The total faults database.


65

Figure 4.12: The attributes table.

4.4 Earthquake scaling laws

In this subchapter the scaling laws used in this dissertation are presented. Generally, these

equations can define various parameters, such as displacement, magnitude, rupture length,

seismic moment, etc. (Billion, 2007). In addition, the validity of models on the mechanics of

seismic rupture can be tested through these empirical relationships (Papazachos et al., 2004).

4.4.1 Wells & Coppersmith (1994)

Displacement vs magnitude and Dmax (maximum displacement) vs length relationships, taken

from Wells & Coppersmith (1994), were applied in this thesis for the estimation of slip rate.

These scaling laws were compiled using a database of approximately 400 seismic events.

Shallow focus, continental, intraplate or interplate earthquakes of magnitude greater than 4.5

are included in this data. On the contrary, there is an exclusion of seismic events that take

place in subduction zones and oceanic labs (Wells & Coppersmith, 1994). In addition, the

rupture width vs magnitude relationship is used for the case that the parameter of width is not

available in the database.

4.4.1.1 Displacement per event (MD) Vs. Magnitude (M)

Figure 4.13: Displacement per event Vs. Magnitude relationship for each type of faults‟ kinematics

(Wells & Coppersmith, 1994).


66

4.4.1.2 Maximum displacement (MD) Vs. Rupture length (SRL)

Figure 4.14: Displacement per event Vs. Rupture length relationship for each type of faults‟

kinematics (Wells & Coppersmith, 1994).

4.4.1.3 Rupture width (RW) Vs. Magnitude (M)

Figure 4.15: Rupture width Vs. Magnitude relationship for each type of faults‟ kinematics (Wells &

Coppersmith, 1994).

4.4.2 Pavlides & Caputo (2004)

Magnitude (Ms) vs maximum vertical displacement (MVD) and surface rupture length

empirical equations are proposed for the Aegean region by Pavlides & Caputo (2004). The

equation used for the purposes of this master thesis is the following magnitude versus

maximum vertical displacement relationship:

( ) ⇒

( ) ( ) ( )

4.5 Estimation of the slip rate – Approaches

The active faults‟ slip rate is one of the most crucial features of seismic hazard analysis.

Except from the literature data, a new database is made in order to present a more

comprehensive distribution for the decrease of parameter uncertainty. The equation that

defines the annual slip rate is associated with the total displacement and the age of each fault

(L. Danciu personal communication):

( )


67

Different approaches have been made for the estimation of the parameter of total

displacement. The stratigraphic age of faults was taken from Kokkalas et al. (2006); Marnelis

et al. (2007); Papanikolaou et al. (2007); Pechlivanidis (2012).

4.5.1 Approach 1 – Historical seismicity

Historical seismicity method is based on data related to historical earthquakes, for which

earthquake magnitude can be estimated. The magnitudes of historical earthquakes can be

correlated with empirical relationships. Therefore, many conclusions can be extracted with

respect to active faults which cause large earthquakes. However, it is widely known that in

some regions the historical data are usually incomplete, so the accuracy of this method is

sometimes limited (Koukouvelas et al., 2010).

This approach is based on the assumption that the total displacement of a fault derives

from the sum of the displacements caused by seismic events that occurred near it. This

contains a degree of uncertainty, because in some areas the correlation between past seismic

activity and known fault structures is impossible (Cornell, 1968). Concerning the seismic

events, the Seismicity Catalog (550 B.C-2010 A.D) (Papazachos et al., 2000; Papazachos et

al., 2010) for magnitude greater than 4.5R is used in order to possess a complete data.

Figure 4.16: Historical seismicity of Greece - application in GIS.

In the next step, a buffer zone of 5km around each fault is made in order to link

seismic events most probably related to the fault with fault‟s displacement. The following

illustration (Fig. 4.17) springs from the GIS software. All the events that fall within the buffer

zone are consider to belong to different ruptures of the fault, their magnitude is used as an


68

input to scaling laws and a displacement value is calculated. The sum of the calculated

displacements is used together with the age of the fault and eq. 4.2 for the computation of slip

rate.

Figure 4.17: Buffer zone of the Argostoli fault, Kefallonia - application in GIS.

4.5.2 Approach 2 – Length of faults

There are many studies and reports relative to the relationship between maximum

displacement and fault length, for the comprehension of fault geometry over many length

scales (Kim & Sanderson, 2005). In this thesis, the following relationship is used (Fig. 4.13)

(Wells & Coppersmith, 1994):

( ) ( ) ( )

where:

: the maximum displacement (km),

: surface rupture length (km),

coefficients.

