# Modeling seismic activity on faults for probabilistic hazard assessment

Thomas Chartier

► To cite this version:

Thomas Chartier. Modeling seismic activity on faults for probabilistic hazard assessment. Sciences of the Universe [physics]. École Normale Superieure de Paris - ENS Paris, 2019. English. NNT: tel-04030083

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# Modélisation de l'activité sismique des failles pour le calcul probabiliste du risque sismique

Soutenue par

Thomas Chartier

Le 31 Octobre 2019

Ecole doctorale n° 560

Sciences de la Terre et de l'Environnement et de Physique de l'Univers, Paris

Spécialité

Terre Environnement

## Composition du jury :

Stéphane, Mazzotti
Pr, Université Montpellier 2
Président du jury

Kuo-Fong, Ma
Pr, National Central University
Rapportrice

Alice-Agnes, Gabriel
Assistant Pr, Munich University
Examinatrice

Nicolas, Chamot-Rooke
CR, Ecole Normale Supérieure
Examinateur

Hélène, Lyon-Caen
Dr, Ecole Normale Supérieure
Directrice de thèse

Oona, Scotti
Dr, Institut de Radioprotection
et de Sûreté Nucléaire
Co-Encadrante de thèse

Aurélien, Boiselet
Dr, Axa
Invité
Résumé

Les taux de sismicité sont un élément clé du calcul probabiliste de l'aléa et du risque sismique. Une méthodologie innovante est développée pour modéliser les taux de ruptures complexes dans un système de failles (SHERIFS). La flexibilité de la méthodologie permet de la partager et de l'appliquer sur des systèmes de failles différents et de s'en servir comme outil de discussion des hypothèses concernant la sismicité sur les failles. Les taux de sismicité dans la partie Ouest du Rift de Corinth en Grèce et dans la région de Marmara en Turquie sont modélisés en explorant l'incertitude épistémique sur le scenario de rupture maximale, la distribution en magnitude et fréquence ou encore les conditions de glissement sur la faille. A Marmara, les hypothèses sont pondérées dans un arbre logique en comparant les taux modélisés aux taux calculés à partir des données et des résultats d'un modèle physique basé sur les équations "rate and state". Pour chaque hypothèse de l'arbre logique, le risque sismique à Istanbul, en termes de probabilité d'effondrement d'un immeuble, est calculé pour deux bâtiments de même type construits respectivement suivant le code de construction de 1975 et celui de 1998. Le risque sismique est six fois plus important pour le bâtiment le plus ancien. Parmi les incertitudes explorées, la source d'incertitude plus importante est liée à la distribution en magnitude et fréquence. L'utilisation des données et du modèle physique permet de réduire l'incertitude sur le risque par un facteur 1.6. Une nouvelle méthodologie de désagrégation du risque permet de montrer que le risque à Istanbul est contrôlé en partie par les séismes de magnitude supérieure à 7 sur la Faille Nord Anatolienne et en partie par les séismes de magnitude modérée (4.5 à 6) dans la sismicité de fond, sur des failles non connues, et à une distance du bâtiment inférieure à 10 km.

Abstract

Earthquake rates are a key component of probabilistic seismic hazard and risk assessment. A novel methodology to model earthquake rates in complex ruptures in a fault system (SHERIFS) is developed. The flexibility of the methodology allows sharing it and applying it to various fault systems as well as using it as a tool to discuss the hypotheses concerning the seismicity on faults. The earthquake rates in the Western Corinth Rift in Greece and the Marmara Region in Turkey are modeled while exploring the associated epistemic uncertainty such as on the maximum rupture scenario, the magnitude frequency distribution or the locking condition of the faults. In Marmara, the hypotheses are weighted in a logic tree by comparing them to the rate calculated from the data (earthquake catalog and paleoseismicity) and the results of a "physics-based" model applying the rate and state equations. For each hypothesis in the logic tree, The seismic risk in Istanbul, represented by the probability of collapse of a building, is calculated for two buildings of the same type but one constructed following the 1975 building code and on following the 1998 building code. The seismic risk is six times larger for the older building. Within the explored uncertainties, the one concerning the magnitude frequency distribution is the largest source of uncertainty on the risk of collapse. By using the data and the physics-based model to weight the logic tree, the uncertainty on the risk is reduced by a factor of 1.6. Through a novel risk deaggregation methodology, we identify two seismogenic sources controlling the risk in Istanbul: the large earthquakes (magnitude larger than 7) on the neighboring North Anatolian Fault and the moderate magnitude earthquakes (between 4.5 and 6) occurring in the background zone, on unknown faults, and at a distance shorter than 10 km from the building.
Remerciements / Acknowledgements

This thesis that you are about to read largely exists because of the continuous support of my family,
friends and colleague without whom I would never have been able to carry on such endeavor.

En premier lieu, je souhaite remercier mes deux directrices de thèse, Hélène et Oona, qui m'ont
permis de me lancer cette thèse. Grâce à leur soutien mais aussi la liberté qu'elles m'ont autorisées dans la
mise en place du projet, le sujet de cette thèse correspond parfaitement à mes ambitions de carrière et à mes
intérêts scientifiques. Peu d'étudiants en thèse ont la chance d'avoir un sujet de thèse taillé sur mesure. Au
cours de la thèse elles m'ont offert un encadrement avec à la fois une grande disponibilité pour la discussion
et une grande liberté en me laissant m'engager dans différentes voie de développement scientifique. Elles
ont sut rester ouvertes à mes idées mais aussi m'orienter lorsque m'ont entêtement naturel me bloquait dans
une seule direction. J'ai pût énormément apprendre de leur rigueur scientifique tout en évoluant dans un
environnement amical rendant chaque journée de travail un vrai plaisir. J'espère pouvoir continuer à interagir
avec elles, à la fois professionnellement mais aussi personnellement.

Merci aux institutions qui ont supporté cette thèse, l'Ecole Normale Supérieure pour m'avoir permis de partir travailler en Californie, l'Institut de Radioprotection et de Sûreté Nucléaire pour un soutien continu depuis plus de cinq ans et le Fond Axa pour la Recherche pour avoir financer ce projet (merci beaucoup à Aurélien pour ton aide dès la mise en place du projet).

A tous mes collègues, maintenant devenu amis, je dis merci. A ceux qui ont partagé la vue et les
plantes du Bureau Banane à l'IRSN : Ludmila, Elif, Arnaud, Flomin, Levent et Rihab. Aux amis du bureau
de l'ENS : Lavinia, Arefeh, Eva, Cédric, Eleonora. A toute l'équipe BERSSIN et du laboratoire de géologie,
merci! Avec de telles équipes, il a été facile de se motiver tous les jours pour aller travailler sachant que
l'entre-aide et l'amitié sera au rendez-vous.

A la ville de Paris, qui est peu à peu devenu ma ville au fil des années. Les longues marches dans
ses rues et dans ses tunnels vont beaucoup me manquer.

A tout mes amis, de la surface et des souterrains, Julia, Arnaud, Julien, Martin, PO, Arthur, Simon,
Anne, Sonia, Célia, Justine, Lucie, Mylène et tant d'autres qui sont toujours près à aller manger un bout ou
boire un coup, et le plus souvent les deux!

Enfin, je voudrais dédier cette thèse à ma grande et belle famille! En particulier à mes parents, qui
m'ont toujours encouragé à faire ce qui me faisait plaisir sans pression sur mes résultats et avec toujours
un enthousiasme contagieux. A ma tante Denise qui a été depuis toujours et est toujours ma principale
interlocutrice pour les discussions scientifiques et qui de plus a été un soutien à la fois logistique et moral
pendant toutes mes études! A mon frère et ma soeur, mes tantes et mes oncles, et mes très nombreux cousins
et cousines dont l'amour constant a forgé la personne que je suis aujourd'hui.
# Contents

Glossaire - Glossary 21

Introduction 23

1 Contexte du projet 24

2 Chaîne de calcul du risque sismique 25

3 Problématiques concernant l'intégration des failles dans le calcul d'aléa sismique 26

3.1 Ruptures complexes 26

3.2 Sismicité sur les failles et sismicité de fond 26

3.3 Contraintes pour la méthodologie à développer 27

4 Problématique de traçabilité des sources du risque sismique et des incertitudes associées 28

5 Plan de la thèse 29

6 Rappel sur les méthodes de calcul de l'aléa sismique 30

6.1 Calcul déterministe 30

6.2 Calcul probabiliste 30

7 Rappel sur les méthodes de calcul du risque sismique 33

7.1 Calcul site spécifique 33

7.2 Calcul de perte pour un ensemble de sites 34
<table><tr><td>Résumé du chapitre</td><td>35</td></tr></table>

<table><tr><td>Structure of the chapter</td><td>37</td></tr></table>

<table><tr><td>1.1 Methodology for earthquake rupture rate estimates of fault networks: example for the western Corinth rift, Greece</td><td>38</td></tr></table>

<table><tr><td>1.1.1 Abstract</td><td>38</td></tr></table>

<table><tr><td>1.1.2 Introduction</td><td>39</td></tr></table>

<table><tr><td>1.1.3 Novel methodology for taking faults into account in PSHA</td><td>41</td></tr></table>

<table><tr><td>1.1.4 Application to the western Corinth rift fault system</td><td>45</td></tr></table>

<table><tr><td>1.1.5 Modeled earthquake rupture rates and comparison with independent data</td><td>49</td></tr></table>

<table><tr><td>1.1.6 Conclusion and perspectives</td><td>54</td></tr></table>

<table><tr><td>1.2 SHERIFS – Open-Source Code for Computing Earthquake Rates in Fault Systems and Constructing Hazard Models</td><td>57</td></tr></table>

<table><tr><td>1.2.1 Abstract</td><td>57</td></tr></table>

<table><tr><td>1.2.2 Introduction</td><td>57</td></tr></table>

<table><tr><td>1.2.3 General methodology applied in SHERIFS</td><td>59</td></tr></table>

<table><tr><td>1.2.4 Model visualization</td><td>68</td></tr></table>

<table><tr><td>1.2.5 Logic Tree Weighting</td><td>68</td></tr></table>

<table><tr><td>1.2.6 Applications of SHERIFS</td><td>69</td></tr></table>

<table><tr><td>1.2.7 Example of a SHERIFS calculation</td><td>69</td></tr></table>

<table><tr><td>1.2.8 Limitations of SHERIFS</td><td>73</td></tr></table>

<table><tr><td>1.2.9 Conclusion and perspectives</td><td>73</td></tr></table>

<table><tr><td>1.3 On sharing SHERIFS</td><td>75</td></tr></table>

<table><tr><td>1.3.1 The struggles of sharing an open-source code</td><td>75</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>1.4</td>
      <td>The pay-offs of sharing an open-source code</td>
      <td>76</td>
    </tr>
    <tr>
      <td>1.4.1</td>
      <td>A more adaptive and reliable code.</td>
      <td>76</td>
    </tr>
    <tr>
      <td>1.4.2</td>
      <td>Discussing input hypotheses</td>
      <td>77</td>
    </tr>
    <tr>
      <td>1.5</td>
      <td>Conclusion</td>
      <td>79</td>
    </tr>
    <tr>
      <td>2</td>
      <td>Modelling the earthquake rates in the Marmara Region and the associated uncertainties</td>
      <td>83</td>
    </tr>
    <tr>
      <td></td>
      <td>Résumé du chapitre</td>
      <td>83</td>
    </tr>
    <tr>
      <td>2.1</td>
      <td>Introduction</td>
      <td>85</td>
    </tr>
    <tr>
      <td>2.2</td>
      <td>The Western North Anatolian Fault System</td>
      <td>87</td>
    </tr>
    <tr>
      <td>2.3</td>
      <td>Earthquake rate modelling</td>
      <td>92</td>
    </tr>
    <tr>
      <td>2.3.1</td>
      <td>The statistical approach: SHERIFS</td>
      <td>92</td>
    </tr>
    <tr>
      <td>2.3.2</td>
      <td>The physics-based approach : RSQSim.</td>
      <td>99</td>
    </tr>
    <tr>
      <td>2.4</td>
      <td>Discussion on the weight of the epistemic uncertainties in the logic tree</td>
      <td>102</td>
    </tr>
    <tr>
      <td>2.4.1</td>
      <td>Uncertainty on the creep</td>
      <td>102</td>
    </tr>
    <tr>
      <td>2.4.2</td>
      <td>Uncertainty on the shape of the MFD target</td>
      <td>104</td>
    </tr>
    <tr>
      <td>2.4.3</td>
      <td>Uncertainty on the largest possible rupture</td>
      <td>105</td>
    </tr>
    <tr>
      <td>2.4.4</td>
      <td>The weighted logic tree</td>
      <td>105</td>
    </tr>
    <tr>
      <td>2.5</td>
      <td>Conclusion and perspectives</td>
      <td>106</td>
    </tr>
    <tr>
      <td>3</td>
      <td>Calculating the Probability of Collapse of a Building in Istanbul</td>
      <td>109</td>
    </tr>
    <tr>
      <td></td>
      <td>Résumé du chapitre</td>
      <td>109</td>
    </tr>
    <tr>
      <td>3.1</td>
      <td>Introduction</td>
      <td>111</td>
    </tr>
    <tr>
      <td>3.2</td>
      <td>Seismic hazard in Istanbul</td>
      <td>113</td>
    </tr>
    <tr>
      <td>3.3</td>
      <td>Methododology for the calculation of seismic risk</td>
      <td>114</td>
    </tr>
    <tr>
      <td>3.3.1</td>
      <td>Probability of damage</td>
      <td>114</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>3.3.2</td>
      <td>Risk deaggregations</td>
      <td>115</td>
    </tr>
    <tr>
      <td>3.4</td>
      <td>Results</td>
      <td>118</td>
    </tr>
    <tr>
      <td>3.4.1</td>
      <td>Probability of collapse for a building in Istanbul</td>
      <td>118</td>
    </tr>
    <tr>
      <td>3.4.2</td>
      <td>Impact of uncertainties on the probability of collapse</td>
      <td>119</td>
    </tr>
    <tr>
      <td>3.4.3</td>
      <td>Seismogenic sources controlling the risk</td>
      <td>122</td>
    </tr>
    <tr>
      <td>3.5</td>
      <td>Discussion</td>
      <td>125</td>
    </tr>
    <tr>
      <td>3.5.1</td>
      <td>Probability of collapse</td>
      <td>125</td>
    </tr>
    <tr>
      <td>3.5.2</td>
      <td>Linking input hypothesis and results</td>
      <td>126</td>
    </tr>
    <tr>
      <td>3.6</td>
      <td>Conclusion and Perspectives</td>
      <td>127</td>
    </tr>
    <tr>
      <td>4</td>
      <td>Conclusions and Perspectives</td>
      <td>129</td>
    </tr>
    <tr>
      <td>4.1</td>
      <td>Modelling earthquake rates in fault systems</td>
      <td>129</td>
    </tr>
    <tr>
      <td>4.1.1</td>
      <td>The system level approach</td>
      <td>129</td>
    </tr>
    <tr>
      <td>4.1.2</td>
      <td>Magnitude Frequency Distribution</td>
      <td>130</td>
    </tr>
    <tr>
      <td>4.1.3</td>
      <td>Complex fault rupture</td>
      <td>130</td>
    </tr>
    <tr>
      <td>4.1.4</td>
      <td>The background seismicity</td>
      <td>131</td>
    </tr>
    <tr>
      <td>4.1.5</td>
      <td>Perspectives on the use of SHERIFS</td>
      <td>131</td>
    </tr>
    <tr>
      <td>4.2</td>
      <td>Physics-based models and alternative approaches of earthquake modelling</td>
      <td>132</td>
    </tr>
    <tr>
      <td>4.2.1</td>
      <td>Possible ruptures</td>
      <td>132</td>
    </tr>
    <tr>
      <td>4.2.2</td>
      <td>Earthquake rates</td>
      <td>132</td>
    </tr>
    <tr>
      <td>4.2.3</td>
      <td>Perspectives on the physics based modelling</td>
      <td>133</td>
    </tr>
    <tr>
      <td>4.3</td>
      <td>The risk oriented approach</td>
      <td>134</td>
    </tr>
    <tr>
      <td>4.3.1</td>
      <td>Identifying the sources of the uncertainties</td>
      <td>135</td>
    </tr>
    <tr>
      <td>4.3.2</td>
      <td>Risk disaggregation</td>
      <td>135</td>
    </tr>
  </tbody>
</table>
List of Figures

1 Chaîne de calcul du risque sismique. 25

2 Étapes du calcul PSHA selon Cornell 1968. 31

1.1 Illustration of the methodology. (a) Set of FtF rupture scenarios. (b) Picking of the magnitude bins and of the sources. (c) Building the target MFD: the black curve is the target MFD anchored at the mean of the three highest magnitude bins (magnitude bin of 0.1). The sum of the resulting MFDs of the six sources has to be equal to the target MFD. (d) Visualization of the partitioning by the iterative methodology of each fault's slip-rate budget (colors correspond to the individual rupture or the FtF rupture; NMS is non-main-shock slip). 42

1.2 Map of the active faults of the western part of the Corinth rift (modified from Boiselet [2014]). The orange polygons are the surface projection of the active faults. The yellow polygons are the surface projection of the blind faults (Pyrgos fault and 1995 fault). Earthquakes of the catalog during the complete period are represented by circles with color and size depending on the magnitude. The date and magnitude of earthquake are indicated. The minimum and maximum values (mm yr⁻¹) of the slip rates of the faults are indicated in the white boxes. The green arrow shows an approximation of the rift extension calculated by projecting horizontally the faults' slip rate, and the pink arrow shows the extensional rate of the rift measured by GPS. 47

1.3 Logic tree explored for this study. 47
1.4 Modeled seismicity for the WCR fault network and comparison to the seismicity rate based on the earthquake catalog of the complete period. (a) Comparison between the modeled moment rates for each FtF scenario set and the seismological rate calculated from the earthquake catalog. Each box represents the SD around a mean and median value represented by a red square and a red line respectively. From left to right: the three first boxes are for each hypothesis scenario set in the logic tree, the fourth box shows the moment rate assuming 100 % of the slip rate of faults is converted into seismic moment, and the fifth box shows the moment rate calculated from the earthquake catalog. (b) Distribution of the ratio of NMS slip resulting from the three deformation models. (c) Comparison between the modeled GR MFD deduced from geological data for the whole fault system and that deduced from the WCR catalog. The models are represented as a colored density function with the red colors for the rates predicted by the higher number of models. The cumulative rates calculated from the catalog are shown as a grey density function. The cumulative number of earthquakes in the catalog is indicated by black bars in the central figure. 51

1.5 Visualization of the way the slip-rate budget of each fault is spent. The color depends on the number of faults involved in the FtF rupture. Minimum and maximum values of the slip rate on each fault is shown in brackets in mm yr⁻¹. 52

1.6 Rate of earthquakes occurring on the Aigion fault for each FtF rupture set. Variability resulting from the exploration of the logic tree is illustrated by the blue boxes. The annual rates of Mw ≥ 6 earthquakes on Aigion fault are indicated for the B14 and B14_hc models. The grey square represents the paleorate (rate of paleoearthquakes) interpreted from Pantosti et al. [2004] with its uncertainties. The green box represents the rate of earthquakes greater than Mw 6 on the Aigion fault inferred from the historical catalog. 53

1.7 Modeling of the background seismicity in seismic hazard and earthquake rate in fault systems (SHERIFS). (a) Expert opinion of the probability of a future earthquake to occur on a modeled fault for magnitude bin. (b) Example of background geometry. (c) Target magnitude-frequency distribution (MFD) modified to take into account the background seismicity. 62

1.8 Flowchart of the overall SHERIFS methodology. BG, Background; FtF, fault-to-fault; NMS, non-mainshock. 63

1.9 SHERIFS data processing workflow. Dsr, sub-divided in slip rate. 64

1.10 SHERIFS iterative process workflow to compute earthquake rates on faults. 66
1.17 Results of the consistency check obtained for three fault-rupture hypotheses for the Betics Fault System, from left to right: single faults ruptures, intermediate ruptures, the whole system ruptures. Each green MFD corresponds to the Gutenberg-Richter distribution (GR) for the whole fault system, modelled from geological data. The green line is the mean of the cumulative annual rates of the samples explored for every magnitude. The garnet MFD corresponds to the seismicity rates extracted from the catalogue. Each MFD is represented as a coloured density function, where the most intense colours correspond to the cumulative annual rates predicted by a higher number of samples in the modelling, and so, they condition the position of the mean. Note that the mean of the maximum magnitudes from the 20 samples explored for each hypothesis is indicated. The seismic moment rate modelled for the whole fault system is also indicated for every hypothesis. It is fundamental to clearly state that differences in this rate for the different hypotheses are due to the fact that each hypothesis implies a different amount of aseismic slip or Non-main-shock slip (NMS). (modified from Gómez-Novell et al. [2018]) 79

1.18 Comparison between the participation rates modelled with SHERIFS (in green, solid line is the mean value, the dashed line are each model of the logic tree) and the Lefevre et al. [2018] paleoearthquake rates (in red) at four sites along the fault. Modified from Marti [2018]. In Set 1 the ruptures in the north are smaller than magnitude 7 and can reach magnitude 7.6 in the south. In Set 2, the ruptures can be larger than magnitude 7.6 both in the north and in the south. 80

1.19 Comparison between the MFD modelled with SHERIFS (in green) and the MFD calculated from the earthquake catalog (in black) and the paleoearthquake rates calculated from Lefevre et al. [2018] (in red). On the left, the MFD when using the GR MFD hypothesis, on the right, the MFD using the modified characteristic MFD hypothesis. Modified from Etienne Marti's Master thesis (Marti [2018]). 81

1.20 Deformation map calculated for Western France from the GPS data. The differential velocity between the point A and B is indicated for the three components. The slip-rate attributed to the fault sections by sharing the A-B differential between parallel sections is indicated in the box next to the fault (in black). Modified from Jacottin [2019]. 81

