<figure><img src="image_26.png" /><figcaption>Figure 2.4: Distribution of earthquakes between the background seismicity and the faults for each background hypothesis.</figcaption></figure>

while exploring the uncertainties on the magnitude of earthquakes, on the completeness period length using a Monte Carlo approach and the uncertainties linked to the low number of earthquakes for the larger magnitudes. Despite this large number of uncertainties explored, the resulting MFD significantly differs from the GR MFD shape.

Like any earthquake catalog, the Turkish catalog is short in comparison with the seismic cycle and it can be argued that the observed shape is a result of the incomplete sample of the phenomenon and that the long term MFD should follow a GR distribution. This debate on the catalog MFD has been present concerning the Californian earthquake catalog as well (Page and Felzer [2015], Parsons et al. [2018]).

In order to reflect the lack of consensus in the community, we explore two hypotheses for the target MFD : one where the target MFD follows a GR truncated between a minimum magnitude and a maximum magnitude, one where the target MFD follows a shape tuned to that of the rates deduced from the catalog. The tuned shape MFD is described by the following equation and is composed of two parts, both defined by a double truncated GR with a b value deduced from by the lower magnitude part of the catalog (4.5 < M < 6.0) that follows an exponential decrease.

$$P_i(M) = \begin{cases} \frac{e^{-\beta \times (M-0.05-M_{min})}}{1-e^{-\beta \times (6.8-M_{min})}} - \frac{e^{-\beta \times (M+0.05-M_{min})}}{1-e^{-\beta \times (6.8-M_{min})}}, & \text{if } M < 6.6 \\ P_i(M = 6.6)/3, & \text{if } M = 6.7 \text{ or } 6.6 \\ P_i(M = 6.3), & \text{if } M = 6.8 \\ P_i(M = 6.8) \times (10^{(b \times (M-6.8))}), & \text{if } M > 6.8 \end{cases}$$

where $P_i$ is the density function depending on M; b describes the linear decrease with M; $\beta = b \times \log 10$; and $M_{min}$ is the minimal magnitude considered in the calculation.

## Set of rupture scenario

The historical catalog doesn't record earthquakes larger than 7.5 since 1700. Based on the statistics of the earthquake catalog, Bohnhoff et al. [2016] consider this value of 7.5 to be the largest possible magnitude in the Marmara region
while earthquakes can reach up to magnitude 8.0 in the Eastern part of the NAFS. A recent review of paleoseismological studies and historical earthquake studies (Dikbaş et al. [2018]) suggests that the largest earthquake having occurred in the region could have been a rupture including both the 1999 Izmit earthquake rupture area and the 1999 Duzce earthquake rupture area resulting in a magnitude 7.7 earthquake. Based on this assumption, we define a Set 1 of more than 300 Fault to Fault (FtF) ruptures allowing a large diversity of ruptures to be possible in the system. Figure 2.5 a) exposes the largest ruptures possible in Set 1.

The resolution of the earthquake records diminishing as we consider older events, it is possible that larger earthquakes occurred in the NAFS but may not have been observed neither in the historical times nor in the paleoseismic records. Furthermore, since most bends in the system could be crossed by a rupture without jumping a large distance or large changes in azimuth, we need to imagine that larger earthquakes might be possible. This hypothesis has been considered in previous studies (Murru et al. [2016], Mignan et al. [2015]). We thus build a Set 2 of FtF ruptures to explore this possibility in which the largest possible ruptures correspond to a magnitude 8.0 earthquake. Figure 2.5 b) exposes the largest ruptures possible in Set 2.

<figure><img src="image_27.png" /><figcaption>**Figure 2.5:** Largest ruptures included in the models using the Set 1 (a) and the Set 2 (b).</figcaption></figure>

## Locking condition of the NAFS in the Western Marmara region

As exposed during the presentation of the NAFS earlier, there is uncertainty concerning the locking condition of the NAF is the western Marmara Sea. Four hypotheses of locking conditions ranging from fully creeping to fully locked are explored in a logic tree to represent the current state of knowledge. The fault parameters for each hypothesis are presented in table 2.1.
## The logic tree

SHERIFS is run with the hypotheses of each of the branch of the logic tree (Figure 2.6). We then compare the modelled annual earthquake rates with the seismicity rates from the earthquake catalog and the paleoseismic records.

<figure><img src="image_28.png" /><figcaption>**Figure 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.</figcaption></figure>

## Results: Earthquake rates modelled by SHERIFS

As we have not considered the entirety of the NAFS but only the faults in the region of Istanbul (figure 2.1), the faults located at the limit of our model are not able to rupture with the sections of the fault we didn't consider. This can involve some modelling issues which will result in a significant portion of the fault slip-rate being spent as NMS slip.

In this study, we only modelled part of the NAF (figure 2.1), therefore some boundary effects might occur on the faults that would rupture with fault outside of the modelled zone. With the aim of modelling the seismic risk in Istanbul, far from the system boundaries, we compare only the rates for a region smaller than the whole modelled system centered on Istanbul (Figure 2.2) that is not affected by boundary effects. In this zone, we extract the earthquakes from the catalog and the modelled rate of ruptures. For ruptures that are only partly located in the zone, the rate is corrected by taking into account the proportion of the fault in the zone.

When compared with the rates calculated from the earthquake catalog for the central zone (figure 2.2), the rates modelled using SHERIFS are slightly higher than the catalog (figure 2.7). However, some combinations of hypotheses lead to better fit to the rate from the catalog than others. The branches using the GR target shape lead to a rate of earthquakes of magnitude between 4.5 and 6.5 that is larger than the observed rate for all models (figure 2.7). The tuned shape (TS) hypothesis is in better agreement with the catalog for this range of magnitudes. Both MFD hypotheses reproduce the rate of large earthquakes equally well. The branches using the Set 2 of rupture scenarios, allowing ruptures up to magnitude 8, have lower earthquake rates than the branches using Set 1 and obtain a better fit with the rates from the catalog. The hypothesis on the creep hypothesis has only a small effect on the earthquake rates
at the level of the central zone. The four hypotheses lead to similar rates (figure 2.7). In conclusion, the branches using
the combination of the TS MFD and the Set 2 of ruptures lead to the best fits with the rates from the earthquake
catalog.

<figure><img src="image_29.png" /><figcaption>**Figure 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.</figcaption></figure>

In Figure 2.8, we compare the participation rate of fault sections where an estimate of the rate of earthquakes is available based on paleoseismic studies. The participation rate is the rate of all the ruptures for which the given fault section is involved in. For most sites, the rate of earthquakes modelled is in general agreement with the rate deduced from the paleoseismicity for all branches of the logic tree.

At the Ganos 1 site (Figure 2.9), the branch “Creep”, assuming a complete creep in the west of the Marmara Sea, leads to rupture rates significantly lower than the paleoseismic rates. For this branch of the logic tree, the Ganos fault spends around 46% of its slip-rate budget as Non Main Shock (NMS) slip. The proportion of NMS slip is the proportion of slip-rate budget that couldn’t be spent in seismic moment rates in SHERIFS. A large NMS (>20-30%)
<figure><img src="image_30.png" /><figcaption>**Figure 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.</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>**Figure 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 is 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.</figcaption></figure>

is indicative of the inability in SHERIFS to satisfy the hypotheses of MFD, slip-rate budget and the set of ruptures. The introduction of a fault completely creeping in the western part of the Marmara Sea limits the number of large earthquakes along the Ganos fault. In the SHERIFS framework, the ability of the Ganos faults to release seismic moment jointly with the faults of the Marmara Sea is required in order for it to spend its full budget.

## 2.3.2 The physics-based approach : RSQSim

### Core principle and main hypotheses

The comparison between the modelled earthquake rates and the data allows to reduce part of the uncertainties explored in the logic tree but some uncertainties still remain, notably the uncertainties concerning the MFD shape and the maximum rupture size.
In the hope of reducing these uncertainties, we implemented our fault system in the physics-based simulator RSQSim (Richards-Dinger and Dieterich [2012]) and analyzed the resulting synthetic earthquake catalogs. RSQSim is a boundary element model that applies the rate and state equation (Dieterich [1978]) where each element of a fault system can be in three different states: loading, nucleating the earthquake rupture or sliding. Elements interactions are considered to be quasi-static therefore neglecting the dynamic influence of seismic waves that would be generated by sliding elements. Where the elements are sliding, they are doing so at a constant slip-rate. These simplifications of the earthquake physics and the rate and state law allow RSQSim to be computationally efficient and to generate long earthquake histories for a large fault network.

RSQSim takes as input the same information as SHERIFS concerning the fault parameters but doesn't require a target MFD shape nor a set of possible FtF ruptures. The MFD of the fault system and the ruptures will be deduced from the synthetic earthquake catalog which result from the combination of the faults loading rates and the rate and state friction law as implemented in RSQSim.

In this study, we will use the same friction parameters a and b for all the elements of the fault system (0.01 and 0.015 respectively). These a and b value are based on empirical measurements from laboratory earthquake experiments and have been widely used for modelling earthquake cycles with the rate and state equation (Marone [1998]). The stress loading rate of the faults in the system is defined using back-slip loading. Back-slip loading calculates the stress rate for each element of the fault that corresponds to the long-term slip-rate of the fault.

We are using triangular elements of 1 km size. For this reason, we will only discuss earthquakes larger than magnitude 6 that rupture a number of elements large enough (around 100) to be representative of an earthquake rupture.

## Earthquake rates in RSQSim

Using the fault geometry and slip-rate with the fully locked hypothesis (table 2.1, figure 2.2) as input for RSQSim, we simulate a 10 000 years long earthquake catalog from which we remove the first 1000 years of seismicity to let the fault system run through several earthquake cycles before starting the statistical analysis.

Richards-Dinger and Dieterich [2012] compared RSQSim with fully dynamic earthquake simulations and have shown that both modelling approaches lead to similar earthquake ruptures in terms of slip history and final slip on the fault. We observe that the scaling of earthquakes in RSQSim is in good agreement with the scaling laws (Tullis et al. [2012]) in terms of geometrical scaling and of stress drop. Interestingly, RSQSim reproduces quite well the rupture extent and magnitude of the 1999 of Izmit and Duzce earthquakes. Based on these comparisons we conclude that even if the physics of earthquake is simplified to allow for cost efficient calculations, the simulated catalog is representative of
the natural system at least to the first order. In order to not over-interpret the results we limit our use of the RSQSim simulated catalog to the discussion of two first order questions: (1) does the long term MFD of the fault system follows a GR law?, (2) do we observe magnitude 8.0 earthquakes in this fault system?