Specifically, the maximum displacement is estimated by knowing the total length of

each fault. This can be applied with the premise that the entire length of the fault ruptures

during the occurrence of a seismic event, although observations have shown the opposite

(Petersen et al., 2011). This can lead to the overestimation of seismic hazard. Then, by

knowing the total displacement and the stratigraphic age of a fault, the slip rate can be

estimated through the basic equation (4.2).


69

4.6 Estimation of minimum & maximum fault depth

For active faults that the values of minimum and maximum seismogenic depth are not

available (i.e. IG-NOA database), some assumptions are made. Then, the maximum depth

value is taken from the depth of Mohorovic (Moho) discontinuity (the boundary between

Earth‟s crust and upper mantle) for each fault. The range of Moho depth in Greece is

presented in the following map:

Figure 4.18: Map of Moho depths in the Greek territory (Tsokas & Hansen, 1997; modified from

Somieski, 2008).

4.7 Fault characterization

4.7.1 Slip rate evaluation

Slip rate is the most crucial parameter of the present investigation. Uncertainties exist, so a

slip rate distribution was made and each fault contained 9 slip rate estimates. As defined by

Eq. 4.2, it derives from the ratio between total displacement and stratigraphic age of fault. For

the estimation of total displacement, two approaches were considered, historical seismicity

(see §4.5.1) and length of faults (see §4.5.2). Two empirical relations were used for this


70

occasion: displacement per event vs magnitude of Wells & Coppersmith (1994) and of

Pavlides & Caputo (2004). The second approach used the surface rupture length vs

displacement empirical relation of Wells & Coppersmith (1994) with the premise that the

entire fault length ruptures during an earthquake (worst case scenario). Thus, for each fault

three values of total displacement were estimated.

The stratigraphic age of faults was derived from the database or from the available

literature. For the reason that uncertainties exist, an average, an upper, and a lower value were

assumed. Each of three values of total displacement was divided with three estimates of

stratigraphic age. Therefore, for each fault 9 slip rate values were resulted.

4.7.2 Conversion of slip rates into seismic activity

According to the methodology of Bungum (2007), fault seismicity derived from slip rates can

be estimated using programs. The initial step of this methodology is the application of the

following two relationships: the cumulative occurrence relationship of Chinnery & North

(1975) (Eq. 4.4) and the total moment release rate equation of Brune (1968) (Eq. 4.5).

( ) ( ) ( ) ( )

where:

N: the number of earthquakes equal to or above magnitude M,

a: the absolute level of activity,

b: the ratio between smaller and larger earthquakes,

M, Mmax: earthquake magnitudes

H: the Heaviside step function.

( )

where:

: the total moment release rate,

μ: the rigidity,

S: the slip rate,

A: the rupture area.

Combining the above Eqs. (4.4)-(4.5), the relationship of Anderson & Luco (1983)

that determines the number of events N for magnitudes 4-5 R is presented below:

( ) (

) (

) ( ) (( ) ) ( )


71

where:

( ( )),

( ( )),

√ ( )) ( ),

,

( ): seismic moment for Ms=0,

d: the magnitude scaling coefficient.

4.7.3 Magnitude-Frequency Distribution (MFD)

Defined by Crowley et al. (2013), MFD consists of a function describing the rate of

earthquakes per year, across all magnitudes (see §2.5). The double truncated Gutenberg-

Richter distribution is frequently used in PSHAs (Crowley et al., 2013).

Figure 4.19: The double truncated Gutenberg-Richter MFD (Crowley et al., 2013).

As described in the previous paragraph, 9 slip rate estimates were calculated for each fault

following two approaches. For each slip rate, the cumulative a value was estimated for

magnitudes from 0-6.5, as can be seen from the following Figure 4.20:


72

Figure 4.20: Cumulative a value vs vMagnitude chart.

The consideration of two approaches provided a wide range of cumulative a-values forming a

zone. Therefore, all distributions were taken into account in the evaluation considering

uncertainties.

4.8 Model implementation

The application of logic trees is an appropriate method of modeling uncertainty. Logic tree

approach allows alternative models assigning in each of them a weighting factor that

represents the probability of that model being correct (Kramer, 1996). In this thesis, two logic

tree approaches are made.

The initial run of the code was done using the nine source models and equal weights to

each one of them (Fig. 4.21). The second run of the code included the b value uncertainty in

the logic tree. The following logic tree of Figure 4.22 contains nine source models and

additionally the b value uncertainty presented in three values (0.9, 1.0, 1.1) with equal

weights to each of them.


73

Figure 4.21: Logic Tree without b value uncertainty.

Figure 4.22: Logic Tree including b value uncertainty for each source file.