2.1 Regional tectonic setting. Modified from Duman et al. [2018]. The active faults are in black except for the North Anatolian Fault Zone (NAFZ) which is in red. The black and red arrows show the plate motion relative to a fixed Eurasia. 86
2.2 Fault system and the earthquake catalog used in this study (Emre et al. [2018]). The fault sections are delimited by the purple lines and the name of the fault sections are indicated in black. Only the earthquake of magnitude greater than magnitude 4.5 and during the complete period (see Table 2.2) are plotted. The year of occurrence of the largest earthquakes (M>7) are indicated. The yellow triangles are the location of paleoseismic studies. 88

2.3 Left : Magnitude Frequency Distribution for the study area calculated from the catalog and the completeness periods presented in Table 2.2. The red dashes are individual Monte Carlo samples on the earthquake magnitude uncertainties and the completeness period. The mean rate value is indicated by black squares and the 16th and 84th percentiles are indicated by the grey area. Right : Depth distribution of earthquakes of magnitude 4.0 and above since 1992 in the Kadirioğlu et al. [2018] catalog and corresponding to the background zone shown in Figure 2.2. 91

2.4 Distribution of earthquakes between the background seismicity and the faults for each background hypothesis. 94

2.5 Largest ruptures included in the models using the Set 1 (a) and the Set 2 (b). 95

2.6 Logic tree explored in this study. For each branch, the scaling law parameters and the slip-rate uncertainties are explored through 10 random samples. 96

2.7 Comparison between the rates calculated from the earthquake catalog (in red with uncertainties in grey) and the model rates (in green) for the central zone of the fault system, close to Istanbul (figure 2.2). The dashed green lines are the MFD for each individual model of the logic tree. The dotted green line are the 16th and 84th percentiles of the distribution and the continuous green line is the mean value of the distribution. Each figure shows the match between model and data for each branch of the logic tree, organized as a table. A fit of 1. is a perfect fit and a value close to 0. expresses a very poor fit. 97

2.8 Comparison of the modelled rupture rates with the rates calculated from the paleoearthquake record at each paleoearthquake site (Figure 2.2). The green curves are the modelled rate of ruptures rupturing the given section. The dashed lines are each individual model of the logic tree. The dotted line are the 16th and 84th percentiles of the distribution and the continuous line is the mean value of the distribution. The paleoearthquake rates and references are exposed in Table 2.3. 98
2.9 Comparison of the modelled rupture rates with the rates calculated from the paleoearthquake record at Ganos 1 site (Figure 2.2) for different branches of the logic tree. The green curves are the modelled rate of ruptures rupturing the Ganos segment. The dashed lines are each individual model of the logic tree. The dotted line are the 16th and 84th percentiles of the distribution and the continuous line is the mean value of the distribution. The paleoearthquake rates are derived from Rockwell et al 2009 and are represented by the purple box. 99

2.10 Left : MFD of the synthetic catalogs generated from the RSQSim simulations exploring a range of input parameters. Right : Normalized MFD of the earthquake catalog, the MFD of the faults modelled using SHERIFS with a GR MFD or a TS MFD (the background seismicity has been removed), and the RSQSim synthetic catalog (a=0.01 b=0.015). 101

2.11 Scoring system allowing the individual weighting of each branch of the logic tree according to both its capacity to spend the fault slip rate budget into earthquake rate, its capacity to reproduce the earthquake rates observed in the data and the agreement between the input hypotheses and the results of the discussion on the physics-based synthetic catalog. 103

2.12 Weighted logic tree established in this study. For each branch, the scaling law parameters and the slip-rate uncertainties are explored through 10 random samples. The weight of each branch is indicated by the bold number. 106

2.13 Distribution of the cumulative earthquake rates in the logic tree for the central zone for different magnitudes. In black : the density distribution when only the scoring according to the NMS is applied. In green : the density distribution weighted according to the fit with the data (catalog and paleo). In purple : the final distribution of earthquake rates, weighted according to the match with the data and the discussion using RSQSim. The vertical bar shows the mean annual earthquake rate of each distribution. The horizontal bar extends between the 16th percentile and the 84th percentile of each distribution. 107

3.1 Map of the Marmara region. The faults are indicated in black (see chapter 2). The site of calculation is the red dot. The red circle has a 10 km radius around the site of calculation. The background zone of the fault system is in green. The SHARE host model(Woessner et al. [2015]), that is to say the area zones for the regions surrounding the fault system are in shaded blue. 111
3.2 Weighted logic tree established in chapter 2. For each branch, the scaling law parameters and the slip-rate uncertainties are explored through 10 random samples. The weight of each branch is indicated by the bold number. GR and TS MFD: Gutenberg-Richter and Tuned Shape Magnitude frequency distribution, Creeping condition in west of the Marmara, Sea Ak2014: Akkar et al. [2014], CY2008: Chiou and Youngs [2014], AC2010: Akkar and Çağnan [2010], Zh2006: Zhao et al. [2006]. 113

3.3 Hazard curves calculated for each branch of the logic tree presented in figure 3.2. The opacity of the curve represents the weight of the branch in the logic tree. 115

3.4 Calculation of the probability of collapse. The opacity of each curve reflects the weight of the branch in the logic tree. From top to bottom: (a) Hazard curves obtained using the logic tree presented in figure 3.2. (b) Incremental hazard curves giving the probability of every PGA value to be the largest observed in 50 years. The dotted line is a building fragility curve linking the probability of the building to collapse or requiring collapse for a given PGA. (c) Convolution of the incremental hazard curves and the fragility function. For each model of the logic tree, the probability of collapse the integral of this curve. (d) Distribution of the probability of collapse in 50 years. Vertical lines indicate the probability of collapse for each individual branch. 116

3.5 Fragility curves giving the probability of the building requiring collapse prevention for the 1975 Turkish building code (TEC75) and the 1998 Turkish building code (TEC98) (Ozmen et al. [2010]). 118

3.6 Probability of collapse in 50 years for a mid-rise RC building in Istanbul built following the 1975 building code (left) or the 1998 building code (right). In black, probability of collapse using the logic tree weighted using the NMS score of the branch. In green, probability of collapse weighted according to the fit between the modelled earthquake annual rates and the annual rates calculated from the data. In purple, the probability of collapse weighted according to the fit between the data and the results of the physics-based modeling. (see chapter 2 for more details) 119

3.7 Probability of collapse over 50 years colored according to the creep hypothesis. 120

3.8 Probability of collapse over 50 years colored according to the choice of GMPE. 120

3.9 Probability of collapse over 50 years colored according to the MFD hypothesis. 121

3.10 Probability of collapse over 50 years colored according to set of scenarios. 121

3.11 Probability of collapse over 50 years colored according to the background hypothesis. 122
# List of Tables

1.1 Fault characteristics in Boiselet [2014]. Mmax values calculated using the equations for normal faults using the rupture area. WC94 refers to Wells and Coppersmith [1994] and Le10 to Leonard [2010] scaling laws. 46

1.2 Rupture scenarios considered in each model. Branch B14_s considers only the single-fault ruptures. Branch B14 considers the single-fault ruptures and the FtF ruptures with a 3 km distance criteria. Branch B14_hc considers the single-fault ruptures and the FtF ruptures with a 3 and a 5 km distance criteria. Mmax values are calculated using the equations for normal faults based on the rupture area. WC94: Wells and Coppersmith [1994]; Le10: Leonard [2010] 48

1.3 Earthquakes updated in the historical and instrumental catalogs of the western Corinth rift. 50

1.4 Completeness hypotheses explored in this study. 50

1.5 Faults Parameters Used for the Example Calculation. 70

2.1 Properties of the faults of the central zone. The full properties table is available in the annexes. 90

2.2 Completeness time used in this study. 91

2.3 Annual rate of M 7.3+ earthquakes based on the paleoseismicity. 92

2.4 Ratio of earthquakes assumed to be on the faults for each background hypothesis. 93

3.1 Description of the hypotheses explored in the logic tree. 114
# Glossaire - Glossary

* **Background Seismicity** - Seismicity that occurs on faults that are not considered in the model.

* **Fault geometries** Note: The following terminology is not a general terminology use across all fields of geoscience but rather in the seismic hazard assessment community and in particular in this study.

- **Fault system** - Ensemble of faults that are in the same region and are part of the same geodynamic unit.

- **Fault segment** - Portion of fault defined by the boundaries that are considered to be the limits of the possible ruptures on this fault.

- **Fault section** - Part of the fault for which a set of paremeter is attributed (slip-rate, dip, ...) but can rupture with neighbouring fault sections.

* **FC** - Fragility Curve - Gives the probability of building dammage for a given ground motion.

* **GMPE** - Ground Motion Prediction Equation - Equation de Prediction du Mouvement Sismique

* **HC** - Hazard Curve - for a range of ground motions, probability of exceeding given ground motion at one site over a period of time.

* **MFD** - Magnitude Frequency Distribution - Distribution en Magnitude et Fréquence

- **GR** Gutenberg Richter distribution (Gutenberg and Richter [1954]).

- **TS** Tuned Shape distribution. Tuned to the shape of the distribution of the catalog (see Chapter 2).

* **NAFS** - North Anatolian Fault System - Système de Failles Nord-Anatolien

* **NMS** - Non Main-Shock slip - See Chapter 1

* **Participation rate** - Annual rate of earthquakes rupturing a given fault section. The ruptures can involve other fault sections.

* **PGA** - Peak Ground Acceleration

* **PGV** - Peak Ground Velocity
* PSA - Pseudo-Spectral Acceleration

* PSHA - Probabilistic seismic hazard assessment - Calcul probabiliste de l'aléa sismique

* RC - Reinforced Concrete

* SHARE - Seismic Hazard Harmonization in Europe

* SHERIFS - Seismic Hazard and Earthquake Rates in Fault Systems

* UCERF - Uniform Californian Earthquake Rupture

* UHS - Uniform Hazard Spectrum - for a range of PSA of different frequencies, the acceleration that can be exceeded with a set probability over a set period of time (e.g. 10% over 50 years).

* WCR - Western Corinth Rift (Greece) Forecast
# Introduction

Depuis les plus jeunes heures de la civilisation humaine, les être humains ont dû soit s'adapter à leur environnement soit le domestiquer afin de pouvoir s'établir durablement dans une région. Parmi l'ensemble des défis qu'une civilisation doit surmonter, les catastrophes naturelles font partie des plus difficiles. Nombreux sont les exemples de civilisations ayant été affaiblies ou simplement effacées par un phénomène naturel trop destructeur pour que les êtres humains puissent se relever. En 464 av.JC, un séisme provoqua la destruction du gymnase de Sparte, tuant une grande partie des jeunes guerriers spatiates et donnant l'opportunité aux Hilotes de se révolter contre leurs oppresseurs de Sparte. En l'an 79, Pompéi fut recouvert par les cendres du Vésuve. Plus récemment, en 2005, l'ouragan Katerina frappa la ville de la Nouvelle-Orléans tuant plus de 1800 personnes et fragilisant l'économie de toute une région des États-Unis (Bankston III et al. [2010]). En 2011, une séisme de magnitude 9 frappa le nord du Japon, générant un tsunami qui s'abattît sur la centrale nucléaire de Fukushima causant une série d'évènements qui mena à la fusion du réacteur et à l'évacuation de plus de 80 000 personnes (Kim et al. [2013]).

Malgré les constructions de murs brises-vagues et d'infrastructures plus résistantes au mouvement sismique, les catastrophes naturelles demeurent aujourd'hui une menace difficile à réduire. La principale raison de cette difficulté est la longue période de récurrence entre deux évènements à un endroit donné, en particulier pour les séismes. Les catastrophes naturelles majeures ont typiquement un temps de retour bien supérieure à la durée de vie humaine et à la mémoire collective d'une société. Ces grands temps de récurrence rendent la prise de conscience du risque difficile à assimiler mais rendent également le phénomène physique difficile à étudier.

Pour comprendre et se protéger contre les catastrophe naturelles, il est nécessaire d'en comprendre l'origine. La cause des séismes resta pendant longtemps une énigme souvent attribuée à une action divine. Au XVIII em siècle, une théorie émergea selon laquelle les séismes seraient provoqués par des gaz circulant dans la croûte terrestre. Nous savons aujourd'hui que les séismes sont produits par le relâchement de contraintes accumulées le long d'une faille. Les temps de récurrence des séismes de taille suffisamment grandes pour être endommageant sont de l'ordre de plusieurs centaines d'années à plusieurs milliers d'années, trop longs pour pouvoir étudier un site donné en utilisant l'observation directe de l'évènement.
La sismologie remédie à ce problème en adoptant une approche ergodique, étudiant les séismes au niveau global, pour comprendre quelles propriétés et caractéristiques tous les séismes partagent et ainsi permettre l'élaboration de théories sur les propriétés d'un potentiel futur séisme dans une région donnée. La géologie s'appuie sur les grandes échelles de temps du passé en étudiant les vitesses de déplacement le long des failles générant les séismes à partir de données géomorphologiques ou les traces d'anciens séismes s'étant produits sur une faille à partir de l'étude de tranchées.

Cette thèse présente une méthodologie qui joint informations géologiques et sismologiques pour évaluer le risque sismique dans les régions où des failles actives ont été identifiées.

# 1 Contexte du projet

En 2014, pendant les études de sûreté nucléaire dans le contexte post-Fukushima, un calcul d'aléa sismique fut conduit pour les 19 centrales nucléaires françaises par l'opérateur des centrales. Je travaillais alors pour l'Institut de Radioprotection et de Sûreté Nucléaire (IRSN) qui a été chargé de l'expertise de ces calculs par l'Autorité de Sûreté Nucléaire (ASN). Ma fonction était de faire l'expertise de la partie probabiliste des calculs présentés par l'opérateur nucléaire. L'une de mes conclusions personnelles fut que pour les sites proches de failles potentiellement actives, les calculs présentés, bien qu'appliquant une approche pouvant être considérée dans son ensemble comme l'état de l'art, ne menait pas à une représentation acceptable des taux annuels de sismicité sur les failles et de l'incertitude associée à ces taux.

Un an plus tôt était présenté le calcul d'aléa sismique pour la Californie, UCERF3 (Uniform Californian Earthquake Rupture Forecast 3) (Field et al. [2014]). Le modèle présenté établit un nouveau standard pour la modélisation des failles pour le calcul d'aléa sismique. Parmi les nouveautés, ce modèle autorise les ruptures sismiques complexes impliquant plusieurs failles tout en approchant le problème à l'échelle du système de faille dans son ensemble et pas seulement au niveau de chaque faille individuellement. De plus, les taux annuels de rupture sont inversés en se basant sur l'ensemble des données disponibles générant ainsi des modèles d'aléa cohérents avec l'état des connaissances à la fois géologiques, géodésiques, sismologiques et paléosismologiques. Malheureusement, l'approche développée pour ce modèle nécessite un niveau de ressources humaines, scientifiques afin de mettre en place des bases de données uniformes et cohérentes, ainsi que des ressources informatiques qui sont hors de portée pour la plupart des études d'aléa sismique dans d'autres régions, notamment en France.

Nous avons mis en place ce projet de thèse après la constatation que le manque de méthodologies et d'outils permettant une représentation des failles dans les modèles d'aléa sismique en accord avec les concepts de la communauté scientifique limitait la prise de décision sur le risque sismique.
Il fut alors clair qu'il était nécessaire de développer une méthodologie et les outils associés à cette méthodologie qui permettent de se rapprocher du standard de UCERF3 dans des régions où moins d'information sur les failles est disponible.

Une seconde conclusion de l'étude post-Fukushima sur les centrales françaises concernait le calcul d'aléa sismique probabiliste en général. Le calcul probabiliste, présenté en détail plus bas, intègre l'ensemble des participations des sources sismiques d'une région et permet une exploration des incertitudes épistémiques associées avec les différentes étapes du calculs. Le résultat est donc difficile à relier aux hypothèses scientifiques sous-jacentes ce qui peut rendre toute prise de décision faite sur la base de ces calculs difficile pour un non spécialiste, en particulier lorsque l'incertitude associée au résultat est forte.

Un second objectif de la thèse fut donc établi: en parallèle de permettre une meilleure modélisation des failles, la méthodologie développée devra également permettre une meilleure communication des incertitudes impactant l'aléa et le risque sismique afin d'aider à la prise de décision.

## 2 Chaîne de calcul du risque sismique

Différents éléments de calculs s'imbriquent pour obtenir une estimation du risque sismique (1). L'aléa sismique est le mouvement du sol pouvant affecter un enjeu (bâtiment, ville, infrastructure ou vie humaine). La réaction de l'enjeu au mouvement sismique est décrit par sa vulnérabilité. La combinaison de l'aléa et de la vulnérabilité permet de calculer le risque sismique.

<figure><img src="image_1.png" /><figcaption>Figure 1: Chaîne de calcul du risque sismique.</figcaption></figure>

Le calcul probabiliste de l'aléa sismique peut être divisé en trois étapes : la description de la géométrie des
sources sismiques, le calcul des magnitudes et fréquences des séismes sur chacune des sources, et le calcul du mouvement sismique au site d'intérêt en fonction de la localisation du séisme par rapport au site, sa magnitude et les conditions de sol du site.

Dans cette étude, nous nous concentrerons sur la modélisation des sources sismiques et du calcul de la fréquence des séismes (figure 1). Cependant, nous réaliserons le calcul du risque sismique en intégrant l'intégralité de la chaîne de calcul (figure 1). Pour le calcul du mouvement sismique, nous utiliserons des GMPEs (Ground Motion Prediction Equation) disponibles dans la littérature qui pour des caractéristiques de séismes données à une distance donnée permettent d'obtenir la probabilité de dépasser un certain niveau de mouvement sismique. Pour la vulnérabilité, nous nous appuierons sur des courbes de fragilité publiées qui décrivent la probabilité qu'un bâtiment soit endommagé lorsqu'il est soumis à un mouvement sismique.

# 3 Problématiques concernant l’intégration des failles dans le calcul d’aléa sismique

## 3.1 Ruptures complexes

La plupart des études d'aléa sismique (Erdik et al. [2004], Woessner et al. [2015], Sesetyan et al. [2018],...) s'appuient sur des modèles de segmentation des failles permettant une modélisation faille par faille des taux de sismicité mais ne permettant pas de de modéliser les ruptures complexes pouvant rompre plusieurs segments simultanément. Le modèle californien UCERF3 permet de s'affranchir des hypothèses de segmentation. Les taux annuels de ruptures d'un segment unique ou de multi-segments sont calculés par inversion à l'échelle du système de faille entier prenant en compte un grand nombre de paramètres. L'approche utilisée dans UCERF3 a changé l'état de l'art et a montré l'importance de considérer un système de failles comme un ensemble et non pas comme une collection de failles isolées. Cependant, l'implémentation de cette approche est complexe et nécessite une bonne connaissance du contexte tectonique du système de faille.

Une méthodologie plus versatile construisant sur les avancées de UCERF3 est requise pour que l'état de l'art définit par UCERF3 puisse être appliqué à d'autres systèmes de failles.

## 3.2 Sismicité sur les failles et sismicité de fond

Les modèles d'aléa sismique prenant en compte les failles établissent une magnitude de troncature (Mt) (Woessner et al. [2015], Sesetyan et al. [2018], Chartier et al. [2017a],...). Les séismes de magnitude supérieure à Mt se produisent
sur les failles modélisées et les séismes de magnitude inférieure à Mt se produisent dans la sismicité de fond, une zone sismotectonique définie autour des failles. Selon des études, Mt peut être comprise entre 5.5 et 6.5. Cette approche a deux impacts potentiels sur l'aléa sismique:

* le modèle ne considère pas la possibilité de séismes de magnitude supérieure à Mt sur des failles inconnues, considérées inactives ou simplement non modélisées. Cela peut entraîner une sous-estimation du risque pour les sites qui ne sont pas à proximité immédiate de telles failles.

* le modèle ne considère pas que les séismes de magnitude inférieure à Mt puissent se produire sur les failles. Cela peut entraîner une sous-estimation du risque pour les sites à proximité immédiate des failles.

Les taux annuels des séismes sur les failles sont calculés à partir de la vitesse de glissement de la faille et les taux de sismicité de fond sont calculés en se basant sur le catalogue de sismicité. Il est possible que, dans certaines régions, ces deux sources d'information ne convergent pas et mènent à des taux de sismicité différents.

Afin d'adresser ces problèmes, il est nécessaire de développer une approche innovante de modélisation des taux de sismicité dans la sismicité de fond.

## 3.3 Contraintes pour la méthodologie à développer

En vue des problématiques exposées précédemment, une nouvelle méthodologie pour les taux de sismicité des failles doit prendre en compte les points suivants:

* suppression des hypothèses de segmentation et ainsi autoriser la possibilité de rupture sismique conjointe de plusieurs segments de failles simultanément.

* une modélisation au niveau du système de faille et non au niveau de chaque segment individuellement.

* l'ensemble des données disponibles concernant un système de failles doit être pris en compte.

* la possibilité d'occurrence de séismes sur des failles non modélisées, c'est à dire dans la sismicité de fond, doit être considérée ainsi que la possibilité d'occurrence de petits séismes sur les failles.

* faciliter l'utilisation de la méthode par des utilisateurs n'étant pas spécialisé dans les méthodes numériques et voulant tester des hypothèses concernant un réseau de faille.

* la méthodologie doit être applicable sur des systèmes de failles variés autant en terme de contexte géodynamique qu'en terme de niveau de connaissance.
## 4 Problématique de traçabilité des sources du risque sismique et des incertitudes associées

Le calcul du risque sismique prend en compte l'ensemble des sources sismiques d'une région, la fréquence des séismes sur ces sources, le mouvement sismique associé à chaque séisme, ainsi que la réaction du bâtiment face au mouvement sismique. L'ensemble de ces paramètres est intégré pour présenter le résultat sous la forme d'une simple métrique telle que la probabilité d'effondrement d'un bâtiment ou la perte financière probable. Après cette intégration, il est difficile d'identifier les sources contrôlant le risque sismique et l'incertitude, étape essentielle afin d'orienter les pistes de recherche future qui pourront améliorer la compréhension du risque sismique.