Considering the MFD of the synthetic catalog, we can reach two conclusions: RSQSim cannot reproduce a GR MFD with the given fault system and the maximum magnitude that can be generated is closer to magnitude 7.7 than to a magnitude 8.0. These two conclusions are not affected by uncertainties on a and b values (figure 2.10).

<figure><img src="image_32.png" /><figcaption>**Figure 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 ($a=0.01$ $b=0.015$).</figcaption></figure>

We also explored the impact of having a region of the fault creeping in the Western Marmara Sea. In a way similar to the “deep creep” model used in SHERIFS, in RSQSim, elements that are below 5km depth were attributed a b value much lower than the a value. The resulting MFD (figure 2.10) leads to the same first order conclusions as for the fully locked hypothesis. This is to be expected. Indeed, the region where creep is suspected is of a negligible size compared to the entire fault system and does not drastically affect the shape at the system level MFD. The creeping condition of the fault in the western Marmara sea most likely affects the participation rates of neighboring faults, however, here we only consider the first order results of the calculation.

The results are compared with the hybrid loading method used in Shaw et al. [2018] with the same input parameters as in the Californian application. The hybrid loading method allows to remove the edge effects on the stress field of the fault that occur with the standard back-slip loading (Shaw et al. [2018]). Different smoothness parameters are tested. The synthetic catalogs do not follow GR MFD, strengthening our previous observation.
## 2.4 Discussion on the weight of the epistemic uncertainties in the logic tree

The flexibility of SHERIFS for modelling the earthquake rates in the NAFS allowed to explore a wide range of uncertainties in a logic tree framework. The SHERIFS approach doesn't contain any physical constraints; it can therefore accommodate the different input hypotheses that are being discussed by the scientific community but also can lead to a large range of uncertainties on the earthquake rates. Since SHERIFS only uses the fault data as input, it is possible to compare the modelled rates with rates calculated from the earthquake catalog and paleoearthquakes which can be considered independent data from the SHERIFS input.

Branches weights in a logic tree are usually set by judging the scientific value of each hypothesis explored in the logic tree but not on the capacity of the modelled earthquake rates in each branch to reproduce the data. The weight of an individual branch of the logic tree is simply the product of the weights of each hypothesis used for the branch. In this discussion, we propose an innovative approach to set the weight of each branch of the logic tree accounting for both the input hypotheses used and the ability to reproduce the independent data.

We set up a quantitative scoring system in order to set the weight of each individual branch of the logic tree. For each branch, four scores are calculated (figure 2.11). One score judges the ability of the combination of input parameters and hypotheses to spend the slip-rate budget of the faults as earthquake rate and not generate a large amount of NMS (S1). Two scores compare the model to the data, judging the capacity of the modelled earthquake rates to reproduce the earthquake rates deduced from the catalog (S2), and to reproduce the earthquake rates deduced from the paleoseismic records (S3). The last score rates a-priory the input hypotheses based on the analysis of the RSQSim synthetic catalog (S4). The final weight of each branch of the logic tree is given by the combination of the four scores (figure 2.11).

### 2.4.1 Uncertainty on the creep

The creep conditions assumed on the Terkidag section play a predominant role in the modeling of earthquake rates on the adjacent Ganos section. The models considering the Terkidag fault as completely creeping have difficulties reproducing the paleoearthquake rates estimated on the Ganos fault (figure 2.9) and lead to a high level of NMS on this fault. In the fully creeping model, the Ganos section is only able to convert 54% of its slip-rate in seismic moment rate and 46% is considered NMS slip. In the partly creeping model, the Ganos section spends 71% of its slip-rate as moment rate. In the deep-creep model and the fully locked model, the Ganos section spends 90% of its slip-rate as seismic moment rate. We calculate the NMS value for each model and each fault section of the central zone. Since
<figure><img src="image_33.png" /><figcaption>**Figure 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.</figcaption></figure>

a large NMS value is likely linked to incompatibilities between input hypotheses, given the SHERIFS framework, a low score is attributed to models with high NMS slip value. For a given model, if the mean NMS value for the fault sections of the central zone is greater than 40% or if the NMS value of one of the faults of the central region is greater than 50%, the score is zero. The score is 1 if the average NMS of the sections of the central region is less than 20%. Between the average values of 20% and 40%, the score linearly decreases from 1 to 0 as the NMS value increases. As a result, the average score of the fully creeping models is 0.27, the average score of the partly creeping models is 0.6 and the average scores of both the deep creep and fully locked models are 0.96.

Figure 2.9 exposes the underestimation of the rate of earthquakes on the Ganos section compared to data when considering the Creep branch of the logic tree. The comparison with the paleoseismicity is done at all sites where
paleoseismicity is available for each model of the logic tree (see above). At each site, the rate of paleo-earthquake is extracted from the literature (table 2.3) and represented as a 2D Gaussian distribution in order to capture the uncertainty both in terms of magnitude and annual rate of occurrence. At each site, the modelled rates are compared to this distribution. The closer the participation rate for a given section is from the maximum of the paleo-earthquake rate distribution the larger the score. The score of the branch is the average score for each paleo-site. The scores for the Creep, Partial Creep, Deep Creep and Fully Locked models are 0.65, 0.73, 0.82 and 0.81 respectively.

## 2.4.2 Uncertainty on the shape of the MFD target

The models imposing a GR MFD as a target shape for the MFD of the fault system show a good agreement with the rate of large earthquakes calculated from both the catalog and the paleoseismicity but overestimate the rate of small to intermediate earthquakes.

However, it can be argued that the deviation of the MFD shape from the GR shape is an artifact of the observation period, which is too short for accurately capturing the full earthquake cycle. Such arguments have been brought forward in California in support for a GR MFD target shape even when the apparent shape of the earthquake catalog close to the faults might differ from the GR shape (Page and Felzer [2015]). Stirling and Gerstenberger [2018] have shown that for four fault systems in New Zealand, while the data doesn't show a good agreement with the GR MFD hypothesis, ETAS simulations suggest that the observation time in the data is too short to accurately calculate the long term rate of a clustered earthquake catalog.

However, the 10 000 years long synthetic catalog generated by RSQSim, complete and representative of the seismic cycle by definition, also diverges from the GR MFD shape. In the RSQSim catalog, there are almost no earthquakes of magnitude between 6.5 and 7.0. According to the scaling laws (Thingbaijam et al. [2017]), 6.5 is the magnitude of an earthquake rupturing the whole fault width. We speculate that in RSQSim, an earthquake rupturing the entire width of the fault, is more likely to rupture neighbouring faults unless stopped by geometrical complexities or the presence of faults that are still in the early part of their cycle. The average length of the straight sections of the faults is around 100 km (figure 2.1), which corresponds to an earthquake of magnitude around 7.2. Ruptures are able to overcome bends and asperities if the neighboring fault is close to rupture leading to larger magnitude earthquakes. Since they require several sections to be close to rupture simultaneously, these ruptures are less frequent. We obtain therefore a bi-modal distribution with the earthquakes up to magnitude 6.3 following a GR, rupturing different portion of the fault plane, very few earthquakes between magnitude 6.3 and 7.0, and a population of earthquakes larger than magnitude 7.0 with the number of earthquake decreasing with the magnitude.

Based on the comparison between the modelled rates with the rates of the earthquake catalog and the results
of RSQSim, and in consideration of the scientific debate around the MFD, we suggest a stronger score (s_mfd) on the "Tuned shape" MFD branch. The branch exploring the "GR MFD" should remain part of the logic tree, however. Consequently, we set the score of the branch "Tuned shape MFD" to 0.8 and the score of the branch "GR MFD" to 0.2.

### 2.4.3 Uncertainty on the largest possible rupture

Based on the comparison between the modelled rates from SHERIFS and the rate calculated from the earthquake catalog and the paleoseismicity studies, it is not possible to weight differently the two branches of the logic tree exploring the uncertainty on the rupture scenarios. While the fit between the modelled rates and the catalog rates using the Set 2 of ruptures, allowing larger ruptures, leads to a slightly better fit than the models using the Set 1 of ruptures, both fits can be considered as satisfying (figure 2.7). Whether ruptures up to magnitude 8.0 are considered or not, the rates in the models are matching the rates from the data when using the TS MFD as a target.

In the several 10 000 years long catalogs simulated by RSQSim, we do not observe earthquake larger than 7.7. In the SHERIFS models, earthquake with magnitude larger than or equal to 8.0 have an annual frequency of 5 10⁻⁴. The likelihood of observing at least one earthquake in a 10 kyr long catalog is 99.3 %. While the bends and other geometrical complexities of the fault trace are crossed by ruptures in the model, no rupture crosses enough complexities to generate such large earthquakes. We can assume that the fault system is very chaotic and having a large number of neighbouring fault sections close to rupture is very unlikely. However, it is important to recall that RSQSim does not fully model the dynamic effects of the earthquake rupture. It is possible that this simplification in the modelling leads to underestimating the likelihood of a rupture propagating through fault complexities. In consideration of these arguments, we set the s_set score of the branch "Set 1" to 0.7 and the s_set score of the branch "Set 2" to 0.3.

### 2.4.4 The weighted logic tree

In the discussion, we established four types of scores for the logic tree branches: the weights established from the analysis of the RSQSim synthetic catalogs and those established from the comparison of the earthquake rates modelled using SHERIFS with the rates calculated from the earthquake catalog and the paleoearthquake record. For each individual branch of the logic tree, these scores are convolved into a final weight unique to the branch (figure 2.11).

The final weight of each hypothesis is calculated by summing all the branches using a given hypothesis (figure 2.12). Due to the high NMS value of the models using the Creeping hypothesis and their underestimation of the paleoearthquake rates, this hypothesis has the lightest weight in the logic tree.

The weights of the MFD hypothesis branches and the Set of Rupture scenario branches are strongly influenced
by the weights imposed after the analysis of the RSQSim synthetic catalog. While the fit to the catalog is better with the TS MFD hypothesis, the fit to the paleoearthquake rates and the ratio of NMS is similar for both branches. Therefore the comparison with the data affects the weight ever-so slightly. The same can be said about the set of rupture scenario branches.

<figure><img src="image_34.png" /><figcaption>**Figure 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.</figcaption></figure>

The weights of the background hypothesis branches are only affected by the comparison with the data. Overall, the background 1 hypothesis reproduces the earthquake rates better than the other two background hypotheses. The scores for the fit to the catalog, the fit to the paleoearthquake rates, and the NMS ratio are respectively 0.54, 0.77 and 0.77 for the background 1; 0.49, 0.76 and 0.70 for the background 2; and 0.48, 0.72 and 0.61 for the background 3. In figure 2.7, we can observe that the modelled MFD tends to be slightly higher than the catalog MFD for the majority of models. Therefore, the background 3, adding more seismicity to the background than the two other hypotheses (table 2.4) necessarily leads to earthquake rates that are in general slightly higher than the observed rates. It is worth noting that we are discussing small differences in trends that are correctly captured by the weights in the logic tree with the three hypotheses having similar weights with a slightly stronger weight for background 1.