74

4.9 Configuration

After the generation of XML files (source model, logic trees, GMPE logic tree), the

compilation of the configuration file (.ini) follows.

The configuration file controls the input model definition and the parameters used in

the calculation. First of all, the structure and basic parameters for seismic hazard are

described. The next steps contain the specification of the area (i.e. polygon, distance, grid

points, etc.) where hazard will be computed, the logic tree processing, the specification of the

discretization level of the mesh that represents faults and the definition of local soil conditions


Nine XML files are the seismic sources model of this implementation. The XML file

of logic tree models the epistemic uncertainty related to seismic sources model and b-value

(see ). The GMPE logic tree (Fig. 4.23) is an XML file that includes the following

approaches considered for active shallow crust:

Akkar & Bommer (2010),

Cauzzi & Faccioli (2008),

Chiou & Young (2008),

Zhao et al. (2006).

Figure 4.23: GMPE Logic Tree.

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CHAPTER 5

RESULTS

5.1 Model A: mean b-value (no-uncertainty)

5.1.1 Hazard maps of Corinth Gulf

After the first OpenQuake execution, the hazard maps were generated for PGA values, for

Spectral Acceleration (SA) of 0.1 sec (referred to a three or four-storey building) and SA of

1.0 sec (referred to a multi-storey structure). Considering the probabilities of exceedance, the

values that are used in this survey are the mean values, for 10% probability of exceedance

(POE) in 50 years (return period of 475 years) and 2% POE in 50 years (return period of 2500

years).

PGA – Return period of 475 years

Figure 5.1: Hazard map of Corinth Gulf, 10% POE in 50 years.



CHAPTER 5 – RESULTS

76

SA 0.1 sec – Return period of 475 years







77



5.1.2 Hazard curves of Patras

Additionally to hazard map calculation, hazard curves for Patras, Aigion and Korinthos were

calculated for 10% probability of exceedance in 50 years and. According to Krinitzsky et al.

(1990), different percentiles reflect the range of uncertainty given by the expert in various

seismic-source characteristics.

Figure 5.7: Hazard curves of Patras for PGA, 10% POE in 50 years.


78

Figure 5.8: Hazard curves of Patras for SA 0.1 sec, 10% POE in 50 years.


5.1.3 Hazard curves of Aigion

Figure 5.10: Hazard curves of Aigion for PGA, 10% POE in 50 years.


79

Figure 5.11: Hazard curves of Aigion for SA 0.1 sec, 10% POE in 50 years.


5.1.4 Hazard curves of Korinthos

Figure 5.13: Hazard curves of Korinthos for PGA, 10% POE in 50 years.


80

Figure 5.14: Hazard curves of Korinthos for SA 0.1 sec, 10% POE in 50 years.


5.1.5 Uniform hazard spectra

Finally, uniform hazard spectra were calculated for 10% POE and for the same cities.

Patras

Figure 5.16: Uniform hazard spectra for Patras, 10% POE in 50 years.


81

Aigion

Figure 5.17: Uniform hazard spectra for Aigion, 10% POE in 50 years.

Korinthos

Figure 5.18: Uniform hazard spectra for Korinthos, 10% POE in 50 years.


82

5.2 Model B: including b-value uncertainty

The second OpenQuake execution contains hazard maps generated for PGA values, for

Spectral Acceleration (SA) of 0.1 sec (referred to a three or four-storey building) and SA of

1.0 sec (referred to a multi-storey structure). Considering the probabilities of exceedance, the

values that are used in this survey are the mean values, 10% POE in 50 years (return period of

475 years) and 2% POE in 50 years (return period of 2500 years).

5.2.1 Hazard maps of Corinth Gulf






83








84



5.2.2 Hazard curves of Patras

Hazard curves for Patras, Aigion and Korinthos were calculated for 10% probability of

exceedance in 50 years and different percentiles.

Figure 5.25: Hazard curves of Patras for PGA, 10% POE in 50 years.



85


5.2.3 Hazard curves of Aigion

Figure 5.28: Hazard curves of Aigion for PGA, 10% POE in 50 years.



86


5.2.4 Hazard curves of Korinthos

Figure 5.31: Hazard curves of Korinthos for PGA, 10% POE in 50 years.



87

Figure 5.33: Hazard curves of Korinthos for SA 1.0sec, 10% POE in 50 years.

5.2.5 Uniform Hazard Spectra

Uniform hazard spectra were calculated for the same towns. These results are comparable to

elastic design spectra of the Greek Seismic Code.

Patras

Figure 5.34: Uniform hazard spectra for Patras, 10% POE in 50 years.

Aigion

Figure 5.35: Uniform hazard spectra for Aigion, 10% POE in 50 years.