De plus, le calcul du risque sismique est le plus souvent réalisé par la communauté des ingénieurs des structures qui s'appuient sur les résultats d'études d'aléa disponibles dans la littérature (Hong and Goda [2006], Iervolino et al. [2018], ...). De ce fait, dans les études de risque sismique, l'accent est en majorité porté sur les techniques de modélisation des structures et très peu sur la modélisation des sources sismotectoniques.

Dans cette étude, les taux de sismicité modélisés sont utilisés pour calculer la probabilité d'effondrement d'un bâtiment. L'impact de chaque hypothèse sur le résultat est analysé afin d'identifier les incertitudes sur les hypothèses d'entrées entraînant les impacts sur le résultat les plus importants. En parallèle, une méthodologie de désagrégation de la probabilité d'effondrement est mise en place afin d'identifier les sources contrôlant le risque.

En adoptant le point de vue du risque sismique, nous souhaitons faire un pas dans la direction de l'amélioration de la communication entre la communauté des géosciences, la communauté des modélisateurs d'aléa sismique et la communauté des ingénieurs. L'illustration des sources d'incertitudes liées aux hypothèses concernant les sources sismotectoniques qui affectent fortement l'estimation du risque sismique peut permettre à la communauté des géosciences d'apprécier quantitativement l'impact de la recherche en géosciences sur la connaissance du risque. Développer des outils d'intégration plus direct de l'aléa et du risque permet également aux communautés des modélisateurs de l'aléa et des ingénieurs d'échanger sur les méthodes de modélisation et d'obtenir une représentation plus réaliste des incertitudes.

Finalement, un résultat d'analyse du risque sismique plus transparent en terme de données utilisées, de méthodes et d'incertitudes associées est une pierre angulaire de la prise de décision concernant les mesures de réduction du risque sismique à mettre en oeuvre.
# 5 Plan de la thèse

Le chapitre 1 se compose de trois parties. La première partie est une publication (Chartier et al. [2017b]) présentant l'élaboration de la méthodologie de calcul des taux annuels de rupture dans un système de faille avec une application sur le réseau de faille du Rift de Corinthe. Le code de calcul appliquant la méthodologie fut développé sous le nom de SHERIFS (Seismic Hazard and Earthquake Rates In Fault Systems). La seconde partie du chapitre est une publication (Chartier et al. [2019]) présentant le fonctionnement du code SHERIFS et les évolutions de la méthodologie vis-a-vis de la première partie. La troisième partie argumente l'intérêt de rendre un code de calcul disponible et présente les discussions les évolutions qui ont été possibles grâce au partage de SHERIFS.

Le chapitre 2 présente une application de SHERIFS pour la faille nord anatolienne en Turquie dans la région de la mer de Marmara. Nombre d'incertitudes pèse sur ce système de faille, parmi lesquelles la condition de bloquage de la faille, la dimension des ruptures possible, la forme de la distribution de la sismicité, et la proportion de séismes pouvant se produire dans la sismicité de fond. Il fut donc possible de tester les capacités de SHERIFS en explorant ces incertitudes dans un arbre logique. Les taux de sismicité modélisés sont comparés aux taux calculés à partir du catalogue de sismicité et des études de paléosismicité disponibles dans la région. Afin d'enrichir la discussion concernant les hypothèses d'entrées du calcul, une modélisation de la sismicité est réalisée avec le code de calcul "physics-based" RSQSim. La comparaison avec les données et les résultats de RSQSim permet d'attribuer des poids à chaque branche de l'arbre logique et ainsi d'obtenir une représentation réaliste de l'incertitude associée aux taux de sismicité dans la région.

Le chapitre 3 s'oriente vers le calcul du risque sismique et se compose de deux parties. Dans la première partie, l'arbre logique construit dans le chapitre 2 est utilisé pour calculer la probabilité d'effondrement de deux immeubles théoriques de 5 étages à Istanbul. L'impact de chaque hypothèse explorée dans l'arbre logique sur la probabilité d'effondrement est discuté. En utilisant une méthodologie innovante de désagrégation du risque sismique, il est possible d'identifier les sources sismique contrôlant la probabilité d'effondrement et d'observer que ces sources diffèrent selon les hypothèses d'entrées et la résistance du bâtiment. Dans la seconde partie, les résultats préliminaires d'un calcul de perte financière sur un portefeuille de 1000 bâtiments dans la région d'Istanbul sont présentés.
# 6 Rappel sur les méthodes de calcul de l'aléa sismique

## 6.1 Calcul déterministe

Dans le calcul déterministe de l'aléa sismique, un scénario sismique est considéré comme ayant une probabilité d'occurrence de 1. Le mouvement sismique est calculé en utilisant une GMPE. Plusieurs approches peuvent être utilisées pour établir ce scénario. Si le site ou les sites d'intérêt sont proches d'une faille active, le scénario peut être définit comme le séisme de magnitude maximal pouvant être envisagé sur cette faille. Si aucune faille active n'est identifiée à proximité du site mais qu'il existe une sismicité diffuse, le scénario est défini par un séisme de magnitude vraisemblable pouvant être généré à proximité du site. Il convient alors d'établir des règles permettant de définir ce qu'est un séisme vraisemblable pour une région.

En France, pour la sûreté nucléaire, c'est cette seconde approche qui est utilisée. Les règles décrivant la manière de définir une magnitude vraisemblable et les marges de sûreté à imposer sont énoncées dans la Règle Fondamentale de Sûreté (RFS - 2001-01).

L'approche déterministe permet de communiquer clairement, à la fois aux ingénieurs et aux décideurs, l'évènement sismique contre lequel il conviendra de se protéger ainsi que les incertitudes épistémiques associées à l'estimation de la magnitude et la localisation de cet évènement. Il est également possible d'explorer les incertitudes épistémiques, pesant sur l'estimation de la magnitude d'un séisme vraisemblable par différent experts ainsi que la GMPE utilisée. En revanche, l'approche déterministe ne permet pas d'explorer les incertitudes aléatoires du mouvement sismique telles que la directivité, ou la chute de contrainte.

## 6.2 Calcul probabiliste

### 6.2.1 L'approche Cornell

L'approche probabiliste, développée par Cornell en 1968 sous le nom PSHA (Probabilistic Seismic Hazard Assessment), permet de prendre en considération l'ensemble des sources sismiques et les incertitudes aléatoires que l'approche déterministe néglige. Les incertitudes aléatoires comprennent l'occurrence aléatoire des séismes qui est représentée par le taux annuel d'occurrence d'un séisme de magnitude donnée sur une source sismique, le mouvement sismique généré par un séisme d'une magnitude donnée à une distance donnée.

L'approche PSHA se compose de quatre étapes (2). Tout d'abord, il convient d'identifier la géométrie de l'ensemble des sources sismiques potentielles proches du site d'intérêt. Ces sources peuvent être des failles actives, des points sources représentant l'occurrence d'un séisme, ou bien des zones de sismicité diffuse où la sismicité est
<figure><img src="image_2.png" /><figcaption>Figure 2: Étapes du calcul PSHA selon Cornell 1968.</figcaption></figure>

considérée uniforme spatialement. Dans un second temps, il faut définir la fréquence et la magnitude des séismes pouvant se produire sur chacune des sources. Le troisième élément est la GMPE, permettant d'obtenir la probabilité de dépasser un certain niveau de mouvement sismique en fonction des caractéristiques du séisme (magnitude, distance, cinématique, ...) ainsi que des caractéristiques du sol au droit du site d'intérêt. La quatrième et dernière étape, qui est la combinaison des éléments des trois premières étapes grâce à l'équation 1, permet d'obtenir la courbe l'aléa sismique. La courbe d'aléa sismique décrit la probabilité de dépasser chaque niveau de mouvement sismique pendant une période donnée.

$$P(A > a^*) = \int_M \int_D \lambda_{M,D} \times P(A > a^* | M, D) \quad (1)$$

Où $\lambda_{M,D}$ est le taux annuel de séismes de magnitude M à la distance D; et $P(A > a^* | M, D)$ est la probabilité du mouvement du sol A d'excéder le mouvement cible $a^*$ étant donnée la magnitude M à la distance D. $P(A > a^* | M, D)$ est calculé grâce à une GMPE.

## 6.2.2 Éléments du calcul probabiliste d'aléa sismique

### a) Géométrie des sources

La géométrie des sources sismiques s'appuie à la fois sur les études géologiques et géophysiques de terrain et sur l'étude du catalogue de sismicité. L'identification des failles actives par les géologues permet de localiser là où peut être attendue la sismicité future. L'analyse du catalogue de sismicité permet de définir les ensembles sismotectoniques en
fonction de la densité de la sismicité enregistrée et ainsi définir des sources sismotectoniques pour lesquelles le potentiel sismogène peut être considéré comme uniforme.

### b) Récurrence des séismes

Les taux de sismicité des zones sismotectoniques sont estimés à partir du catalogue de sismicité. L'instrumentation sismologique des territoires s'étant développée à partir des années 1960, les catalogues de sismicité instrumentale sont courts comparés à la récurrence des séismes endommageant qui peut être de plusieurs siècles. Des catalogues de sismicité historique sont construits à partir des témoignages de ressentis de séismes ayant eu lieu avant la période instrumentale. Le seuil de détectabilité des séismes s'est amélioré au cours du temps, aussi bien pour les détections instrumentales que pour la survie des témoignages historiques. Pour chaque gamme de magnitude est établie une date à partir de laquelle le catalogue peut être considéré complet. Le nombre de séismes observés pendant la période complète permet de calculer le taux annuel de séismes pour chaque gamme de magnitude.

### c) GMPEs

Les GMPES sont établies empiriquement par analyse statistique des mouvements sismiques enregistrés, à partir des bases de données d'accélérogrammes, des relations entre les paramètres du séisme, notamment la magnitude et la distance à la station, et des indicateurs de mouvement sismique issus de l'accélérogramme. Parmi les indicateurs, le plus couramment utilisé est le PGA (Peak Ground Acceleration) qui est la valeur maximale de l'accélération enregistrée à la station lors du séisme. Le PGA étant un indicateur plutôt représentatif du contenu haute fréquence du séisme, des accélérations pseudo-spectrales (PSA for Pseudo-Spectral Acceleration) sont également calculées à partir de l'accélérogramme. Les PSA sont la réponse au mouvement sismique d'oscillateurs harmoniques à une dimension avec un amortissement de 5% de différentes fréquences propres. Le PGV (Peak Ground Velocity) qui est la vitesse maximale enregistrée est également utilisé.

Ces différents indicateurs correspondent à différentes fréquences de réponse de la structure des bâtiments et sont ainsi utiles pour calculer les dégâts potentiels. Par exemple, un bâtiment de 3 étages a une fréquence propre proche de 3Hz, ainsi un calcul de la probabilité d'occurrence d'un PSA de 3Hz sera un indicateur utile pour calculer la probabilité de dégât pour ce bâtiment.

### 6.2.3 La désagrégation

Le calcul probabiliste agrège la participation à l'aléa sismique de l'ensemble des sources sismiques présentent dans une région. Afin d'identifier les sources participant en majorité à la probabilité de dépassement d'un niveau d'aléa sismique donné, il est possible de désagréger le calcul. Pour cela il est nécessaire de séparer les probabilités conditionnelles
de dépassement d'un niveau d'aléa sismique en fonction de la magnitude, de la distance, et/ou de l'emplacement géographique de la source sismique.

Il est également possible de faire la désagrégation en epsilon de la distribution de probabilité de la GMPE qui permet de tracer la participation de mouvements sismiques prédits par la GMPE proches de la moyenne ou bien des extrêmes de la distribution de probabilité.

### 6.2.4 L'approche par simulation de catalogues de sismicité synthétiques

Il existe des approches alternatives à l'approche Cornell pour calculer l'aléa sismique probabiliste. L'approche "event-based" (Bommer et al. [2002]) utilise les mêmes ingrédients que l'approche Cornell décrite précédemment mais ne s'appuie pas sur le formalisme probabiliste de l'équation 1. Par une approche Monte-Carlo, elle simule un catalogue de sismicité synthétique de plusieurs milliers d'années et calcule le mouvement sismique associé à chaque séisme. En analysant l'historique des mouvements sismiques synthétiques enregistrés à un site donné, il est possible de calculer la probabilité annuelle de dépassement d'un niveau sismique. Cette approche présente l'avantage d'illustrer clairement le mouvement sismique lié à chaque évènement du catalogue et ainsi présenter un résultat plus simple à appréhender par une audience peu familière avec le calcul probabiliste. La simulation d'un catalogue synthétique peut également permettre de modéliser des séquences sismiques de manière simple et explicite tandis que leur probabilisation est plus compliquée à modéliser mais également à communiquer. En revanche, afin d'explorer les incertitudes aléatoires sur l'occurrence des séismes pour chacune des sources sismogéniques et sur le mouvement sismique généré au site pour un séisme donné, il est nécessaire de générer des catalogues de plusieurs millions, voire milliards de séismes. Ceci est extrêmement coûteux en terme de puissance de calcul et de mémoire et mène souvent à négliger l'exploration des incertitudes épistémiques pesant sur la définition des sources.

## 7 Rappel sur les méthodes de calcul du risque sismique

### 7.1 Calcul site spécifique

Le calcul du risque sismique pour un site spécifique, pour un site critique tel qu'une central nucléaire ou un barrage, se base sur le calcul d'aléa sismique au site et la désagrégation. Pour une période de retour fixée, en d'autres termes une probabilité fixée, la désagrégation présente les sources sismiques contribuant au dépassement de l'aléa sismique. Une sélection d'accélérogrammes correspondant aux magnitudes et distances participant majoritairement à l'aléa sismique dans la désagrégation est extraite des bases de données (Rizzo et al. [1975]).

Cette sélection d'accélérogrammes est ensuite utilisée par les ingénieurs des structures comme sollicitation
sismique qui, en utilisant des modèles numériques, propagent le mouvement au sein de la structure afin d'évaluer les potentiels endommagements.

Afin de faciliter le calcul, il est également possible de s'appuyer sur des courbes de fragilité. Développées empiriquement ou synthétiquement par des ingénieurs des structures, elles relient un paramètre de mouvement du sol à la probabilité d'endommagement d'un bâtiment. Le paramètre peut être le PGA ou un PSA d'une fréquence correspondant à la fréquence propre du bâtiment.

Utiliser une courbe de fragilité simplifie grandement la mise en place du calcul car aucun calcul supplémentaire de la réaction du bâtiment au mouvement sismique n'est nécessaire. En revanche, le fait d'utiliser un seul indicateur du mouvement sismique entraîne l'omission d'une part de la complexité du mouvement sismique telles que la présence de différents contenus fréquentiels, la durée, ou encore la polarisation.

## 7.2 Calcul de perte pour un ensemble de sites

Lorsqu'un séisme se produit, il peut endommager un grand nombre de bâtiments simultanément. Pour calculer la probabilité de perte il faut donc considérer la possibilité que plusieurs bâtiments soient endommagé pendant le même évènement sismique. L'approche Cornell (Cornell [1968]) ne permet pas de prendre en compte la probabilité conditionnelle d'endommagement d'un bâtiment sachant qu'un autre bâtiment est endommagé.

Afin de calculer cette probabilité, l'approche "event-based" est utilisée. Un catalogue de sismicité synthétique est simulé à partir du même type de modèle de taux annuel d'occurrence des séismes utilisés dans l'approche Cornell. Pour chaque séisme du catalogue synthétique, un champ de mouvement sismique est simulé grâce à une GMPE. L'incertitude du mouvement sismique prédit par la GMPE peut être explorée en prenant en compte la corrélation spatial du mouvement sismique (Jayaram and Baker [2009]). La probabilité d'endommagement de chaque bâtiment est calculé en utilisant une courbe de fragilité adaptée au type de bâtiment. Différentes métriques peuvent être utilisées pour présenter le risque, telle que le nombre de bâtiments affectés ou effondrés, la perte financière associée au dégâts, ou encore le nombre de victimes. L'analyse statistique du catalogue synthétique de dégât permet de calculer la probabilité du risque et les séismes qui entraînent les pertes les plus importantes ou les plus fréquentes (Hong and Goda [2006]).
# Chapter 1

# Methodology for modelling earthquake rates
in fault systems

## Résumé du chapitre

La fréquence annuelle de séismes sur les failles est un élément essentiel du calcul probabiliste de l'aléa et du risque sismique. Dans ce chapitre, nous présentons une méthodologie novatrice pour calculer la fréquence annuelle des séismes dans un réseau de faille à partir de la vitesse de glissement et de la géométrie des failles. Cette méthodologie considère le système de failles dans son ensemble et permet de modéliser les fréquences annuelles de ruptures complexes impliquant plusieurs sections de failles. En plus de la géométrie et de la vitesse de glissement des failles dans le réseau, des hypothèses sur les ruptures possibles et sur la distribution en magnitude et fréquence (MFD) de la sismicité sont requises. La méthodologie permet également de considérer la possibilité que des séismes futurs arrivent sur des failles inconnues, donc dans la sismicité de fond.

La méthodologie est implémentée dans le code SHERIFS (Seismic Hazard and Earthquake Rates in Fault Systems) de telle sorte à être utilisable aisément par des utilisateurs sans expérience de programmation. SHERIFS est assez flexible pour modéliser des systèmes de failles diversifiés et pour explorer une grande variété d'incertitudes épistémiques, notamment concernant les hypothèses de ruptures complexes et de MFD. En comparant les taux modélisés au taux calculés à partir du catalogue de sismicité et aux taux calculés à partir des études de paléosismicité, il est possible de discuter et pondérer les hypothèses d'entrées explorées.

Une application sur le système de failles de la partie occidentale du Rift de Corinth en Grèce est présentée. Il est observé que malgré le fait que la sismicité du réseau de faille suit une MFD de type Gutenberg-Richter, localement,
les failles peuvent présenter une MFD proche d'un séisme caractéristique. De plus, afin de reproduire les taux de sismicité observés dans le catalogue et dans la paléosismicité, il est nécessaire de considérer possible la rupture conjointe de plusieurs sections de faille durant le même séisme.

Au travers des différents exemples d'application de SHERIFS, nous exposons les difficultés mais également et surtout les avantages de partager un code appliquant une méthodologie novatrice. L'utilisation de SHERIFS par des personnes extérieures à son développement à permis d'améliorer la méthodologie et de faire avancer les discussions concernant un système de failles en comparant avec d'autre systèmes de failles modélisés.
# Structure of the chapter

This chapter presents a novel methodology for modelling earthquake rates in faults systems and is composed of three sections.

The first section is an article published in 2017 exposing a proof of concept for an earthquake rate modelling methodology with an application on the Western Corinth Rift in Greece (Chartier et al. [2017b]). It lays down the concepts of the methodology and relies on the fault system parameters established during the PhD thesis of Aurélien Boiselet.

The second section of the chapter is an article published in 2019 presenting the code SHERIFS (Seismic Hazard and Earthquake Rates In Fault Systems) that applies the methodology presented above (Chartier et al. [2019]). This article exposes the details of the algorithm and provides an example of application. The additional features of the code added since the application on the Western Corinth Rift are also presented. The goal of the article is to be a support for any user. The SHERIFS code and a user manual is available online at https://github.com/tomchartier/SHERIFS.

The third and final section of the chapter is a discussion about the process of developing and sharing an open-source and user-friendly code such as SHERIFS. In this section, the difficulties of the process are fully exposed as well as the outcomes of the sharing. A large number of scientific discussions were made possible only because the code was available for others to apply in different study areas. The goal of the section is to argue for the open sharing of scientific codes and convince PhD students that the benefits of sharing a code drastically outweighs the time and energy costs.
# 1.1 Methodology for earthquake rupture rate estimates of fault networks: example for the western Corinth rift, Greece

## 1.1.1 Abstract

Modeling the seismic potential of active faults is a fundamental step of probabilistic seismic hazard assessment (PSHA). An accurate estimation of the rate of earthquakes on the faults is necessary in order to obtain the probability of exceedance of a given ground motion. Most PSHA studies consider faults as independent structures and neglect the possibility of multiple faults or fault segments rupturing simultaneously (fault-to-fault, FtF, ruptures). The Uniform California Earthquake Rupture Forecast version 3 (UCERF3) model takes into account this possibility by considering a system-level approach rather than an individual-fault-level approach using the geological, seismological and geodetical information to invert the earthquake rates. In many places of the world seismological and geodetical information along fault networks is often not well constrained. There is therefore a need to propose a methodology relying on geological information alone to compute earthquake rates of the faults in the network. In the proposed methodology, a simple distance criteria is used to define FtF ruptures and consider single faults or FtF ruptures as an aleatory uncertainty, similarly to UCERF-3. Rates of earthquakes on faults are then computed following two constraints: the magnitude frequency distribution (MFD) of earthquakes in the fault system as a whole must follow an a priori chosen shape and the rate of earthquakes on each fault is determined by the specific slip rate of each segment depending on the possible FtF ruptures. The modeled earthquake rates are then compared to the available independent data (geodetical, seismological and paleoseismological data) in order to weight different hypothesis explored in a logic tree. The methodology is tested on the western Corinth rift (WCR), Greece, where recent advancements have been made in the understanding of the geological slip rates of the complex network of normal faults which are accommodating the ~ 15 mm.yr⁻¹ north-south extension. Modeling results show that geological, seismological and paleoseismological rates of earthquakes cannot be reconciled with only singlefault-rupture scenarios and require hypothesizing a large spectrum of possible FtF rupture sets. In order to fit the imposed regional Gutenberg-Richter (GR) MFD target, some of the slip along certain faults needs to be accommodated either with interseismic creep or as post-seismic processes. Furthermore, computed individual faults' MFDs differ depending on the position of each fault in the system and the possible FtF ruptures associated with the fault. Finally, a comparison of modeled earthquake rupture rates with those deduced from the regional and local earthquake catalog statistics and local paleoseismological data indicates a better fit with the FtF rupture set constructed with a distance criteria based on 5 km rather than 3 km, suggesting a high connectivity of faults in the WCR fault system.
1.1.2 Introduction

The goal of probabilistic seismic hazard assessment (PSHA) is to estimate the probability of exceeding various groundmotion levels at a site (or a map of sites) given the rates of all possible earthquakes. The first step of PSHA following a Cornell-McGuire approach (Cornell [1968]; McGuire [1976]) is the characterization of the seismic sources. For regions where active faults have been identified and their slip rates are known, several methods have been proposed in order to calculate the rate of earthquakes occurring on these faults. The most commonly used methods consider faults as independent structures on which the strong earthquakes are located (e.g., SHARE project in Europe, Woessner et al. [2015]; Yazdani et al. [2016], in Iran; TEM model in Taiwan, Wang et al. [2016]). In these PSHA studies, a background seismicity will generate earthquakes up to a threshold magnitude (Mw) of 6.0 or 6.5, beyond which earthquakes are generated on the faults. The rate of earthquakes for these larger magnitudes is based on geological and paleoseismological records, and the maximum magnitudes depend on the physical dimensions of the fault under consideration. In the resulting model, the rate of lower magnitudes is controlled by seismological information and the rate of stronger magnitudes by geological information. In cases where large historical earthquakes are associated with multiple fault segments, the individual fault segments described by the geologists in the field are regrouped in a larger fault source and a mean slip rate is attributed to the fault source. A specific magnitude frequency distribution (MFD), often Gutenberg-Richter (GR) (Gutenberg and Richter [1944]) or characteristic earthquake (Wesnousky [1986]), describing the mean sliprate-based earthquake rate on the fault is attributed to each fault source. This process requires simplifying fault complexity in terms of geometry and slip rate and does not allow complex ruptures that propagate from one fault source to an adjacent one.

