3.part4__computer models of probable maximum loss

8/9/2019 3.Part4__computer Models of Probable Maximum Loss

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PART 4: COMPUTER MODELS OF PROBABLE

MAXIMUM LOSS

Chapter 6.0 Seismi Ris! M"#e$s by Dionne Gesink Law

6.% I&tr"#'ti"&

The purpose of this chapter is to address the questions: What are the seismic risk models

doing and how can they be critically examined? The objective of this section is to explain

seismic risk modelling in greater depth, for the purposes of model examination andassessment of model output The steps outlined in a generic seismic risk model will be

discussed in further detail by reviewing the components of the model This includes the

insurance inputs, the seismic ha!ard module, the vulnerability module, and the financialoutputs

As the awareness of the threat of a catastrophic earthquake along the south-west coast ofBritish Columbia motivates the individual to purchase more earthquake insurance, thethreat of insolvency within the insurance and reinsurance industry also grows. Thisconcern has created an effort by both government and the industry to determine acompanys e!posure to seismic risk, and methods of managing that risk.

"n attempts to prevent insolvency in the event of a catastrophic earthquake, the federal#ffice of the $uperintendent of %inancial "nstitutions $%"' has distributed a

questionnaire to insurers and reinsurers regarding earthquake risk assessment. %rom thissurvey, #$%" hopes to ascertain the severity of the loss e!posure of the industry as awhole, and amend the best practices recommendations to include a strategy for effectiverisk management &$tratton, personal communication'. %or e!ample, several largerinsurance and reinsurance companies use seismic risk models to(

) determine their e!posure to insured earthquake losses,

) develop a risk management strategy,

) aid in underwriting.

As the potential costs of a catastrophic earthquake near an urban centre become fullyrealised, strategies to manage seismic risk will be crucial in preventing insolvency. "t is inthe best interest of all insurance and reinsurance companies to use AT *+A$T T#methods of risk analysis, whether they be mathematical equations or sophisticatedcomputer models. owever, model users should be aware that different methods can produce different results. These discrepancies can either confuse the user, or drawattention to the uncertainty involved in seismic risk modelling. As risk analyses are

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performed, it will become increasingly imperative that those individuals responsible forrisk management of the e!posures understand the methods and models used, and themeaning of the results produced.

There are several natural haard risk models that can be used to assess both the Canadian

e!posure to a haard, and the potential insured losses in the event of a catastrophe. $omeof the natural haards which pose the greatest threat to Canadians are floods, droughts,earthquakes, hail storms, tornadoes and severe winter storms &reviewed in section /.0,above'. 1ue to the important economic and industry implications of an earthquake nearan urban centre, this review of risk models will be restricted to those that analyse insuredlosses resulting from earthquakes in Canada.

The purpose of this chapter is to(

2. 3rovide an overview of seismic haard4/. +!plain seismic risk modelling4 and

5. 3rovide an approach to evaluate the various seismic risk models available to theinsurance industry.

6any of the available seismic risk models estimate damage and losses due to seismicshaking, fire following, landslide, liquefaction, and tidal wave inundation. $eismicshaking, however, will be the only portion of the model reviewed and evaluated in depthsince it is responsible for most of the damage associated with an earthquake. %uturestudies should review the other modules in the seismic risk model, especially sincelandslides in estern Canada are not yet thoroughly understood.

istorically, the 6ontreal-7uebec City region has been susceptible to earthquakes. 6ore

recently, geologists and seismologists have begun to acknowledge a seismic threat fromtwo types of activity in southern British Columbia. The first is a ma8or subductionearthquake &9uttenberg-:ichter magnitude 6;


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and e!ecution of elaborate models which will assist in predictingEestimating the potentialimpact of a natural haardEdisaster in a defined area of interest.D &+3C, unpublished'. ?+6AT"$ is intended to aid in natural haard disaster management. "t can help planners identify vulnerable areas, improve emergency preparedness, and assist with pre-disaster mitigation &+3C, unpublished'. %or e!ample, if a potential risk e!ists in an area,

amendments to city plans, oning laws, and building codes can help to minimisee!posure.

Emergency Information Systems "n the event of a ma8or earthquake, monitoring the disaster in real-time will require anemergency information systems &+"$' such as the +arly 3ost-+arthquake 1amageAssessment Tool &+3+1AT', which was developed by +7+CAT for the California+arthquake Authority. +3+1AT has a lag time of 2> to 50 minutes and can optimise thedischarge of emergency response and repair units, enable hospitals in high damage areasto prepare for incoming casualties, and begin initial estimates of total dollar loss whichcan be updated regularly. "n effect, +3+1AT performs a lifeline analysis during a

catastrophe. "n Canada, $oft:isk is used for floods.

Lifeline Analysis Models *ifeline analysis involves assessing the impact of an earthquake on emergency response,communication lines, transportation routes, and power lines. $ince this task has a high priority in California, +7+CAT has developed the **+7+ model to perform suchanalyses. "n Canada, 6unich :e and :escan performed an e!tensive study on theeconomic and insured impact of a severe earthquake in the British Columbia lowermainland &6unich :e, 20'. The 6unich :e economic model addressed the effect of anearthquake with respect to structural and content damage, infrastructure damage, onsitein8ury and loss of life, and offsite damage for seismic shock, ensuing fire, landslide, and

inundation. The insured losses model focused on damages due to seismic shaking and firefollowing. Assuming an earthquake of 6;F.>, total economic losses were estimated torange from G2.5 to 5/.2 billion, while the total insured loss estimation ranged fromGF.FH to 2/.H/ billion.

