Earthquake Risk Assessment from Insurance Perspective
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Abstract
The assessment of earthquake and risk to a portfolio, in urban or regional scale, constitutes an important element in the mitigation of economic and social losses due to earthquakes, planning of immediate postearthquake actions as well as for the development of earthquake insurance schemes. Earthquake loss and risk assessment methodologies consider and combine three main elements: earthquake hazard, fragility/vulnerability of assets and the inventory of assets exposed to hazard. Challenges exist in the characterization of the earthquake hazard as well as in the determination of the fragilities/vulnerabilities of the physical and social elements exposed to the hazard. The simulation of the spatially correlated fields of ground motion using empirical models of correlation between intensity measures is an important tool for hazard characterization. The uncertainties involved in these elements and especially the correlation in these uncertainties, are important to obtain the bounds of the expected risks and losses. This paper looks at the current practices in regional and urban earthquake risk assessment, discusses current issues and provides illustrative applications from Istanbul and Turkey.
6.1 Introduction
In UNISDR terminology, “Risk” is defined as “the combination of the probability of an event and its negative consequences”, and “Risk assessment” is defined as “a methodology to determine the nature and extent of risk by analyzing potential hazards and evaluating existing conditions of vulnerability that together could potentially harm exposed people, property, services, livelihoods and the environment in which they depend”.
Earthquake risk can be defined as the probable economic, social and environmental consequences of earthquakes that may occur in a specified period of time and is determined by using earthquake loss modeling procedures. In this context, the loss is the reduction in the value of an asset due to earthquake damage and risk is the quantification of this loss in terms of its probability (or uncertainty) of occurrence. In simpler terms, the “loss” is the reduction in value of an asset due to damage and the “risk” represents the uncertainty of this “loss”.
Earthquakes, which have annually caused an average of USD 34.7 billion in damages (Munich 2016), are one of the most destructive natural perils and can lead to severe economic, social and environmental impacts. Rapid urbanization and the accumulation of assets in seismic areas have led to an increase of earthquake risk in many parts of the world. The 2011 Great East Japan Earthquake was the costliest earthquake with USD 210 billion in economic losses followed by the HanshinAwaji earthquake (Kobe earthquake) in 1995 with USD 100 billion in economic losses (Munich 2016). Similarly, loss estimates from a 7.8 magnitude earthquake in Southern California would cause over USD 200 billion in economic losses (USGS 2008).
Public and private enterprises analyze their portfolio of assets to assess and to manage their earthquake risk. In calculating the earthquake risk of each asset, social and economic losses, due to not only physical damage to buildings and facilities but also to the nonstructural damage, consequential damage and business interruption are considered. In insurance terminology, these risk assessments and estimations are called as the Catastrophe (or simply, “Cat”) Modeling. Insurance companies use these cat models for insurance pricing, portfolio management, to monitor their capital requirements and solvency and to determine their reinsurance needs. Cedents can use the cat models to assess the appropriate structure of their outwards program and to compare technical prices of outwards treaties to market prices.
For a given inventory of elements (location and physical characteristics) exposed to seismic hazard, the important ingredients of this earthquake risk estimation flowchart are Ground Motion, Direct Physical Damage, Induced Physical Damage, and Direct/Indirect SocioEconomic Losses.
Almost all earthquake risk assessment schemes rely on the quantification of the earthquake shaking as intensity measure parameters using probabilistic or deterministic earthquake hazard models. For a given ground motion (intensity measure) the direct physical damage is determined by the fragility/vulnerability relationships that provide the probability of damage/loss, conditional on the level of intensity measure. Each step of the process incorporates stochastic or random variation associated with all aspects of the modeled phenomenon. Consequently, the earthquake risk estimations should consider the uncertainties in these steps.