In the past decades, the quality of observations has improved and our understanding of earthquakes has grown (proceedings of the 2017 Fault2SHA meeting). We observe more and more complex earthquake ruptures propagating on several neighboring faults. There is thus a need for hazard models to accurately represent the fault and rupture complexity observed in the field by geologists and to correctly distinguish aleatory from epistemic uncertainties.

Toro et al. [1997] define epistemic uncertainty as “uncertainty that is due to incomplete knowledge and data about the physics of the earthquake process. In principle, epistemic uncertainty can be reduced by the collection of additional information”. Aleatory uncertainty, on the other hand, is an “uncertainty that is inherent to the unpredictable nature of future events”; in this respect a fault-to-fault (FtF) rupture should be treated as an aleatory uncertainty since it is linked to the randomness of the seismic phenomenon.

In order to allow FtF ruptures, the Working Group on California Earthquake Probabilities (WGCEP-2003) for the San Francisco Bay region developed a methodology that explores possible FtF ruptures in a logic tree. Each branch of the logic tree represents a seismic hazard model, and the rate of the corresponding FtF rupture scenario is
obtained by weighting the branches. In the hazard study of the Marmara Region in Turkey, Gülerce and Ocak [2013] used this approach and set the weight of each branch (or rupture scenario) such that the mean seismicity rate modeled by the logic tree fits the recorded seismicity rate around the fault of interest. This method treats the uncertainty of FtF ruptures as an epistemic uncertainty in the PSHA calculation.

The Uniform California Earthquake Rupture Forecast version 3 (UCERF-3) model was developed using a novel methodology that treats all possible combinations of FtF rupture scenarios within the same branch of the logic tree as an aleatory uncertainty (Field et al. [2014]). Per their terminology, faults are divided into smaller sections and all possible section-to-section ruptures are investigated. The possibility of ruptures happening is controlled by a set of geometric and physical rules and the rate of earthquakes is computed using a “grand inversion” of the seismological, geological, paleoseismological and geodetical data available in California. The regional GR MFD of earthquakes of California and the geodetical deformation are used as a target for the total earthquake rupture forecast in each deformation model. This grand inversion relies also on estimates of the creep rate on faults deduced from local deformation data when available.

For many fault networks, only sparse seismological and geodetical data are available, and the geological record is often the most detailed source of information concerning the faults' activity. In such cases, it is necessary to develop a methodology that allows building seismic hazard models relying only on geological data and yet allowing FtF ruptures as an aleatory uncertainty. The sparse geodetical, seismological and paleoseismological data can then be used as a means of comparison to help weighting the different input hypothesis.

In this study we propose such a methodology based on the slip-rate budget of each fault, FtF ruptures hypothesis and assumptions on the shape of the MFD defined for the fault system as a whole. The methodology is developed so as to be flexible and applicable to regions where data on faults, geodesy and seismicity may be sparse. The rate of earthquakes on faults computed using geological information (slip rates) and is then compared to other sources of information such as the regional and local earthquake catalogs and the paleoseismic data in order to weight the different epistemic uncertainty explored in the logic tree. Moreover, it is also known that faults accommodate important amounts of slip in either post-seismic slip or in creep events (e.g., L'Aquilla earthquake 2009; Cheloni et al. [2014]; Napa earthquake 2014; Lienkaemper et al. [2016]). These phenomena, called non-main-shock slip (NMS) later on, are integrated in the slip rates deduced from geological information and should not be converted into earthquake rates when computing seismic hazard. The methodology presented in this study allows part of the geological slip rate to be considered as NMS slip rate.

We use this methodology to generate fault-based hazard models for the western Corinth rift (WCR), Greece, which has been studied for the past decade by the Corinth Rift Laboratory Working Group (CRL-WG) Lyon-Caen et al. [2004]; Bernard et al. [2006]; Lambotte et al. [2014]). A large number of active faults have been identified in
this area, and a consensus about their possible geometries and activity rates has been reached within the CRL-WG (Boiselet [2014]). We used this geologic information to test our modeling approach and explore different epistemic uncertainties in a logic tree. Finally, we compared the modeled earthquake rates of each fault with seismological and paleoseismological data in order to weight the hypothesis in the logic tree.

### 1.1.3 Novel methodology for taking faults into account in PSHA

In most regions of the world the amount of data available to model faults in a PSHA study is often sparse and uncertain. However, the need to consider such data in PSHA is increasing, and the methods to properly incorporate the available geological information in the hazard models are still missing. In this context, we propose building a methodology that allows considering all the available information on faults, allows setting rules to define FtF ruptures and considers single faults or FtF ruptures as an aleatory uncertainty.

Our iterative method allows converting the slip-rate budget of each individual fault rate of earthquakes by requiring that the resulting regional MFD of earthquakes in the whole fault system follows an imposed shape. The MFD shape of each individual fault will thus be a result of the iterative process and not an imposed parameter.

The proposed method is presented here in a nutshell and illustrated in figure 1.1.

1. The necessary input data include the following:

* A definition of the 3-D geometry of the fault system.

* An estimate of the geological slip rates of each individual fault that determines the slip-rate budget of the fault.

2. Setting up the methodology requires the following:

* Choosing suitable scaling laws to estimate the maximum magnitude each fault can host.

* Assuming the minimum magnitude of earthquakes possible on the faults (Mw 5.0 in this study).

* Hypothesizing FtF rupture scenarios based on some rules. In this study only a simple distance rule is used to define FtF ruptures. In future developments, more physics-based approaches could be explored. In the example presented in figure 1.1 a, the three faults (fault 1, fault 2 and fault 3) are considered to be sufficiently close to each other; thus, they can either rupture individually (F1, F2, F3) or in FtF ruptures (F1 + F2, F2 + F3 or F1 + F2 + F3).

* Imposing a shape for the target MFD for the whole fault system. In this study a GR MFD distribution is assumed.
<figure><img src="image_3.png" /><figcaption>**Figure 1.1:** Illustration of the methodology. (a) Set of FtF rupture scenarios. (b) Picking of the magnitude bins and of the sources. (c) Building the target MFD: the black curve is the target MFD anchored at the mean of the three highest magnitude bins (magnitude bin of 0.1). The sum of the resulting MFDs of the six sources has to be equal to the target MFD. (d) Visualization of the partitioning by the iterative methodology of each fault's slip-rate budget (colors correspond to the individual rupture or the FtF rupture; NMS is non-main-shock slip).</figcaption></figure>

3. Three pre-computational steps are performed to carry out the following:

* To calculate all possible magnitude bins each fault and FtF rupture scenario can accommodate according to each scaling law considered (figure 1.1b).

* To calculate the number of incremental quantities of slip rate (dsr) contained in each fault budget. In the
example, fault 1, fault 2 and fault 3 have a slip-rate budget of 5, 3.2 and 4 mm yr⁻¹ respectively (figure 1.1d). Therefore, considering a dsr size of 0.01 mm yr⁻¹, the faults budgets will be consumed after 500, 320 and 400 dsr respectively. The sliprate budget of each fault may be spent along individual faults and/or FtF rupture scenarios.

* To convert the target MFD, expressed in terms of rate of earthquakes, into moment rates (figure 1.1b). This target MFD will be used to pick the magnitude bin on which an increment dsr will be spent. Notice that the formulation in terms of moment rate implies that greater magnitudes are more likely to be picked.

4. Iterative process is described as follows:

* First, the bin of magnitude (of width 0.1) where a dsr will be spent is picked according to the target MFD for the whole fault system in terms of moment rate.

* Then, in this bin of magnitude $M_i$, a seismotectonic source $Si$ (an individual fault or an FtF scenario) that can host this magnitude is picked randomly. The increment of moment rate $d\dot{M}_0$ for this source is calculated following Eq. (1), and the rate of earthquakes increment dre is calculated using Eq. (2).

$$d\dot{M}_0 = \mu \cdot A \cdot dsr \qquad (1.1)$$

$$dr_e(M_i) = \frac{d\dot{M}_0}{M_0(M_i)}, \qquad (1.2)$$

where $d\dot{M}_0$ is the increment of moment rate for the source $Si$, $\mu$ the shear modulus of the fault, A the area of the source, dsr the increment of slip rate spent, $dr_e(M_i)$ the increment of the rate of magnitude $M_i$, and $M_0(M_i)$ the seismic moment of a moment magnitude $Mw$ defined by Hanks and Kanamori [1979]:

$$Mw = \frac{2}{3}\log(M_0) - 10.7. \qquad (1.3)$$

* At each iteration, the slip-rate budget of the faults participating in the scenario accommodating the earthquakes of the three highest magnitude bins (0.3 being the range of uncertainties in the scaling laws used to assess the maximum magnitude) is checked:

* If there is still a portion of the slip-rate budget to be spent, the dre calculated is added to the rate of earthquakes of magnitude $M_i$ for the source $Si$.

* If one of the faults of the FtF rupture generating the largest earthquake has exhausted its sliprate budget, the final rates of the highest magnitude earthquakes are reached. Then, knowing the shape of the imposed target MFD, the target rate at the fault system level for all magnitudes bins is known (figure 1.1c). At this stage, an additional check is performed:
* if adding the dre calculated for magnitude *M*ᵢ onto the source Si leads to the exceeding of the target MFD for this magnitude, then this dre is not added to the source Si and the increment dsr of this computation step is considered as NMS slip;

* if adding the dre to the source Si does not lead to the exceeding of the target MFD, this dre is added to the source Si.

* The increment of slip rate dsr is then removed from the slip-rate budget of the fault or the faults involved in source Si.

* If the slip-rate budget of each fault is exhausted, the fault and the corresponding FtF rupture scenarios the fault is involved in are removed and cannot be picked anymore in subsequent iterations of the computation.

* These steps are repeated until all the slip-rate budgets of all the faults in the system are spent either on single-fault ruptures, FtF ruptures or NMS slips.

The output of this process is an earthquake rupture rate for different magnitudes for each fault and FtF rupture scenario in the model, considered as aleatory uncertainty. We also record how the slip-rate budget of each fault is partitioned between the different FtF ruptures and how much NMS slip was needed on each fault in order to fit the target MFD shape (here GR MFD) with a given set of FtF rupture scenarios (figure 1.1d). In the example, fault 1 spends 43 % of its budget on single-fault ruptures (blue color), 7 % on F1 + F2 ruptures (dark green), 23 % on F1 + F2 + F3 ruptures (dark grey) and 27 % on the NMS slips (light grey). On the other hand, 100 % of the slip-rate budget of the slower moving fault (i.e., fault 2) is converted into earthquake rates (0 % NMS) and limits the rate of the largest magnitude earthquakes (F1 + F2 + F3) (see Annex 1).

A simplified example of the application of this methodology based on only two faults is presented in the Supplement to this paper (see Annex 1). This example illustrates step by step the way in which the proposed methodology allows the transformation of slip-rate budgets of faults into earthquake rates.

Post-processing then includes the following:

* Exploring the epistemic uncertainties: Many assumptions have to be made when setting up the methodology (scaling law, FtF rupture set, faults parameters, etc.), and the different possible hypothesis should be explored in a logic tree.

* Reality checks: The last step of the methodology involves comparing the modeled earthquake rates with independent data, such as the seismicity rates deduced from the catalog and paleoearthquake rates deduced from trench studies. Each branch of the logic tree is then weighted according to its performance with these independent data.
In this study, we applied the proposed methodology to a well-documented rifting zone in the Aegean Sea (figure 1.2).

### 1.1.4 Application to the western Corinth rift fault system

The east-west striking Corinth rift is the most seismically active structure in Europe with several earthquakes larger than Mw 5.5 recorded in the historical times as well as in the instrumental period (e.g., Jackson et al. [1982]; Papazachos and Papazachou [2003]; Makropoulos et al. [2012]). The Corinth Rift Laboratory was set up in 2001 in the western and most seismically active part of the rift (Lyon-Caen et al. [2004]) with the goals of understanding the rifting process and providing key elements for the seismic hazard assessment of the region.

The geodetical deformation measured by Global Positioning System (GPS) shows a highly localized opening of the Corinth rift at a rate of 10 mm yr⁻¹ in the east and 15 mm yr⁻¹ in the west (Avallone et al. [2004]) over a width of less than 20 km, inducing a high strain rate. This deformation is accommodated by a complex network of both north- and south-dipping normal faults. Geological studies of these faults have shown that the north-dipping faults located on the southern coast have a higher slip rate than the south-dipping northern faults, giving the rift its asymmetrical structure. In the south, the Peloponnese is uplifted by the activity of these faults (Armijo et al. [1996]; Ford et al. [2013]), and in the north the coast line is subsiding.

The western Corinth rift fault slip rates were inferred from the displacement of geologic markers in the field or from seismic profiles on each individual fault, with the exception of the two blind faults identified by their recent seismic activity (1995 fault, Bernard et al. [1997] and Pyrgos fault, Sokos et al. [2012]) and for which the microseismicity recorded close to the fault was transformed into the slip rate on the fault plane. These latter slip rates are therefore subject to a very large uncertainty. The estimated geological extension rate expressed by the sum of the horizontal projection of the geological slip rates of the faults is in the range of 3 to 6 mm per year, which is three times less than the geodetical extension rate. Given this disagreement, the WCR is a good candidate to test whether the earthquake rates calculated using our methodology, which relies only on geological information, can account for the occurrence of the large earthquakes that have been documented in the region (Albini et al. [2017]).

The WCR fault system has been described in detail by Boiselet [2014], who defined a model for the fault system, including geometries and slip rates for each fault (figure 1.2, table 1.1) and a set of possible FtF ruptures (hereafter model B14). The B14 model proposes a set of FtF rupture scenarios (table 1.2) assuming that two neighboring faults can make up an FtF scenario only if they are less than 3 km apart. In this paper, we also explore a logic tree branch for an alternative rupture set (see figure 1.3) with higher fault connectivity (B14_hc), where faults can break together if their fault traces are separated by 5 km or less, therefore allowing a wider spectrum of possible FtF rupture
<table><caption>Table 1.1: Fault characteristics in Boiselet [2014]. Mmax values calculated using the equations for normal faults using the rupture area. WC94 refers to Wells and Coppersmith [1994] and Le10 to Leonard [2010] scaling laws.</caption><thead><tr><th rowspan="2">Fault name</th><th rowspan="2">ID</th><th rowspan="2">Length (km)</th><th rowspan="2">dip</th><th colspan="2">Seismogenic depth (km)</th><th colspan="2">Slip rate mm.yr<sup>-1</sup></th><th colspan="2">Mmax</th><th rowspan="2">Time-frame of the data</th></tr><tr><th>Upper</th><th>Lower</th><th>Min</th><th>Mean</th><th>Max</th><th>WC94</th><th>Le10</th></tr></thead><tbody><tr><td>Psathopyrgos fault</td><td>f1</td><td>8.5</td><td>60</td><td>0</td><td>6</td><td>4.6</td><td>5</td><td>5.5</td><td>5.8</td><td>5.7</td><td>2 kyr</td></tr><tr><td>Neos Erineos fault</td><td>f2</td><td>11.4</td><td>55</td><td>0</td><td>7</td><td>2.3</td><td>3.2</td><td>4.1</td><td>6.0</td><td>5.9</td><td>3-4 kyr</td></tr><tr><td>Aigion fault</td><td>f3</td><td>8.6</td><td>60</td><td>0</td><td>7</td><td>3.5</td><td>4</td><td>4.6</td><td>5.8</td><td>5.8</td><td>50-60 kyr</td></tr><tr><td>East Helike fault</td><td>f4</td><td>14.5</td><td>55</td><td>0</td><td>7</td><td>3</td><td>3.5</td><td>4</td><td>6.1</td><td>6.0</td><td>10-12 kyr</td></tr><tr><td>West Helike fault</td><td>f5</td><td>11.2</td><td>55</td><td>0</td><td>7</td><td>0.5</td><td>0.9</td><td>1.4</td><td>6.0</td><td>5.9</td><td>800 kyr</td></tr><tr><td>Trizonia fault</td><td>f6</td><td>10.6</td><td>65</td><td>0</td><td>7</td><td>1.3</td><td>1.4</td><td>1.5</td><td>5.9</td><td>6.0</td><td>800 kyr</td></tr><tr><td>West Channel fault</td><td>f7</td><td>10.8</td><td>45</td><td>0</td><td>2.5</td><td>0.4</td><td>0.45</td><td>0.5</td><td>5.6</td><td>5.5</td><td>240-400 kyr</td></tr><tr><td>South Eratini fault</td><td>f8</td><td>12</td><td>45</td><td>0</td><td>6.5</td><td>0.6</td><td>1</td><td>1.4</td><td>6.0</td><td>6.0</td><td>800 kyr</td></tr><tr><td>East Channel fault</td><td>f9</td><td>22</td><td>45</td><td>0</td><td>4.5</td><td>1</td><td>1.4</td><td>1.8</td><td>5.7</td><td>5.7</td><td>1500 kyr</td></tr><tr><td>North Eratini fault</td><td>f10</td><td>11.5</td><td>60</td><td>0</td><td>6</td><td>2.4</td><td>4</td><td>5.6</td><td>5.9</td><td>5.8</td><td>12 kyr</td></tr><tr><td>Marathias fault</td><td>f11</td><td>17.4</td><td>60</td><td>0</td><td>6.5</td><td>1.39</td><td>1.4</td><td>1.41</td><td>6.1</td><td>6.0</td><td>400 kyr</td></tr><tr><td>1995 fault</td><td>f12</td><td>14</td><td>35</td><td>8</td><td>12</td><td>0.5</td><td>3.2</td><td>7</td><td>6.0</td><td>6.0</td><td>5 yr</td></tr><tr><td>Pyrgos fault</td><td>f13</td><td>11</td><td>35</td><td>6</td><td>11</td><td>0.5</td><td>3.2</td><td>7</td><td>6.1</td><td>6.0</td><td>5 yr</td></tr></tbody></table>
<figure><img src="image_4.png" /></figure>

**Figure 1.2:** Map of the active faults of the western part of the Corinth rift (modified from Boiselet [2014]). The orange polygons are the surface projection of the active faults. The yellow polygons are the surface projection of the blind faults (Pyrgos fault and 1995 fault). Earthquakes of the catalog during the complete period are represented by circles with color and size depending on the magnitude. The date and magnitude of earthquake are indicated. The minimum and maximum values (mm yr⁻¹) of the slip rates of the faults are indicated in the white boxes. The green arrow shows an approximation of the rift extension calculated by projecting horizontally the faults' slip rate, and the pink arrow shows the extensional rate of the rift measured by GPS.

scenarios (additional scenarios in bold in table 1.2). For a comparison with classical fault PSHA studies, we explore a branch with only a simple fault rupture called B14_s. In this branch no FtF rupture is allowed.

<figure><img src="image_5.png" /><figcaption>**Figure 1.3:** Logic tree explored for this study.</figcaption></figure>

The target MFD is chosen to be in the shape of a GR MFD with a b value of 1.15 ± 0.05, which is a typical value for extensional systems (Schorlemmer et al. [2005]).