88

Korinthos

Figure 5.36: Uniform hazard spectra for Korinthos, 10% POE in 50 years.

5.3 Comparison

In this chapter we examine the differences between the hazard calculations performed in this

thesis and between the published results for the region of Corinth Gulf, Greece. The first

hazard calculation procedure in this thesis didn‟t include the b value uncertainty (Run #1), in

contrast with the second hazard calculation (Run #2) during which the b-value was varied by

0.1.

5.3.1 Difference between 10% probability of exceedance for mean PGA values between

Run #1 and Run #2

Subtracting the acceleration values of both hazard calculations, the difference between Run #1

and Run #2 does not exceed the range ±0.1g. As it can be seen from the following maps, the b

value uncertainty increased slightly the resulting hazard values.

Figure 5.37: Difference map between Run #1 and Run #2 (Run#1 – Run#2) for mean PGA values,

return period of 475 years.


89

5.3.2 Difference between 2% probability of exceedance for mean PGA values between

Run #1 and Run #2

Figure 5.38: Difference map between Run #1 and Run #2 (Run#1 – Run#2) for mean PGA values,

return period of 2500 years.

Finally, the conclusion that is made shows that the variability of b-value is not

significant when the return period is increased. The same applies to the other hazard

calculations.

5.4 Comparisons with the Greek Seismic Code

The first comparison is made between the New Hazard Map of Greece and the hazard results

of Run #2, which is considered as the “worst case scenario”.

Figure 5.39: Hazard maps for the comparison of PGA values. 10% probability of exceedance for the

next 50 years (return period of 475 years).


90

Although a direct comparison of the results is not easy (the hazard map of Greece is the

result of a zonation thus cannot be compared with discrete values. Anyway, it can be observed

that our results gave higher values than the corresponding 0.24g of Greek Seismic Code. Our

highest values range between 0.5g and 0.6g. The Greek Seismic Code is considering the

seismicity while here we considered individual faults.

The uniform hazard spectra (UHS) of our results (Run #2) and of the Greek Seismic

Code for Soil Class A (bedrock) were also compared. The uniform hazard spectrum of the

Greek Seismic Code was adjusted to our study area, so the acceleration has the value 0.24g

because it belongs to Seismic Hazard Zone II and the parameter γ (Importance Factor) has the

value 1.00 because the research is referred to ordinary residential and office buildings,

industrial buildings, hotels, etc.

Figure 5.40: Comparison between Patras UHS & Greek Seismic Code. 10% probability of

exceedance for the next 50 years.

Figure 5.41: Comparison between Aigion UHS & Greek Seismic Code. 10% probability of



91

Figure 5.42: Comparison between Korinthos UHS & Greek Seismic Code. 10% probability of


The comparison between the second hazard calculation and the Greek Seismic Code

leads us to the same conclusions. Mean UHS of Korinthos is below the standards of Greek

Seismic Code and mean UHS for the cities of Patras and Aigion are upper the regulations.

Thus, it is proposed that the Greek Seismic Code requires a new approach and methodology

in order to be more precise principally for regions that present high levels of seismicity, such

as the Corinth Gulf.

5.5 Comparisons with previous studies

The aim of this subchapter is to compare our estimates with some previous studies. The

results are checked in order to validate the approach that we have made.

SHARE

Figure 5.43: Hazard maps for the comparison of PGA values. 10% probability of exceedance (return

period of 475 years).


92

This project is a strong argument considering the checking of our results, because it

consists of a combination of area sources model, seismotectonic characteristics, historical

seismicity, fault sources and strain deformation rates. Comparing the values of PGA

distribution for our survey and for SHARE project, it can be noticed that our estimates (0.35g-

0.55g approximately) agree with the corresponding approach of SHARE (0.40g-0.45g

approximately) for a return period of 475 years.

Tselentis & Danciu (2010)



Tselentis & Danciu (2010) examined seismic hazard maps of Greece and of the

surrounding regions including some significant engineering parameters (PGA, PGV, Arias

intensity, cumulative absolute velocity). Considering the mean PGA estimates (0.4g-0.6g

approximately) for Corinth Gulf of the above presented seismic hazard map, there is a very

good correlation with our results (0.35g-0.55g approximately) for the same region.

Segkou (2010)

The seismic hazard estimation for the Greek territory was carried out following some various

approaches relative to seismological, geological and geophysical observations. The linear

source model, the random seismicity model of shallow earthquakes and a seismic source

model of intermediate depth was applied for this implementation.


93



For the reason that Segkou (2010) took into account both an approach that includes

source models and historical seismicity, it can be observed that our results distribution (0.35g-

0.55g approximately) agrees in significant degree with these depicted in Figure 5.16 (0.30g-

0.45g approximately).