The impact of the weights on the annual earthquake rates are presented in figure 2.13. The weighting leads to lower earthquake rates for the small and intermediate magnitudes and larger rates for the magnitudes greater than 7.0. This is due to the reduced weight of the branches using the GR hypothesis.

## 2.5 Conclusion and perspectives

In this study, we calculated earthquake rates in the Marmara region relying on the fault slip-rate and geometry as primary information. We combined two innovating approaches, the SHERIFS approach that relies on statistical rules and the RSQSim approach that relies on physical rules.
<figure><img src="image_35.png" /><figcaption>**Figure 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.</figcaption></figure>

With SHERIFS, we explored an extensive logic tree of uncertainties concerning the locking condition of the NAF fault in the Marmara region, the shape of the MFD, the ratio of seismicity between the background and the faults, the largest possible rupture as well as uncertainties on the slip-rates and the maximum magnitude predicted by the scaling law. Rather than basing the weights of the branches of the logic only on the expert judgment of each hypothesis, we also take advantage of model performance by comparing results with data (earthquake catalog and paleoearthquake) and weigh the branch accordingly. In addition, the analysis of the synthetic catalog simulated by RSQSim showed a MFD diverging from a GR and didn't contain any earthquakes of magnitude larger than 7.7. This allowed us to attribute a stronger weight to the branches of the logic tree showing similar features leading to a final weighted distribution of modelled annual rates that properly represents the state of knowledge of the NAFS in the vicinity of Istanbul (figure 2.13).

In the next chapter of this study, we carry out a PSHA using the weighted logic tree and calculate the risk of collapse of a building in Istanbul. We expose the impact of each uncertainty of the logic tree on the probability of collapse and we deaggregate the risk results in order to identify the sources controlling the seismic risk.
# Chapter 3

# Calculating the Probability of Collapse of a
Building in Istanbul

## Résumé du chapitre

En utilisant les taux de sismicité modélisés dans le chapitre 2, nous calculons la probabilité d'effondrement d'un bâtiment à Istanbul sur une période de 50 ans. Pour chaque branche de l'arbre logique, nous calculons grâce au calcul de l'aléa probabiliste, la courbe d'aléa au site, décrivant la probabilité d'être dépassée pour un ensemble d'accélérations du sol. En convoluant cette courbe d'aléa avec la courbe de fragilité du bâtiment, qui décrit la probabilité d'effondrement du bâtiment en fonction de l'accélération du sol, nous obtenons la mesure du risque qui est la probabilité d'effondrement.

Nous calculons cette probabilité d'effondrement pour deux types de bâtiments représentant la majorité des bâtiments à Istanbul: un immeuble de moyenne élévation (3 à 7 étages), en béton armé, l'un construit en suivant le code de construction de 1975 (TEC75) et l'un construit en suivant le code de construction de 1998 (TEC98).

La probabilité d'effondrement du bâtiment TEC75 en 50 ans est de 2.8 à 8.1% et celle du bâtiment TEC98 est de 0.4 à 1.3%. L'évolution du code de construction entre 1975 et 1998 réduit donc le risk d'effondrement par un facteur 6. La pondération de l'arbre logique en utilisant la comparaison aux données et au catalogue synthétique de RSQSim a permis de réduire l'incertitude par un facteur 1.6 pour le bâtiment TEC75 et par un facteur 1.8 pour le bâtiment TEC98.

Grâce à l'utilisation de l'arbre logique, nous calculons l'impact de chaque incertitude explorée sur l'estimation du risque. L'incertitude sur la forme de la MFD entraine le plus d'incertitude sur la probabilité d'effondrement, suivie par le choix du set de rupture, de la GMPE et de l'hypothèse de sismicité de fond. A cause de la distance d'environ 70
km entre la zone de creep potentiel et le site, l'incertitude sur l'hypothèse de creep n'entraîne que peu d'incertitude sur l'estimation du risque à Istanbul.

Nous présentons une méthode de désagrégation du risque sismique permettant d'identifier les sources sismotectoniques contrôlant la probabilité de collapse. Pour le cas du bâtiment à Istanbul, deux sources participent au risk d'effondrement: les séismes de magnitudes supérieures à 7 sur la section de la faille Nord Anatolienne la plus proche et les séismes de magnitudes inférieures à 6.5 dans la zone de sismicité de fond à une distance inférieure à 10 km du site. Les séismes de magnitude 4.5 à 5.5 participent à la probabilité d'effondrement du bâtiment TEC75 mais ne génèrent pas de mouvements du sol suffisant pour entrainer l'effondrement du bâtiment TEC98.

L'approche développée dans ce chapitre nous permet d'identifier les pistes de recherches qui permettront d'améliorer la connaissance du risque sismique à Istanbul.
**3.1 Introduction**

The city of Istanbul being located in the vicinity of the North Anatolian Fault (NAF) (figure 3.1), the seismic hazard estimate has been a growing concern over the past decades (Erdik et al. [1999]). Since the 1999 Izmit earthquake that occurred on the NAF, East of the Marmara Sea, about 50 km east of Istanbul, several studies have assessed the seismic hazard in Istanbul (Erdik et al. [2004], Woessner et al. [2015], Giardini et al. [2018], Sesetyan et al. [2018]). These studies provided results in the form of hazard maps of the Peak Ground Acceleration (PGA) and of various frequencies of Pseudo Spectral Acceleration (PSA) that have a 10% or 2% probability of being exceeded in 50 years.

<figure><img src="image_36.png" /><figcaption>**Figure 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.</figcaption></figure>

In this study, rather than presenting hazard metrics, we present the result of the analysis in terms of a risk
assessment metric, the probability of collapse in a period of 50 years for a building in Istanbul. Probabilistic seismic
risk studies have been used in the past but they have been carried on by structural engineers, thus focusing more on
the modelling of the building response to the ground motion rather than the modelling of the seismic sources. In this
study, we will focus our attention on the impact that different hypotheses on the modelling of the seismicogenic sources
have on the risk assessment.

Using a risk targeted approach, Iervolino et al. [2018] show that "generally, design procedures are such
that seismic structural reliability tends to decrease with increasing seismic hazard of the building site, despite the
homogeneous return period of exceedance of the design seismic ground-motion". Despite using a building code
constructed using a hazard that represents the PGA at 10% over 50 years over the whole Italian territory, the risk
of damage of buildings is much higher in area where the hazard is higher. Using a hazard map presenting a uniform
probability of exceeding a given ground motion (e.g. 10% over 50 years) can mislead the audience of the map (decision maker and the public) and make them think that the risk level is also uniform over the territory. Iervolino et al. [2018] showed that, in Italy, the risk level is not uniform.

In order to increase the chances of seismic hazard results reaching a wider audience, the company Temblor (through its website temblor.net) presents risk results that integrate both the hazard results and the building response. This allows to frame the question in terms that can be more easily understood by non-PSHA practitioners.

Hong and Goda [2006] have shown that when looking at the risk for a specific building, the seismicogenic sources controlling the hazard at a site can differ from the sources controlling the risk.

Most PSHA studies present the hazard as a 10% chance of exceedance in 50 years which is the classical value used for the establishment of codes for residential buildings. This value of 10% is set as an acceptable level of risk to be taken for general use buildings. For critical structures such as chemical or nuclear plants this value is 2%, 0.5% or even lower. However, since this value on the hazard level doesn't directly reflects the risk level (Iervolino et al. [2018]), presenting the hazard without consideration of the risk can be misleading for the decision making process.

In more general terms, the hazard map poorly answers the question posed by the general public and decision makers alike: what is the probability of damage for a building during a given period of time?

In this study, the seismic hazard (probability of exceeding different levels of ground motion) is calculated using the earthquake rates modelled in the chapter 2 exploring a wide logic tree of epistemic uncertainties (figure 3.2, table 3.1). We also explore uncertainties on the Ground Motion Prediction Equation (GMPE) through a logic tree set up by Sesetyan et al. [2018].

Using the probability of exceeding different levels of ground motion (e.g. the hazard curve) and the probability of a building to collapse given a ground motion level (e.g. the fragility curve), we calculate the probability of collapse for a building in Istanbul over a period of 50 years. We perform the calculation using two different fragility curves both corresponding to a 5 floors reinforced concrete building but for two different building codes, the TEC75 building code and the TEC98 building code (Ozmen et al. [2010]).

We track the impact on the probability of collapse of each uncertainty explored in the logic tree and show the leading sources of uncertainty on the probability of collapse.

Using a novel approach for risk deaggregation, we expose the earthquake sources that control the probability of collapse of a building in Istanbul for different models and input hypotheses.
<figure><img src="image_37.png" /><figcaption>**Figure 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]</figcaption></figure>

## 3.2 Seismic hazard in Istanbul

In this study, we assess the seismic hazard at a site in Istanbul (figure 3.1) using the Cornell McGuire approach (Cornell [1968], McGuire [1976]) based on the following equation 1.

$$P(A > a^*) = \int_M \int_D \int_{\epsilon} \lambda_{M,D} \times P(A > a^*|M, D, \epsilon) \quad (3.1)$$

With $\lambda_{M,D}$ the annual rate of earthquakes of magnitude $M$ at the distance $D$; and $P(A > a^*|M, D)$ the probability of the ground motion $A$ to exceed the target level $a^*$ given the magnitude $M$ at the distance $D$. $P(A > a^*|M, D, \epsilon)$ is obtained using a Ground Motion Prediction Equation (GMPE) with the $\epsilon$ value. $\epsilon$ is defined as the number of standard deviations by which an observed logarithmic spectral acceleration deviates from the mean logarithmic spectral acceleration of a GMPE.

Based on the earthquake rates modeled using SHERIFS (chapter 2), we conduct the Probabilistic Seismic Hazard Assessment (PSHA) using the code Openquake (Pagani et al. [2014]). Each branch of the Seismic Source Characterization (SSC) logic tree set up in the chapter two is ran with four Ground Motion Prediction Equation (GMPE). This GMPE logic tree was constructed in a former PSHA of Turkey (Sesetyan et al. [2018]) and we chose to use it with the same GMPE weights (figure 3.2).