In this study we explore other epistemic uncertainties having a potential impact on the modeled earthquake
<table><caption>Table 1.2: Rupture scenarios considered in each model. Branch B14_s considers only the single-fault ruptures. Branch B14 considers the single-fault ruptures and the FtF ruptures with a 3 km distance criteria. Branch B14_hc considers the single-fault ruptures and the FtF ruptures with a 3 and a 5 km distance criteria. Mmax values are calculated using the equations for normal faults based on the rupture area. WC94: Wells and Coppersmith [1994]; Le10: Leonard [2010]</caption><thead><tr><th rowspan="2">FtF sets</th><th colspan="2">Faults involved in the scenario</th><th colspan="2">Mmax</th></tr><tr><th></th><th></th><th>WC94</th><th>Le10</th></tr></thead><tbody><tr><td colspan="2">B14, B14_hc, B14_s</td><td>All the single-fault ruptures</td><td colspan="2">see table 1.1</td></tr><tr><td>3 km</td><td>f3</td><td>f2</td><td>6.2</td><td>6.2</td></tr><tr><td>distance</td><td>f3</td><td>f2</td><td>6.4</td><td>6.2</td></tr><tr><td>criteria</td><td>f2</td><td>f1</td><td>6.2</td><td>6.0</td></tr><tr><td></td><td>f4</td><td>f5</td><td>6.2</td><td>6.0</td></tr><tr><td>B14</td><td>f1</td><td>f13</td><td>6.2</td><td>6.2</td></tr><tr><td>B14_hc</td><td>f4</td><td>f12</td><td>6.4</td><td>6.2</td></tr><tr><td></td><td>f4</td><td>f8</td><td>6.4</td><td>6.2</td></tr><tr><td></td><td>f4</td><td>f8</td><td>6.5</td><td>6.4</td></tr><tr><td></td><td>f4</td><td>f8</td><td>6.5</td><td>6.4</td></tr><tr><td></td><td>f8</td><td>f9</td><td>6.2</td><td>6.0</td></tr><tr><td>5 km</td><td>f11</td><td>f6</td><td>6.3</td><td>6.3</td></tr><tr><td>distance</td><td>f11</td><td>f6</td><td>6.4</td><td>6.5</td></tr><tr><td>criteria</td><td>f11</td><td>f6</td><td>6.5</td><td>6.5</td></tr><tr><td></td><td>f11</td><td>f6</td><td>6.6</td><td>6.5</td></tr><tr><td>B14_hc</td><td>f3</td><td>f5</td><td>6.2</td><td>6.2</td></tr><tr><td></td><td>f3</td><td>f7</td><td>5.8</td><td>5.8</td></tr><tr><td></td><td>f3</td><td>f9</td><td>6.2</td><td>6.1</td></tr><tr><td></td><td>f3</td><td>f8</td><td>6.4</td><td>6.5</td></tr><tr><td></td><td>f3</td><td>f4</td><td>6.5</td><td>6.6</td></tr><tr><td></td><td>f4</td><td>f7</td><td>6.2</td><td>6.2</td></tr><tr><td></td><td>f4</td><td>f8</td><td>6.4</td><td>6.5</td></tr><tr><td></td><td>f4</td><td>f8</td><td>6.5</td><td>6.5</td></tr><tr><td></td><td>f8</td><td>f10</td><td>6.3</td><td>6.3</td></tr><tr><td></td><td>f3</td><td>f6</td><td>6.5</td><td>6.5</td></tr><tr><td></td><td>f3</td><td>f6</td><td>6.5</td><td>6.5</td></tr><tr><td></td><td>f3</td><td>f12</td><td>6.2</td><td>6.3</td></tr><tr><td></td><td>f3</td><td>f4</td><td>6.3</td><td>6.3</td></tr><tr><td></td><td>f8</td><td>f9</td><td>6.3</td><td>6.2</td></tr><tr><td></td><td>f3</td><td>f4</td><td>6.6</td><td>6.7</td></tr></tbody></table>
rates (figure 1.3) in addition to the different FtF rupture sets previously described; two scaling laws (Wells and Coppersmith [1994]; Leonard [2010]) have been used to calculate the maximum magnitude based on rupture area for normal faults, and two values of the shear modulus *μ* have been used: 30 GPa, a commonly used value in hazard studies, and 20 GPa to represent the low-shear wave velocity in the WCR region recently estimated based on ambient noise tomography (Giannopoulos et al. [2017]). For each branch, 20 random samples are drawn from triangular distributions in order to explore the epistemic uncertainty affecting the *b* value of the target MFD (1.15 ± 0.05), the slip rate of the faults and the uncertainty within the scaling law.

### 1.1.5 Modeled earthquake rupture rates and comparison with independent data

Using our method, the modeled rate of earthquakes for the WCR is then compared to the rate of earthquakes observed in the catalog. The seismicity catalog considered in this study (figure 1.3) is the SHEEC catalog (Stucchi et al. [2013]; Grünthal et al. [2013]) developed in the framework of the SHARE project updated for six historical earthquakes (Albini et al. [2017]) and three instrumental earthquakes (based on Baker et al. [1997]; and P. Bernard from the 3HAZ Corinth project, personal communication, 2017). The updates and their implication on the catalog are summarized in table 1.3. We propagate the earthquake magnitude uncertainties in the estimate of seismic moment rate and earthquake rate calculations by randomly sampling the magnitude of each earthquake within their uncertainties (Stucchi et al. [2013]; Albini et al. [2017]) and by using two hypotheses of completeness. In table 1.4 the time of completeness of the catalog for Greece calculated by the SHARE project (Stucchi et al. [2013]) and the times calculated by Boiselet [2014] using the approach proposed by Stepp [1972] at the scale of the Corinth rift region are reported.

A first reality check is performed to compare the modeled and the catalog seismological moment rates. The seismological moment rate is calculated directly using the rates of earthquake of each magnitude in the catalog based on the moment magnitude relation (Eq. 3) The seismic moment rates in models B14 and B14 are in good agreement with the seismic moment rate deduced from the catalog, whereas B14_s predicts a higher seismic moment rate (figure 1.4a). This comparison provides a better confidence in the models where FtF ruptures are possible than in the B14_s model. In the single rupture model (B14_s), 90 % to nearly 100 % of the geological slip rate is converted into seismic moment rate with only less than 10 % interpreted as NMS slip rate. On the other hand, when FtF ruptures are possible (B14 and B14 Editorial), 25 % of the geological slip-rate budget of the faults is interpreted as NMS slip (figure 1.4b).

A second reality check consists in comparing modeled and catalog MFDs (figure 1.4c). The B14_s model does not manage to reproduce the rate of earthquakes deduced from the catalog, as it predicts a higher rate of Mw 5 earthquakes and no earthquakes of Mw 6.3 and above. On the other hand, we observe a good agreement of the MFDs of models B14 and B14 Editorial with the catalog. B14 reproduces the cumulative earthquake rate for Mw of 5.6 to 6.1 well, whereas model B14 Editorial reproduces the cumulative rate of earthquakes of Mw 5.0 to 5.5 better.
<table><caption>Table 1.3: Earthquakes updated in the historical and instrumental catalogs of the western Corinth rift.</caption><thead><tr><th>Date</th><th>Type of update</th><th>Old parameters</th><th>New parameters</th><th>Special implication for the catalog</th></tr></thead><tbody><tr><td>14 May 1748</td><td>Magnitude</td><td>Mw = 6.4 ± 0.25</td><td>Mw = 5.9 (5.4–5.9)</td><td>Not in the complete period for this range of magnitudes</td></tr><tr><td>23 Aug 1817</td><td>Magnitude</td><td>Mw = 6.6 ± 0.25</td><td>Mw = 6.5 (6.0–6.5)</td><td></td></tr><tr><td>26 Dec 1861</td><td>Location</td><td>(38.22, 22.139)</td><td>(38.28, 22.24)</td><td>Not associated with Aigion fault</td></tr><tr><td>9 Sep 1888</td><td>Magnitude</td><td>Mw = 6.3 ± 0.4</td><td>Mw = 6.2 (5.7–6.2)</td><td></td></tr><tr><td>25 Aug 1889</td><td>Location and magnitude</td><td>(38.25, 22.08)<br>Mw=6.24 ± 0.25</td><td>(38.50, 21.33)<br>Mw=6.4 (6.4–6.6)</td><td>Earthquake outside the WCR</td></tr><tr><td>3 Mar 1965</td><td>Depth and magnitude</td><td>Depth = 10 km<br>Mw = 6.5</td><td>Depth = 55 km<br>Mw = 6.8</td><td>Earthquake associated with the subduction zone, not with the WCR fault system</td></tr><tr><td>15 Jun 1995</td><td>Location and magnitude</td><td>(38.37, 22.15)<br>Mw=5.8</td><td>(38.36, 22.20)<br>Mw=6.3</td><td></td></tr><tr><td>5 Nov 1997</td><td>Location</td><td>(22.28, 38.41)</td><td>(22.28, 38.36)</td><td></td></tr></tbody></table>

<table><caption>Table 1.4: Completeness hypotheses explored in this study.</caption><thead><tr><th colspan="2">SHARE project Woessner et al. [2015]</th><th colspan="2">Boiselet [2014]</th></tr><tr><th>Magnitude range</th><th>Date of completeness</th><th>Magnitude range</th><th>Date of completeness</th></tr></thead><tbody><tr><td>4.1–5.1</td><td>1970</td><td>5.0–5.4</td><td>1958</td></tr><tr><td>5.1–5.7</td><td>1900</td><td>5.5–6.0</td><td>1904</td></tr><tr><td>5.7–6.5</td><td>1650</td><td>6.0–6.5</td><td>1725</td></tr><tr><td>≥ 6.5</td><td>1450</td><td>6.5–7.0</td><td>1725</td></tr></tbody></table>
<figure><img src="image_6.png" /></figure>

**Figure 1.4:** Modeled seismicity for the WCR fault network and comparison to the seismicity rate based on the earthquake catalog of the complete period. (a) Comparison between the modeled moment rates for each FtF scenario set and the seismological rate calculated from the earthquake catalog. Each box represents the SD around a mean and median value represented by a red square and a red line respectively. From left to right: the three first boxes are for each hypothesis scenario set in the logic tree, the fourth box shows the moment rate assuming 100 % of the slip rate of faults is converted into seismic moment, and the fifth box shows the moment rate calculated from the earthquake catalog. (b) Distribution of the ratio of NMS slip resulting from the three deformation models. (c) Comparison between the modeled GR MFD deduced from geological data for the whole fault system and that deduced from the WCR catalog. The models are represented as a colored density function with the red colors for the rates predicted by the higher number of models. The cumulative rates calculated from the catalog are shown as a grey density function. The cumulative number of earthquakes in the catalog is indicated by black bars in the central figure.
Slip-rate budget repartition

The way the slip-rate budget is spent between FtF ruptures, single-fault ruptures and the NMS slip ratio of the fault depends on the slip rate of the fault and the FtF ruptures the fault is involved in. Slow slipping faults that are involved in large FtF rupture scenarios (Neos Erineos or West Helike) have the majority of their slip-rate budget consumed by these large FtF ruptures (figure 1.5). On the contrary, the fast slipping faults that are involved in few FtF ruptures scenarios (1995, Pyrgos, North Eratini) spend their budget predominantly on single-fault ruptures producing a high number of small to medium magnitude earthquakes, which leads to easily exceeding the GR regional target and thus implies a higher proportion of NMS slip rate on these faults.

<figure><img src="image_7.png" /><figcaption>**Figure 1.5:** Visualization of the way the slip-rate budget of each fault is spent. The color depends on the number of faults involved in the FtF rupture. Minimum and maximum values of the slip rate on each fault is shown in brackets in mm yr⁻¹.</figcaption></figure>

Models B14 and B14 HC have a similar mean 25 % ratio of NMS slip ratio (figure 1.4), but this ratio is not distributed in the same way between the different faults in each model. However, an important NMS proportion on the blind faults (Pyrgos and 1995-fault) and the offshore North Eratini fault is found for both models. There are three main factors that can induce this result: either the FtF sets are not realistic, the slip rates explored on those faults are not realistic and do not include enough complex ruptures with these faults, or there is a mechanism of NMS slip such as creep or slow slip events happening on these faults.
Earthquake rupture rate on the Aigion fault

We now choose to focus our interest on the Aigion fault. Since this fault is one of the most active faults of the WCR and crosses the city of Aigion, it represents a major source of seismic hazard and risk for the region.

The earthquake rate modeled on the Aigion fault depends of the FtF rupture set allowed in the model (figure 1.6). The resulting MFD of the Aigion fault has the shape of a GR MFD for model B14 and B14_s, with a steeper slope for the B14_s model. In the B14_hc, the MFD computed for the Aigion fault resembles a characteristic earthquake distribution of magnitude close to Mw 6.0, similar to the maximum magnitude of earthquakes rupturing only the Aigion fault. It is worth noting that the larger magnitude earthquakes in figure 1.6b and c involve not only the Aigion fault but also the neighboring faults participating in the FtF ruptures (figure 1.5, table 1.2).

Using the paleoseismological data presented by Pantosti et al. [2004], it is possible to propose rates of large magnitude earthquakes on the Aigion fault (figure 1.6). This paleorate (rate of paleoearthquakes) is subject to large uncertainties but can be used to validate or invalidate the different FtF rupture set hypothesis. In the B14_s model where faults only break on their own, the Aigion fault is not able to accommodate the paleoearthquake magnitudes. In the B14 model, where fault rupture is only allowed between faults separated by 3 km or less, the modeled earthquake rates are lower than the rates inferred from the paleoseismological study. In the B14_hc model, where FtF ruptures are allowed for faults separated by 5 km or less, the modeled earthquake rates agree well with the paleorate, within the margin of uncertainty.

<figure><img src="image_8.png" /><figcaption>**Figure 1.6:** Rate of earthquakes occurring on the Aigion fault for each FtF rupture set. Variability resulting from the exploration of the logic tree is illustrated by the blue boxes. The annual rates of Mw ≥ 6 earthquakes on Aigion fault are indicated for the B14 and B14_hc models. The grey square represents the paleorate (rate of paleoearthquakes) interpreted from Pantosti et al. [2004] with its uncertainties. The green box represents the rate of earthquakes greater than Mw 6 on the Aigion fault inferred from the historical catalog.</figcaption></figure>

According to the recent reappraisal of the historical seismicity (Albini et al. [2017]), the Aigion fault is most
likely the source of the 1817 Mw 6.5 (6.0–6.5) and the 1888 Mw 6.2 (5.7–6.2) earthquakes. This leads to estimates of annual rates of Mw > 6 earthquakes on the Aigion fault of 0.005 to 0.007 (figure 1.6) depending on the date of completeness of the catalog used (table 1.4). The model B14_s does not manage to reproduce the great magnitudes earthquakes observed in the catalog. The annual rates for earthquakes Mw > 6 of 0.0034 and 0.0051 predicted by models B14 and B14_hc respectively are statistically compatible with the rate inferred from the catalog.

### Weighting the logic tree branches

The comparison with independent local data allows suggesting weights for the different FtF rupture set hypothesis (figure 1.3) for hazard calculation.

The B14_s branch, where faults can only rupture independently, fits neither the annual moment rate nor the earthquake rate of the catalog of the region, nor the paleoearthquake magnitude on the Aigion fault (figure 1.4 and figure 1.6). We conclude that this branch should not be used for a hazard calculation in the western Corinth rift.

Between the two branches where FtF ruptures are possible, B14_hc manages to match the earthquake rates of the catalog for a range of magnitudes where statistics are stronger (14 earthquakes Mw 5.0 and above) compared to the B14 model (matching only 4 earthquakes of Mw 6.0 and above in the catalog) (figure 1.4). The B14_hc branch matches the Aigion fault earthquake rates inferred from the paleoseismology and the historical catalog better than the B14 model (figure 1.6). The agreement with the earthquake rate in the regional catalog and the better reproduction of the Aigion fault data of the B14_hc model lead us to propose a stronger weight for this model compared to the B14 model for the estimate of hazard for Aigion city.

### 1.1.6 Conclusion and perspectives

The methodology presented in this study uses a system-level approach rather than an individual-fault-level approach to estimate the rate of earthquakes on faults based on the geological data collected for each fault and allowing FtF rupture in the hazard model as an aleatory uncertainty. The application of the methodology to the WCR fault network shows that, in order to match a GR MFD for the whole fault system, part of the fault slip rates have to be spent as a non-main-shock slip. The way the fault slip rate is partitioned among single or FtF ruptures and the resulting shape of the individual fault MFD depends on the location of the fault in the network and the fault's characteristics. The earthquake rates modeled using the geological data on the faults are compared with the local earthquake catalog and paleoseismic data in order to weight the different epistemic hypothesis. In the case of the WCR, and for future seismic hazard assessment for the city of Aigion, these reality checks suggest attributing a stronger weight to the branch allowing FtF ruptures between faults with the 5 km distance criteria (B14_hc), a lower weight to that based on the 3
km criteria (B14) and a null weight to the model where only single-fault ruptures are allowed (B14_s).

The fault network used for the application concerns only the western part of the Corinth rift fault network. Integrating the rest of the network in the model could modify the final outcome and should be explored in future developments.

More reality checks will be implemented in the future in order to weight the different uncertainties of the logic tree based on the results of the ongoing microseismicity studies in the WCR (i.e., use the possible presence of repeater earthquakes on the Aigion fault to validate NMS slip ratio, Duverger et al. [2015]).

The methodology presented in this article can be applied to other fault systems in different tectonic environments. In order to implement this approach, the geometries and slip rates of the faults have to be known within uncertainties, FtF rupture scenarios sets have to be defined, and the shape of the regional MFD needs to be assumed or inferred from the regional catalog. If for the WCR the GR distribution seems suitable, it has been shown that a Youngs and Coppersmith distribution (Youngs and Coppersmith [1985]) can be more appropriate for other fault systems (e.g., by Hecker et al. [2013]). Given the flexibility of our methodology any other target MFD can be easily implemented in the methodology.

The earthquake rupture rate calculated using this methodology is very sensitive to the choice of possible FtF rupture scenarios. The comparison with the earthquake catalog and local data, such as the paleoseismological data, can provide guidance to the strength of each hypothesis. Nevertheless, the choice based on distance between faults should be supported by more physical approaches in the future such as Coulomb stress modeling (Toda et al. [2005]) and/or dynamic modeling of ruptures (Durand et al. [2016]).

The methodology at this stage does not consider the background seismicity. The example of the dense WCR fault system allowed setting aside this issue in order to test our methodology and focus on the FtF ruptures. Future developments of the methodology need to allow part of the modeled seismicity rate to be in the background. If performing hazard calculation for a region wider than the fault system itself, it is necessary to combine the models built with this methodology with classical area sources.
The following section is an article (Chartier et al. [2019]) presenting the evolution of the methodology since Chartier et al. [2017b] and the code (SHERIFS) that applies the methodology. The aim of this following article is to be a support for a user of the code, explaining in detail the algorithm rather than focusing on a specific application.
## 1.2 SHERIFS – Open-Source Code for Computing Earthquake Rates in Fault Systems and Constructing Hazard Models

### 1.2.1 Abstract

Modelling the seismic potential of active faults and their associated epistemic uncertainties is a fundamental step of probabilistic seismic hazard assessment (PSHA). SHERIFS (Seismic Hazard and Earthquake Rate In Fault Systems) is an open-source python code that builds hazard models including earthquake ruptures involving several fault sections or Fault-to-Fault (FtF) ruptures. It contains user-friendly tools to calculate the annual rate of FtF ruptures in a fault system based on the slip rate estimates and accounting for associated background seismicity.

SHERIFS applies a forward incremental approach following three rules: (1) the FtF ruptures allowed in the fault system are defined as input by the user and explored randomly, (2) the magnitude frequency distribution (MFD) of the modelled seismicity in the fault system must follow an imposed shape, (3) the slip-rate budget attributed to each fault section must be preserved in the calculation if the first two rules allow it. Indeed, in some cases, a fraction of the slip rate budget must be considered as being spent in Non-Main-Shock events (NMS) such as creep or post-seismic slip. Background seismicity rates are defined by the hazard modeler as the ratio of on-fault/off-fault seismicity for different ranges of magnitude.

Given a coherent set of input hypotheses, SHERIFS allows end-users to build the seismic hazard fault model thanks to an interactive user-friendly interface. It aims to help interactions between field data collectors and hazard modelers to explore and weight epistemic uncertainties affecting the input hypotheses. To do so, SHERIFS includes tools to compare modeled earthquake rates to the available local data (earthquake catalog and paleoseismological data). This comparison can be used to weigh different hypotheses explored in a logic tree and discard the hypotheses that are not in agreement with the data. SHERIFS's outputs are in a format that can be used directly as inputs for PSHA in the OpenQuake Engine (Pagani et al. [2014]).

### 1.2.2 Introduction

Developing a hazard model for a region where active faults have been described requires to convert the geological and geophysical data into 3D fault geometries and slip rates and then into earthquake rates. Most commonly seismic hazard modelers have to develop their own approach to manage the available data. Each modeler has a different approach for translating slip rates into earthquake rates on faults which sometimes does not allow a straightforward understanding of the resulting hazard model. Some assumptions have to be made when building a hazard model and, in the ideal case, the data collectors are involved in the modeling process to insure the working hypotheses are acceptable.
In order to help data collectors build hazard models, some tools are available (FiSH, OpenQuake toolkits). The FiSH (Pace et al. [2016]) modeling approach provides estimates of earthquake rates and time dependent probability of earthquakes in the period of interest for the hazard assessment using the data available on a fault. This MATLAB code can easily be operated by a user with limited coding skills. FiSH can be used to explore a range of epistemic uncertainties affecting the earthquake rates of the modeled fault. Since the approach in FiSH focuses on one fault only, multi-fault ruptures can only be modeled by considering average parameters for the whole structure. The OpenQuake toolkits allow building hazard models using as input shapefiles containing information on the faults but considering as well a fault by fault approach and not a fault system approach.

Thus, in most hazard models (e.g. Woessner et al. [2015]; TEM Wang et al. [2016]), small faults are usually grouped into large structures in order to allow for larger magnitude earthquakes. Moreover, background earthquakes are handled using a truncated approach in which earthquakes with a magnitude lower or equal to M6.4 occur only in the background zone with a rate defined by the rate in the earthquake catalog whereas magnitudes higher than M 6.4 are located on the faults with a rate defined using the average slip-rate of the fault. This approach allows integrating faults within area zones while avoiding double counting. However, it can lead to discontinuities in the regional MFD since the rate of low magnitude earthquakes and the rate of high magnitude earthquakes are calculated from different sources of information (Danciu et al. [2018]). Last but not least, magnitudes stronger than M6.4 may potentially occur in the background as well, especially in regions of slow tectonic deformation and in the presence of concealed faults (e.g. Dartfield earthquake, Hornblow et al. [2014]).

It has been known for a long time that several fault sections of a fault or of several faults can rupture during a single FtF rupture event (e.g. Knuepfer [1989], Barka and Kadinsky-Cade [1988] and Wesnousky [1988]). It is therefore paramount to have modelling procedures that allow a large set of possible FtF ruptures to occur in an aleatory fashion in the hazard model while reflecting the individual slip-rate of each section.

The Californian model UCERF3 (Field et al. [2014]) tackles this issue and allows FtF ruptures to occur in the model by relaxing the segmentation assumption and treating the problem at the faults system level. The annual rate of FtF ruptures is inverted in a “Grand Inversion” process considering the large amount of data available in California. UCERF-3 allows all possible ruptures in the fault system that follow a set of plausibility rules. The individual slip-rates of each section, the earthquake rates at the level of California and at the level of the paleo-seismic sites are some of the constraints used to invert for the rate of each rupture. This model also allows small earthquakes to happen on faults and large earthquakes to happen in the area sources by defining off-fault seismicity without appealing to the artificially truncated distribution commonly used.