Vamvakaris (2010)

The estimation of maximum PGA values was made using attenuation relationships adjusted in

each type of hypocentric depth (low, intermediate, high).




94

Comparing the hazard maps for a return period of 475 years it can be implied that the

correlation of PGA distributions are quite good. The estimates of Vamvakaris (2010) range

between 0.30g and 0.50g, while our results range between 0.35g and 0.55g.

95

CHAPTER 6

SUMMARY and CONCLUSIONS

6.1 Summary

The dissertation examined the seismic hazard assessment for a seismic prone region, Corinth

Gulf (north Peloponnese, Greece), considering the active faults that surround this area. Two

fault databases were used, GreDaSS‟s and Institute of Geodynamics‟.

Three source categories were defined, according to the level of data completeness. The first

category included faults with adequate level of data (i.e. slip rate, dip, rake, etc.), the

corresponding second category included intermediate amount of information (i.e. maximum

magnitude, length) and the third category contained faults with poor level of data (i.e. length).

The unknown values of critical parameters (i.e. displacement, maximum magnitude, length,)

in the attributes table were estimated by the application of empirical laws.

Nine different slip values per fault were calculated. A distribution of slip rates was made

dividing the total displacement with the stratigraphic age of each fault after the assumption of

two approaches, historical seismicity and fault length.

Slip values were converted to seismic activity compiling some Matlab scripts (see Appendix).

The hazard calculation of OpenQuake Engine was divided in two parts. The first part included

the logic tree that contained the seismic sources model without the b value uncertainty. On the

contrary, the second part considered the b value uncertainty in the calculation. Thus, a

comparison of them was made.

We used OpenQuake in order to compute hazard maps-hazard curves and uniform hazard

spectra for PGA, SA (0.1sec & 1.0sec) and uniform hazard spectra for bedrock soil

conditions. All of them are referred to return periods of 475 & 2500 years and compared with

previous research.

The GMPE‟s used in this study were the Akkar & Bommer (2010), Cauzzi & Faccioli (2008),

Chiou & Young (2008) and Zhao et al. (2006) considered for the active shallow crust of

Greece.

CHAPTER 6 – SUMMARY and CONCLUSIONS

96

6.2 Results

The scope of this thesis was the estimation of seismic hazard of Corinth Gulf considering

active faults for bedrock soil conditions. The OpenQuake engine, developed by GEM, was

used for this purpose. It is a software that uses an innovative methodology for hazard

calculation. The execution is performed using a configuration file and XML files (seismic

sources model, logic tree, GMPE model). The epistemic uncertainty (i.e. slip rate, b-value)

can also be modeled.

The comparison of two hazard calculations drew the conclusion that b-value uncertainty did

not reflect our estimates. The differences between Run #1 and Run #2 were smoothed when

the return period was increased.

The fault database needs more enhancement because there was a lack of information

considering the slip rate estimates.

Previous implementations considering seismic hazard assessment for PGA and return period

of 475 years were compared with our study and showed that our results are correlated

significantly with their corresponding estimates.

The Greek Seismic Code needs a better and more detailed approach in order to be more

precise, especially for seismic prone areas. The comparison of our uniform hazard spectra

with the corresponding of Greek Seismic Code for the cities of Patras, Aigion and Korinthos

showed that the hazard suggested by the Greek Seismic Code could be underestimated.

97

APPENDIX

PROGRAMMING

Openquake operates by using the NRML format, which is an alternative version of XML data

schema. In order to create these files, some Matlab scripts and functions were compiled for

the purposes of XML-file construction (source model, logic tree) and the conversion of slip

rates to seismic activity, a necessary parameter for SHA. All of them are extensively

presented in the Appendix.

The aim of basic Matlab script is to introduce some fundamental parameters deduced

from the ArcGIS Shape Files (.shp), give specific values to significant parameters (slip rate,

aspect ratio) and create the appropriate XML files needed for the structure of the basic source

model of Openquake. The purpose of this action is to produce several XML files that contain

all faults for nine different slip rates. These nine slip rate values were derived from the

application of :

Displacement vs magnitude relationships of Wells & Coppersmith (1994) and

Pavlides & Caputo (2004) in the historical seismicity approach.

Displacement vs length scaling law of Wells & Coppersmith (1994) in the

length of fault approach.

Three estimates of fault age (minimum, medium and maximum stratigraphic

age)

Thus nine values of slip rate were calculated per fault i.e. three scaling laws and three

fault ages. In addition, this script uses some features from the attributes table of active faults‟

shape files, such as the name, coordinates, dip and rake, which are parameters included in the

XML files. Then, the seismic activity rate is estimated by using the methodology proposed by

Bungum (2007).