The logic tree presented in figure 3.2 explores a large number of uncertainties on the input hypotheses of the fault modelling (table 3.1). This translates into a large uncertainty in the hazard result (figure 3.3). In this study, we will not expose the impact of each uncertainty on the hazard metric but rather we will present how each uncertainty
<table><caption>Table 3.1: Description of the hypotheses explored in the logic tree.</caption><thead><tr><th>Logic Tree node</th><th>Hypothesis name</th><th>Short description</th></tr></thead><tbody><tr><td rowspan="4">Locking Model</td><td>Creeping</td><td>NAF creeping in the Western Marmara Sea</td></tr><tr><td>Partial Creep</td><td>NAF 50% creeping in the Western Marmara Sea</td></tr><tr><td>Deep Creep</td><td>NAF creeping at depth in the Western Marmara Sea</td></tr><tr><td>Fully Locked</td><td>NAF is locked</td></tr><tr><td rowspan="2">Magnitude Frequency Distribution</td><td>GR</td><td>The modelled seismicity follows a Gutenberg Richter distribution</td></tr><tr><td>TS</td><td>The modelled seismicity follows a distribution similar to the one observed in the earthquake catalog</td></tr><tr><td rowspan="4">Background Seismicity</td><td></td><td>Ratio of the seismicity on the faults for each magnitude range</td></tr><tr><td></td><td>4.0 | 4.5 | 5.0 | 5.5 | 6.0 | 6.5 | 7.0 | 7.5 | 8.0+</td></tr><tr><td>BG_1</td><td>0.8 | 0.8 | 0.8 | 0.8 | 0.8 | 0.9 | 1.0 | 1.0 | 1.0</td></tr><tr><td>BG_2</td><td>0.7 | 0.7 | 0.7 | 0.7 | 0.7 | 0.8 | 0.9 | 1.0 | 1.0</td></tr><tr><td></td><td>BG_3</td><td>0.4 | 0.4 | 0.4 | 0.45 | 0.5 | 0.6 | 0.8 | 1.0 | 1.0</td></tr><tr><td rowspan="2">Scenario Set</td><td>Set_1</td><td>The largest rupture possible in the system are in the size of the largest historical earthquakes (M7.7)</td></tr><tr><td>Set_2</td><td>The largest rupture possible in the system (M8.0) exceeds the historical earthquakes</td></tr></tbody></table>

impacts the risk, expressed as the probability of collapse of a building.

## 3.3 Methodology for the calculation of seismic risk

### 3.3.1 Probability of damage

In this study, we set up an approach to explore the impact of the different epistemic uncertainties considered in the logic tree through the lens of the probability of collapse. The hazard curve resulting from each branch of the logic tree is convolved with a fragility curve describing the building response to the seismic solicitation. The hazard curve shows the probability of exceedance of a given ground motion (e.g. PGA) during a given time period (e.g. 50 years). From this hazard curve, we create an incremental hazard curve giving the probability of a ground motion to be the strongest
<figure><img src="image_38.png" /><figcaption>**Figure 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.</figcaption></figure>

ground motion observed during the given time period. This probability is then multiplied by the probability of the ground motion to damage the building according to the predictions of a given fragility curve. The integration on the ground motion level gives us a probability of damage of the building during the time period (equation 2).

$$P(damage) = \sum_{A} P(A = a_n) \times P(damage|a_n) \qquad (3.2)$$

With A the ground motion level, P(A) the probability of the ground motion being the largest ground motion observed in the time period according to the hazard curve, P(damage|A) the probability of damage with a ground motion of A according to the fragility curve.

### 3.3.2 Risk deaggregations

Convolving hazard and fragility curves provides a single risk indicator, such as the probability of damage, give us a better idea of how different input hypotheses impact risk, it also makes it more difficult to understand what are the earthquake sources contributing the most to this risk. Similarly to the deaggregations developed by McGuire (McGuire [1995]) for hazard deaggregation, we identify the participation of each source to risk by developing a methodology to deaggregate the probability of damage. First, deaggregations of the hazard results are carried out for a range of ground motions, ranging from very small ground motion with a negligible change of damaging a building to very large ground motions with a negligible probability of exceedance. Each deaggregation gives the conditional probability of exceedance of the ground motion for each range of distance, magnitude, and epsilon value (eq 4). The epsilon value $\epsilon$ is the number of standard deviation from the mean ground motion predicted by the GMPE. $\epsilon = 0$ indicates the mean
<figure><img src="image_39.png" /><figcaption>**Figure 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.</figcaption></figure>
value participates to the hazard, $\epsilon = -1$ means that the values of acceleration one standard deviation smaller than the mean participate to the hazard, and a $\epsilon = 1$ means that acceleration one standard deviation larger than the mean participate to the hazard.

$$P(A > a_n) = \sum_D \sum_M \sum_{\epsilon} P(A > a_n|M, D, \epsilon) \quad (3.3)$$

In order to obtain the conditional probability of the ground motion to be the largest observed in the time period of interest, each conditional probability is reduced by the conditional probability of exceeding a stronger ground motion (eq 4)

$$P(A = a_n) = \sum_D \sum_M \sum_{\epsilon} P(A > a_n|M, D, \epsilon) - P(A > a_{n+1}|M, D, \epsilon) = \sum_D \sum_M \sum_{\epsilon} P(A = a_n|M, D, \epsilon) \quad (3.4)$$

Where, $P(A > a_n|M, D, \epsilon)$ is the conditional probability of exceeding the ground motion $a_n$ given the magnitude $M$, the distance site to source $D$ and $\epsilon$ value; and $P(A > a_{n+1}|M, D, \epsilon)$ is the conditional probability of exceeding a ground motion such as $a_{n+1} > a_n$.

In order to obtain a precise result, the hazard deaggregation ($P(A > a_n|M, D, \epsilon)$) needs to be calculated for a large number of ground motion $a_n$. However, because deaggregation can be computationally expensive, the number of ground motion level calculated needs to be optimized depending on the computational capacities.

$$P(damage|M, D, \epsilon) = \sum_n P(A = a_n|M, D, \epsilon) \times P(damage|a_n) \quad (3.5)$$

where $P(damage|M, D, \epsilon)$ is the probability of a building being damaged over the time period of interest for a given set of magnitude, distance and epsilon value.

Deaggregating the probability of damage provides a better understanding of the sources contributing to the seismic risk for a building and allows a more efficient targeting of future studies aiming to reduce risk uncertainties.

This approach also offers the possibility to use magnitude, distance and/or source dependant fragility curves where the probability of damage $P_{M,D,\epsilon}(damage|a_n)$ can be calculated using the following equation if such fragility curves are available.

$$P(damage) = \sum_M \sum_D \sum_n P(A = a_n|M, D) \times P_{M,D}(damage|a_n) \quad (3.6)$$
## 3.4 Results

### 3.4.1 Probability of collapse for a building in Istanbul

Several fragility curves describing the building response to ground motions are available for Turkish buildings. In this study, we use the fragility curves for mid-rise reinforced concrete (RC) buildings developed by Ozmen et al. [2010]. RC buildings is the most common construction type in the Marmara region with 75% of the total building stock (Bal et al. [2008]). Fragility curves provide the probability of the building being in a state of "collapse prevention" where structural elements of the building have been damaged and the reuse of the building is not safe. In order to simplify the language, we will address the "probability of collapse prevention" as the "probability of collapse". Ozmen et al. [2010] provide fragility curves for two types of RC buildings, following the Turkish building code established in 1975 (TEC75) and following the building code established in 1998 (TEC98). The probability of collapse according to the PGA is shown in figure 3.5. These building models are representative of the majority of building stock in Turkey (Ozmen et al. [2010]). Ozmen et al. [2010] also provide fragility curves giving the probability of the building to be no longer suitable for immediate occupancy and for life safety.

<figure><img src="image_40.png" /><figcaption>**Figure 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]).</figcaption></figure>

Using the hazard curves giving the probability of exceedance of PGA over 50 years presented in figure 3.4, we calculate the probability of collapse.

Comparing the probability of collapse of a building in 50 years for the two building codes, indicates a reduction of a factor 6 for the TEC98 building with respect to the TEC75 building (figure 3.6). For a TEC75 building, the information gained from adding the comparison to the data in the weighting of the logic tree reduces the uncertainty on the probability of collapse from between 3.4% and 11.8% to between 3.2% and 10.3%. Adding the weighting suggested by the physics-based modelling, the uncertainty on the probability of collapse is brought down to between 2.8% and
<figure><img src="image_41.png" /><figcaption>**Figure 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)</figcaption></figure>

8.1%. In total, the uncertainty is reduced by a factor 1.6.

Similarly, for a TEC98 building, the information gained from adding the comparison to the data in the weighting of the logic tree reduces the uncertainty on the probability of collapse from between 0.48% and 2.23% to between 0.44% and 1.88%. Adding the weighting suggested by the physics-based modelling, the uncertainty on the probability of collapse is brought down to between 0.35% and 1.31%. In total, the uncertainty is reduced by a factor 1.8.

### 3.4.2 Impact of uncertainties on the probability of collapse

In order to understand the impact of each uncertainty explored in the logic tree on the probability of collapse, we illustrate the results according to each branch of the logic tree (figures 3.7 to 3.11).

The probability of collapse is not dependent on the creep hypothesis used in the model (figure 3.7). The distance between Istanbul and the creeping section of the fault prohibits a strong influence of this distant source on the seismic hazard.

The choice of GMPE does affect the probability of collapse with the Akkar and Cagnan 2010 GMPE leading to significantly lower probabilities compared to the high values of Zhao et al. 2006 GMPE (figure 3.8).
<figure><img src="image_42.png" /><figcaption>**Figure 3.7:** Probability of collapse over 50 years colored according to the creep hypothesis.</figcaption></figure>

<figure><img src="image_43.png" /><figcaption>**Figure 3.8:** Probability of collapse over 50 years colored according to the choice of GMPE.</figcaption></figure>

Using the GR hypothesis as a target shape leads to a significantly larger probability of collapse over 50 years than using the TS hypothesis (figure 3.9). The models using the GR hypothesis predicts a larger rate of earthquakes of magnitude 4.5 to 6.5 than the TS hypothesis, leading to a probability of collapse around two times larger.

Allowing larger ruptures to occur in the Set 2 branch consummates a large portion of the moment rate budget of the faults which leads to lower annual rate of rupture for earthquakes of all magnitudes. This change in the balance of the moment rate budget leads to probabilities of collapse smaller for Set 2 and for Set 1 by a factor of around 1.5 (figure 3.10).