Insured Loss Estimation Models $everal seismic risk models have been developed for use by the insurance industry. Thesemodels include( 6unich :e, :isk 6anagement $olutionIs ":A$, +7+CATIs+7+AJA:1 or +7+Canada, and :isk +ngineeringIs +7Canada. Though developedfor slightly different purposes, all attempt to provide additional information for riskmanagement strategies.

To evaluate the different seismic risk models available for insured loss estimation, it isimperative that the modelling process be understood. The process of seismic riskmodelling will be e!plained in four stages(

2. A generic seismic risk model will be presented./. Components of the generic model will be e!plained in more depth with reference

to the @ancouver and surrounding area.

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5. A framework to e!amine seismic risk models will be provided.. The 6unich :e, ":A$, and +7+Canada models will be presented using the

suggested framework.

At the end of the chapter, recommendations will highlight further work in this area.

6.( )e&eri Seismi Ris! M"#e$

The purpose of this section is to provide an overview of the process of seismic riskmodelling. The modeller inputs insurance information into the model, and specifies anearthquake magnitude and location. This information is used by the seismic haardmodule to estimate shaking intensity at a sight. $haking intensity is used in thevulnerability module to estimate damage. 1amage is used in the financial module toestimate insured losses

$ome seismic risk models have been developed to aid the insurance industry with riskmanagement via the estimation of the probable ma!imum loss. 3robable ma!imum loss&36*' is an insurance term for the estimated likely ma!imum cost that could be incurredin the event of an earthquake of a given magnitude.

6ost seismic risk models are comprised of three modules &%igure F.2'. The seismichaard module simulates actual earthquake shaking. The vulnerability module relatesseismic shaking to structural and property damage. The financial module assigns a cost tothose damages and calculates the ma!imum potential andEor e!pected losses. This process of seismic risk modelling is outlined in the following steps.

Step 1 Insurance Inputs The information contained in an insurance companyIs portfolio is used as input for theseismic risk model. "t is vital that this information be as complete as possible4 otherwiseuncertainty in the results is inflated. This includes data on(

• building location - by cresta one or postal code &5-F digit'4

• building construction - building type, building age, building height4

• building use4

• building contents4 and

• policy information - building value, deductibles, reinsurance, co-insurance.

The location and magnitude of the earthquake are also specified at this stage. Thelocation of the earthquake, usually identified by its epicenter, is specified by a sourceone &see $ection F.'. A continental plate earthquake near an urban centre poses thegreatest threat to both Canadians and the insuranceEreinsurance industry. Thus, whenanalysing a worst-case scenario, most users will place the epicentre, or centre of theearthquake, in the source one closest to @ancouver. The magnitude of an event, isusually specified using either(

• a return period,

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• the 9uttenberg-:ichter scale &6', or

• peak ground acceleration &39A',

and these measures can be either(• user defined,

•

based on a specific historical event,• an average of several historical events, or

• a proposed ma!imum magnitude event.

Step ! Seismic "a#ard Module The seismic haard module uses the location and magnitude of an earthquake, specifiedin step 2, to estimate the probability of seismic haard for either individual sites, or theinsurance portfolio as a whole. ere, seismic haard refers to any physical phenomenonassociated with an earthquake including ground motion, fire-following, landslide,liquefaction, tsunami, and inundation. 6ost of the damage incurred by a structure duringan earthquake is the result of seismic ground motion. The longer the shaking, the greater

the damage. The ob8ective of the seismic haard module is to estimate the intensity ofshaking at sites within the insurance companyIs portfolio &++:", 2


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according to "BC classes which are based on the ?ational Building Code of Canada&?BCC' standards. Thus, the ?BCC structural information is converted to ATC-25equivalents to be used in the vulnerability functions. This conversion is a potential sourceof error in the calculation of 36*. The sie of this error is unknown, and worthy offurther investigation.

1amage estimates to structures are presented as probable ma!imum damage &361'andEor probable e!pected damage &3+1'. #ften 361 is calculated at the 0th or >th percentile. 3+1 is usually calculated around the >0th percentile &see $ection F.>'.

Step & 'inancial Module and Insurance (utputs 1amage estimates from the vulnerability module are used in the financial module tocalculate the probable ma!imum loss &36*' and probable e!pected loss &3+*' of anearthquake, based on the companys portfolio. 36* is a function of 361 and the insuredvalue of the building. 6ost risk models calculate losses due to structural damage, damageto property and contents, and business interruption. These estimates are presented either

as a percent of the total value of the structure, or as a dollar value. The net 36* iscalculated by including deductibles, and the appropriate layers of reinsurance and co-insurance. $ome models will also provide a measure of uncertainty with the net 36* estimate.

6./ I&s'ra&e I&p'ts

The first step is seismic risk modelling involves insurance information. "n addition tospecifying the magnitude, duration, and location of an earthquake during analysis, themodeller must provide information on building location, building inventory andinsurance structure.

"t is the responsibility of the insurance company to provide portfolio information as inputto the risk models. This includes data on building location, building inventory, andinsurance structure. The records within the portfolio can be complete or incomplete, sitespecific or aggregated. %or site specific analysis, incomplete data are usually handled bythe model by assigning weighted averages. This introduces uncertainty into the analysisand elevates the potential for errors. The accuracy and reliability of the earthquake lossestimates calculated by the model can only be improved by increasing the rigor of theinsurance and database inputs.

The distance of a structure from the centre of an earthquake will influence the degree of

shaking, and hence damage, incurred by the structure. Thus, the $"ati"& of a structure isan e!tremely important piece of information. 1ata on structure location can range fromsite specific, such as street address or postal code, to regionally aggregated, such asearthquake accumulation assessment ones - otherwise known as cresta ones &%igureF./'. This information is used in the seismic haard module attenuation equations todetermine(

• the distance from building site to earthquake source, and

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• site conditions which can strongly influence ground motion attenuation.