APPENDIX – PROGRAMMING

98

THE BASIC MATLAB SCRIPT

*Original code was provided by Dr. Laurentiu Danciu

function ok = write_simple_fault(filename_shp)

%% Load fault source

rShape=shaperead(filename_shp);

names = fieldnames(rShape)

for j=1:9 % loop over slip rates

for i=1:length(rShape) % loop over faults

%Fields of the attributes table of each .shp file

code{i}=rShape(i).CODE;

name{i}=rShape(i).NAME;

longitude{i}=rShape(i).X;

latitude{i}=rShape(i).Y;

dip(i)=rShape(i).DIPP;

upper_depth(i)=rShape(i).MINDEPTH;

lower_depth(i)=rShape(i).MAXDEPTH;

rake(i)=rShape(i).RAKE;

maxmag(i)=rShape(i).MAXMAG;

fault_length=rShape(i).LENGTH;

%aspect ratio_GreeDass_database

% if ((rake(i)==170) || (rake(i)==173) || (rake(i)==-

20))

% aspect_ratio(i)=4;

% else

% aspect_ratio(i)=1;

% end

%aspect ratio_Geodynamic_Institute_database

if (rake(i)==180)

aspect_ratio(i)=4;

else

aspect_ratio(i)=1;

end

% prepare the name of the slip rate definition (1-9)

slip_R = ['rShape(i,1).SLIPRT' num2str(j)];

slipRate = eval(slip_R)*0.1; % convert to cm/year


99

% case slip = 0

if slipRate==0

slipRate =0.0001;

end

% get a_value

a_cum_value_max(i)=calc_fsz_activity2(fault_length,upper_depth

(i),lower_depth(i),dip(i),maxmag(i),slipRate);

end

% get values for XML file

filenamexml=['SLIP_RATE_' num2str(j) '.xml'];

ok =

writefxml(code,name,longitude,latitude,dip,upper_depth,lower_d

epth,aspect_ratio,maxmag,a_cum_value_max,rake,filenamexml)

end

end

MATLAB FUNCTION FOR THE COMPUTATION OF

CUMULATIVE A VALUE

*Code provided by Dr. Laurentiu Danciu

function [ a_cum_value_max ] = calc_fsz_activity2(

length,upper_depth,lower_depth,dip,maxmag,slipRate)

% Script to compare total moment of seismicity with moment

% determined for fault parameters

% Incoming:

% fBvalue : b-value

% fS : Slip rate (mm/year)

% fD : Average slip (m)

% fLength : Fault length (m)

% fWidth : Fault width (m)

% fM00 : M0(0) for Ms = 0, c in logM0=c-dM

% fMmin : Minimum magnitude

% fBinM : magnitude binnning

% fMmax : Maximum magnitude

% fDmoment : d in logM0=c-dM

% fRigid : Rgidity in Pascal

% Model 2: Anderson and Luco

% Units are in CGS

%% Calculate moment from faults


100

% Parameters for Seismic Moment from Faults

% b-value

bVal = 1.00;

% Rgidity in GPascals --> miu =30GPa

% convert to dyne/cm2 (CGS units) --> or (N/m^2) (SI units)

% convert shear modulus from Pa (N/m^2, kg/(m * s^2))

% to dyn/cm^2, 1 dyn = 1 g * cm/s^2 = 10^-5 N

% 1 GPa = 10^9 kg/(m * s^2) = 10^12 g/(m * s^2) = 10^10 g/(cm

*s^2)

% = 10e10 dyn/cm^2

miu = 30 * 1.0e10; % this is dyne/cm^2

% d in logM0=c-dM

dKanamori = 1.5;

% c in logM0=c-dM

cKanamori = 16.05;

% : Fault length (km) -->cm (*1.0e05)

fLength = length * 1.0e05;

% Fault width (km) -->mm

fWidth=(abs(upper_depth-lower_depth))/sind(dip)*1.0e05;

% aspect ratio

%aspectRatio = fLength/fWidth;

% fWidth= 10 * 1.0e05;

% Minimum magnitude

Mmin = 0;

% Maximum magnitude

fMmax=maxmag;

% magnitude binnning

deltMFD = 0.1;

% parameters for Recurrence Model

% bbar value

b_bar = bVal * log(10);

% Magnitude scaling coefficient

d_bar = dKanamori * log(10);

% Fault slip-length ratio

alpha = 1.0e-04;


101

% Seismic Moment-Magnitude scaling for Mw=0, units are

dyne/cm^2

momZero = 10^cKanamori;