In this paper we propose an alternative approach to calculate the earthquake rates in a fault system that preserves the main philosophy of UCERF-3. The aim of the proposed approach, named SHERIFS (Seismic Hazard
and Earthquake Rates In Fault Systems), is to provide a user-friendly tool with a graphical interface that allows data collectors and fault modelers to build hazard models in a forward processing scheme with an exploration of the epistemic uncertainties. The approach consists in the conversion of the slip-rate budget of each fault of the system into rupture rates for all possible single fault and FtF ruptures. SHERIFS relies on a forward modeling incremental method with a simple lay out of the assumptions about the input model which leads to an easy construction of the logic tree. The only required input data are an estimate of the geometry and slip-rate of the modeled faults.

The theoretical background of the methodology is presented in Chartier et al. (2017).

In this paper we present how this methodology has been implemented in SHERIFS, an open source tool coded in the Python language. The objective of SHERIFS is not only to provide the optimal hazard model but rather to allow the exploration of a large range of epistemic uncertainties and we recommend using it as such. By providing an easy-to-use tool for modeling faults in hazard models, we wish to promote discussions and feedbacks between data-providers and hazard modelers, one of the main objectives of the Fault2SHA ESC working group (https://Fault2SHA.net/). SHERIFS includes a set of tools allowing to compare the modelled earthquake rates to the local earthquake catalog or paleoseismological data and to discuss the different input hypotheses. Thus, SHERIFS can be useful not only to hazard modelers but also to geologists as a means to test the coherency of the rupture hypotheses that best describe the seismic potential of a fault system.

This tool creates hazard models for fault systems that can be used as inputs for OpenQuake (Pagani et al. [2014]) but since most PSHA computing codes use similar entries, the output of SHERIFS could easily be adapted to provide inputs for other codes as well (e.g. OpenSHA, Field et al. [2003]; CRISIS, Ordaz et al. [2017])

### 1.2.3 General methodology applied in SHERIFS

The SHERIFS code allows end-users to build the fault model thanks to an interactive user-friendly interface. The logic tree structure and the input files can be easily modified for a re-run if different parameters need to be tested.

This section of the article synthesizes the main steps of the methodology implemented in SHERIFS as presented in Chartier et al. [2017b]. This methodology requires as input data fault section geometries and slip-rate estimates for all the faults of the fault system in order to calculate the earthquake rupture rates.

The SHERIFS iterative methodology requires first establishing possible FtF earthquake rupture scenarios in the fault system and fixing the shape of the target MFD for the entire fault system. At each iteration, a magnitude is randomly picked based on the target MFD and an earthquake rupture scenario able to host such magnitude is selected. For this scenario, an increment of the slip-rate budget of the involved faults is converted into earthquake rupture rate
for the considered magnitude. At the beginning of the iterative process, the absolute value of the target MFD is not
known, only the shape is imposed. In SHERIFS we explore different criteria to set the MFD target value that are
detailed below. The iterative computation continues until the slip-rate budget of the faults is exhausted.

Required information and input working hypotheses

At first, the limits of the fault system have to be set. If the specific extent of the fault system is clearly limited in the field, we suggest using the enclosing boundary. In some applications, the fault system can be much larger than the area of interest for the hazard study. In such a case, the part of the system considered should be large enough to make sure that an extension of the system would not affect the rupture rates inside the zone of interest. If the fault network of a region is composed of distinctive sub-regions where it is believed that no rupture can go through, we suggest treating them as different fault systems.

Within the defined fault system, the geometry (trace, dip, and upper and lower seismogenic depth), the slip-rate (with uncertainties) and the kinematics (normal, strike-slip, reverse or the rake) of the fault sections must be provided. For partly creeping faults, we suggest the user to correct the geological/geodetic slip-rate input to reflect the “seismic” slip-rate that should be considered in SHERIFS. Alternatively, the shear modulus and/or the geometry of the creeping sections can also be adapted in order to model only the locked part of the fault.

We suggest defining typical lengths of fault sections to be on the order of the seismogenic depth. Faults with a
longer length should be cut in smaller sections (that can rupture together). The sections should be defined as small as
necessary in order to account for local information. For example, a change in slip-rate, rake or dip should be considered
for defining the sections. The SHERIFS approach is based on the assumption that the seismicity of the fault system
taken as a whole follows the shape of a known MFD (i.e. Gutenberg and Richter [1944] hereafter GR or Youngs and
Coppersmith [1985], hereafter YC). If the local seismicity data doesn't show clearly a distinct shape, SHERIFS allows
the user to explore several hypotheses in a logic tree.

a) **Hypothesis on the FtF ruptures**
One of the most important working hypothesis of the SHERIFS methodology concerns the definition of possible FtF ruptures allowed in a given fault system. SHERIFS doesn't impose the way to choose the set of FtF ruptures, and only requires a list. The user is free to use rules (as done in UCERF3) or rely on physical simulations to define possible FtF ruptures. As the rules to define FtF ruptures are subject to discussion (i.e. Schwartz [2018]), SHERIFS allows to explore different sets of possible FtF ruptures.

In order to implement in SHERIFS single and FtF ruptures following the OpenQuake formalism, a single fault rupture is defined in the input files with either the “simple” or “complex fault” typology, depending on the user’s choice,
and can host magnitudes starting from the minimal magnitude up to the maximum magnitude that the single fault can
accommodate (scaling law- dependent value). The “simple fault” typology is defined by the fault trace, the dip and
the upper and lower seismogenic depth and the “complex fault” typology allows more details in the fault geometry
such as listricity or seismogenic depth variable along strike. A FtF rupture, on the other hand, is defined with the
“characteristic fault source” typology, hosting only the greater magnitudes activating the entire fault surface included in
the FtF rupture.

**b) Sampling the model space of uncertainties** The slip rate of the faults, the magnitude scaling parameters and the b value are usually associated with important uncertainties. In SHERIFS, uncertainty bounds are considered and explored based on the user-defined number of random samples. For each branch of the logic tree, SHERIFS will create a number of models equal to the number of random samples. For each model, a slip-rate value is picked uniformly within the uncertainty bounds of the slip-rate attributed to each fault, the parameters of the scaling law are picked independently following a Gaussian distribution within their error bounds; and a b-value is picked within the box-car range of b-values considered by the user. The first sample provided in the output file (model number 1) is always the mean value of the slip-rate, scaling law and b-value parameters.

In order to explore slip-rate value uncertainties of neighboring sections, the user can choose between a
"correlated" or "random" sampling method. If the "random" option is chosen, slip-rate values are selected in the
distribution without consideration of the values sampled in neighboring fault sections. Therefore, a section of the fault
can be sampled in the lower part of its distribution when its neighboring section of the same fault can be sampled
in the upper part of this distribution. If the "correlated" option is chosen, sections that can rupture together in FtF
scenarios will always be sampled in the same part of their distribution. In practice, the distribution of possible slip-rate
on each fault is divided in four quarters and if two faults can rupture together, their slip-rates will be sampled in the
same quarter of the distribution for this model. We suggest that the "correlated" option be used when working with
long fault systems where long faults have to be discretized in smaller sections. In the case where two very different
opinions concerning the slip-rate of the faults are available, for example slip rates based on geological or geodetic
considerations, we suggest building two different models rather than exploring these options in one single distribution.

Concerning the magnitude scaling relationships, the user can choose a set of published options (Wells and
Coppersmith [1994], Leonard [2010], Thingbaijam et al. [2017]) and explore them in a logic tree. For some options,
it is possible to choose which dimension of the fault to use (length or area). A new branch of the logic tree will be
created for each chosen option. Within this branch the uncertainty affecting the estimate of the maximum magnitude
is explored by random sampling of the parameters of each scaling relationship.
<figure><img src="image_9.png" /><figcaption>**Figure 1.7:** Modeling of the background seismicity in seismic hazard and earthquake rate in fault systems (SHERIFS). (a) Expert opinion of the probability of a future earthquake to occur on a modeled fault for magnitude bin. (b) Example of background geometry. (c) Target magnitude-frequency distribution (MFD) modified to take into account the background seismicity.</figcaption></figure>

**c) Setting the background** Fault-based PSHA models usually take into account the possibility of an earthquake occurring on an unknown fault by defining a background zone around the faults. The seismicity rate of this background zone is usually deduced from the catalog and follows a GR distribution between the minimum magnitude Mmin and a truncated magnitude Mt (usually 5.8< Mt <6.5). The earthquakes with a magnitude larger than Mt are confined to the modelled faults and their rates are defined by the slip-rate and geometry of the faults.

In SHERIFS, earthquake rates are deduced from the geological information and are partitioned between background and faults (figure 1.7a). In order to define the background zone geometry the user can rely on simple distance criteria (for example, 10 or 20 km distance from the faults) to draw the background zone around the fault system (figure 1.7b). The background geometry and properties should be defined specifically for each model considered for the fault system. The seismicity rate of the background is defined by the user by setting the ratio, R, of the seismicity occurring on the modelled faults versus in the background. In the graphical interface this ratio has to be set for each magnitude M>Mmin of the distribution and is likely to increase with magnitude. To help set this ratio the user may rely on analysis of the distance between earthquakes and modeled faults. In SHERIFS, the MFD for the whole system has been defined to follow a target shape. The ratio R defined by the user for each magnitude bin is used to deduce the target shape for the faults. At the end of the iterative process, when the absolute MFD value of the fault system is known, the MFD of the background is then calculated using this ratio (figure 1.7c).

Since R is very difficult to determine, several background hypotheses are meant to be explored. This straight forward definition of the background has been introduced in SHERIFS since the version used in Chartier et al. [2017b]. We hope to encourage the discussion about the expert opinion on the matter of the background seismicity and its effect
Flowchart of the SHERIFS methodology

<figure><img src="image_10.png" /><figcaption>**Figure 1.8:** Flowchart of the overall SHERIFS methodology. BG, Background; FtF, fault-to-fault; NMS, non-mainshock.</figcaption></figure>

on the seismic hazard assessment.

## Workflow of the SHERIFS tool

SHERIFS workflow includes three tools that should be used sequentially (figure 1.8). The first tool sets up and runs the SHERIFS calculation and the logic tree exploring the epistemic uncertainties with the help of a graphical interface. The second tool allows visualizing the hazard model and comparing the modeled earthquake rates to available data. After a critical analysis of this comparison, the third tool allows the end-user setting the weights of the logic tree branches. The final outputs can then be directly used to perform probabilistic seismic hazard assessment.

Once the necessary information are in the input files and the python file1\_SHERIFS.py has been filled with information concerning the run, SHERIFS opens a series of windows using a graphical interface. The purpose of these windows is to help the user build the logic tree and the input files necessary for the PSHA calculation. The detail of each
<figure><img src="image_11.png" /><figcaption>**Figure 1.9: SHERIFS data processing workflow. Dsr, sub-divided in slip rate.**</figcaption></figure>

of the windows is explained in the user manual (provided with the code: www.github.com/tomchartier/SHERIFS). It is worth noting that the use of the graphical interface is not required by SHERIFS; an advanced user with a good knowledge of the required information and files structure can run SHERIFS independently of the graphical interface. It is also possible for the user to modify some hypotheses of the calculation or add or delete a logic tree branch and rerun the calculation.

The workflow for the calculation of the earthquake rates is described in figure 1.9 and figure 1.10.

The first steps consist in formatting the inputs provided by the user in order to run SHERIFS (figure 1.9). The slip-rate budget of each fault is sub-divided in slip rate increments (dsr). The maximum magnitude is deduced using the geometry of each section of the maximum FtF rupture scenario and the scaling law. The shape of the target MFD is then corrected for the proportion of the seismicity assumed to occur in the background and then converted in terms of moment rate.

SHERIFS iterative methodology spends the slip-rate budget of each fault until the target MFD is reached and the slip-rate budgets of each fault are exhausted (figure 1.10). In some cases, the target is reached before the budget of all faults is exhausted; the remaining slip-rate budget is then considered as (Non-Main Shock (NMS) slip and not converted into earthquake rates. The proportion of NMS slip on a specific fault of the system is an output of the methodology resulting from the combination of faults parameters, the set of FtF scenarios explored and the imposed
shape of the regional MFD.

More specifically, at each iterative loop, one magnitude bin of size 0.1 is randomly picked using the MFD
defined in terms of moment rate and a source (single fault or FtF rupture) able to host such magnitude is selected
(figure 1.10). If the target is not already set or not reached for this bin of magnitude, the rate of this magnitude for the
picked source is increased and the slip-rate budget of the fault or faults involved in the source is reduced by one dsr
increment; if the target is reached, the dsr increment is considered as NMS slip.

The selection of fault or FtF scenario that can host the picked magnitude is realized with faults preferentially
picked according to the ratio of remaining slip rate budget over the slip-rate initial budget. This ad hoc rule has been
set up in order to help isolated faults that don't break in any large scenarios spend their slip rate budget.

The absolute value of the target MFD is set when the system reaches one of the following:

1 - the budget of at least one of the faults participating in the largest magnitude earthquakes is exhausted.
The target is then set because it is not possible to change the rate of earthquakes of the three largest magnitude bins,
since the budget of one of the faults participating in the largest magnitude FtF ruptures is exhausted. Using the shape
of the regional target MFD, the absolute value of the target earthquake rate for all magnitude bins can then be set
(figure 1.11a). The choice of the three largest bins was made in order to allow flexibility around the target shape for the
largest bins and avoid that a single odd rupture scenario in the last magnitude bin limits the rates of the whole system.

2 - the rate of the two largest magnitude bins is limited by the budget of a fault being exhausted but the third
largest one is not. The annual rate on the latter bin is then limited to twice the rate of the mean of the two largest
bins in order to limit the differences of earthquake rates between the last magnitude bins and keep the consistency of
the target MFD shape set (figure 1.11b).

3 - the seismic moment required in order to fit the target shape and the rate of the largest magnitude
earthquakes is equal to the remaining seismic moment in the system at a given moment of the iterative process. This
ad hoc rule then sets the target in order to ensure that the rate of the smaller magnitude earthquakes will also reach
the set target (figure 1.11c). Rule 2 and 3 were newly introduced since the version of the code used in Chartier et al.
[2017b] in order to better model the target shape of certain fault systems proposed by some beta users. Additional
novelties introduced in the latest version of SHERIFS are discussed in the electronic supplement (see Annex 1).

SHERIFS will check if the resulting MFD of the fault system matches the shape of the target imposed by the
user. In the event that the shape doesn't match, which occurs when the slip-rate increment is not small enough, then
the model is rerun with a slip-rate increment divided by two. After three re-runs, the model is accepted but a warning
is displayed.
<figure><img src="image_12.png" /><figcaption>**Figure 1.10: SHERIFS iterative process workflow to compute earthquake rates on faults.**</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure 1.11:** The three cases of setting the target in the iterative process. (a) Case 1: limiting slip-rate budget, (b) case 2: limiting earthquake rate difference, and (c) case 3: limiting remaining moment rate.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 1.12:** Logic tree for the example calculation in which BG1 and BG2 are the two background hypotheses, set 1 and set 2 are the two rupture scenario set hypotheses, and MFD GR (Gutenberg–Richter) and MFD YC (Youngs and Coppersmith) are the two MFD shape hypotheses.</figcaption></figure>

It is important to point out that SHERIFS is not modelling earthquake ruptures as an earthquake simulator would do but only converting slip-rate on faults into earthquake rates. Each spending of a slip-rate increment is not the modeling of a true earthquake but is converted into rate of earthquakes that can be allowed on a specified fault.

## Non Main Shock slip

Non Main Shock slip is the proportion of slip-rate budget of a fault section that couldn't be transformed into earthquake rates within the SHERIFS procedure. A high NMS proportion signifies that the input slip-rate for this fault section is not compatible with the set of scenarios, the target MFD and the input slip-rate of the neighboring faults given the assumptions and rules of SHERIFS. In this case, NMS can be regarded as an error or misfit of the model. Models that predict a very high NMS, typically over 30 to 40%, need to be reconsidered in detail to understand the origin of this NMS. Similarly, the high NMS possibly calculated for some fault sections needs to be understood. The reason for this NMS can be diverse: the set of scenario involving the fault section or/and the fault slip rate set in input for this section are not realistic or the target MFD is not suitable for the fault system. Large NMS slip can also results from miscalculations in the code, when using a too large slip-rate increment for example. NMS slip differs from what could
be strictly called a misfit or error by the fact that it can be explained by physical phenomena and should therefore not necessarily be reduced to zero. NMS can reflect that part of the slip-rate deduced from geology or geodetic inversions which can be dissipated in non-seismic processes such as after-slip, creep or slow slip events but cannot be taken as a definitive proof of the existence of these phenomena in a specific fault system as it could reflect some limitations of the SHERIFS approach.

### 1.2.4 Model visualization

This tool allows extracting and visualizing numerous results that can be easily compared with the seismicity catalog of the region and plotted on a map. The user needs to specify in the python file the name of the run and the data files to use as well as the spatial limits of the maps. The user can select the type of information to plot, very useful when running a large fault model. The user manual describes in more details the use of this tool.

The produced figures include the distribution of MFDs of the whole model and of each individual branch of the logic tree. These MFDs can be compared to the MFD of the local earthquake catalog. The local catalog is extracted using the geometry of the background defined by the user. The uncertainties of both the completeness period of the catalog and the magnitude of the earthquakes can be explored. A user who wishes to study the MFD of a region smaller than the whole system can define a sub-area. The code will extract the MFD of the faults within this sub-area and the MFD of the catalog for this sub-area. This tool also plots the MFD of individual faults and fault sections and compares the results to the rate of historical or paleo-earthquakes when this information is available for single faults.

The user can use this tool to extract statistics concerning the amount of NMS slip in the model, the maximum magnitude for each branch, the repartition of the moment budget between single fault ruptures and complex FtF ruptures.

Maps of each FtF rupture scenario are generated allowing the user to check that the input scenarios were correctly set up.

### 1.2.5 Logic Tree Weighting

Once the content of the logic tree has been analyzed and compared to the local data (catalog and paleo-seismicity), the user needs to attribute weights to each branch of the logic tree. This tool opens a graphical interface to help building the logic tree file used as an input for the PSHA calculation.

SHERIFS aims to promote the discussion of the uncertainties affecting the earthquake rates on faults. The Logic Tree Weighting tool should not be run before a proper discussion of each branch of the logic tree.
## 1.2.6 Applications of SHERIFS

### Past applications of SHERIFS

The proof of concept of the SHERIFS methodology was realized on the Western Corinth Rift (WCR) fault system (Chartier et al. [2017b]). In this methodological exercise, a Gutenberg-Richter FMD target shape was considered and three sets of FtF scenarios where tested: B14_s that considered only single fault scenarios; B14 that considered FtF ruptures with a distance criteria of 3km between two faults; and B14_hc that considered a higher connectivity within the fault-system and allowed FtF ruptures separated by 5 km or less.

SHERIFS was run with these hypotheses and sanity checks where performed.

The comparison of the fault model results with the seismicity revealed that the B14_s branch of the logic tree implied seismicity rates that were incompatible with the rates computed from the catalog. Moreover, the B4_s branch didn't produce the large earthquakes observed in the historical catalog. Finally, comparison of the modeled rates with paleoseismic data available for the Aigion fault, clearly indicated that the B14_s branch cannot reproduce the rate of large earthquakes deduced from paleoseismic data. On the other hand, for the B14 and the B14_hc branches, where FtF ruptures were allowed, the agreement between the modeled rates and the instrumental/historical seismicity and paleoseismic rate improved, with the 5 km criteria used in B14_hc explaining better the data than the 3 km distance criteria used in B14. The discussion of these results lead to the conclusion that the model B14_s should be discarded from the logic tree and the model B14_hc could have a stronger weight than B14.

The SHERIFS methodology is presently being tested on different types of fault systems in France, Italy, Israel, Spain, Ecuador, India and Turkey. A comparison exercise was also performed between SHERIFS and alternative methodology that are currently being developed within the FAULT2SHA ESC working group (https://Fault2SHA.net/) using a fault system in northern Italy (Visini et al. [2019]).

## 1.2.7 Example of a SHERIFS calculation

We present here a simplified example of application of SHERIFS for the five southern faults of the WCR (Greece) with a discussion of the resulting models. We hope this can be used as an illustration of the type of discussion that can be supported by SHERIFS. Two key features of SHERIFS have been used: a hazard model has been generated and a fundamental discussion on the input hypotheses has taken place. All the calculations files for this example can be found with the SHERIFS code at https://github.com/tomchartier/SHERIFS. Using the SHERIFS graphical interface, the model was run (please refer to the user manual for a detailed description of the user interface). For this example, the logic tree presented in figure 1.12 is used with 20 random samples on Mmax, b value (between 0.95 and
<table><caption>Table 1.5: Faults Parameters Used for the Example Calculation.</caption><thead><tr><th rowspan="2">Model Name</th><th rowspan="2">Fault Name</th><th rowspan="2">Dip</th><th rowspan="2">Oriented</th><th rowspan="2">Mechanism</th><th colspan="2">Seismogenic depth (km)</th><th colspan="3">Slip-rate (mm.yr<sup>-1</sup>)</th><th rowspan="2">Shear Modulus (GPa)</th></tr><tr><th>Upper</th><th>Lower</th><th>Min</th><th>Mean</th><th>Max</th></tr></thead><tbody><tr><td>Example _Model</td><td>F1</td><td>60</td><td>N</td><td>N</td><td>0</td><td>6</td><td>4.8</td><td>5.0</td><td>5.2</td><td>30</td></tr><tr><td>Example _Model</td><td>F2</td><td>55</td><td>N</td><td>N</td><td>0</td><td>7</td><td>3.0</td><td>3.2</td><td>3.4</td><td>30</td></tr><tr><td>Example _Model</td><td>F3</td><td>60</td><td>N</td><td>N</td><td>0</td><td>7</td><td>3.8</td><td>4.0</td><td>4.2</td><td>30</td></tr><tr><td>Example _Model</td><td>F5</td><td>60</td><td>N</td><td>N</td><td>0</td><td>7</td><td>3.3</td><td>3.5</td><td>3.7</td><td>30</td></tr></tbody></table>

1.05) and the slip rates of the faults (table 1.5). For this run, an increment of slip rate dsr of 0.001 mm/yr was chosen.