"t is also important that information on building class, height, and year of construction beas complete as possible because ,'i$#i& i&+e&t"r- information is used in thevulnerability module to estimate the damage resulting from an earthquake. "t is assumed

that the quality of materials and workmanship used during construction are to ?ationalBuilding Code of Canada standards. nfortunately, evidence following the 2 Barrietornado &Allen, 2


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• the sufficiency of the data and databases used in the seismic haard module. Data

s'iie&- issues of data quality, quantity, availability, ob8ectivity, resolution andcompleteness apply to both data input into the program, and data stored indatabases within the program. "f seismic data are deficient, again, the reliability of the results will be compromised. This elevates the uncertainty associated with the

outputs. "ssues of data sufficiency need to be discussed along with the previoustwo issues. Thus, this chapter will address data sufficiency inherently within theseismicity and model sufficiency sections. The impat " #ata s'iie&- i&m"#e$ #e+e$"pme&t is &"t 3e$$ 'erst""# a re*'ires 'rther i&+estiati"&.

)*&*1 Seismicity The fundamental properties of seismicity are generally well understood by the scientificcommunity &see $ection /..2'. owever, conflicting assessments in a given geographicalarea can still arise. %or e!ample, the seismic activity of the Cascadia subduction one,2>0 km off the coast of @ancouver and ashington, is currently under debate. ere, theKuan de %uca, 9orda, and +!plorer plates are being subducted, or over-ridden, by the

?orth American continental plate &%igure F.5'. Because of the absence of ma8or historicalseismic activity in this area &9uttenberg-:ichter magnitude, 6 L H', subduction has beenconsidered relatively aseismic by some researchers &Campbell, unpublished'. Campbell&unpublished' argues that since the Kuan de %uca plate is young, thin and smooth,subduction is occurring aseismically, and may cease altogether within 200 years. esuggests that, at worst, the est coast will e!perience a few moderate earthquakes &6 ; >to H.>' over the ne!t few centuries. :ogers &2' and Atwater et al. &2>' have anopposing interpretation based on evidence from both the Cascadia subduction one andsimilar subduction ones around the world. They note that the largest recordedearthquake &6 ; .>' occurred in Chile in 2F0 along a young, thin, smooth subducting plate, much like the Cascadia subduction one &$mith, 2F4 Atwater et al., 2>4 :ogers,

2'. They have also found evidence suggesting that a ma8or earthquake &6 ;


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should use seismic risk models to assess their e!posure. +specially since the absence ofevidence is not evidence of absence.

)*&*! Module Sufficiency The purpose of the seismic haard module is to use ground motion attenuation equations

to estimate ground motion, or shaking, at a site some distance from the centre of anearthquake. 9round motion moves in si! directions( north, south, east, west, up and down&%igure F.'. Thus there are two horiontal a!es &northEsouth, eastEwest', and one vertical&upEdown'. "n Canada, there are very few recordings of strong ground motion, particularly horiontal, and so accurate simulation is compromised. $ince ground motionattenuation equations are the foundation of every seismic haard module, this will affectthe model results. Kust how much the results are affected requires further e!ploration.Accordingly, the data input, databases, and equations used within the model need to be asrigorous as possible for the model to be considered sufficient. ere sufficient refers to themodel adequately or satisfactorily representing the Canadian est Coast seismicsituation.

9round motion attenuation describes how ground shaking subsides with distance. Thisrelationship is dependent on earthquake source conditions, event magnitude and groundshaking, and site conditions. 9round motion attenuation equations are based on seismicdata from pre- and post-instrumentation events around the world. The validity of theattenuation results are dependent on the reliability of historical accounts, and the rigor ofmeasures for currently active seismic areas. Thus, it is important that the analysis ofhistoric events be as accurate as possible.

9lobally, large magnitude earthquakes occur rarely &on the order of hundreds of years'and without warning, so that traditionally it has been difficult to measure and study them.

Canada has not yet had a catastrophic earthquake, and so the severity of its e!posure isunclear. owever, in efforts to minimise e!posure, Canada has built over 200 seismicmonitoring stations for research purposes. These stations record seismic parametersincluding the location of each epicenter, duration, and magnitude for all earthquakes. Theepicentre is the surficial location of the source of an earthquake, and is found directlyabove the hypocentre. "n areas with enough seismograph stations, such as southwesternBritish Columbia, the depth of the hypocentre is also measured. The hypocentre is theactual location of the source of an earthquake. This is usually at some depth beneath theearthIs surface along a rupturing fault. *arger earthquakes are e!amined more thoroughlyand include measures of earthquake intensity, fault dimensions and orientation, causalstress fields and so on &:ogers, personal communication'. hile this level of detail will be of use in the future, current researchers and models must rely on historic seismicevents for risk analysis. A ma8or proportion of these events occurred before sophisticatedinstrumentation became available for measuring seismicity. "t is e!tremely difficult totranslate historical data into current settings with any kind of accuracy &:ogers, personalcommunication'. Therefore there is a high degree of uncertainty inherently associatedwith any earthquake risk analysis.

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9enerally, ground motion attenuation at a site is a function of distance from the source&d', depth to hypocentre &:', earthquake magnitude &6', and site parameters describingregional geology and site soil conditions &9i'. As seismic waves pass through the ground,they encounter different mediums which either amplify or dampen their movement. %rom%igure F.> it can be seen that ground motion attenuates e!ponentially with increasing

distance from the epicentre.