% beta coeficient Model 2: Anderson and Luco

beta_numerator = alpha * momZero;

beta_denominator = miu * fWidth;

beta = sqrt(beta_numerator/beta_denominator);

% MFD

vMagnitude = Mmin:deltMFD:fMmax;

%% Calculation factors for Recurrence MOdel No 2

fFac1 = (d_bar-b_bar) / d_bar;

fFac2 = slipRate / beta;

fFac3 = exp(b_bar * (fMmax - vMagnitude));

fFac4 = exp(-(d_bar / 2) * fMmax);

%% Bungum Equations 7: Originally by Anderson and Luco, BSSA,

1983

vCumNumber = fFac1 * fFac2 * fFac3 * fFac4;

vMagnitude = Mmin:deltMFD:fMmax;

%% compute aGR-value

% cumulative

a_cum_value_max1 = log10(vCumNumber) + bVal * vMagnitude;

a_cum_value_max=a_cum_value_max1(1,1)

MATLAB FUNCTION FOR THE CONSTRUCTION OF XML FILES


function ok =

writefxml(code,name,longitude,latitude,dip,upper_depth,lower_d

epth,aspect_ratio,maxmag,a_cum_value_max,rake,filename_xml)

%construction of XML file

docNode=com.mathworks.xml.XMLUtils.createDocument('nrml');

nrml=docNode.getDocumentElement;

nrml.setAttribute('xmlns:gml','http://opengis.net/gml');

nrml.setAttribute('xmlns','http://openquake.org/xmlns/nrml/0.4

');

%write source model

source_model_element=docNode.createElement('sourceModel');


102

source_model_element.setAttribute('name','Simple Fault

Model');

nrml.appendChild(source_model_element);

%write simple faults source element

for q=1:numel(name) %use of 'for' loop - type all faults in

one XML file

simple_fault_source_element=docNode.createElement('simpleFault

Source');

simple_fault_source_element.setAttribute('id',num2str(code{q})

); %%%

simple_fault_source_element.setAttribute('name',name{q}); %%%

%tectonic region-Active Shallow Crust

simple_fault_source_element.setAttribute('tectonicRegion','Act

ive Shallow Crust');

source_model_element.appendChild(simple_fault_source_element);

%add simple fault geometry

simpleFaultGeometry_element=docNode.createElement('simpleFault

Geometry');

simple_fault_source_element.appendChild(simpleFaultGeometry_el

ement);

gml_LineString=docNode.createElement('gml:LineString');

simpleFaultGeometry_element.appendChild(gml_LineString);

%add the vertex list of each polyline in clock-or counter

clock wise

gml_posList=docNode.createElement('gml:posList');

gml_LineString.appendChild(gml_posList);

llon=longitude{q}

llat=latitude{q}

for i=1:length(llon)-1 %coordinates of each fault

gml_posList.appendChild(docNode.createTextNode([num2str(llon(i

)) ' ' num2str(llat(i)) ' ']))

end


103

%add dip

dip_element=docNode.createElement('dip');

simpleFaultGeometry_element.appendChild(dip_element);

dip_element.appendChild(docNode.createTextNode(num2str(dip(q))

)); %%%

%add upper seismogenic depth element

upperSeismoDepth_element=docNode.createElement('upperSeismoDep

th');

simpleFaultGeometry_element.appendChild(upperSeismoDepth_eleme

nt);

upperSeismoDepth_element.appendChild(docNode.createTextNode(nu

m2str(upper_depth(q)))); %%%

%add lower seismogenic depth element

lowerSeismoDepth_element=docNode.createElement('lowerSeismoDep

th');

simpleFaultGeometry_element.appendChild(lowerSeismoDepth_eleme

nt);

lowerSeismoDepth_element.appendChild(docNode.createTextNode(nu

m2str(lower_depth(q)))); %%%

%add magnitude scaling relationship

magScaleRel_element=docNode.createElement('magScaleRel');

simple_fault_source_element.appendChild(magScaleRel_element);

magScaleRel_element.appendChild(docNode.createTextNode('WC1994

'));

%add rupture aspect ratio

ruptAspectratio_element=docNode.createElement('ruptAspectRatio

');

simple_fault_source_element.appendChild(ruptAspectratio_elemen

t);

ruptAspectratio_element.appendChild(docNode.createTextNode(num

2str(aspect_ratio(q)))); %%%

%%add truncGutenbergRichterMFD_element

truncGutenbergRichterMFD_element =

docNode.createElement('truncGutenbergRichterMFD');

truncGutenbergRichterMFD_element.setAttribute('aValue',

num2str(a_cum_value_max(q)));

truncGutenbergRichterMFD_element.setAttribute('bValue',

num2str(1.0));

truncGutenbergRichterMFD_element.setAttribute('maxMag',

num2str(maxmag(q))); %%%


104

truncGutenbergRichterMFD_element.setAttribute('minMag',

num2str(4.5));

simple_fault_source_element.appendChild(truncGutenbergRichterM

FD_element);