In the branch BG1, 100% of the seismicity of all magnitudes is considered to be modeled on the faults. In the hypothesis BG2, 60%, 70%, 80%, 90%, 95%, and 100% of the seismicity is considered to be on the faults for magnitude 4.0, 4.5, 5.0, 5.5, 6.0, and Mw 6.5 and more respectively. In the set of rupture scenarios Set 1, faults F1, F2 and F3 can rupture together in scenarios of two or three faults and fault F5 can only rupture alone. In the branch Set 2, all four faults can rupture together. Finally, two hypotheses of target MFD are explored: GR and modified Youngs and Coppersmith YC (see supplementary material for the complete formulation of the modified YC equation, see Annex 1).

After running the model visualization tool, it is possible to compare the modelled earthquake rates to those of the catalog for each hypothesis of the logic tree.

SHERIFS is a tool that allows to discuss how each branch and each hypothesis of the logic tree performs against the earthquake catalog and paleo earthquake data. This analysis also allows us to understand which hypotheses on this simple fault system are able to reconcile the geologic data (slip-rate, geometry of the faults) with the seismological and paleoseismic data.

Models using a target MFD shape GR match the rate of the catalog better than the YC MFD (figure 1.13). Given the large discrepancy between the modelled rates and the catalog rates for the YC hypothesis, this branch can have a weight of 0 in the logic tree. Between the Set 1 and Set 2, Set 1 leads to slightly higher rates than Set 2 which matches the rate of the catalog better. In this respect, the branch Set 1 can be weighted stronger than the branch Set 2 in the logic tree. The modelled rate can be compared at the fault level with the rate calculated from paleoseismology data (figure 1.14). Here for Fault 3, where some trenches have been conducted, we compare the rate of all earthquake ruptures that involved Fault 3 with the rate calculated from the paleoseismology study.

While both rupture sets hypotheses agree with the rate of paleo earthquakes, within the range of uncertainty,
<figure><img src="image_15.png" /></figure>

**Figure 1.13:** For each hypothesis of MFD shape and rupture scenario set, comparison between the modeled MFD of the whole logic tree and the earthquake rate calculated from the catalog. Dashed green lines are the MFD of each individual model, the solid green line is the mean MFD, and green patches represent the uncertainty (16-84 percentiles). The dotted black line is the rate from the catalog with uncertainties. The ratio of NMS is indicated for each background hypothesis.

<figure><img src="image_16.png" /></figure>

**Figure 1.14:** Each green dotted line is the sum of the rates of all different ruptures passing through this fault. The solid green line is the mean rate. The purple dot is the paleoearthquake rate and the purple box is the associated uncertainty. The red dot is the historical earthquake rate and the red box is the associated uncertainty.
<figure><img src="image_17.png" /><figcaption>**Figure 1.15:** Map of the NMS slip ratio for each branch of the logic tree.</figcaption></figure>

the Set 2 hypothesis leads to an average annual rate closer to the paleoseismic rate and therefore could be weighted stronger than Set 1. Interestingly even though the regional target MFD is of the shape of a GR, the participation rates of the fault can, and often do, differ from the GR distribution. Similar observations have been made with different system level approaches such as integer programming (Geist and Parsons [2018]) and simulated annealing (Field et al. [2014]).

On the NMS slip map (figure 1.15), we can identify, which faults have trouble spending their slip rate budget given the set of hypothesis. This can help identifying some possible issues with the model input hypotheses.

A NMS ratio of more than 30% for a fault might indicate some modeling issues for a particular model. In this example, all branches of the logic tree lead to large NMS slip on most of the faults of the system. This is due to the fact that this example system is a subset of the faults of the western Corinth Rift fault system and not including the other faults of the system and therefore the possible FtF ruptures with those faults leads to some difficulties to accommodate the input slip-rate as seismic slip-rate in the SHERIFS approach. In other words, identifying the faults that belong to a fault system is paramount.
1.2.8 Limitations of SHERIFS

Although SHERIFS allows considering faults systems as a whole and modeling complex earthquake ruptures in seismic hazard assessment models, it remains a simplification of the natural systems and several limitations have to be noted before any use of this methodology. Although, SHERIFS explores a wide range of epistemic uncertainties, a full exploration of the epistemic uncertainty would require comparison with other fault modeling approaches (Geist and Parsons [2018], Field et al. [2014], Visini et al. [2019]).

SHERIFS is not able to consider complex slip distributions along strike for a given rupture. In the present version, the methodology considers that the spending of slip-rate budget is uniform for all faults participating in a given rupture. SHERIFS being an open-source code, it can be modified at will and we encourage any user willing to develop and test this feature to do so.

When considering only a part of a fault system, SHERIFS will not resolve the rates at the edge of the system correctly because it is likely that ruptures with faults that lie outside of the modelled area were omitted. Users should verify that the sites of interest are located in the center of the modelled area, where the hazard assessment is not sensitive to changes in the definition of the limits of the modelled area, ensuring that all sources potentially contributing to the hazard for the site are correctly modelled.

Testing of SHERIFS on different fault systems has led to important improvements regarding the versatility of the code. Although many cases can now be supported by SHERIFS, it is not impossible that some applications may require further adaptations of the code. Hence, we suggest that SHERIFS be used with care and that the results be always checked by the end-user.

In order to allow the code to be applicable to very diverse fault systems and hypotheses, a few controls on the input files have been implemented. It is the duty of the user to make sure the input files are consistent with the hypotheses wanted for the calculation. SHERIFS provides output files and figures to help judging the validity of the results. The output figures of SHERIFS are not in any case exhaustive and we encourage any user that requires more specific outputs to take part in the development of python routines producing these outputs and to share these developments with the community under the same GNU Lesser General Public License.

1.2.9 Conclusion and perspectives

SHERIFS is an open-source python tool to calculate the rate of earthquakes in a fault system while relaxing segmentation hypotheses. It relies on three basic ingredients: an assumption on the shape of the regional MFD, hypotheses on the possible FtF ruptures and preservation of slip rate variability along faults, if needed. SHERIFS's objective is to provide
data collectors and fault modelers with a friendly and easy-to-use interface to explore coherency of input hypotheses
and the impact of uncertainties in data and input hypotheses on the resulting seismic hazard.

Output files from SHERIFS are formatted to be directly usable as input files for the PSHA calculation. Future
developments will include tools to analyze the hazard outputs with complex logic trees.

We hope the seismic hazard models generated using SHERIFS can represent more accurately the vision of the
data providers.

**Data and resources** SHERIFS can be accessed free of charge on (https://github.com/tomchartier/SHERIFS) and can be used under the license (GNU Lesser General Public License). This open source code can be freely modified by the user as long as the modified code is also available with the same license. Questions about SHERIFS can be asked on the google group https://groups.google.com/forum/#!forum/sherifs. This google group aims to be a platform to share the questions related to the use of SHERIFS for the modelling of fault systems. We hope to be able to answer the questions and to improve the points where users have identified short-comings of SHERIFS.
## 1.3 On sharing SHERIFS

This section presents my experience of sharing the SHERIFS code, the difficulties that came with it but also the numerous scientific payoffs. Hopefully this section can help convincing other PhD students to spend the time and energy required for sharing their codes.

### 1.3.1 The struggles of sharing an open-source code

Building an operational scientific calculation code from the ground up is not an easy task, especially for someone who is not a trained programmer as it is the case for most PhD students in earth sciences. After having adapted the theoretical background to be numerically compatible and tested different parts of the code, the code is often only usable by the few persons having participated closely to its development.

#### Choosing a programming language

The choice of the programming language needs to consider four aspects: the popularity of the language in the community, the easiness to install program in the language, the easiness to code in the language for the main developer and the computing efficiency.

For SHERIFS, the language filling the four boxes was python. Python is the most commonly used language at the time, it is easy to install on any platform, development in python is intuitive and it is efficient enough to calculate earthquake rates on faults. For other projects, Matlab could be more suitable if the popularity of Matlab in the community out-weights the difficulties to get access to Matlab (e.g. licence costs). If the computing efficiency is at the essence, Fortran or C could be a better choice.

#### Making a "user friendly" code

Depending on the target audience, the meaning of the term "user-friendly" can vary widely. In the case of SHERIFS, users can be seismologists, hazard modelers or geologists. Some users might be dazzled by using computer codes and command lines. In order to help these users to get a head start, I set up a user interface for SHERIFS.

The main factor affecting user-friendliness is the availability of a complete user manual. The user manual should be detailed enough that a new user can use the code to its full extent on its own which means that writing the user manual takes a considerable amount of time.
Assessing the usability of the code by outside parties requires beta-testers. Finding beta-testers is a relatively easy task if the code offers practical solution to a problem. For the case of SHERIFS, many geologists and seismologists in the Fault2SHA Working Group (http://fault2sha.net/) were interested in modelling the seismic activity in the fault system they are studying. Before SHERIFS only the FiSH (http://fish-code.com/) modeling code, that considers faults individually and not as fault systems was available (Pace et al. [2016]).

Within the Fault2SHA working group, we organized a training workshop with a dozen participants. Before the workshop, the code was sent to the participants so they could try to run the test making sure every component of the code would work during the training. SHERIFS runs with python and relies on common python libraries and should be easy to install on every platform (Linux, Mac or Windows). However, some aspects of the code, in particular the writing and reading of text files was different depending on the platform.

The workshop took time and resources for the organization but allowed direct interactions between developer and users. Through these interactions, changes were made in the code to permit the usability by everyone on every platform. Discussion on the meaning of each term used in the manual about fault modelling clarified the different points of views. After this beta testing, changes were made to both the code and the user manual that made the code more easy to use as intended.

# 1.4 The pay-offs of sharing an open-source code

## 1.4.1 A more adaptive and reliable code.

The SHERIFS code was developed for an application to the fault system of the Western Corinth Rift, a normal fault system of moderate size but with high slip-rate values. Even though the SHERIFS approach is in theory applicable for any fault system, in practice, the code needed to be adapted to correctly handle larger systems.

The main beta tester of SHERIFS has been Octavi Gomez-Novell with an application to the Betics fault systems in South Eastern Spain (Gómez-Novell et al. [2018]). In this fault system and for certain hypothesis on the set of ruptures that are possible, different constrains for setting the target MFD where added. We also added tests to guarantee that the target was respected in the resulting modelled MFD. This exercise made the code more versatile and more reliable.
1.4.2 Discussing input hypotheses

The main gain of SHERIFS has been the increased ability for discussing scientific hypotheses concerning fault systems.

Having a versatile and user-friendly code allowed different users to apply the methodology on their fault system and to compare the modelled earthquake rates with the available data. Using a common language, we were able to discuss some modelling questions that were shared in several fault systems. I will present here some of these, still on-going, discussions.

Rupture scenarios

Octavi Gomez Novel (Gómez-Novell et al. [2018]) applied SHERIFS on the 400 km long Betics Fault system, South Eastern Spain (figure 1.16), dominated by SW-NE left-lateral strike slip faults, some of which are oblique reverse faults. They discussed the uncertainty concerning the possible multi-fault ruptures in the system and developed a logic tree exploring different hypotheses on the ruptures allowed in the system. The comparison of the modelled rate (earthquake catalog and paleoseismicity) with the data allowed to narrow the number of possible hypotheses, eliminating the branch where the faults rupture only independently and the branch where the rupture can propagate across the whole system (figure 1.17).

During Etienne Marti's master thesis (Marti [2018]), we were able to test rupture hypotheses brought forward by the paleoseismic records along the left lateral Dead Sea Fault. After compiling the available paleosismic data, Lefevre et al 2018 suggested that in the Dead Sea Fault System (DSFS), earthquake magnitudes might be limited to magnitude less than 7. in the North while they might reach magnitude 7.6 in the South. Marti tested different sets of rutpure scenarios and concluded that in order to spend the slip-rate budget of the faults, earthquakes larger than magnitude 7.5 are required in the North as well as in the South (figure 1.18). In this exercise, SHERIFS was used as a tool to test paleoseismic hypotheses.

Magnitude Frequency Distribution

In the DSFS, two MFD hypotheses were explored in order to model the seismicity rate, the GR hypotheses and a
modified characteristic MFD (Chartier et al. [2019]). Only the modified characteristic MFD was able to reproduce
both the catalog seismicity rates and the rates of paleo-earthquakes along the fault (figure 1.19).

The divergence from the GR MFD is also observed for the NAFS (chapter 2) and the San Andreas Fault System (SAFS) (Youngs and Coppersmith [1985]). Page and Felzer [2015] argue that this observation for the SAFS is due to an observation bias. In other applications of SHERIFS, in normal fault system of the Western Corinth Rift (see
<figure><img src="image_18.png" /></figure>

**Figure 1.16:** Location of the study area within the Iberian Peninsula. B. Tectonic scheme of the Eastern Betics Shear Zone (EBSZ). Faults considered in the present study are depicted in red. CF: Carboneras fault; PF: Palomares fault; LTF: Los Tollos fault; CAF: Carrascay fault; BSF: Bajo Segura fault; AMF: Alhama de Murcia fault. C. Seismicity map inferred from the earthquake catalogue used in this study (IGN-UPM working group, 2013), which covers from year 1048 to 2011. The buffer area used to extract the seismicity is indicated. The white arrow represent the converge between the African and the Iberia plates. (modified from Gomez-Novell et al submitted)

section 1), in strike slip fault system of the Betics (Gomez Novel et al submitted), and in the strike slip fault system of the Armoric Region of France (Jacottin [2019]), the GR MFD hypothesis managed to reproduce the local data. Additional data in these regions might change this observation. After analysis of the paleo-seismic records and the earthquake catalog of several faults in New Zealand, Stirling and Gerstenberger [2018] concluded that the data is too sparse to be conclusive and this uncertainty on the faults MFD should be explored in hazard models. In chapter 3, we show that this uncertainty on the MFD target is the leading source of uncertainty on the estimation of the probability of collapse for a building in Istanbul.

## Background seismicity

Hypotheses on the background seismicity modelling are not usually explored in seismic hazard assessment studies, mostly due to a lack of modelling tools. The system level approach implemented in SHERIFS allows testing a range of possibilities for the ratio of earthquakes in the background and on the faults in a very simple way. In chapter 3, we show how the hypotheses on background seismicity can affect the estimation of the seismic risk in Istanbul. In Istanbul, the seismicity rates on the faults reflect the slip-rate of the fault since they are calculated locally based on geological
<figure><img src="image_19.png" /></figure>

**Figure 1.17:** Results of the consistency check obtained for three fault-rupture hypotheses for the Betics Fault System, from left to right: single faults ruptures, intermediate ruptures, the whole system ruptures. Each green MFD corresponds to the Gutenberg-Richter distribution (GR) for the whole fault system, modelled from geological data. The green line is the mean of the cumulative annual rates of the samples explored for every magnitude. The garnet MFD corresponds to the seismicity rates extracted from the catalogue. Each MFD is represented as a coloured density function, where the most intense colours correspond to the cumulative annual rates predicted by a higher number of samples in the modelling, and so, they condition the position of the mean. Note that the mean of the maximum magnitudes from the 20 samples explored for each hypothesis is indicated. The seismic moment rate modelled for the whole fault system is also indicated for every hypothesis. It is fundamental to clearly state that differences in this rate for the different hypotheses are due to the fact that each hypothesis implies a different amount of aseismic slip or Non-main-shock slip (NMS). (modified from Gómez-Novell et al. [2018])

and geodetic information. The background is added to this seismicity following the ratio set as input for SHERIFS.

In her Masters thesis (Jacottin [2019]), Marie Jacottin modelled the seismicity rates on the 350 km long South Armorican Fault System, Bretagne, Western France. Since no slip rate estimates were available for this slow moving fault, the slip rates were based on a strain map calculated from the GPS displacement field. Therefore hypotheses on how the slip-rate is distributed between the faults and the background were made (figure 1.20).

The modelled seismicity rates can then be compared with the recorded seismicity and those hypotheses on the background seismicity that reproduce the data can be weighted more strongly in a logic tree.

## 1.5 Conclusion

While the work of sharing a code can be tedious, especially for research oriented PhD students, the availability of the code brings a community together and allows discussion on modelling issues that are shared in different study regions. Enabling the use of a methodology in a given region by the local experts often leads to interesting scientific discussions.

Finally, this move towards open sciences helps sharing the hazard models, therefore increasing the number
<figure><img src="image_20.png" /><figcaption>**Figure 1.18:** Comparison between the participation rates modelled with SHERIFS (in green, solid line is the mean value, the dashed line are each model of the logic tree) and the Lefevre et al. [2018] paleoearthquake rates (in red) at four sites along the fault. Modified from Marti [2018]. In Set 1 the ruptures in the north are smaller than magnitude 7 and can reach magnitude 7.6 in the south. In Set 2, the ruptures can be larger than magnitude 7.6 both in the north and in the south.</figcaption></figure>

of people able to review and discuss the models. The open source hazard and risk calculation software OpenQuake (Pagani et al. [2014]), has greatly improved the sharing of hazard models and has allowed easy comparison between hazard estimates which in turn led to a better understanding of the epistemic uncertainties that affect the models. We hope that SHERIFS can be a step in the same direction and improve the discussion around modelling the earthquake rates in fault systems.
<figure><img src="image_21.png" /></figure>

**Figure 1.19:** Comparison between the MFD modelled with SHERIFS (in green) and the MFD calculated from the earthquake catalog (in black) and the paleoearthquake rates calculated from Lefèvre et al. [2018] (in red). On the left, the MFD when using the GR MFD hypothesis, on the right, the MFD using the modified characteristic MFD hypothesis. Modified from Etienne Marti's Master thesis (Marti [2018]).

<figure><img src="image_22.png" /></figure>

**Figure 1.20:** Deformation map calculated for Western France from the GPS data. The differential velocity between the point A and B is indicated for the three components. The slip-rate attributed to the fault sections by sharing the A-B differential between parallel sections is indicated in the box next to the fault (in black). Modified from Jacottin [2019]
# Chapter 2

## Modelling the earthquake rates in the Marmara Region and the associated uncertainties

### Résumé du chapitre

Dans ce chapitre, nous utilisons la méthodologie SHERIFS pour calculer les taux de sismicité dans la région de la Mer de Marmara dans le but d'estimer le risque sismique pesant sur la ville d'Istanbul en Turquie. Istanbul se trouve à une vingtaine de kilomètres de la faille Nord Anatolienne qui a une vitesse de glissement proche de 20 mm/an. La faille Nord Anatolienne est localisée sous la Mer de Marmara sur une longueur d'environ 200 km; son étude est donc un challenge. Au travers d'un arbre logique, nous explorons un ensemble d'incertitudes ayant le potentiel d'affecter le taux de sismicité modélisé.

Quatre hypothèses concernant le blocage de la faille dans la partie occidentale de la Mer de Marmara sont explorées: une hypothèse où la faille n'est pas bloquée et n'accumule donc pas d'énergie élastique sur cette section, une hypothèse où la faille n'accumule que 50% du glissement en énergie élastique, une hypothèse où la faille est bloquée sur les 5 premiers km et glisse dans sa partie plus profonde, et enfin une hypothèse où la faille est totalement bloquée et accumule 100% du glissement en énergie élastique.

La MFD calculée à partir du catalogue de sismicité ne suit pas une distribution du type Gutenberg-Richter (GR): la fréquence d'occurrence des séismes de magnitude supérieure à 7 est plus forte que ce que la décroissance
logarithmique d'une courbe du type GR prédirait. La réalité d'une telle distribution pour un système de faille est débattue dans la communauté scientifique, certains argumentant que cette observation est biaisée par la courte période de complétude du catalogue comparée à la longueur du cycle sismique. Nous établissons donc deux branches dans l'arbre logique: une des branches utilise une MFD suivant une distribution du type GR et l'autre une MFD de la forme de la MFD du catalogue.

Deux hypothèses sont considérées pour la rupture la plus large possible dans le système de failles. La première considère un séisme de l'ordre de magnitude 7.7, rompant les deux ruptures de 1999 simultanément. La seconde envisage que des ruptures plus grandes, générant des séismes de magnitude 8 sont possibles dans le système, cette hypothèse ayant été considérée par d'autres études.

Nous utilisons les capacités de SHERIFS pour modéliser trois hypothèses différentes pour la sismicité de fond, se produisant sur des failles non connues ou non considérées dans le calcul. Ces hypothèses vont d'une considération que la grande majorité des séismes se produisent sur les failles connues, y compris les séismes de magnitudes modérées (de 4.5 à 5.5), à une considération que la majorité de magnitudes modérées se produisent sur des failles non connues et qu'il est possible que des séismes de magnitude 7 se produisent sur des failles considérées inactives ou non connues.

Enfin, pour chaque branche de l'arbre logique, 10 tirages aléatoires sont effectués sur les vitesses de glissement et les paramètres de la loi d'échelle reliant la dimension des ruptures à la magnitude.

Afin de pondérer chaque hypothèse de l'arbre logique, les taux de sismicité sont comparés aux taux calculés à partir du catalogue de sismicité et des études de paleosismicité. Ces données, étant un échantillon court du cycle sismique de la faille, ne permettent pas de choisir clairement une hypothèse entre les deux possibilités de MFD et les deux possibilités de rupture maximale. Pour compléter cette discussion, nous modélisons un catalogue de sismicité synthétique avec le code RSQSim qui simule un catalogue de séismes à partir des lois de friction "rate ans state". Ce catalogue de 10 000 ans ne présente pas de séismes plus grand que magnitude 7.7 et sa MFD diverge de la GR MFD.