In 1990, under the UNIDNDR (International Decade for Natural Disaster Reduction) program the RADIUS (Risk Assessment Tools for the Diagnosis of Urban Areas against Seismic Disasters) project promoted the earthquake risk assessment and mitigation in the international scale (UNISDR 2000). One of the most used methodologies of earthquake risk assessment originate from HAZUS (www.fema.gov/hazus) where, HAZUSMH MR4 is a damage and lossestimation software developed by FEMA to estimate potential losses from natural disasters. The World Bank’s CAPRA (http://www.ecapra.org/) project has also developed the widely used probabilistic risk assessment tools and software. Besides, several European Projects have also contributed to the development of comprehensive methodologies and tools for earthquakerisk assessment. In this regard, the following projects can be cited: RISKUE (Mouroux and LeBrun 2006); LESSLOSS (Calvi and Pinho 2004; Spence 2007, http://www.risknat.org/baseprojets/ficheprojet.php?num=55&name=LESSLOSS); SYNERG (Pitilakis et al. 2014a, b, http://www.vce.at/SYNERG/files/dissemination/deliverables.html) and; NERA (www.neraeu.org).
The Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe (SERA, http://www.seraeu.org/en/home/) as a Horizon 2020supported program, works to develop a comprehensive framework for seismic risk modelling at European scale. This risk modeling involves: European capacity curves, fragility, consequence and vulnerability models; European seismic risk results in terms of average annual loss (AAL), probable maximum loss (PML), and risk maps in terms of economic loss and fatalities for specific return periods and; Methods and data to test and evaluate the components of seismic risk models.
GEM initiative (www.globalquakemodel.org), which started in 2006 to develop global, opensource earthquake risk assessment software and tools, has contributed profoundly to the earthquake hazard and risk assessment standards, developed guidelines, the OpenQuake (www.globalquakemodel.org/openquake) software and the global earthquake hazard and risk maps (https://www.globalquakemodel.org/gem).
6.2 Probabilistic Earthquake Risk
where:
P(D > dIM) represents the socalled fragility function and; λ(IM > im) is the total frequency, which IM exceeds an intensity measure level “im” and, essentially, represents the seismic hazard at the site.
where P_{k}(DSIM) represents the probability for the given inventory element k at a given Damage State (DS) and constitutes the element of the Damage Probability Matrix (DPM) for the inventory element k and CDR_{k}(DS) represents the Central Damage Ratio for the given inventory element k at the given DS. The DPM, for a given inventory element k, provides the damage probability distribution for different DS (represented by CDR) and the IM.
The development of PerformanceBased Earthquake Engineering (PBEE) has created a rigorous and comprehensive framework for Probabilistic Seismic Risk Analysis (PSRA) (Cornell and Krawinkler 2000; Krawinkler 2002). This PBEEPSRA framework is based upon a chain of four conditional random variables: the ground motion intensity measure (IM); the engineering demand parameter (EDP), the componentspecific damage measure (DM or damage state DS) and, the decision variable (DV). The IM term is a quantitative measure of ground motion shaking intensity such as peak ground acceleration or spectral displacement. The EDP term is a quantitative measure of peak demand on the asset (e.g. interstory drift ratio, peak floor acceleration for a building). The DS term represents a discrete component damage state. The Decision Variables, DV, is the outcome of the earthquake risk (such as the annual earthquake loss or the exceedance of damage limit states). These parameters are and need to be carefully defined. For example, an efficient IM should be able to predict EDPs with low uncertainty.
where: λ(DV) is the annual rate of exceeding the decision variable, DV;
G(DVDM) is the probability of exceeding the decision variable given the damage measure, DM;
G(DMEDP) is the probability of exceeding the damage measure, DM, given the engineering demand parameter, EDP;
G(EDPIM) is the probability of exceeding the engineering demand parameter, EDP, given the intensity measure, IM, and;
λ(IM) is the annual rate of exceeding the ground motion intensity measure and;
dG(DVDM), dG(DMEDP)λ and dλ(IM) are the differentials of the respective terms.