%add rake

rake_element=docNode.createElement('rake');

simple_fault_source_element.appendChild(rake_element);

rake_element.appendChild(docNode.createTextNode(num2str(rake(q

))));

end

xmlwrite(filename_xml,docNode);

ok=1;

MATLAB FUNCTION FOR THE CONSTRUCTION OF LOGIC TREE

XML FILE


function [kk]=logic_tree(filename_xml)

%construction of logic tree XML file

docNode=com.mathworks.xml.XMLUtils.createDocument('nrml');

nrml=docNode.getDocumentElement;

nrml.setAttribute('xmlns:gml','http://opengis.net/gml');

nrml.setAttribute('xmlns','http://openquake.org/xmlns/nrml/0.4

');

logic_tree_element=docNode.createElement('logicTree');

logic_tree_element.setAttribute('logicTreeID','lt1');

nrml.appendChild(logic_tree_element);

%1st branching level for the source models

logic_tree_branching_level_element=docNode.createElement('logi

cTreeBranchingLevel');

logic_tree_branching_level_element.setAttribute('branchingLeve

lID','bl1');

logic_tree_element.appendChild(logic_tree_branching_level_elem

ent);


105

logic_tree_branch_set_element=docNode.createElement('logicTree

BranchSet');

logic_tree_branch_set_element.setAttribute('uncertaintyType','

sourceModel');

logic_tree_branch_set_element.setAttribute('branchSetID','bs1'

);

logic_tree_branching_level_element.appendChild(logic_tree_bran

ch_set_element);

logic_tree_branch_element=docNode.createElement('logicTreeBran

ch');

logic_tree_branch_element.setAttribute('branchID','b1');

logic_tree_branch_set_element.appendChild(logic_tree_branch_el

ement);

uncertainty_model_element=docNode.createElement('uncertaintyMo

del');

logic_tree_branch_element.appendChild(uncertainty_model_elemen

t);

uncertainty_model_element.appendChild(docNode.createTextNode('

SLIP_RATE_1a.xml'));

uncertainty_weight_element=docNode.createElement('uncertaintyW

eight');

logic_tree_branch_element.appendChild(uncertainty_weight_eleme

nt);

uncertainty_weight_element.appendChild(docNode.createTextNode(

num2str(0.111)));


ch');



ement);


del');


t);


SLIP_RATE_2b.xml'));


eight');


nt);


num2str(0.111)));


ch');



106


ement);


del');


t);


SLIP_RATE_3c.xml'));


eight');


nt);


num2str(0.111)));


ch');



ement);


del');


t);


SLIP_RATE_4d.xml'));


eight');


nt);


num2str(0.111)));


ch');



ement);


del');


t);


SLIP_RATE_5e.xml'));


eight');


nt);


107


num2str(0.112)));


ch');



ement);


del');


t);


SLIP_RATE_6f.xml'));


eight');


nt);


num2str(0.111)));


ch');



ement);


del');


t);


SLIP_RATE_7g.xml'));


eight');


nt);


num2str(0.111)));


ch');



ement);


del');


t);


108


SLIP_RATE_8h.xml'));


eight');


nt);


num2str(0.111)));


ch');



ement);


del');


t);


SLIP_RATE_9i.xml'));


eight');


nt);


num2str(0.111)));

%2nd branching level for b_value

logic_tree_branching_level_element=docNode.createElement('logi

cTreeBranchingLevel');

logic_tree_branching_level_element.setAttribute('branchingLeve

lID','bl2');

logic_tree_element.appendChild(logic_tree_branching_level_elem

ent);

logic_tree_branch_set_element=docNode.createElement('logicTree

BranchSet');

logic_tree_branch_set_element.setAttribute('uncertaintyType','

bGRRelative');

logic_tree_branch_set_element.setAttribute('branchSetID','bs21

');

logic_tree_branching_level_element.appendChild(logic_tree_bran

ch_set_element);


ch');



109


ement);


del');


t);

uncertainty_model_element.appendChild(docNode.createTextNode(n

um2str(0.9)));


eight');


nt);


num2str(0.333)));


ch');



ement);


del');


t);


um2str(1.0)));


eight');


nt);


num2str(0.334)));


ch');



ement);


del');


t);


um2str(1.1)));


eight');


nt);


110


num2str(0.333)));

%type the logic tree XML file

xmlwrite(filename_xml,docNode);

type(filename_xml);

end

111

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