In chapter 2, the results of the physics-based model RSQSim suggested giving less weight to both the GR hypothesis and the Set 2 hypothesis. The impact of this weighting on the probability of collapse can be observed in figure 3.6. However, in this particular case, the GR hypothesis leads to a higher risk and the Set1 to a lower risk. The
combined influence of these branches makes weighting less influential on the mean value of collapse but the overall
uncertainty is reduced.

<figure><img src="image_44.png" /><figcaption>**Figure 3.9:** *Probability of collapse over 50 years colored according to the MFD hypothesis.*</figcaption></figure>

<figure><img src="image_45.png" /><figcaption>**Figure 3.10:** *Probability of collapse over 50 years colored according to set of scenarios.*</figcaption></figure>

We evaluate (figure 3.12) the contribution of the uncertainties of each node of the logic tree by calculating
the absolute difference between the distribution of the branches presented in figures 3.7 to 3.11. The most influential
branches of the logic tree show the largest differences between the different distributions. For both building codes, the
largest source of uncertainty is the choice of target MFD followed by the choice of the set of rupture scenario. The
uncertainty with the less impact on the risk is the choice of locking model. For the TEC75 building, the background
hypothesis node of the logic tree is generating a similar uncertainty on the risk to the choice of GMPE node. However,
for the TEC98 building, while both nodes generate more uncertainty, the choice of GMPE is a larger source of
uncertainty.
<figure><img src="image_46.png" /><figcaption>**Figure 3.11:** Probability of collapse over 50 years colored according to the background hypothesis.</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>**Figure 3.12:** Relative impact of each uncertainty on the probability of collapse for TEC75 (left) and TEC98 (right). The length of the line is relative to its impact on the uncertainty. The lengths are normalized. The uncertainties are from top to bottom: the background hypothesis, the rupture set, the MFD, the GMPE and the locking model of the NAF in the western Marmara Sea.</figcaption></figure>

### 3.4.3 Seismogenic sources controlling the risk

The deaggregation of the risk is ran for the 3 branches that have the strongest weight in the logic tree to analyze the impact on the risk. For comparison purposes, deaggregation is also computed using the faults and background model developed within the SHARE project. For each model, the two fragility curves TEC75 and TEC98 are used (figure 3.13).

For all models, the deaggregation of the seismic risk shows a clear bi-modal participation with a contribution of the distant large M7 and greater earthquakes occurring on the NAF and the participation of close small to moderate earthquakes occurring in the background. The choice of background hypothesis affects the participation of small to moderate earthquakes (figure 3.13 a and b). The choice of target MFD is the most impacting with a drastic increase of the participation of small earthquakes to the risk when the GR MFD is used compared to the TS MFD (figure 3.13 a
and c). While the probability of an M5 earthquake damaging a building is relatively small, the rate of M5 earthquakes in the background, e.g. close to the site, is larger in the GR hypothesis than in the TS one.

The SHARE model leads to a greater probability of collapse than the models from the logic tree proposed in this study (figure 3.13) due to higher estimates of both background seismicity rates and of M6.5 to 7.0 earthquakes on the faults compared to those proposed in this study (figure 3.14).

The contribution of each magnitude-distance bin to the probability of collapse depends strongly on the fragility curve considered for the building. Between figure 3.13 b and f, we can observe the decrease of the participation of M4.5 to 5.5 earthquakes when considering a TEC75 or a TEC98 building. As shown by the epsilon value close to 2 (figure 3.13 b), M4.5 to 5.5 earthquakes have a non negligible probability of generating PGA that are damaging for TEC75 building (around 0.4 g, cf figure 3.5). For a TEC98 building, a damaging PGA are around 0.8g; a PGA value unlikely to be generated by the M4.5 to 5.5 earthquakes (epsilon value are superior to 2.5 in figure 3.13 f).

In SHARE, 100% of earthquakes are in the background for magnitude lower or equal to 6.3 and 100% of the earthquakes are on the faults for magnitudes greater or equal to 6.4. This artificial separation is clearly visible in the deaggregation (figure 3.13). In the SHERIFS models, especially using the BG3 hypothesis, the rate of 4.5 <M< 5.5 earthquakes on the faults is non-negligible. However, since the fault is almost 20 km away from the site of calculation, these moderate magnitudes don't participate to the risk of collapse in this case. The participation of the earthquake source to the risk of collapse is directly linked to the spatial distribution of the rate of earthquakes vis-a-vis the calculation site.

From the hazard source model, we extracted the magnitude frequency distribution (MFD) of the section of the NAF closest to Istanbul and the background MFD from a circular zone of 10 km radius around Istanbul (figure 3.1, figure 3.14). The 10 km radius was chosen to be representative of the distance up to which earthquakes are participating to the risk in the background region of Istanbul (figure 3.13). The larger rate of earthquakes assumed in the SHARE model (figure 3.14), both for the background seismicity and the faults, explains the stronger probability of collapse over 50 years. In SHERIFS, seismicity is shared between background and faults over the entire magnitudes range with the exception of the largest one (for the largest magnitude bin the ratio of earthquakes in the background is 0, for M> than 7.0 in BG1 and M>7.5 in BG2 and BG3). For low magnitude earthquakes ( 4.5 <M< 5.5) this ratio is 0.2 in BG1, 0.3 in BG2 and 0.6 in BG3 (table 3.1).

For all models, the contribution of earthquakes for magnitude between 4.5 and 6.5 is linked to PGA in the upper part of the GMPE distribution (mean epsilon > 2). Probability of collapse of the TEC98 building is linked to higher epsilon of the GMPE than for the TEC75 building. In order to lead to the collapse the TEC98 building, the PGAs are linked to the upper part of the GMPE distribution.
<figure><img src="image_48.png" /><figcaption>**Figure 3.13:** Deaggregation of the probability of collapse over 50 years using the building code TEC75 (a,b,c,d) and TEC98 (e,f,g,h) and the GMPE Ak14. Three different models from the logic tree are used: all with partial creep model and the Set 1 of rupture scenario, the BG1 and TS MFD (a,e), BG3 and TS MFD (b,f) and BG2 and GR MFD (c,g). Figure d and h use the fault and background model from the SHARE project. The color represent the mean of the epsilon value of the GMPE for each bin. PC : Probability of Collapse. BP : Background Participation. The figures are normalized vertically since the vertical scale is the conditional probabilities.</figcaption></figure>
<figure><img src="image_49.png" /></figure>

**Figure 3.14:** For the four models used in figure 3.13 : participation rate of the fault section closest to the site (solid line) and for the background seismicity (dashed line) for a 10 km radius (figure 3.1) around the site. Three models from the logic tree are used: the BG1 and TS MFD (blue), BG3 and TS MFD (green) and BG2 and GR MFD (black). The fault and background MFD SHARE are in red. All models include the background zone north of Istanbul that crosses the 10km radius (figure 3.1) shown in purple.

**3.5 Discussion**

**3.5.1 Probability of collapse**

The methodology used in the study allows to describe the differences in seismic risk estimates when considering two buildings following different construction codes in Istanbul (TEC75 and TEC98 type buildings). The TEC75 buildings have a probability of collapse in 50 years of 2.8 to 8.1% whereas the TEC98 buildings have a probability of collapse in 50 years of 0.4 to 1.3% (figure 3.6). The evolution of the building code between TEC75 and TEC98 leads to a 6 fold reduction of the risk of collapse over 50 years.

We used the data and the discussion based on the RSQSim modelling to weigh the logic tree (see chapter 2).
Because of the weighting, the uncertainty on the risk is reduced by a factor of 1.6 for the TEC75 building and by a
factor of 2.0 for the TEC98 building.
### 3.5.2 Linking input hypothesis and results

In this study we explore a larger range of epistemic uncertainties that is usually explored in the risk assessment studies and we observe the impact of these uncertainties by computing the probability of collapse. By using a streamlined methodology, we are able to expose the impact of each uncertainty on the final probability of collapse and therefore give an orientation for future research with a strong potential for improving the risk assessment.

#### The Magnitude Frequency Distribution

The largest source of uncertainty is on the choice of the target MFD (figure 3.12), especially for the TEC75 building. Future work on the earthquake catalog, both on the historical and the instrumental part, might be able to shed new light on the long term MFD in the western NAFS. However, since the number of large magnitude earthquakes will remain relatively low, the statistical analysis will still suffer from uncertainties in the large magnitude range.

After analyzing the MFD of several fault systems in New Zealand, Stirling and Gerstenberger [2018] advise to always explore this uncertainty in the logic tree for hazard studies. Since our results show the important impact of this uncertainty on the uncertainty concerning the risk, we also support the exploration of this uncertainty by default in future studies in order to have a proper estimation of the uncertainty on the risk.

However, reducing this uncertainty is possible. The long synthetic catalogs generated using "physics-based" model RSQSim show a clear deviation from the GR MFD. Taking into account this observation in the weighting of the logic tree significantly reduces the uncertainty on the probability of collapse (figure 3.6, figure 3.9). More studies with alternative "physics-based" approaches might be able to reduce even more the uncertainty.

Finally, a worldwide comparison of the MFD similar fault systems (e.g. San Andreas Fault System, Dead Sea Fault System, Hope Fault System in New Zealand...) could bring some new information on the validity of a MFD different from the GR MFD for a strike-slip fault system.

#### The largest possible rupture

The probability of collapse in 50 years is reduced in Set 2 compared to Set 1 (figure 3.10). Including larger earthquakes in a fixed moment rate budget system leads to reducing the overall rate of earthquakes. Since the ground motion generated by magnitude 7.5 earthquakes have the potential to already lead to the collapse of buildings (figure 3.13), the reduction of their annual rates has a greater impact on the probability of collapse than considerations of potential larger magnitude earthquakes, hence leading to an overall reduction of the probability of collapse for Set 2.
In chapter 2, the comparison between the model and the data (earthquake catalog and paleoseismicity) was not sufficient to discard the possibility of a magnitude 8 earthquake on the NAF close to Istanbul. It is possible that future paleoseismic studies reveal the occurrence of magnitude 8 earthquakes in the Marmara region. In order to reduce this uncertainty, we modelled the NAF with RSQSim. The absence of magnitude 8 earthquakes in the RSQSim synthetic catalogs allowed to set a stronger weight to the Set 1 branch and therefore reducing the uncertainty on the probability of collapse due to the rupture set branch. However, RSQSim doesn't capture the dynamic effects of the earthquake rupture which could allow for larger earthquakes than the ones suggested by RSQSim. Further physics-based modelling of the NAF have the potential to reduce even more the uncertainty caused by this branch of the logic tree.

## The background seismicity

The uncertainty on the way the background seismicity is modelled is not usually explored in seismic risk analysis. Using the background modelling approach of SHERIFS, we explored three hypotheses of seismicity ratio between the faults and the background (table 3.1). This uncertainty has a large impact on the probability of collapse (figures 3.11 and 3.12); the larger the proportion of earthquakes in the background, the larger the probability of collapse.