Hazard Analysis represents the annual rate of exceedance of certain intensity measures (IMs), where λ(IM) quantifies the annual rate of exceeding a given value of seismic intensity measure (IM) (i.e. the outcome of the PSHA).

In the structural analysis, one creates a structural model of the building in order to estimate the response, measured in terms of a vector of engineering demand parameters (EDP), conditioned on seismic excitation represented by a set of IMs [G(EDPIM)].

Damage Analysis yields the conditional probability function, G(DMEDP), that relates Damage Measures (DMs) and EDP. The DM distributions are generally characterized in terms of fragility curves.

Loss Analysis uses Decision Variable (DV) as the random variable and produces the conditional probability function, G(DVDM), for given DMs, to describe the earthquake risk (e.g. the annual losses, the exceedance of damage limit states).
In Eq. 6.5 all four variables (IM, EDP, DM, and DV) are continuous random variables. However, Eq. 6.5 is generally modified as the summation of discrete terms, since in the current practice; the damage measures are not continuous but rather a set of discrete damage states. The integration of scenario losses provided by the triple integral (Eq. 6.5) over the entire range of occurrence probability will result in the quantification of seismic risk in terms of the Expected Annual Loss (EAL) (Dhakal and Mander 2006).
6.2.1 Fragility Functions
where FR(x) denotes the fragility function for a specific loss for a given IM = x and λ(Loss) is the annual rate of exceedance of the specific Loss.
where, λ(EDP) is the annual rate of exceeding a specified demand level EDP≥edp; G(EDPIM) is the probability of exceeding the engineering demand parameter, EDP, given the intensity measure, IM and; λ(IM) is the annual rate of exceeding the ground motion intensity measure, IM. For the assessment λ(EDP), the result of probabilistic seismic demand analysis can be used.
6.3 Ground Motion Intensity Measures (IM)
Estimates of damage to structures are made on the basis of a given level of ground motion intensity. The strength of an earthquake ground motion is often quantified by an IM (Baker and Cornell 2005). Macroseismic intensity and peak ground motion parameters (e.g. peak ground acceleration, velocity, and displacement, PGA, PGV and PGD, respectively) as well as the spectral acceleration/displacement at the fundamental vibration period of the structure, have been traditionally used in earthquake vulnerability assessment studies (Calvi et al. 2006). The use of a particular intensity measure for fragility or vulnerability assessment depends on the damageability characteristics of the element under the direct and indirect actions induced by an earthquake.
6.3.1 Ground Motion Prediction Models
where ln(IM) is the logarithm of ground motion intensity measure that is modeled as a normally distributed random variable. The terms \(\overline {\ln \left( {IM} \right)} \left( {M,R,\Theta } \right)\) and \(\sigma \left( {M,R,\Theta } \right)\) are the predicted mean and standard deviation of the ln(IM), respectively. They are functions of magnitude, M, sourcesite distance, R and other estimator parameters such as rupture mechanism, soil conditions and etc. that are collectively referred in vector Θ. The parameter ε is a standard normal random variable and represents the variability in ln(IM). Positive ε produces larger thanaverage values of ln(IM), whereas negative ε values yield smallerthanaverage values of ln(IM).
6.3.2 Spatial Correlation of Ground Motion
 (1)
The eventwide correlation of IMs through the betweenevent (intraevent) variability (i.e. a systematic lower or higher ground motion of an event, for instance, due to a higher or lower stress drop at the source) and:
 (2)
The tendency of local IMs being lower or higher than the GMPMs predicted median, through the withinevent (intraevent) variability (i.e. nearfault directivity effects and wave propagation paths). (e.g. Wang and Takada 2005; Goda and Hong 2008a, b; Jayaram and Baker 2009; Esposito and Iervolino 2011). The intraevent residuals at different sites are correlated, as a function of their separation distance. This correlation would be larger as the distance between the sites become smaller.
As such, when modeling ground motion fields for a scenario earthquake, a sample of the interevent residuals for all the sites/cells, for the event, should be taken and combined with the intraevent residual at each site/cell, obtained through a spatial correlation model (e.g. Crowley et al. 2008).
Empirical models of spatial correlation of ground motion intensity measures exist only for a few seismic regions in the world, such as Japan, Taiwan, California and Marmara Region in Turkey, since a dense observation of strong earthquake ground motion is necessary for this purpose.
where, Σ_{xy} is the covariance matrix between sites x and y, stored as the (xth, yth) element of the n × n (n is number of sites/cells) covariance matrix Σ. Covariance formulation has a significant computational expense and can only be used for a modest number of sites.
6.3.3 Correlation Between IMs at the Same Site