The Canadian est Coast is susceptible to two types of earthquakes( shallow continental,and deep subduction. $hallow earthquakes close to @ancouver, such as in the $trait of9eorgia, are analysed using attenuation curves from California &:ogers, personalcommunication'. California attenuation equations are based on peak ground acceleration&39A', local magnitude, depth to hypocentre, and distance to epicentre &Campbell, 2


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,et3ee& the seismi s"'re a str't'ra$ $"ati"& a& misreprese&t sha!i&

i&te&sit- at the site.

"t is the ob8ective of the attenuation function to determine shaking intensity at a site giventhe original ground motion magnitude, and distance from the source. To better understand

ground motion attenuation, each component of the attenuation equation can be addressedseparately. This includes( the source parameters, ground motion parameters and site parameters.

Source Parameters An earthquake is the result of elastic strain released via rupturing along a fault line M theearthquake source. The larger the rupture, the larger the earthquake and surrounding areaaffected. $eismic waves originate at the source and decay as they move radially outwardsfrom it. "n order to determine the level of ground motion at a site, it is important to havesome measure of where the source is in relation to the site-to-source parameter. Theseismic source can be described by several parameters including the fault location, down-

dip e!tent of the of the plate boundaries, depth of the hypocentre, and location ofepicentre.

U&$ess seismi ati+it- has ,ee& ",ser+e# a$"& a a'$t5 its $"ati"& "r eiste&e5

remai&s '&!&"3&. %or instance, the 2> Nobe earthquake in Kapan &6;F.' occurredalong a previously unknown fault. "f an area is thought to have seismic potential and yetlittle to no physical evidence e!ists to support the hypothesis, source ones are often usedto identify the location of a fault. %rom 2>F< to 2


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$ince the movement of a seismic wave attenuates with distance, most attenuationequations have a site-to-source parameter. This suggests a measure from the structurelocation to the hypocentre. As mentioned earlier, hypocentre measurements are notalways available or reliable. owever, unlike depth to hypocentre, the epicentre, locateddirectly above the hypocentre at the surface, is a straight forward and reliable seismic

measurement. Therefore, it is usually used to measure site-to-source distance. $eismichaard modules account for depth of hypocentre by ad8usting the source-to-site distance.

Ground Motion 9round motion is induced by seismic energy release at the source. "t is usually measured by magnitude, seismic shaking intensity, and peak ground acceleration, which can bequantified using seismographs or accelerograms. The 200 seismograph stations in Canadacontinuously record all seismic activity in Canada with magnitude 6 L 5.>, including 6 ; 5.> for populated areas &:ogers, personal communication'. 9round motion shakingintensity is responsible for much of the damage to structures. Thus, as shaking durationincreases, so does the amount of damage.

olding all other factors constant, a subduction earthquake will often produce moredamage than a continental earthquake because its larger rupture surface increases theduration of strong shaking &:ogers, 2'. "n the various seismic risk models, the userspecifies a seismic event magnitude using either a 9uttenberg-:ichter scale magnitude,6, or a recurrence probability. As the magnitude of an event increases, its return periodtends to decrease. The recurrence period is used in a recurrence model to assign themagnitude of an event based on the probability of e!ceeding the event in a given numberof years &*amarre et al., 2/'.

The )'tte&,erRihter sa$e is the scale most commonly used to measure a seismic

event. "t describes the Itotal energy of the seismic waves radiating outwards from anearthquake as recorded by the amplitude of ground motion traces on seismographs at anormalised distance of "##km from the sourceI &$mith, 2F'. $ince it was firstdeveloped, the 9uttenberg-:ichter scale has been modified to include data from modernseismic measurement devices, and local and regional conditions. hile the localmagnitude scale is acceptable for measuring smaller earthquakes &6 less than or equal toF.>', the moment magnitude scale is more appropriate for larger events &6 L F.>'. Thelocal magnitude $% & ' is the logarithm of the corrected ground motion in micrometers&2mm ; 20-5 mm'. %or e!ample, a seismic wave amplitude of 0.> mm &>00 mm' willhave an 6* of /.H &log &>00' ; /.H', while to achieve 6* ;


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movement, and the rigidity of ground material. Though 6 L >.> accounts forappro!imately 2P of all earthquakes in the world, they are responsible for 0P of allseismic energy released &$mith, 2F'.

The 9uttenberg-:ichter scale does not include ground shaking intensity, duration, or

frequency, which are necessary to infer potential damages. Accordingly, the 6 is usuallyconverted in the seismic module to a M"#iie# Mera$$i Ie 7MMI8. 66" provides ameasure of seismic ground shaking intensity by assigning a numerical value to the humanobservations of felt ground motion and the e!tent of physical damage to buildings andundeveloped land. An e!perienced individual will rate the intensity of an earthquake from66" ; 2, not felt e!cept by a very few under e!ceptionally favourable circumstances, to66" ; Q"", total destruction &wave seen on ground surface, lines of sight and leveldistorted, ob8ects thrown into the air4 see Table F.'.

Though 66" is e!tremely sub8ective, it can be argued that it is no less scientific than9uttenberg-:ichter $cale measurements since seismologists can disagree on the e!act

rating of the magnitude of an event. "n addition to providing information on the spatialdamage pattern after an earthquake, 66" is applicable to pre-instrumentationearthquakes.

66" has since been modified to be more ob8ective by relating each inde! increment to ameasure of pea! r"' ae$erati"& &see Table F./'. 39A is the peak value ofhoriontal ground acceleration at a site. The advantage of 39A is that it is ob8ective anddirectly measurable. owever, 39A does not provide a measure of duration or frequencyof ground motion which are important factors for determining damage to structures&Ansary et al., 2>'.