Basé sur ces observations, il est alors possible d'attribuer un poids plus important pour ces deux hypothèses dans l'arbre logique. Le résultat de cette étude est une estimation des taux de sismicité dans le réseau de faille et de leurs incertitudes représentant clairement l'état des connaissances actuel.
## 2.1 Introduction

The North Anatolian Fault System (NAFS) runs through the North of Turkey for a distance of more than 1500 km (Figure 2.1) accommodating the westward extrusion of the Anatolian plate with a right lateral motion of around 25 mm/yr (Reilinger et al. [2006]). Along the western portion of the NAFS, this right lateral motion is partitioned between to fault branches with the northern branch accommodating most of the motion (Reilinger et al. [2006]). This northern branch of the NAFS crosses the Sea of Marmara 20 km south of the city of Istanbul (Figure 2.2). The last earthquakes having occurred in the Marmara Sea, severely damaging the city of Istanbul, date back to 1766 and 1894 (Ambraseys [2002]). Growing from a population of less than one million in 1950, Istanbul is now a city of more than fifteen million. The 1999 Izmit earthquake that ruptured the fault eastward of the Marmara Sea has been a reminder of the hazard faced by Istanbul. The NAFS is expected to be the major source of seismic hazard looming on the megalopolis. Motivated by better constraining the seismic hazard, the two decades following the 1999 earthquake have been rich in geological, geophysical and geodetic studies of the Marmara Region (Ergintav et al. [2014]). These studies have brought new light on the structure (Armijo et al. [1999], Le Pichon et al. [2001], Le Pichon et al. [2003] ...) and dynamics (Hergert and Heidbach [2010], Ergintav et al. [2014], Bohnhoff et al. [2017] ...) of the NAFS and raised important questions such as the locking condition of the fault and the possibility of a large rupture in the Marmara Sea.

Building on the findings of these studies, several Earthquake Rate Forecast (ERF) models and hazard maps have been developed (Erdik et al. [2004], Gülerce et al. [2017], Murru et al. [2016], Sesetyan et al. [2018], Demircioğlu et al. [2018]). While these studies improve our understanding on the hazard for Istanbul, none of them fully explore the epistemic uncertainties in the parametrization of the ERF parameters that have the potential to affect the seismic hazard in Istanbul.

The NAFS being offshore on its portion closer to Istanbul, satellite-based geodesy (GPS and INSAR) are not able to resolve accurately the locking condition of the fault which remains debated (Klein et al. [2017]). The possibility of creep in the Marmara Sea might have an impact on the seismic hazard for Istanbul and should be explored in the seismic hazard assessment.

Past studies (Erdik et al. [2004], Demircioğlu et al. [2018]) have used the classic approach to model faults and background seismicity in seismic hazard. The rate of earthquakes in the background is based on the local seismic catalogue up to a threshold magnitude (M5.5) and the rate of larger magnitude earthquakes are based on the slip-rate of the faults. This approach can lead to several limitations in Probabilistic Seismic Hazard Assessment (PSHA) and eventually in the seismic risk assessment. First, this approach lacks the consideration that earthquakes with a magnitude larger than the threshold magnitude can occur in the background as it has been observed in July 2019 in California where a magnitude 7.1 earthquake occurred on a fault that was not modelled as active in the UCERF3
<figure><img src="image_23.png" /></figure>

**Figure 2.1:** Regional tectonic setting. Modified from Duman et al. [2018]. The active faults are in black except for the North Anatolian Fault Zone (NAFZ) which is in red. The black and red arrows show the plate motion relative to a fixed Eurasia.

model (Brandenberg et al. [2019], Field et al. [2014]). However, the possibility of such earthquake occurring in the background was considered (Field et al. [2014]). Second, this approach when used with a spatially uniform distribution of the seismicity, cannot consider that intermediate magnitude earthquakes (lower than the threshold magnitude) can be more likely to occur on the fault than on any given point of the background.

In this study, we will use the recently developed SHERIFS code (Chartier et al. [2019]) that allows exploring these uncertainties using a logic tree approach. Furthermore, SHERIFS considers a system level approach, in which different rupture scenarios are explored in an aleatory manner, relaxing fault segmentation and defining complex multi-faults ruptures.

Through the SHERIFS approach we can also address two issues (1) the uncertainty on the size of the largest rupture that may occur along the NAFS and (2) the shape of the Magnitude Frequency Distribution (MFD).

The geometry of the network could potentially host larger ruptures than the one observed in the historical time. For example, the change of azimuth in the geometry of the fault in front on the Princes Island (Figure 2.2) that was not crossed by the 1999 Izmit earthquake could be crossed by a future earthquake as it has been shown by Oglesby
et al. [2008] and Aochi and Ulrich [2015] using dynamic rupture modelling. Furthermore, ruptures that run through more complex fault geometries have been observed in fault systems (e.g. the 2016 Kaikoura earthquake, Klinger et al. [2018]).

It has been long observed that the number of earthquakes in a region decreases with the magnitude of the earthquake. Gutenberg and Richter [1954] established the logarithmic decrease of the number of earthquake with the magnitude (noted as GR law hereafter). However, when analyzing the MFD of the earthquake catalog in the Marmara region we can observe a larger number of earthquakes of magnitude 7.0 and above than predicted by the GR law. Since there are only 6 earthquakes larger than magnitude 7.0 in the catalog, the long term representativity of this divergence from the GR law can be debated. Several studies have discussed this aspect of earthquake statistics along the San Andreas strike slip fault systems; either arguing for the divergence (Schwartz and Coppersmith [1984]) or the GR law (Page and Felzer [2015]). Recently, Stirling and Gerstenberger [2018] have analyzed several fault zones in New Zealand and have argued for the systematic exploration of the uncertainty on the shape of the MFD when modelling faults in seismic hazard assessment. We explore this uncertainty in this study.

The earthquake rates modelled with SHERIFS using each combination of uncertainties will be compared to the earthquake rates calculated from the earthquake catalog and the paleoseismic records in order to give a score to each model. However, for some hypotheses, the comparison with the data is not sufficient for rating one hypothesis against another. We tackle this issue by modelling a synthetic earthquake catalog using the earthquake simulator RSQSim (Richards-Dinger and Dieterich [2012]) along the fault system. By analyzing the statistics of the synthetic catalog, we are able to discuss the physical validity of the different hypotheses explored and preferentially weight the branches of the logic tree that are more compatible with physically-based models.

Because the aim of this study is to better understand the seismic risk in Istanbul, in chapter 3, the uncertainties concerning the modelling of the earthquake rates in the fault system are propagated in the calculation of the probability of collapse of a building in 50 years. The impact of each uncertainty on the uncertainty of the estimation of the probability of collapse is quantified and discussed.

## 2.2 The Western North Anatolian Fault System

Fault traces and some of the slip rate estimates along the North Anatolian fault system have been recently updated in the Emre et al. [2018] and references within. In this study, we rely on their map (available online at http://www.mta.gov.tr/v3.0/hizmetler/yenilenmis-diri-fay-haritalari, last accessed August 2019) to digitize the fault traces (Figure 2.2).
<figure><img src="image_24.png" /></figure>

**Figure 2.2:** Fault system and the earthquake catalog used in this study (Emre et al. [2018]). The faults sections are delimited by the purple lines and the name of the fault sections are indicated in black. Only the earthquake of magnitude greater than magnitude 4.5 and during the complete period (see Table 2.2) are plotted. The year of occurrence of the largest earthquakes (M>7) are indicated. The yellow triangles are the location of paleoseismic studies.
The faults parameters of the main faults used in this study are presented in Table 2.1. Slip rates are taken from Hergert and Heidbach [2010] who inverted the GPS velocity field in a geomechanical model in order to calculate the slip-rate of the fault network. These slip-rates are in general agreements with the slip-rate calculated by Flerit et al. [2004] and Ergintav et al. [2014]. Since they agree with the long-term geological slip-rate of the faults, these values of slip-rate have been preferred to those estimated by Reilinger et al. [2006] calculated at a larger scale and that tend to overestimate the slip-rate compared to the geological estimate (Hergert and Heidbach [2010]). Uncertainties on the slip-rate value (Table 2.1) are taken into account by a random exploration in a uniform distribution between the minimal slip-rate value and the maximal slip-rate value set from the literature (Hergert and Heidbach [2010], Klein et al. [2017]) and weighted in order to give a central weight to the mean value. It can be noted that the range of the slip-rate explored in this study does not include values that vastly differ from the geological estimate (23 mm/yr according to Le Pichon et al. [2003]), since they integrate the deformation on a wider area than the fault fault itself.

The scientific community has been debating over the possibility of the NAF been creeping in the Western Marmara region, along the Terkidag, Central basin, Kumburgaz and Acvilar sections of the fault (table 2.1, figure 2.2). Creep has been observed on other strike-slip faults in the world (San Andreas Fault – Nason [1973], Longitudinal Fault Taiwan – Hsu and Bürgmann [2006]) and is expected to release an important part of the tectonic load of the fault without producing major earthquakes hence possibly reducing the seismic hazard in the region. The large scientific efforts of the past two decades have led to conclude that the Eastern part of the fault in the Marmara Sea is locked (Diao et al. [2016]). However, the distance from the fault to the shore in the western part of the sea remains a challenge for traditional land-based or satellite-based geodetic instruments. While novel sea-floor geodesy experiments seem to suggest that the fault is locked at the surface at least at some places (Lange et al. [2019]), these conclusion are still under discussion (Yamamoto et al. [2019]). Relocated microseismicity and the identification of repeater earthquakes suggest that the lower part of the fault might be creeping (Schmittbuhl et al. [2016b], Schmittbuhl et al. [2016a]). Based on the latest studies of the fault in this area, we propose to explore four models of locking condition for the NAF that represent the current state of knowledge. The “creep” hypothesis considers the fault as fully creeping, thus reducing its contribution to the seismic slip-rate budget to 0. The “partial creep” hypothesis considers the fault releasing half of its slip-rate as creep and half as seismic moment, reducing its slip-rate by half. The “deep creep” hypothesis considers that the fault is fully locked for the first 5 kilometers and creeping below, and the “fully locked” hypothesis considers that 100% of the fault slip-rate can be released as earthquakes.

For the faults within the Armutlu peninsula located between the northern strand and the southern strand of the NAF, south of the Izmit section and north of the Iznik section (figure 2.2), we are not able to find slip-rate estimates. However, the velocity field shows very little deformation (Ergintav et al. [2014]) within the Armutlu peninsula. Based on this observation, we assume the slip-rate of these faults to be less than 1 mm/yr. It is worth noting that these faults are relatively far from Istanbul in comparison to the NAF and their participation in the seismic hazard affecting
<table><caption>Table 2.1: Properties of the faults of the central zone. The full properties table is available in the annexes.</caption><thead><tr><th>Fault Name</th><th>Rake</th><th>Creep hypothesis</th><th>Seismogenic depth (km)</th><th>Min slip-rate (mm/yr)</th><th>Mean Slip-rate (mm/yr)</th><th>Max slip-rate (mm/yr)</th></tr></thead><tbody><tr><td>Ganos</td><td>180</td><td>Fully Locked</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td rowspan="4">Terkidag</td><td rowspan="4">180</td><td>Creeping</td><td>15</td><td>0.</td><td>0.</td><td>0.</td></tr><tr><td>Partial Creep</td><td>15</td><td>7.5</td><td>8.</td><td>8.5</td></tr><tr><td>Deep Creep</td><td>5</td><td>17</td><td>18</td><td>19</td></tr><tr><td>Fully Locked</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td rowspan="4">Central Basin</td><td rowspan="4">180</td><td>Creeping</td><td>15</td><td>0.</td><td>0.</td><td>0.</td></tr><tr><td>Partial Creep</td><td>15</td><td>7.5</td><td>8.</td><td>8.5</td></tr><tr><td>Deep Creep</td><td>5</td><td>17</td><td>18</td><td>19</td></tr><tr><td>Fully Locked</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td rowspan="4">Kumburgaz</td><td rowspan="4">180</td><td>Creeping</td><td>15</td><td>0.</td><td>0.</td><td>0.</td></tr><tr><td>Partial Creep</td><td>15</td><td>7.5</td><td>8.</td><td>8.5</td></tr><tr><td>Deep Creep</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td>Fully Locked</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td rowspan="4">Acvilar</td><td rowspan="4">180</td><td>Creeping</td><td>15</td><td>7.5</td><td>8.</td><td>8.5</td></tr><tr><td>Partial Creep</td><td>15</td><td>7.5</td><td>8.</td><td>8.5</td></tr><tr><td>Deep Creep</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td>Fully Locked</td><td>15</td><td>17</td><td>18</td><td>19</td></tr><tr><td>Adalar</td><td>-168</td><td>Fully Locked</td><td>10</td><td>12.2</td><td>14.3</td><td>16.5</td></tr><tr><td>Cinarcik</td><td>-147</td><td>Fully Locked</td><td>15</td><td>2.2</td><td>3.6</td><td>5</td></tr><tr><td>Izmit</td><td>180</td><td>Fully Locked</td><td>15</td><td>18</td><td>20</td><td>22</td></tr><tr><td>Adaparazi</td><td>180</td><td>Fully Locked</td><td>15</td><td>16</td><td>18</td><td>20</td></tr><tr><td>Karadere</td><td>180</td><td>Fully Locked</td><td>15</td><td>11.8</td><td>15</td><td>18</td></tr><tr><td>Duzce</td><td>180</td><td>Fully Locked</td><td>15</td><td>11.8</td><td>15</td><td>18.2</td></tr></tbody></table>

the city is expected to be negligible.

In this study, we combined two catalogs : the earthquake catalog from Kadirioğlu et al. [2018] homogenized in Mw for the period 1900-2012 and the catalog SHEEC (Stucchi et al. [2013]) for the period 1000-1899. The completeness period used in this study are based on these two studies and presented in Table 2.2.
<table><caption>Table 2.2: Completeness time used in this study.</caption><tr><td>Completeness from</td><td>4.0 - 4.7</td><td>4.8 - 5.2</td><td>5.3 - 5.7</td><td>5.8 - 6.2</td><td>6.3 - 6.7</td><td>6.8 - 7.2</td><td>7.3 - 7.7</td><td>7.8+</td></tr><tr><td>SHARE (Woessner et al. [2015])</td><td>1987</td><td>1952</td><td>1900</td><td>1850</td><td>1750</td><td>1700</td><td>1700</td><td>1700</td></tr><tr><td>Kadirioğlu et al. [2018]</td><td>1992</td><td>1977</td><td>1937</td><td>1850</td><td>1750</td><td>1700</td><td>1700</td><td>1700</td></tr></table>

<figure><img src="image_25.png" /></figure>

**Figure 2.3:** Left: Magnitude Frequency Distribution for the study area calculated from the catalog and the completeness periods presented in Table 2.2. The red dashes are individual Monte Carlo samples on the earthquake magnitude uncertainties and the completeness period. The mean rate value is indicated by black squares and the 16th and 84th percentiles are indicated by the grey area. Right: Depth distribution of earthquakes of magnitude 4.0 and above since 1992 in the Kadirioğlu et al. [2018] catalog and corresponding to the background zone shown in Figure 2.2.

In this study, based on the analysis of the depth distribution of earthquakes in the instrumental catalog (Kadirioğlu et al. [2018]) and of the rupture inversion of the Izmit earthquake, we have limited the seismogenic thickness of the fault to a depth of 15km. 80% of the earthquakes are in the first 15km of the crust in the region of interest (Figure 2.3). The Izmit rupture inversions show that most of the slip during the earthquake was contained in the first 15km of the crust (Reilinger et al. [2000]).

Dikbaş et al. [2018] present a review of the paleoseismic studies that have been carried on the Izmit, Adapazari, Karadere and Duzce segments of the fault. They propose an interpretation of the rupture history of these segments. Based on the number of ruptures observed in one location and the length of the observation period, we estimate the annual rate of earthquakes with a magnitude larger or equal to 7.2 +- 0.1 for different sections of these segments. The location of these segments are presented in figure 2.2 and the estimated rates are presented in table 2.3. At the West of the Marmara Sea, for the Ganos segment, the paleoearthquake rates have been calculated from Rockwell et al. [2009] and Meghraoui et al. [2012]. Both studies lead to similar rates for earthquakes larger than 7.2 (table 2.3). The paleoearthquake rates are calculated by dividing the number of events by the observation time, the uncertainty reflects the statistical uncertainty due to the small number of observation assuming a poissonian process.
<table><caption>Table 2.3: Annual rate of M 7.3+ earthquakes based on the paleoseismicity.</caption><thead><tr><td>Site</td><td>Reference</td><td>Number of events</td><td>Observation time</td><td>Annual rate</td><td>Uncertainty</td></tr></thead><tbody><tr><td>Ganos 1</td><td>Rockwell et al. [2009]</td><td>4</td><td>1000</td><td>0.00357</td><td>0.001</td></tr><tr><td>Ganos 2</td><td>Meghraoui et al. [2012]</td><td>5</td><td>1600</td><td>0.003</td><td>0.001</td></tr><tr><td>Izmit 1</td><td>Klinger et al. [2003]</td><td>4</td><td>1600</td><td>0.0025</td><td>0.0013</td></tr><tr><td>Izmit 2</td><td>Dikbaş et al. [2018]</td><td>5</td><td>1600</td><td>0.0032</td><td>0.0014</td></tr><tr><td>Izmit 3</td><td>Dikbaş et al. [2018]</td><td>5</td><td>1600</td><td>0.0032</td><td>0.0014</td></tr><tr><td>Adaparazi 1</td><td>Dikbaş et al. [2018]</td><td>3</td><td>1600</td><td>0.0018</td><td>0.001</td></tr><tr><td>Karadere 1</td><td>Dikbaş and Akyüz [2011]</td><td>3</td><td>1600</td><td>0.0018</td><td>0.001</td></tr><tr><td>Duzce 1</td><td>Pantosti et al. [2008]</td><td>4</td><td>1600</td><td>0.0025</td><td>0.0013</td></tr></tbody></table>

## 2.3 Earthquake rate modelling

In this section, we describe two approaches for calculating earthquake rates in fault systems. The first approach is SHERIFS (Chartier et al. [2019]), a statistical approach that converts the slip-rate of the faults into earthquake rates built to respect a given shape of MFD at the system level. The second approach is RSQSim that generates a long catalog of synthetic ruptures using the loading rates and the rate and state equation (Richards-Dinger and Dieterich [2012]). SHERIFS allows to explore a wide range of epistemic uncertainties on the input hypotheses and RSQSim allows to discuss which of these hypotheses are physically plausible.

### 2.3.1 The statistical approach: SHERIFS

#### Core principle and main input hypothesis

SHERIFS uses an iterative budget spending approach of the slip-rate of the fault to calculate the annual rate of occurrence of each rupture of a predefined set of ruptures. In an iterative manner, SHERIFS randomly selects user-defined rupture scenarios for which involved faults have slip-rates budget to spend. The random selection is done in order to ensure that the resulting system level MFD has the shape imposed as input (b value in the case of a Gutenberg-Richter MFD, for example). It is important to recall that SHERIFS doesn't simulate earthquakes but only converts slip-rates into earthquake rates. For this reason, SHERIFS is computationally light which allows aleatory (combination of ruptures) and epistemic (logic tree) uncertainties concerning the fault system to be easily explored.

SHERIFS takes as input the geometry and slip-rate of the faults, the set of multi-fault ruptures that can be expected in the fault network, and the shape of the MFD defined at the fault system level. Before the calculation, the
actual value of the MFD and the shape of the MFD of each individual fault are not known. They will be deduced from the fault slip-rate budget and the other hypotheses. Depending on the combination of input hypotheses and faults parameters, SHERIFS can consider part of the slip-rate budget of some fault as Non Main Shock (NMS) slip in order to respect the target MFD shape. A NMS of more than 30% is most likely to be an indication that the combination of input hypotheses used doesn't agree with the faults parameters in the SHERIFS framework and that they should be reconsidered.

## Background seismicity

One uncertainty that SHERIFS allows to explore is the proportion of seismicity that can occur in the background, on faults that are unknown or not considered as active in the model. In most PSHA, this is taken into account by a background zone with a GR MFD truncated at a given Mt.

In SHERIFS, it is possible to define a-priori the proportion of earthquakes that can be expected on the faults and the proportion in the background for each range of magnitude. In order to assess these proportions, we analyze the distance of each earthquake to the closest fault in the model. Considering the poor knowledge on the epicentral location of the historical earthquakes, we only consider the instrumental catalog after 1970. Since we are interested in the hazard in Istanbul, we only consider the spatial distribution of earthquakes around the sea of Marmara (the central zone in Figure 2.2).

In order to represent the epistemic uncertainty associated with the proportion of seismicity considered on the faults versus that on the background, we set up three branches of the logic tree. The proportion of earthquakes considered to occur on the faults for each branch is presented in Table 2.4. Studies of the NAFS off-fault deformation might bring some light on these value in the future (Şengör and Zabcı [2019]).

<table><caption>Table 2.4: Ratio of earthquakes assumed to be on the faults for each background hypothesis.</caption><thead><tr><th>Magnitude</th><th>4.0</th><th>4.5</th><th>5.0</th><th>5.5</th><th>6.0</th><th>6.5</th><th>7.0</th><th>7.5</th><th>8.0+</th></tr></thead><tbody><tr><th>Background 1</th><td>0.8</td><td>0.8</td><td>0.8</td><td>0.8</td><td>0.8</td><td>0.9</td><td>1.0</td><td>1.0</td><td>1.0</td></tr><tr><th>Background 2</th><td>0.7</td><td>0.7</td><td>0.7</td><td>0.7</td><td>0.7</td><td>0.8</td><td>0.9</td><td>1.0</td><td>1.0</td></tr><tr><th>Background 3</th><td>0.4</td><td>0.4</td><td>0.4</td><td>0.45</td><td>0.5</td><td>0.6</td><td>0.8</td><td>1.0</td><td>1.0</td></tr></tbody></table>

## MFD

The annual rate of earthquakes obtained by analysis of the Kadirioğlu et al. [2018] catalog in the Central Zone (Figure 2.2) indicates a MFD diverging from a GR MFD for magnitudes larger than 6.5 (figure 2.3). The rates are obtained