Weatherill et al. (2013) provides a comprehensive description of the generation random fields of ground shaking considering the interperiod correlation of the ground motion residuals.
6.4 Probabilistic Seismic Hazard Assessment (PSHA)
where: λ(M > m_{min}) is the annual rate of earthquakes with magnitude greater than or equal to the minimum magnitude m_{min}, r is the source distance, m is the earthquake magnitude and; f_{M}(m) and f_{R}(r) are the probability density functions (PDFs) for the magnitude and distance. It should be noted that: this equation is indicated for a single earthquake source zone and the integration is over all considered magnitudes and distances. The integration process can be extended to encompass other earthquake sources as well.
6.4.1 Monte Carlo Simulation
MonteCarlo method can be utilized to estimate the probabilistic seismic hazard, instead of the computation through the total probability integral given by Eq. 6.22. The same also holds for probabilistic seismic risk applications through the total probability integral given by Eq. 6.5. As such, for seismic hazard and risk assessment applications, it is rational to carry out a numerical evaluation of the probabilistic earthquake risk using a Monte Carlo simulationbased approach.
Monte Carlo method is based on a multitudinous resampling of an earthquake catalog to construct synthetic earthquake catalogs and then to find earthquake ground motions from which the hazard values are found (Ebel and Kafka 1999). For PSHA assessment first element of the Monte Carlo simulation technique is to generate synthetic earthquake catalogs (Stochastic Event Sets) for each source zone by drawing random samples from the assumed PSHA model components (Musson 2000; Scherbaum et al. 2004). Subsequently, the ground motion intensitymeasures (IMs) can be evaluated for each earthquake contained in the catalog and, for all earthquakes in the catalog, a history of ground motion IM estimates is obtained at each site. These estimates are reorganized to develop a list of the annual maximum IMs in ascending order, to yield the seismic hazard curve through a plot of the sorted annual maximum IMs as a function of the probability of exceedance.
6.4.2 Ground Motion Distribution Maps
Groundmotion IM Field Maps describes the geographic distribution of a given IM obtained considering an earthquake rupture and a GMPM. The spatial correlation of the intraevent residuals can be considered in the generation of the field.
The earthquake shaking can be determined theoretically for assumed (scenario) earthquake source parameters through median ground motion prediction models or, for postearthquake cases, using a hybrid methodology that corrects the analytical data with empirical observations. These type of maps are generally called as “ShakeMaps” (Wald et al. 2006, https://earthquake.usgs.gov/data/shakemap/). In insurance industry, postearthquake ShakeMaps are used with industry exposure data to calculate insured loss estimates (Parametric Earthquake Insurance).
For the analysis of seismic risk (especially for distributed assets), it is necessary to produce a spatially correlated field of ground motion. The ground motion IM across a region should be defined in a manner that is consistent with either a given earthquake scenario or a given return period. Pitilakis et al. (2014b) refers to these maps as a “Shakefield”.
6.4.3 RiskBased Earthquake Hazard: RiskTargeted Hazard Maps for Earthquake Resistant Design
The earthquake resistant design of structures requires the definition of design basis ground motion for a given return period, with the assumption that the probability of collapse for buildings is uniform regardless of the location. However, for a rigorous and explicitly uniform probability of collapse, the hazard maps should essentially be riskbased. In ASCESEI codes, risk target is taken as 1% probability of collapse in 50 years).
The distribution of the collapse capacity in terms of a specific IM can be defined by a cumulative lognormal function with log mean, β, and log standard deviation, β. Luco et al. (2007), using a β = 0.8, found a probability of collapse of 10% at 2475year ground motion level in the USA. Douglas et al. (2013), using a β = 0.5, found a probability of collapse of 10–5 at the 475year return period design ground motion level, for new buildings in France.
6.5 Assets Exposed to Earthquake Hazard, Building Inventories
Assets Exposed to Hazard is represented by the Exposure Model that contains the information regarding the assets (such as building inventories) within the area of interest for the assessment of earthquake risk.
To perform a seismic risk assessment, building inventories are determined based on specific classification systems (taxonomies).
Building taxonomies define structure categories by various combinations of use, time of construction, construction material, lateral forceresisting system, height, applicable building code, and quality (FEMA 2003; EMS98Grunthal 1998 and RISKUE 2004).
Publicly available data, at country and regional spatial scale, includes: UNHousing database, UNHABITAT, UN Statistical Database on Global Housing, Population and Housing Censuses of individual Countries (https://en.wikipedia.org/wiki/Population_and_housing_censuses_by_country), the World Housing Encyclopedia (WHE) database developed by EERI and IAEE (http://www.worldhousing.net).