$ome researchers believe that Arias I&te&sit- is a more ob8ective measure of shakingintensity and ground motion characterisation &Arias, 2H04 Nayen et al., 24 Nayan and6itchell, 2F'. Arias intensity is calculated by integrating the entire seismogram waveform, including amplitude and duration of ground motion. The ob8ective is to find thetotal seismic energy absorbed by the ground either at the surface, or at some depth below.nlike 39A, which uses a single, high frequency, point in the seismogram, Ariasintensity considers the full range of frequencies recorded for all points in the seismogram.Arias "ntensity is also directly quantifiable and verifiable, as opposed to 66" &Nayen etal., 24 Nayen and 6itchell, 2F'. owever, Arias intensity is still relatively young,and an e!tensive database is still being developed. There is also the question of how, oreven if, Arias intensity can deal with historic earthquakes. As well, Arias "ntensity isdependent on the seismic record, and seismograms may not always be available, ortriggered, to measure seismic activity. Though this measure does show promise for thefuture, 66" will likely continue to be used for seismic haard modelling for some time.

Site Parameters 9round motion is strongly affected by site conditions. As such, it is important to consider site effects in any ground motion attenuation function. %or instance, seismic motion inshallow soils & less than or equal to 20 m' is amplified, while in deep soils & L 20 m' it is

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attenuated &Campbell, 2


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Ca$i"r&ia a "ther s',#'ti"&

2"&es are represe&tati+e "5

a app$ia,$e t"5 the sit'ati"& "

3ester& Ca&a#a.

$eismic haard modelling is highly dependent on the occurrence of seismic events in the past. $ince the ability to directly measure seismic activity is relatively recent, it isassumed that qualitative descriptions of historic events are sufficiently accurate to enablethe event to be consistently converted to a value of 66". As a corollary, it is assumedthat 66" can adequately quantify historic ground shaking intensity. Assuming that thequality of building construction and materials is uniform around the world, this could befeasible. owever, the world is composed of a mosaic of building practices that have been developing through time at different rates. An earthquake resistant building designfor the kraine may not be sufficient by Californian standards. Accordingly, anearthquake of equal magnitude in either area may produce completely different damage

results, and hence different measures of 66". %or international comparison of seismicshaking intensity, 66" is highly uncertain. owever, within a given 8urisdiction, 66" provides a common forum. $eismic measurement is still limited. That is(

• not all seismic parameters are confidently measurable yet, such as depth to

hypocentre,• not all seismically active areas are equipped with instrumentation, and

• often, in areas that are equipped, the instruments are either not triggered, or not

immediately triggered, during an event.

$ince no alternative measure for historic events is currently available, there is no reason

to discontinue using 66" and the 66"-damage relationship in seismic risk modelling&Tung et al., 2'.

Sensiti+ities %or many models, the most sensitive parameter is also the most sub8ective - 66". 1ue tothe sub8ective nature of many of the seismic haard inputs, some form of sensitivityanalysis should be performed to determine how alternative inputs for important parameters will affect model results and, ultimately, decisions made based on theseoutputs &++:", 2


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• attenuation equations, and

• parameter measurement and estimation.

%or e!ample, *amarre et al. &2/' have attempted to quantify uncertainty by applyingthe bootstrap method. The bootstrap method is a statistical approach which deals with

incomplete datasets. Their ob8ective was to evaluate uncertainty due to(• incompleteness of the earthquake catalogue4

• errors in magnitude measurement and conversion &6 to 66"'4

• mismatching of the recurrence and attenuation models with reality4 and

• the final seismic haard estimates.

There is also the potential for uncertainty to be associated with the seismic parametersthemselves. This pertains to data sufficiency issues. %or instance, depth to hypocentre,used in many attenuation equations, is difficult to measure because of limitations ininstrumentation and modelling.

6ost models obtain Canadian seismic source and site condition information from the9eological $urvey of Canada. $ince all models use the same soil data for Canada, all aresub8ect to the same uncertainties associated with the collection, completeness, accuracyand resolution of the data. Thus, there is again an underlying commonality between themodels. ith so many commonalties between the seismic haard models, aside from thedata limitations, discrepancies in the results are not well understood.

6.9 '$&era,i$it- M"#'$e

The third step in seismic risk modelling involves modelling structural vulnerability todamage. The purpose of the vulnerability module is to estimate the degree of damage to

structures and contents, as well as the potential cost of business interruption for a givenearthquake. To do this, the shaking intensity estimated in step two is used in vulnerabilityfunctions.

"n the vulnerability module, #amae is estimate# 'si& +'$&era,i$it- '&ti"&s 3hihre$ate r"' m"ti"& t" #amae "r +ari"'s str't'res. $ince Canada has not had aserious earthquake, damage information is limited, and so, the vulnerability functions are based on observations of historic and recent earthquake damage from around the world.As with the attenuation laws, it is therefore necessary to have a complete understandingof how historical shaking intensities are converted to estimates of damage &see $ectionF.'.

Building inventory information, including "nsurance Bureau of Canada class and age ofstructure, are converted to Applied Technology Council :eport &ATC-25' equivalents toinfer the relative vulnerability of a structure to failure. sing modified ATC-25vulnerability functions, the percent of structural damage is estimated based on relativevulnerability of the building and 66" shaking intensity at the site.

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The ATC-25 vulnerability functions, developed in 2 by a group of $tructural+ngineers from the Applied Technology Council, describe the modes of failure fordifferent types of structures given earthquake shaking intensity. They also provide ameasure of the likely cost of repair for a structure given its construction type, defined bythe ATC-25 classification system &Table F.>'. 66" was used as the measure of shaking

intensity because it was available for historic and more recent earthquakes. Additionalmeasures of structural damage were obtained from field and shake table investigations.1amage and shaking intensity were then used to estimate structural vulnerability tofailure in the event of an earthquake, with functions developed for each construction type&%igure F.th, percentile on the vulnerability curve&%igure F.th percentile can provide the modeller with anunwarranted sense of confidence in the damage estimates. owever, events with a higherreturn period can have more detrimental effects if the confidence level is decreased. %ore!ample, 3robable +!pected 1amage &3+1' is calculated at the >0th percentile on thevulnerability curve &%igure F.