Reducing this uncertainty will remain a challenge since the number of damaging earthquakes in a given area is too small for a conclusive statistical analysis. Geodetic strain maps and geologic investigations of deformation away from the major faults could provide pieces of information useful for setting the seismicity ratio between the faults and the background.

## The creep condition model

In this study, the hypothesis of creep on the fault in the western Marmara Sea has the smallest impact on the uncertainty concerning the risk of collapse. The potentially creeping section is more than 50 km away from the risk calculation site in Istanbul. Because of this large distance, the risk is much more sensitive to the modelling parameters affecting the fault section directly in front of Istanbul.

## 3.6 Conclusion and Perspectives

Rather than exposing hazard metrics such as the 10% probability of exceedance of a PGA over 50 years, we chose to present risk metric such as the probability of collapse of a building in 50 years. Using a risk assessment approach we can draw the following conclusions :

* The probability of a 5 story RC building to require collapse prevention in Istanbul over a period of 50 years is 2.8
to 8.1 % for a TEC75 building and 0.4 to 1.3% for a TEC98 building.

* The evolution of the building code between TEC75 and TEC98 decreases the probability of collapse by a factor of 6 according to our study.

* By using the comparison with the data and the physics-based catalog from RSQSim, the uncertainty on the probability of collapse was reduced by a factor of 1.6 for the TEC75 building and by a factor 1.8 for the TEC98 building.

* The leading source of uncertainties is the choice of MFD followed by the choice of rupture set, the GMPE and the background hypothesis. The locking condition of the NAF doesn't affect the probability of collapse since the potentially creeping section is 70km away from Istanbul.

* Both magnitude 7+ earthquakes occurring on the NAF and moderate earthquakes of magnitude between 4.5 and 6.5 occurring within 10 km from Istanbul participate to the probability of collapse.

Identifying the sources controlling the hazard and the risk allows to target future studies that aim to reduce this uncertainty. For example, in Istanbul, the use of RSQSim has reduced uncertainties by allowing more weight on some branches. Alternative models could help to know if the GR MFD branch should be removed from the logic tree completely, thus further reducing the uncertainty.

Risk oriented studies have the potential to improve communication between two isolated communities that are the geosciences community and the engineering community by developing tools with which both hazard modeler and engineers can discuss. In this study, we only use PGA fragility curves. More fragility curves could be explored and multi dimensional (PGA, PSA, duration,..) fragility curves could also be used in this type of studies.

The approach presented in this study could also be used to draw maps of probability of collapse for different types of buildings. Such type of outputs could help public authorities to set up risk mitigation plans.
# Chapter 4

## Conclusions and Perspectives

This chapter presents the main conclusions and perspectives of this thesis. It is structured in three sections presenting each the conclusions and perspectives of an aspect of the thesis:

* Modelling earthquake rates in fault systems

* Physics-based modelling

* The risk oriented approach

A final section gives the general conclusions of the thesis.

### 4.1 Modelling earthquake rates in fault systems

#### 4.1.1 The system level approach

In this study, we present a system level approach for earthquake rate modelling in fault systems, taking as input the slip-rate and geometry of the faults, an hypothesis on the MFD of the fault system, and an hypothesis on the ruptures that are possible in the system. Through an iterative procedure, the fault slip-rate budget is converted into annual rate of rupture. In order to accommodate the different input hypotheses, part of the slip-rate budget of a fault cannot be converted into annual rate of ruptures and is thus considered as aseismic. A proportion of the seismicity can be attributed in the background zone surrounding the fault system, representing the possibility of an earthquake happening on non-modelled faults. It is possible to explore a wide range of epistemic uncertainties in a logic tree. By comparing the modelled earthquake rates with the local data (earthquake catalog and paleoseismicity), a weighting of
the logic tree branches is proposed. Through this approach, the uncertainties affecting the modelling of the earthquake rates on faults are properly propagated in the seismic risk assessment.

### 4.1.2 Magnitude Frequency Distribution

In chapter 2, after analysis of the earthquake rates in the catalog, we observe a shape of the MFD that diverges from the GR distribution. We explored two hypotheses in a logic tree, the MFD following the GR distribution and the MFD following a shape tuned to that of the catalog MFD (TS MFD). Between the epistemic uncertainties explored in the logic tree in chapter 2, we found that the MFD is the leading cause of uncertainty on the probability of collapse in 50 years of a building in Istanbul. Following the conclusions of Stirling and Gerstenberger [2018], we suggest that this uncertainty should be explored for seismic hazard assessment.

The synthetic earthquake catalog generated by the physics based model RSQSim shows a clear divergence from the GR distribution towards a more characteristic distribution of the seismicity. Using this analysis, we were able to set a stronger weight to the TS MFD branch in the logic tree and therefore reduce the uncertainty on the assessment of the probability of collapse.

At the system level, the earthquake rates follow the MFD set as input. However, at the fault level, the participation rate (or rate of rupture going through the fault) can be very different from the regional MFD, sometimes tending towards a characteristic earthquake MFD even when a GR MFD is imposed at the system level. Similar observations can be made for the participation rates in the UCERF3model (Field et al. [2014]). As the intensity of the ground motion decreases with the square of the distance between the source and the site of calculation, the local seismogenic sources often control the hazard. Hence, the participation rate MFD can have a very strong impact on the hazard estimate. In Istanbul, the models constructed using SHERIFS lead to very different probability of collapse estimates than the models based on SHARE (see chapter 3). SHARE uses the classical fault level approach to model the faults and imposes a GR MFD on each fault, the risk disaggregation shows the impact of this hypothesis on the risk estimate. Allowing the local MFD to be different than the system level MFD is one of the features of the system level approach that has the largest impact on the risk estimate.

### 4.1.3 Complex fault rupture

Allowing ruptures to propagate between fault sections, moves the discussion from segmentation of the fault to possible ruptures in the system. This allows an easy exploration of the epistemic uncertainty on the maximum rupture that is possible in the fault system. Comparing the modelled earthquake rates with the rates from the earthquake catalog and the paleoseismicity studies can eliminate some rupture hypotheses and therefore reduce the epistemic uncertainty. This
allowed to test some rupture hypotheses laid out by paleoseismologists and compare how they perform against data.

### 4.1.4 The background seismicity

In SHERIFS, a novel methodology for modelling background seismicity is introduced. The proportion of seismicity on the faults and in the background is user-defined for each magnitude as an input. It acknowledges the intrinsic lack of knowledge of a given region and several hypothesis are easily explored. Due to a lack of modelling tools, this uncertainty is usually not explored in seismic hazard studies. In the Istanbul example, we showed that the background seismicity, depending on how it is considered in the fault model, can be an important source of uncertainty for the estimate of the probability of collapse. This uncertainty should be systematically explored for a complete picture of the epistemic uncertainty affecting a risk estimate.

### 4.1.5 Perspectives on the use of SHERIFS

While SHERIFS is operational and has been applied to a variety of fault systems, it has never been applied to a subduction zone. In theory, the methodology should be applicable in the same way; however, unforeseen challenges may arise. The application of this methodology to a subduction would allow to explore different approaches and developments to model the coupling of the interface.

Many aspects of SHERIFS could be improved, especially in term of computational efficiency. Faster computation enables the user to explore a wider range of uncertainties on a laptop computer. Features like automatic consistency checks could be implemented. For example if a rupture set is not compatible at all with the other hypotheses in the system, SHERIFS could notify the user and prevent him from interpreting a flawed set of input hypotheses.

Several additional refinements could be added to SHERIFS, one of which being the modelling of complex slip-distribution along the ruptures. At present SHERIFS spends the same amount of slip-rate budget for all the faults involved in a given rupture, the possibility of using other distributions can be implemented.

So far, SHERIFS calculates only time-independent rate of earthquakes in the fault system which is the first step towards building a time-dependent model. In time-dependent models, depending on the elapsed time since the last earthquake, the probability of an earthquake in the near future is modified by a probability function. Several functions are possible and UCERF3-TD (time dependent, Field et al. [2015]) presents how this approach can be applied to system level approaches. The way to model time dependency is still under discussion in the scientific community and, to my knowledge, no national building code relies on such models. It would be interesting to transform SHERIFS in a tool allowing users to join this discussion and to explore the impact of different hypotheses on the risk assessment.
Finally, SHERIFS is a community tools used by geologists and hazard modelers. By sharing the risk calculation codes, we could bring engineers in this community. Working as a community to address the problems of seismic risk is the most efficient way to bring the best available science into the decisions on risk mitigation measures. We can follow the example of the SCEC community (Southern California Earthquake Center) that has enabled advances in the field of seismic hazard assessment (UCERF - Field et al. [2014], CyberSHAKE - Graves et al. [2011], ...).

## 4.2 Physics-based models and alternative approaches of earthquake modelling

### 4.2.1 Possible ruptures

In accordance with dynamical modelling results of Aochi and Ulrich [2015], we define earthquake ruptures that can run through the fault bend of the NAF in the vicinity of Istanbul.

On the NAF, no earthquakes larger than 7.7 have been observed in the historical time. However, since the length of the historical catalog is limited to several hundred years, it is possible that larger earthquakes with long recurrence times may occur along the western NAF. Therefore we explore this hypothesis in a logic tree branch that allows earthquake ruptures corresponding to a magnitude 8 earthquakes.

The 10 000 years long synthetic earthquake catalogs generated using the earthquake simulator RSQSim didn't contain any earthquake of magnitude greater than 7.7. This observation suggests a stronger weight for the branch of the logic tree that doesn't include the larger rupture. Since the set of possible ruptures has an impact on the probability of collapse, the weighting of the logic tree allows to reduce the uncertainty on the risk.

### 4.2.2 Earthquake rates

In the Marmara region, the MFD calculated from the earthquake catalog shows a divergence from the GR MFD. However, it can be argued that this observation is due to an incompleteness of the earthquake catalog or the uncertainty of the historical magnitudes. Nevertheless, we set up logic tree branches exploring this hypotheses: a GR MFD and a MFD tuned to the shape of the catalog (Tuned Shape TS).

The MFD of the 10 000 years long catalog simulated using RSQSim follows a MFD significantly different from a GR MFD. Therefore, we set a stronger weight to the branch using the TS MFD. The choice of the MFD being the leading source of uncertainty on the risk, the setting of the weight led to an important reduction of the uncertainty affecting the assessment of the probability of collapse in 50 years of a building in Istanbul.
However, it is worth noting that RSQSim simplifies the dynamics of the earthquake rupture and it is not excluded that other physics-based models could predict larger ruptures or a different MFD shape. At the time of writing this thesis, there are no simulators able to generate long earthquake histories of an extensive 3D fault network while integrating the full earthquake dynamics.