The “Global Exposure Database for the Global Earthquake Model” project, under the Global Earthquake Model (GEM—www.globalquakemodel.org) framework, is concerned with the compilation of an inventory of assets at risk (Gamba et al. 2014 and Dell’Acqua et al. 2012). The USGS—Prompt Assessment of Global Earthquakes for Response (PAGER) (Wald et al. 2010) undertaking has also developed a comprehensive global inventory of assets exposed to earthquake hazard (Jaiswal et al. 2010).
6.6 Fragility, Consequence and Vulnerability Relationships
Fragility Relationships (Models) describe the probability of exceeding a set of damage states, given an intensity measure level. HAZUS (FEMA 1999) uses four damage states as the: slight, moderate, extensive and complete damage. Combining the fragility information with consequence (damage to loss) functions, which describe the probability distribution of loss given a performance (damage) level, allows for the derivation of vulnerability functions. Vulnerability functions can be used to directly estimate economic losses, where the loss ratio could be the ratio of cost of repair to the cost of replacement for a given building typology.
where, σ_{EDPIM} is the standard deviation of the logarithmic EDP distribution given by EDP = a (IM)^{b} or ln(EDP) = ln a + b ln(IM), (a and be are regression coefficients resulting from the response data) and; Φ(•) is the standard normal distribution function.
Numerous approaches exist towards “direct” estimation of fragility and vulnerability functıons at various levels of resolution. Approaches that are generally used for the “direct” estimation fragility and vulnerability functıons are empirical, analytical and hybrid.
Analytical (or predicted) fragility refers to the assessment of the expected performance of buildings based on calculation and building characteristics. The capacity spectrum method, originally derived by Freeman (1998), is first implemented within the HAZUS (FEMA 2003) procedure as well as in many other earthquake loss estimation analyses (e.g. SELENA—Molina and Lindholm, 2010 and ELER (Erdik et al. 2008; Hancılar et al. 2010). DBELA (DisplacementBased Earthquake Loss Assessment) method (Crowley et al. 2004; Bal et al. 2008) relies on the principles of direct displacementbased design method of Priestley (2003).
Mean damage ratios for EMS’98 damage grades
Several compilations of literaturebased fragility and vulnerability functions exist. Such as: GEM database of vulnerability and fragility functions for buildings (YepesEstrada et al. 2016; YepesEstrada et al. 2014) and SYNERG database for infrastructure fragilities (Pitilakis et al. 2014b; Crowley et al. 2014).
Correlation of Vulnerability/Fragility Uncertainties
In general, fragility and vulnerability function correlations are incorporated only for limit cases of independent or perfectly correlated component damage states and, it is generally not possible to do more than an estimate the losses, with and without vulnerability uncertainty correlation, to constrain the results. Evidence of correlation of vulnerability and fragility function uncertainties can be obtained from postearthquake damage surveys.
6.7 Metrics Used in Risk Assessment and CAT Modeling
For the measurement of risk for a single asset or portfolio of assets, several metrics, in physical and financial loss terms, are used. Following is a brief explanation of these metrics.
The Loss Exceedance (or Exceedance Probability, EP) curves, the Average Annual Loss (AAL) and Probable Maximum Loss (PML) constitute the primary metrics of the probabilistic risk/loss assessment. In engineering terms, the losses associated with the building stock are generally quantified in terms of Los Ratio (LR), defined as the repair cost divided by the replacement cost. LR is also called as the damage factor, damage ratio and fractional loss.
Loss Exceedance Curves (EP Curves) describe losses versus probability of exceedance in a given time span (generally, annual). EP Curves are used for cat modelling, as it is beneficial to identify attachment or exhaustion probabilities, calculate expected losses within a given range, or to provide benchmarks for comparisons between risks or over time.
Occurrence Exceedance Probability (OEP) is the probability that the associated loss level will be exceeded by any event in any given year. It provides information on losses assuming a single event occurrence in a given year. Aggregate Exceedance Probability (AEP) is the probability that the associated loss level will be exceeded by the aggregated losses in any given year. It provides information on losses assuming one or more occurrences in a year.
The AEP and OEP can be used for managing exposure both to single large event and to multiple events across a time period. They can be similar when the probability of two or more events is very small; they are identical when there is zero probability of two or more events. However, AEP can be very different from the OEP when the probability of two or more events is significant.