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potentially to the point where costs outweigh gains. As data isaggregated to reduce costs and compensate for incompletedata, uncertainty in model results is increased, potentially tounacceptable levels. Accordingly, compromises must be madeto enable seismic risk modelling.

Three assumptions should be made when the ATC-25 vulnerability functions are appliedto estimate damage in western Canada(

2. lag period between ?BCC changes and implementation4/. level of ?BCC enforcement4 and5. given equal magnitude earthquakes, damage will be worse in @ancouver and the

surrounding area, than in California. This is because @ancouverIs ?BCC standardsfor earthquakes are not as rigid as those for California. &owever, this could be

updated soon.' As well, much of @ancouver is powered by natural gas whichcould have serious repercussions in the event of fire-following.

ow do these assumptions change the results produced by the vulnerability functionsR%ailure to account for these assumptions could lead to severe under-estimation of potential damages.

66" is a sub8ective and sensitive parameter. $ince there is a non-linear relationship between shaking intensity and level of structural damage, small changes in 66" willresult in large differences in structural damage. *evel of damage also depends strongly onstructural vulnerability. "ncomplete building inventory information is usually

compensated for either by calculating a weighted average for the construction types inthat area, or by querying the database for an appropriate inventory distribution. owever,this can result using the wrong construction type to determine the vulnerability function4therefore, structural information must be as precise and complete as possible.

As with the seismic haard module, there is uncertainty associated with each step in thevulnerability module. As the comple!ity of a structure increases &e.g. multiple! buildings', the uncertainty also increases since collapse of these structures are not wellunderstood &+7+CAT, unpublished'. This can result in over-estimation of damage. Aswell, it is assumed that structures are built to code, and maintained over time, which isnot always the case. %ailure to account for the condition of a structure could result in an

under-estimation of potential damage. %inally, the conversions from "BC class to ATC-25class may further introduce uncertainty into the vulnerability module. There are severalother sources of uncertainty in the vulnerability module which require furtherinvestigation.

6.6 Fi&a&ia$ M"#'$e

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The final step in seismic risk modelling involves the estimation of losses in the financialmodule. The purpose of the financial module is to calculate the insured losses of anearthquake based on three factors( insurance structure, structural damages estimated bythe vulnerability module and cost to repair the damages incurred.

A ma8ority of seismic risk models have financial modules which estimate probablema!imum loss &36*' for property, contents and business interruption. To estimate grossloss, the cost of repair is calculated for each insured structure using the percent damageincurred by the structure. ?e!t, the insured value of the structure and policy limits areconsidered. The same is done for contents and business interruption.

?et 36* is calculated by considering the insurance structure. That is, the layers ofreinsurance, coinsurance, and retrocession are subtracted from the gross 36*. %orindividual analysis, each site is considered independently. %or a portfolio analysis, thelosses are statistically aggregated. $ome financial modules also estimate probablee!pected losses &3+*', based on a worst-case-scenario, and e!pected annual losses

&+A*', which account for all possible earthquakes that may affect a site over a period oftime.

*oss estimations are directly linked to the cost of repairing damage. owever, followinga catastrophe, the high demand for scarce materials and labour tends to drive up the costsof repair. The cost of inflation can be substantial and therefore should be considered inthe calculation of 36*. $ome models include the cost of inflation by ad8ustingcoinsurance and deductibles, others have built-in inflation factors and some do notacknowledge the issue. As well, the final 36* estimate should include the cost ofremoving debris from the site before repairs can be made.

"n addition to calculating loss estimates, another important function of the financialmodule is to quantify the uncertainty that pervades each component of the seismic riskmodel. $ince the model is a decision making tool, some measure of uncertainty should beassociated with the loss estimates. This can be in the form of a level of confidence,standard deviation, confidence interval, or a range of loss estimates.

6.; Re+ie3 " Seismi Ris! M"#e$s

This section poses some questions that should be considered before modelling seismicrisk. "t also e!amines three seismic risk models currently available to the insuranceindustry to aid in decision making and seismic risk management. $ome attempt to

validate the results of the models has already been put forth by some of the modellingcompanies &see Kones et al., 2>'.

There are several decisions that must be made before an appropriate seismic risk modelcan be selected. %irst, and foremost, the company must decide what it hopes to achieve byusing a seismic risk model. This can be addressed by answering a few questionsconcerning the modelling effort. That is(

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2. ow will results from the model be used to assess the risk of a companyR That is,will the results be used as the final estimation of probable ma!imum loss &36*',or will they be used to improve inputs for a more comprehensive and tailored36* estimation methodR This will help determine both the necessary resolutionof the data for input, and which model to use for the analysis.

/. hich cost calculations should be performedR %or e!ample, if only an estimate of 36* is required, there is no need to use a model that also calculates probablee!pected losses &3+*', e!pected annual losses &+A*', or other loss calculations.

5. hat factors should be included in the model calculation of costR This includescost of seismic shaking given property damage, content damage, businessinterruption, andEor secondary costs due to fire-following, landslide, liquefaction,or inundation. Addressing this question can aid in model selection.

$econd, assessment of a companyIs risk can be performed either at the portfolio level, theindividual level, or both, depending on the model used. Before beginning an assessment,the insurance company must decide at what level they wish to perform their analysis.

This will likely produce different 36* estimates. 1epending on the resolution of thecompanyIs input data, this decision could already be made. That is, if the companyIs datais aggregated according to cresta one, it is not possible to perform a site-specificanalysis.