### 4.2.3 Perspectives on the physics based modelling

In this study, we have demonstrated how physics based modelling can be used to improve seismic risk estimates by using RSQSim as a discussion tool. In order not to over-interpret the results of RSQSim, given the modelling limitation, we limited the discussion to two first order questions concerning the NAF: are magnitude 8 earthquakes possible and can the MFD differ from a GR distribution?

As physics-based models continue to improve and evolve, the answers to these questions can be more accurate in the future and more detailed questions can be asked. For example, the local participation rate of a fault section is extremely important for assessing the seismic risk of neighbouring sites. Participation rates from statistical methods such as SHERIFS could be compared to those produced from physics based models.

In this study, we didn't focus on the ground motion prediction aspect of the seismic hazard assessment and used GMPE available in the literature. GMPE are empirically constructed and their accuracy to represent the ground motion can only be as good as the data used to derive them. As very few ground motion have so far been recorded near faults, GMPEs predictive power is reduced for sites located less than 10 km away from the seismogenic source, typically the sites exposed to the highest risk levels. Dynamic rupture models have the potential to provide the synthetic data needed to complement the ground motion database on which GMPEs are constructed.

Finally, one can imagine that fully physics-based hazard models will come to replace the traditional statically and empirically based hazard models of the Cornell approach, such as the ones constructed in this study. By linking earthquake rupture simulation and wave propagation for a long synthetic catalog, it is possible to calculate the probability of exceeding a given damaging ground motion (Shaw et al. [2018]), even extract some non-Poissonian behaviours of the system. Such model could have the potential to generate an earthquake hazard forecast as efficiently as meteorological model can forecast the weather. Efforts for the integration of physics-based geosciences in hazard assessment are carried on within SCEC (Southern Californian Earthquake Center) (Shaw et al. [2018]) and international projects such as ChEESE (https://cheese-coe.eu).

While the physics of the earthquake rupture and the wave propagation can be properly written into equations and, in theory, integrated in a 3D calculation software; one major roadblock stands in the way of a fully physics based hazard assessment: the large epistemic uncertainties affecting geophysical systems. Physics based models require an
important level of detail for the geometry and properties both of the fault and of the medium where the wave is propagating. This is required in order to be able to simulate the large bandwidth of frequency content of a ground motion that can damage a building. Meteorological models solve similar issues by comparing the models to the data and gradually improving. However, the weather is a constantly occurring phenomenon for which most parameters can be assessed by in-situ sampling or through light-waves observation. Earthquakes and solid earth parameters are for the most part only accessible when earthquakes occur and rarely with direct in-situ measurements of the parameters. Therefore, since most of the parameters will likely never be known with a sufficient detail for all points of a model, exploring the epistemic uncertainty is necessary but is computationally very impractical with these detailed models.

Nonetheless, pursuing the development of fully physics based hazard model will allow improving our general knowledge of the earthquake phenomena and, equally importantly, will generate interactions between different sectors of the geosciences community by creating a common goal as well as shared methodologies and modelling tools that can be used to inform traditional models. In my opinion, these beneficial outcomes have the potential to drastically improve the seismic hazard assessment even if the practical applicability of a fully physics based hazard model seems impossible in the foreseeable future.

In the annex, I discuss the use of Machine Learning methods for the seismic risk assessment.

## 4.3 The risk oriented approach

In this study, we have deliberately chosen to present the result in term of risk (e.g. probability of collapse) and not in the more classical terms of hazard (e.g. expected acceleration associated to a given probability of being exceeded). The reasons for this choice are twofold.

First, the usual hazard metrics such as the UHS (Uniform Hazard Spectrum) or the hazard map are presented for a given probability of exceedance, for example 10% over 50 years. While 50 years is a comprehensive universal number representing the average time of occupancy of a building by an individual, the 10% is a political choice for an acceptable level of risk taken which can change drastically depending on the application of the study. In this study, we don't have a given application in mind but simply want to expose and understand the seismic risk that affects a building in Istanbul, therefore the probability of collapse is a more adapted and comprehensive metric.

Second, using a risk oriented approach is an opportunity to open the discussion of this study, about the seismogenic sources controlling the risk and its uncertainty, to a wider audience than the hazard modelers community, bringing together geosciences and engineering. In order to reach this aim we developed tools easily used by both geoscientists and hazard modelers to identify the sources contributing to the seismic risk and the origins of the
uncertainties. At the same time, the same tools allow engineers to appreciate the reduction of risk when more precise
geological/seismological hypotheses are available for the faults.

4.3.1 Identifying the sources of the uncertainties

Concerning the probability of collapse for a mid-rise RC building in Istanbul, we identified the MFD of the fault system as the leading source of uncertainty. We were able to reduce this uncertainty using the discussion with RSQSim. The other uncertainties explored in the logic tree (the rupture scenario set, the background seismicity, the creep model of the fault, and the GMPE) all have an impact. The choice of creep model hypothesis has a minimal impact on the risk estimate due to the 70km distance between the potentially creeping section of the fault and the site of calculation.

By weighting the logic tree using the comparison between the modelled earthquake rates and the data as well
as the discussion based on the RSQSim synthetic catalog, we were able to enhance the accuracy of the risk assessment
by a factor 1.6 for the older 1975 building and by a factor of 2 for the 1998 building. According to our calculations, the
evolution of the building code between TEC75 and TEC98 leads to a 6 fold reduction of the risk of collapse over 50
years.

4.3.2 Risk disaggregation

We developed a methodology for risk disaggregation that exposes the contributing seismogenic sources of the probability
of collapse for a building during a period of time, here 50 years.

In Istanbul, the probability of collapse is controlled by two sources, the magnitude 7+ earthquakes occurring
on the nearest section of the NAF 17km away and the magnitude 4.5 to 6.5 earthquakes occurring in the background
seismicity occurring within 10 km from the site. The relative participation to the risk of the background compared to
the fault is variable depending on the background hypothesis used, ranging from 30 to 60% of the participation.

The TEC75 building is more sensitive to the background hypothesis than the TEC98 building. The disag-
gregation also shows that the ground motion that can lead to the collapse of the TEC98 building are more extreme
compared to the mean ground motion of the GMPE than the ground motion that lead to the collapse of the TEC75
building.
### 4.3.3 Perspectives on the risk calculation

The methodology set up in this study is implemented in a code that takes the outputs of SHERIFS and OpenQuake to calculate the risk of building damage and the disaggregation. The work needed to make this code user friendly and available will be carried in the future. The experience of sharing SHERIFS showed important improvements in the discussion of modelling earthquake rates on faults. Sharing the risk calculation has a potential to enhance communication between the seismic hazard community and the engineering community.

So far, the methodology only considered as input the fragility curve provided by the engineer. With more exchanges with the engineers, it could be possible to imagine other types of inputs such as multi-dimensional fragility curves that can take several ground motion parameters as input instead of one.

The methodology can also be used to generate other types of outputs such as a map of the probability of collapse for a given type of building or a map of the uncertainties, a useful tool to orient risk mitigation measures. This could identify areas where the risk is potentially high but very uncertain and help setting up future studies in order to reduce this uncertainty.
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Annex 1 : Annexes of chapter 1

A1.1 Supplementary material of Chartier et al. [2017]

Figure 1, presents an example of the earthquake rates calculation step by step for a fault system composed of three faults.
<figure><img src="image_50.png" /><figcaption>**Figure 1:** Illustration of the methodology step by step.</figcaption></figure>
# A1.2 Supplementary material of Chartier et al. [2019]

## A1.2.1 The Modified Young and Coppersmith (1985)

For some fault systems, depending on the spatial scale of the study, the Gutenberg and Richter (1954; hereafter, GR) magnitude-frequency distribution (MFD) might not be appropriate. It has been shown that a combined MFD with a log decrease with magnitude and a characteristic earthquake might be more appropriate to explain the rate observed at different time scales (Young and Coppersmith, 1985, hereafter, YC; Zielke [2018]). The YC MFD aims to better represent this bimodal distribution. The bimodal distribution proposed by YC concentrates an important proportion of the moment rate on the higher magnitude range of the distribution. When working with a fixed moment-rate budget as SHERIFS does, it implies then that the overall absolute value of the earthquake rate will be very dependent on the maximum magnitude in the fault system. Because SHERIFS allows exploring the maximum magnitude within the range admitted by the scaling law, a change of 0.1 in Mmax between two models with the same overall moment rate can result in an important difference in the rate of lower magnitude earthquakes (figure 2).

To minimize this effect, we propose the following modified YC MFD expression

$$p = \begin{cases} \frac{\beta e^{-\beta(M_{max} - 1.5 - M_{min})}}{1 - e^{-\beta(M_{max} - M_{min})}} \times \frac{\phi((M - (M_{max} - 0.25)) \times 5)}{\phi(0)} \times s, & \text{if } M_{max} - 0.5 < M < M_{max} \\ \left(\frac{\beta e^{-\beta(M - M_{min})}}{1 - e^{-\beta(M_{max} - M_{min})}}\right) \times e^{\frac{1}{b(M_{max} - M_{min})}}, & \text{if } M_{min} < M < M_{max} - 0.5 \\ 0, & \text{if } M > M_{max} \end{cases}$$

in which b is the slope of the logarithmic part of the distribution, $\beta = \ln(10) \times b$, $M_{max}$ is the maximum magnitude in the fault system, $M_{min}$ is the minimal magnitude of earthquakes considered for the model, $M_f$ is the optimal maximum magnitude (see the definition in the next paragraph), $\phi$ is a normal probability distribution of mean = 0 and $\sigma = 1$ and $s$ is the scaling factor for the rate of characteristic earthquakes (default value = 1.0).

This expression allows reducing the variation of the rate of smaller earthquakes when the maximum magnitude varies but the moment rate of the MFD remains constant. In this formulation, the relative shape between the exponential part and the characteristic part of the distribution becomes dependent on the difference between the actual Mmax and Mf, the optimal Mmax. The user needs to define a magnitude Mf within the SHERIFS code such that when Mmax = Mf the distribution is in the shape of an YC distribution in which the characteristic part is a Gaussian distribution of width 0.5, centered on Mmax 0.25. If Mmax < Mf, the rate of earthquakes in the characteristic part is increased in proportion to the exponential part of the distribution. If Mf < Mmax, this rate is decreased. Figure S1 illustrates how this allows reducing the variability of the rate of small-magnitude earthquakes while exploring the maximum magnitude.