Value at Risk (VaR) is equivalent to the Return Period, and measures a single point of a range of potential outcomes corresponding to a given confidence. The VaR is the fractile value on an EP curve corresponding to a selected probability level.
Tail Value at Risk (TVaR) measures the mean loss of all potential outcomes with losses greater than a fixed point. When used to compare two risks, along with mean loss and Value at Risk, it helps communicate how quickly potential losses tail off.
VaR and TVaR are both mathematical measures used in cat modelling to represent a risk profile, or range of potential outcomes, in a single value.
Conditional Value at Risk (CVaR) is the area under the EP curve below a selected cumulative probability level, p, normalized by the probability of exceedance (1 − p). CVaR, accounts for the rare events in terms of their severity and frequency by taking the conditional expectation of the EP curve.
Average Annual Loss (AAL) (or Annual Estimated Loss—AEL or Pure Premium) is the expected value of a loss exceedance distribution and can be computed as the product of the loss for a given event with the probability of at least one occurrence of event, summed over all events. AAL is the average loss of all modeled events, weighted by their probability of annual occurrence (EP curve) and corresponds to the area underneath the EP curve. If the loss ratio (LR) is used for the quantification of loss, then the term Average Annual Loss Ratio (AALR) is used in lieu of AAL. For earthquake insurance purposes, the AAL or AALR is of particular importance in determining the annual pure premiums.
Pure Premium represents the average of all potential outcomes considered in the analysis, and could be considered to be the breakeven point if such a policy is to be written for very large number of times.
The Probable Maximum Loss (PML) is one of the most popular metrics in financial risk management, and there are several definitions. PML can be associated with the OEP or the AEP. Conventionally, PML was defined as a fractal of the loss corresponding to the return period of 475 years. In Japan, the PML is defined as the (conditional) 0.9fractile value for a scenario that corresponds to a selected probability level (typically, return period of 475 years).
ASTM E202616A use specific nomenclatures for seismic risk assessment of buildings. are in use:
Scenario Upper Loss, based on deterministic analysis) (SUL) is defined as the earthquake loss to the building with a 90% confidence of nonexceedance (or a 10% probability of exceedance), resulting from a specified event on specific faults affecting the building. If the specified earthquake hazard is the 475year return period event, then this term can be called the SUL475, and this term is the same measurement as the traditional PML defined above.
Scenario Expected Loss, based on deterministic analysis, (SEL) is defined as the average expected loss to the building, resulting from a specified event on specific faults affecting the building. If the specified earthquake is the 475year return period event, then this term can be called the SEL475.
The Probable Loss, based on probabilistic analysis, (PL) is defined as the earthquake loss to the building(s) that has a specified probability of being exceeded in a given time period from earthquake shaking. The PL is commonly taken as the loss that has a 10% probability of exceedance in 50 years, which is called the PL475, because it corresponds to a return period of 475 years.
6.8 Earthquake Risk Assessment Models and Example Applications
The estimation of the earthquake risk due to deterministic earthquake scenarios is of use for communicating seismic risk to the public and to decision makers. However, a probabilistic assessment of earthquake risk (generally called, Probabilistic Seismic Risk AnalysisPSRA) is needed for risk prioritization, risk mitigation actions and for decisionmaking in the insurance and reinsurance sectors.
Seismic risk for a single element at risk can be calculated through the convolution of a hazard curve with a vulnerability relationship quantifying the probability of a given consequence occurring under different levels of ground shaking. For geographically distributed elements, the use of hazard curves calculated with conventional PSHA, may overestimate the total loss since the conventional PSHA does not distinguish the inter and intraearthquake variability of ground motion (Crowley and Bommer 2006).
Since the PSRA encompasses multitude sources of uncertainties stemming from hazard, inventory and vulnerability (or fragility and consequence) functions, Monte Carlo simulations are routinely employed to facilitate the orderly propagation of these uncertainties within the process. Using Monte Carlo simulations, a value of the interearthquake variability can be sampled for each earthquake and then values of the intraearthquake variability are sampled at each location for this earthquake. Such eventbased simulation involves suites of probabilistically characterized deterministic risk scenarios (e.g. Crowley and Bommer 2006; Silva et al. 2013).
Similar to PSHA, the results of a PSRA can also be deaggregated to identify the components of the overall system (i.e. earthquake scenarios) that are contributing significantly to the seismic risk (e.g. Goda and Hong 2008a, b; Jayaram and Baker 2009).