%inally, the company must also decide whether to have the analysis performed as aservice by the model provider, or to license the model for in-house analysis. There areadvantages and disadvantages for both of these options. sing the model as a serviceensures that a qualified individual with a thorough understanding of the model performsthe analysis. owever, the disadvantage is that the service modeller may not have athorough understanding of the insurance data provided, or of the insurance industry.

*icensing a model both

2. enables that an individual with a thorough understanding of the companys dataand the insurance industry performs the risk analysis, and

/. enables the company to get a better sense of the limitations, uncertainties andsensitivities of the program, and also enables more e!perimentation and tailoringof the program to the companyIs needs.

owever, there are many startup costs associated with licensing from hardware tolearning the program. As well, it is possible that the uncertainty and error could increaseinitially depending on the skills, or e!perience, of the in-house modeller. "f the analysis is performed as a service, usually the insurance company must provide detailed informationregarding portfolio building inventory, insurance structure, and assumptions.

The information provided during the review of the seismic haard module &$ection F.'can be used as a framework for both other modules in the seismic risk model, and for theseismic risk model as a whole. This method of e!amination has been summarised in%igure F..

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%irst, the sie&e behind the what is being modelled should be investigated. %or instance,how well is damage to structures understood by engineers, and then modelled by thevulnerability module. "f the scientific community does not have a good understanding ofthe haard, modelling will be inherently limited.

$econd, potential users should review the p'rp"se5 app$iati"& a appr"ah of eachmodel. This allows the user to match the needs of the company with the appropriatemodel.

Third, all models simplify reality. Therefore, it is important to e!amine the integrity of amodel. This includes how well a haard is modelled, or what the "mp"&e&ts " them"#e$ are. This requires looking at the entire modelling process from user inputs, todatabase inputs, to each module through which the data is manipulated, to outputs. "norder to determine how well the seismic risk model simulates the damages attributable toseismic shaking, the model components must be e!amined. This includes the insuranceinputs, and the seismic haard, vulnerability, and financial analysis modules. Certain

assumptions make this simplification possible, and these assumptions must not violate thelaws of physics. As well, since the seismic risk models are used as a decision makingtool, their sensitivities, uncertainties, and limitations also need to be understood.

%inally, there are issues of #ata *'a$it- a *'a&tit-. The quality of data affects modelresults. Data *'a$it- is affected by the data sources, collection procedure, accuracy,resolution, and completeness. %or e!ample, in #ntario, the soil maps produced by the9eological $urvey of Canada &9$C' differ from those produced by the #ntario9eological $urvey $' because of collection procedure. 9iven the same soil type -H0P sand and 50P silt - the 9$C will describe the soil as a sandy silt, while the #9$ will call it a silty sand. "f these differences occur in #ntario, it is likely that a similar

problem could e!ist in other provinces and with respect to other measurements. Data*'a&tit- is affected by the frequency of earthquakes, and the ability to measure them.#ne of the problems with estimating insured losses due to earthquakes along the estCoast of Canada is the rarity of events. This limits the quantity and availability ofattenuation and damage data. "n addition, there are issues of sub8ectivity in the collection procedure, such as the case with 6odified 6ercalli "ntensity measurement &66"'.%inally, issues of data matching and transfer functions need to be investigated since thiscan decrease the accuracy and increase the uncertainty associated with the data. %orinstance, converting peak ground accelerations to 66", or "BC classes to ATC-25classes. These issues are usually addressed throughout the model review.

The ob8ective now is to review some of the seismic risk models available to the insuranceindustry using the proposed e!amination scheme. There are some areas

which overlap between the models, such as in the scientific understanding and datasufficiency of seismic haard. These areas need not be compared, but rather addressed asin the seismic haard section &F.'.

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)*-*1 ./e Models A preliminary e!amination of the 6unich :e 3robable 6a!imum *oss Calculationmodel, the :6$ - ":A$ model, and the +7+CAT - +7+aard model was performedusing the proposed evaluation scheme as a guideline. Before comparing the models, theyshould be briefly reviewed.

%unich (e ) *robable %aximum &oss +alculation %odel The purpose of the 6unich :e model is to calculate the 36* resulting from anearthquake, for a given property portfolio &%igure F.20'. The model uses a probabilisticapproach to calculate loss based on damage from 2/00 earthquakes. 36* is calculatedfor losses due to property and contents damage, and business interruption givenearthquake shaking and fire following. The model can be used to determine theeffectiveness of an underwriting strategy, and as a decision making tool regardingreinsurance protection. By using a probabilistic approach, some measure of uncertainty isinherently provided with the results. Though the 6unich :e model has been criticised for performing loss estimation by cresta one, at the time of its development this was the

only level of insurance data available. "n response to improvements in insurance portfolioinformation, 6unich :e is developing F-digit postal code site analyses capabilities for itsmodel. The model is currently provided as a free service to its clients.

(isk %anagement olutions ) -(. %odel

The purpose of :isk 6anagement $olutions &:6$' ":A$ model is to educate people onrisk associated with an earthquake &%igure F.22'. This can be performed using bothdeterministic and probabilistic methods at the site-specific or portfolio levels. *osses arecalculated primarily from damages due to less severe, but more frequent earthquakeshaking, with estimates for landslide, liquefaction, and fire following. :esults from the

analysis are meant to(

• provide information for input into the risk analysis methods of the company4

• aid in underwriting and portfolio management4

• assess the quality of current rates4 and

• evaluate incremental load risk placed on a portfolio.

At this time, ":A$ is the model most commonly used to assess risk in Canada. The riskmodel can be provided as a service by :6$, or licensed to the insuranceEreinsurancecompany.