The parameter s allows increasing or decreasing the ratio between the logarithmic part of the distribution and the characteristic part. If s = 1, the rate at the center of the normal distribution defining the characteristic earthquake is equal to the rate in the logarithmic distribution for a magnitude equal to the maximum magnitude minus 1.5; if s > 1, this rate is higher, if s < 1 this rate is lower.

We choose to define the characteristic part of the distribution using a normal distribution. Wells and
Coppersmith (1985) use a boxcar distribution instead. Because of the lack of data in most fault systems for characterizing the rate of large earthquake precisely, this choice is open to discussion. SHERIFS being an open-source code, we encourage the user to try other distributions if needed.

In the SHERIFS methodology, modeled earthquake rates are compared with the rates calculated from the earthquake catalog, mostly populated with low-magnitude earthquakes. Because the actual size and shape of the characteristic part of the MFD cannot be constrained by the too few large earthquakes in the catalog; with the proposed MFD, it is possible; given a fixed moment-rate budget to explore uncertainties on the maximum magnitude in the system while keeping the rate of low-magnitude earthquakes stable.

<figure><img src="image_51.png" /><figcaption>**Figure 2:** Illustration of (a) the YC MFD and (b) the modified characteristic MFD proposed in this article. The exponential part of the distribution has a b-value of 1, the Mf value of the modified characteristic distribution is fixed at 7.5 and the scaling factor s = 1. Three maximum magnitudes are explored: 7.0 (light gray curve), 7.5 (dark gray curve), and 8.0 (black curve). All of the six MFDs have the same moment rate of 1020 N·m. Solid curves are the cumulative distribution (M m) and dotted curves are the incremental distributions.</figcaption></figure>

### A1.2.2 Host Models

SHERIFS hazard model for the fault system can be easily incorporated into a larger “host model.” The host model can be any model for the region in the form of an OpenQuake input file. This allows the user to run calculations integrating other types of sources such as area zones for the regions surrounding the fault system and to use the resulting model for hazard and risk studies for sites outside of the background zone.

SHERIFS cuts an imprint in the host model using the user-defined background shape and then pastes the background and the modeled fault sources in the cut. The geometries and earthquake rates of the host model cropped sources are then automatically redefined. The seismic activity of the modified host zones is reduced to take into account the reduction of area where the background zone defined around the faults overlaps with the zone. The seismic activity of the host area sources is not recalculated using the earthquake catalog.
Bibliography

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# Annex 2 : Discussion on Machine learning application in seismic risk assessment

Machine learning allows fast calculation for complex systems after the model has been trained on a dataset (Bergen et al. [2019]). The data can be actual observations or output of models. Machine learning algorithms can extract trends that would be difficult to identify using statistical analysis alone. The resulting algorithm can have a tremendous predictive power for other areas of application and be very computationally efficient.

However, the resulting algorithm can only be as good as the data it's trained on. While there are many possible applications in the field of seismology (Kong et al. [2018]), for seismic hazard and risk assessment technical limitations are likely to reduce the applicability of these methods.

Hazard is often mostly controlled by local sources since the intensity of the ground motion decreases with the square of the distance of the source to the site. Since the number of records of large earthquakes in a given region is very sparse, ergodic assumptions would be required in order to gather an amount of data large enough to train and test an algorithm.

Machine learning doesn't aim to explain a phenomenon but rather aims to produce an operational tool that can be used even without a full understanding of the mechanisms at work. Algorithms can be tested against independent data in order to assess their accuracy. For seismic hazard and risk assessment, dealing with rare and extreme events, the amount of data for testing is likely to be too small.

Furthermore, users of hazard and risk estimates are decision makers who don't necessarily have a scientific background. The robustness of the products are under intense scrutiny since they can have important social and economical impacts. If the model is based on state of the art modelling and hypotheses about earthquakes, the decision makers can understand the validity and limitations of the results and elaborate strategies accordingly. The statistical test of the validity of a PSHA results remains an extremely difficult task due to the low probability of moderate or large events that affect the hazard. However, each component of the model can be tested against data (earthquake rate, ground motion prediction equation).

In the case of a model relying on machine learning, proving the statistical validity against independent data will be difficult. Machine learning generates "black box" algorithms in which the different components cannot be independently tested against data. It will be difficult for decision makers to rely on these models that offer less visibility.

The start-up company One Concern developed a risk mitigation tool based on machine learning that has been used by different public entities including the city of San Francisco. After realizing the lack of consistency between different outputs and the lack of transparency of the model, the city of San Francisco has decided to terminate the contract with One Concern. According to the head of the city's emergency management department : "We can't be cutting-cutting edge without knowing for sure that we can validate data" (https://www.nytimes.com/2019/08/09/us/emergency-response-disaster-technology.html).

Nonetheless, while a direct application of the machine learning algorithms to seismic risk assessment seems limited due to the lack of transparency of the algorithms and the fundamental lack of training and testing data, the
many possible applications in the fields of seismology, dynamic modelling and geodesy (Bergen et al. [2019]) will provide
improved inputs for the classical PSHA approaches. Recent studies using machine learning showed very promising
results that will likely lead to improvements in the accuracy of seismic hazard assessment.

For example, Rouet-Leduc et al. [2018] have demonstrated the capability of machine learning for inferring
stress evolution surrounding a laboratory fault from acoustic emissions only once the algorithm has been trained.
Rouet-Leduc et al. [2017] have trained an algorithm to predict the time to future rupture in the laboratory. These
type of studies will bring valuable information for the calibration of physics based models and for the setting of new
probability functions that can be used in time-dependant probabilistic seismic hazard assessment.

In the same way that physics-based models do not have to be perfect to be able to bring valuable input to the
risk assessment and to reduce the uncertainty, as we have shown in this study, the machine learning algorithms will
bring new insight on problems that classical models have trouble investigating adequately.
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# Annex 3 : List of contributions

## A3.1 Articles

* Methodology for earthquake rupture rate estimates of fault networks: example for the western Corinth rift, Greece. Thomas Chartier, Oona Scotti, Hélène Lyon-Caen, Aurélien Boiselet, Natural Hazards and Earth System Sciences 2017

* SHERIFS: Open-Source Code for Computing Earthquake Rates in Fault Systems and Constructing Hazard Models. Thomas Chartier, Oona Scotti, Hélène Lyon-Caen. SRL. 2019

* Computational Tools for Relaxing the Fault Segmentation in Probabilistic Seismic Hazard Modelling in Complex Fault Systems. F Visini, A Valentini, T Chartier, O Scotti, B Pace - Pure and Applied Geophysics, 2019

* Modelling earthquake multi-fault ruptures across complex fault systems based on geological data: the Eastern Betics Shear Zone. Octavi Gomez-Novell, Thomas Chartier, Julian Garcia-Mayordomo, María Ortuño, Eulalia Masana, Juan Miguel Insua- Arévalo, Oona Scotti. Engineering Geology. submitted.

* Transposing an active fault database into a seismic hazard fault model for nuclear facilities-Part 1: Building a database of potentially active faults (BDFA) for metropolitan France. Jomard, Hervé and Cushing Edward Marc and Palumbo Luigi and Baize Stéphane and David Claire and Chartier Thomas. Natural Hazards and Earth System Sciences. 2017

* Transposing an active fault database into a fault-based seismic hazard assessment for nuclear facilities - Part 2: Impact of fault parameter uncertainties on a site-specific PSHA exercise in the Upper Rhine Graben, eastern France, Chartier Thomas and Scotti Oona and Clément Christophe and Jomard Hervé and Baize Stéphane, Natural Hazards and Earth System Sciences. 2017

## A3.2 Posters and Presentations

* 2017

– Journées des thèses IRSN

– Congrès des doctorants ED

* 2018

– EGU

* Seismic Hazard and Earthquake Rate In Fault Systems-SHERIFS: a python tool for earthquake geologists, fault-hazard modelers and decision-makers. Thomas Chartier, Scotti Oona, Lyon-Caen Hélène

* Earthquake rupture hypotheses at the Eastern Betic Shear Zone (SE Spain): what does the SHERIFS approach tell about their magnitude-frequency distributions? Octavi Gómez-Novell, Julián García-Mayordomo, María Ortuño, Eulàlia Masana, Robert López, Thomas Chartier, Oona Scotti
- SCEC Annual Meeting: Constraining epistemic uncertainties on hazard models in the Marmara region using SHERIFS (Seismic Hazard and Earthquake Rates in Fault Systems). Thomas Chartier, Oona Scotti, Hélène Lyon-Caen

- Fault2SHA 2018 KAUST

* Seismic Hazard and Earthquake Rates in Fault Systems: The SHERIFS methodology applied in the Marmara region (Turkey). Thomas Chartier, Oona Scotti, Keith Richards-Dinger, James Dieterich, and Hélène Lyon-Caen.

* Need for inclusion of physics-based fault models into seismic hazard assessment: The example of the Dead Sea Fault. Thomas Chartier, Etienne Marti, Oona Scotti, Yann Klinger

- Journées des thèses IRSN

- Congrès des doctorants ED

- 2019

- Fault2SHA Barcelona: REDUCING UNCERTAINTIES IN SEISMIC RISK ESTIMATES IN ISTANBUL BY COMBINING STATISTICS- AND PHYSICS-BASED APPROACHES by: Thomas Chartier, Oona Scotti, Hélène Lyon-Caen, Keith Richards-Dinger, Jim Dieterich, Aurélien Boiselet.

- EGU: Physics-based earthquake simulators as a tool in Fault-PSHA: example for the Marmara region, Turkey. Thomas Chartier, Oona Scotti, Keith Richards-Dinger, James Dieterich, and Hélène Lyon-Caen.

- Journées des thèses IRSN

- Congrès des doctorants ED

### A3.3 SHERIFS GitHub and User Manual

SHERIFS code is available at https://github.com/tomchartier/SHERIFS with a user manual.
<figure><img src="image_52.png" /><figcaption>**Figure 1:** Screen shot of the SHERIFS user manual. Available at https://github.com/tomchartier/SHERIFS.</figcaption></figure>
# 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 Corinthe 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.

# MOTS CLÉS

Taux de Sismicité, Faille, Système de Failles, Aléa Probabiliste, Risque Sismique, Istanbul, Faille Nord Anatolienne, Désagrégation

# 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 (magnitude between 4.5 and 6) occurring in the background zone, on unknown faults, and at a distance shorter than 10 km from the building.

# KEYWORDS

Earthquake Rates, Fault, Fault System, Probabilistic Hazard, Seismic Risk, Istanbul, North Anatolian Fault, Deaggregation