CAPRA GISEarthquake module, http://www.ecapra.org/software

EQRM, http://www.ga.gov.au/scienti.ictopics/hazards/earthquake/capabilties/modelling/eqrm

ERGO (MAEviz/mHARP), http://ergo.ncsa.illinois.edu/?page id = 48

HAZUSMH earthquake module, http://www.fema.gov/hazus

OpenQuake, https://www.globalquakemodel.org/openquake/

ELER,http://www.koeri.boun.edu.tr/Haberler/NERIES%20ELER%20V3.16 176.depmuh

RiskScapeEarthquake, https://riskscape.niwa.co.nz/

SELENA, http://www.norsar.no/seismology/engineering/SELENARISe/
The OpenQuake Engine (https://www.globalquakemodel.org/) is GEM ‘s stateoftheart software for seismic hazard and risk assessment at varying scales of resolution, from global to local. It is opensource, fully transparent and can be used with GEM or userdeveloped models to carry out scenariobased and probabilistic hazard and risk calculations and produce a great variety of hazard and loss outputs. Spatial correlation of the ground motion residuals and correlation of the uncertainty in the vulnerability can be modeled. Main calculations performed in connection with the earthquake loss assessment can be listed as: Scenario risk; Scenario damage; Classical PSHAbased risk; Probabilistic eventbased risk and; Retrofitting benefitcost ratio. Comprehensive global earthquake risk maps were provided by GEM (https://www.globalquakemodel.org/gem).

Deterministic Risk/Loss Calculation (analysis due to a single earthquake scenario);

Probabilistic Risk/Loss Calculation (an analysis that considers a probabilistic description of the earthquake events and associated ground motions) and;

Classical PSHABased Risk/Loss Calculation (analysis based on conventional probabilistic earthquake hazard assessment).
6.8.1 Deterministic Earthquake Risk/Loss Calculation
Following are some earthquake risk assessment examples, where, deterministic earthquake loss calculation procedure is used.
6.8.1.1 Deterministic Loss Assessment for Buildings in a Region in Istanbul
6.8.1.2 Deterministic Earthquake Loss Assessment in the Zeytinburnu District of Istanbul
Deterministic Earthquake Risk Assessments for İstanbul
A comprehensive earthquake risk assessment study was conducted by Boğaziçi University, OYO International and GRM Ltd. for İstanbul Metropolitan Municipality (İBB) in 2009 (http://istanbulolasidepremkayiplaritahminlerininguncellenmesil_sonuc_rapor_2010.09.pdf). This study was updated in 2018 by Boğaziçi University for the İBB (http://depremzemin.ibb.istanbul/wpcontent/uploads/2020/02/dezim_kandilli_depremhasartahmin_raporu.pdf). The 2009 study was based on a single scenario earthquake (Mw7.5), rupturing the Main Marmara Fault to simulate the socalled pending “İstanbul Earthquake” with an annual probability of occurrence of about 2–3%. Intensity and spectral accelerationbased fragilities were considered. Loss ratios for the buildings, as well as other losses, were determined for median and 84percentile probabilities. In addition to this Mw7.5 scenario earthquake, the 2018 study also considered single stochastic ground motion simulations for several rupture alternatives and the official PSHA map for different return periods, for the earthquake ground motion. The aggregate building damage results for different damage states, obtained from different rupture scenarios, do not differ much from the results of the Mw7.5 scenario earthquake. The risk in both studies was computed using a classical simple deterministic approach, with no consideration of spatial variation of ground motion intensity.
The building damage rates that would result from the occurrence of the Mw 7.5 Istanbul earthquake scenario indicate that the medıan damage ratios for buildings with no, light, medium, heavy and very heavy/collapse damage status are respectively found to be about 60, 26,11, 2 and 1%. Noting that as of 2020 there are about 1.1 million buildings and 3.9 million housing units in the İstanbul Province, one can estimate that about 0.44 million buildings (about 1.6 million housıng units) will receive some degree of damage after exposure to the “İstanbul Earthquake”. In monetary terms, this structural damage will correspond to about USD 6.5 billion.
6.8.2 Probabilistic Earthquake Risk Calculation
Following are some earthquake risk assessment examples, where, probabilistic earthquake loss calculation procedure is used.
Probabilistic Earthquake Risk Assessments for İstanbul
Turkish Catastrophe Insurance Pool (TCIP) Loss Modeling
6.8.3 Classical PSHABased Earthquake Risk Calculation
Turkish Catastrophe Insurance Pool (TCIP) AALR Models
6.8.4 Effect of the Spatial Correlation of Ground Motion on Earthquake Loss Assessments
The effect of the consideration of spatial correlation of IMs, can be assessed from the examples provided for both deterministic and probabilistic earthquake loss applications: Sect. 6.8.1.1 Deterministic Loss Assessment for Buildings in a Region in Istanbul and Sect. 6.8.1.2 Deterministic Earthquake Loss Assessment in the Zeytinburnu District of Istanbul. The findings in these sections essentially follow those obtained by Park et al. (2007) who has performed stochastic simulation of ground motion fields to compute seismic losses within two portfolios of structures. Annual Mean Rate of Exceedance (essentially, EP) curves, for building portfolios with large and small footprints are assessed for six different models for the correlation coefficient, varying from no correlation at all distances to fully correlated ground motion fields, to study their effect on the EP curves. Park et al. (2007) has observed that: for either portfolio type, no correlation related losses associated with low probabilities of exceedance are significantly underestimated compared to the cases with correlation. The relative underestimation of losses associated with low probabilities of exceedance are evident for portfolios with small footprint than that with the large footprint and the effect of spatial correlation on the entire portfolio was found to be larger if the correlation length is comparable or larger than the footprint of the portfolio.
6.9 Uncertainties in Risk Assessments