/0/+.T ) /0/1a!ard The purpose of +7+CATs +7+aard model is to evaluate the risk due to an earthquake by estimating catastrophic event losses for an individual risk or portfolio &%igure F.2/'. A probabilistic approach is used to estimate probable ma!imum loss, net e!pected loss, andannual e!pected losses. 3roperty, contents and business interruption losses are calculatedfor earthquake shaking, fault rupture, fire following, liquefaction, landsliding, tsunami,inundation, and haardous material release. The ob8ectives are to( facilitate policy writingfor underwriters4 evaluate e!isting books4 develop strategies for managing catastrophes4

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determine pure premium4 and test scenarios. +7+CAT has had limited activity in Canada,however, it is gaining

attention. 1ue to its comple! nature, +7+aard has been offered as a service. owever,+7+CAT hopes to have the model ready for licensing by 2H.

)*-*! E0amination of t/e Seismic isk Models Table F.F reviews the preliminary results of the proposed e!amination scheme for the6unich :e, :6$, and +7+CAT models. The models are compared generally. The purpose and applications of each model is revisited, followed by a brief review of theapproaches used to estimate seismic risk and losses, that is, deterministic vs. probabilisticmodelling. The primary and secondary consequences of an earthquake accounted for bythe models are assessed based on the modules within the seismic risk models. %ore!ample, the 6unich :e model investigates the cost of earthquake shaking and firefollowing. The :6$ model uses earthquake shaking and fire loss, and also includeslandslide and liquefaction losses. "n addition to these modules, the +7+CAT model

includes loss estimates due to inundation, fault rupture, and haardous materials release.

:epresentation of seismic haard is e!plored by reviewing the components of the model(the insurance inputs, seismic haard, vulnerability, and loss calculations &Table F.H'."nsurance inputs are nearly identical for all three models, e!cept that the 6unich :emodel currently uses cresta one to specify building location. The seismic haardmodules differ in their treatment of ground motion, attenuation, and site conditions. %ore!ample, the 6unich :e model uses 9uttenberg-:ichter magnitude, then 6odified6ercalli "ntensity &66"' to measure ground motion while the :6$ and +7+CATmodels use peak ground accelerations &39A' and 66". As well, the :6$ and +7+CATattenuation equations differ. The :6$ attenuation equation is a function of site to source

distance and peak ground acceleration. $ite conditions are accounted for in a separatestep. "n contrast, +7+CAT uses a logic tree approach to weight the average of threeattenuation equations which are functions of rupture length, site to source distance, 39A, shaking duration, and site conditions. +ach model uses modified vulnerability functionsto estimate damages, and each model calculates loss in a different way.

6odel integrity is e!amined by reviewing the ma8or assumptions, sensitivities,uncertainties and limitations of the three models &Table F.


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e!tent of damage at the site based on the site seismic shaking. %inally, each model has afinancial module that

calculates the potential insured losses given the e!tent of property and content damage, business interruption, and insurance structure.

The seismic risk models #ier in their purposes, applications, secondary effectsconsidered, attenuation and vulnerability functions, assumptions, sensitivities, and othermore minor functions. They will also differ in services and support provided, andoperation costs.

The purpose of this section has been to e!plain the process of seismic risk modelling, andto provide a method by which to e!amine the models currently available for riskmanagement. "n addition to this, other questions should be considered, this timeregarding the company producing the model. This includes how often databases areupdated, what kind of support is offered by the company, how credible the company is,

and what time and space costs will be incurred.

ecommendations

2. atch ?ational 9eographics documentary on natural haards( 2orn of 'ire* /. This analysis should also be performed for +astern Canada.5. A similar e!amination of the +'$&era,i$it- a i&a&ia$ modules should be

undertaken. The seismi ha2ar# portion of the risk models should be studied ingreater detail.

. Las$i#e5 $i*'eati"&5 i&'ati"&5 a ire "$$"3i& m"#'$es were notaddressed in this document and need to be evaluated in a similar manner.

>. Other ris! m"#e$s, such as :isk +ngineersI +7Canada, should also be reviewed.F. This analysis should be repeated for =i M"#e$s.

Reere&es

Allen, 1. +. &2. $cale( 2(20 000 000.

Ansary, 6. A., Samaaki, %., Natayama, T. &2>'. $tatistical analysis of peaks anddirectivity of earthquake ground motion. /arthquake /ngineering and tructural 8ynamics /( 2>/H-2>5.

Arias, A. &2H0'. A measure of earthquake intensity. "n( eismic 8esign for 9uclear *ower *lants ansen, :. K. &ed.'. 6"T 3ress, Cambridge.


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Atwater, B. %., ?elson, A. :., Clague, K. *., Carver, 9. A., Samaguchi, 1. N., Bobrowsky,3. T., Bourgeois, K., 1arieno, 6. +., 9rant, . C., emphill-aley, +., Nelsey, . 6.,Kacobi, 9. C., ?ishenko, $. 3., 3almer, $. 3., 3eterson, C. 1. and :einhart, 6. &2>'.$ummary of coastal geologic evidence for past great earthquakes at the cascadiasubduction one /arthquake pectra 22( 2-2


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*amarre, 6., Townshend, B. and $hah, . C. &2/'. Application of the bootstrap methodto quantify uncertainty in seismic haard estimates 2ulletin of the eismological ocietyof .merica eology and >eological 1a!ards of the ancouver (egion, outhwestern 2ritish +olumbia, 6onger, K. . .&ed.'. >eological urvey of +anada, 2ulletin etting the %ost out of the (esults. Technical $ervices Bulletin. Ale!ander owden Canada *imited, 2F.

3.part4__computer models of probable maximum loss

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