Hazard uncertainty (seismic source characterization and ground motion modeling)

Vulnerability uncertainty

Uncertainty in the assumptions and specifications of the risk model

Portfolio uncertainty (location and other attributes of the building classes).
In general, there exist two types of uncertainties that need to be considered in earthquake risk/loss assessments: aleatory and epistemic. Aleatory uncertainty accounts for the randomness of the data used in the analysis and the epistemic uncertainty accounts for lack of knowledge in the model.
Aleatory variability, that generally affects the loss distributions and exceedance curves is directly included in the probabilistic analysis calculations through the inclusion of the standard deviation of a GMPM considered in the analysis. Epistemic uncertainties, which can increase the spread of the loss distributions, are generally considered by means of a logic tree formulation with appropriate branches and weights associated with different hypotheses. Similarly, MonteCarlo techniques can also be used to examine the effect of the epistemic uncertainties in loss estimates.
Demand Surge and Loss Amplification represent the socalled Post Event Inflation elements in earthquake risk assessment. They arise due to: Shortages of labor and materials, which cause prices to rise; Supply/demand imbalances delay repairs, which results in structural deterioration and; Political issues (due to the size of the disaster and under pressure from politicians, insurers are encouraged to settle claims generously).
The general finding of the studies on the uncertainties in earthquake loss estimation is that the uncertainties are large and at least as equal to uncertainties in hazard analyses (Stafford et al. 2007; Strasser et al. 2008). It should also be noted that the estimates of human casualties are derived by uncertain relationships from already uncertain building loss estimates, so the uncertainties in these estimates are rather compounded (Coburn and Spence 2002).
6.10 Conclusions

Earthquake risk and loss assessment is needed to prioritize risk mitigation actions, emergency planning, and management of related financial commitments. Insurance sector have to conduct the earthquake risk analysis of their portfolio to assess their solvency in the next major disaster, to price insurance and to buy reinsurance cover.

Due to the research and development on rational probabilistic risk/loss assessment methodologies and studies conducted in connection with several important projects, today we have substantial capability to analyses the risk and losses ensuing from lowprobability, high consequence major earthquake events.

In this regard, the selection of an appropriate set of GMPMs, that are compatible with the regional seismotectonic characteristics, and the selectıon of vulnerability (or fragility and consequence) relationships that are compatible with the IMs and appropriate with the inventory of assets in the portfolio are of great importance. The mean damage ratio (MDR) is highly sensitive to the consequence models (i.e. loss ratios assigned to each damage state).

The probability distribution function for the loss to a portfolio depends on the spatial correlatıon of the ground motion and the vulnerability of the buildings. The consideration of the spatial correlatıon does not change the mean loss but increases the dispersion in the loss distribution, which can have a profound influence in loss and insurance related decisions. When spatial correlation is considered, the losses at longer return periods increase. On the opposite side, the losses at shorter return periods may be overestimated if the spatial correlation is not included in the analysis.

The reduction of the uncertainties in earthquake risk/loss assessment is an important issue to increase the reliability and to reduce the variability between the assessments resulting from different of earthquake risk/loss models. In this connection, earthquake risk/loss assessment models should explicitly account for the epistemic uncertainties in the components of analysis, especially in the inventory of assets and vulnerability relationships.

The practice of risk assessment is now established. However, a number of research issues, such as: uncertainty correlation in vulnerability, logictree modeling of epistemic uncertainties and treatment of uncertainties in exposure modeling, remain for treatment in future applications.
Notes
Acknowledgements
The valuable contribution of my colleagues (listed in alphabetical order) Prof. Dr. Sinan Akkar, Assoc. Prof. Dr. Zehra Çağnan, Dr. Yin Cheng, Dr. Mine Betül Demircioğlu, Dr. Karin Şeşetyan and Dr. Thomas Wagener, in the preparation of this paper are gratefully acknowledged.
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