a basic introduction to quantitative seismic hazard

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Journal of Earthquake and Tsunami, Vol. 1, No. 2 (2007) 99–118c© World Scientific Publishing Company

A BASIC INTRODUCTION TO QUANTITATIVESEISMIC HAZARD ASSESSMENT

JEROEN TROMP

Seismological LaboratoryCalifornia Institute of Technology

Pasadena, CA 91125 USA

We provide an overview of some of the issues that need to be considered in the contextof quantitative seismic hazard assessment. To begin with, one needs to inventory andcharacterize the major faults that could produce earthquakes that would impact theregion of interest. Next, one needs a seismographic network that continually recordsground motion throughout the region. Data from this network may be used to assessand locate seismicity, calibrate ground motion simulations, and to conduct seismic early-warning experiments. To assess the response of engineered structures to strong groundmotion, seismographs should also be installed at various locations within such engineeredstructures, e.g., on bridges, overpasses, dams and in tall buildings. The ultimate goalwould be to perform ‘end-to-end’ simulations, starting with the rupture on an earthquakefault, followed by the propagation of the resulting seismic waves from the fault to anengineered structure of interest, and concluding with an assessment of the response ofthis structure to the imposed ground motion. To facilitate accurate ground motion andend-to-end simulations, one needs to construct a detailed three-dimensional (3D) seismicmodel of the region of interest. In particular, one needs to assess the slowest shear-wavespeeds within the sediments underlying the metropolitan area. Geological information,and, in particular, seismic reaction and refraction surveys are critical in this regard. Inthe context of end-to-end simulations, detailed numerical models of engineered structuresof interest need to be constructed as well. Data recorded by the seismographic networkand in engineered structures after small to moderate earthquakes may be used to assessand calibrate the seismic and engineering models based upon numerical simulations.Once the seismic and engineering models produce synthetic ground motion that matchthe observed ground motion reasonably well, one can perform simulations of hypotheticallarge earthquakes to assess anticipated strong ground motion and potential damage.Throughout this article we will use the Los Angeles and Taipei metropolitan areas asexamples of how to approach quantitative seismic hazard assessment.

1. Introduction

The purpose of this extended abstract for the 2007 Singapore Workshop on Earth-quakes and Tsunamis: From Source to Hazard is to summarize some of the basicingredients that are required to perform quantitative seismic hazard assessment.This summary is largely based upon experiences with such assessments in south-ern California (Krishnan et al., 2006a, b) and Taipei (Lee et al., 2007b). We willcover the need for an inventory and characterization of the major faults that couldproduce earthquakes that would produce strong motion in the area of interest, theimportance of a seismic network, and the necessity of instrumenting engineered

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structures. Data recording, archiving, and distribution is an integral part of seis-mic hazard assessment, because such data are critical for the characterization ofground motion in the region of interest, and the validation of numerical simulationsof seismic wave propagation and building responses.

In order to perform quantitative hazard assessment, detailed three-dimensional(3D) models of the region of interest need to be constructed. This requires theinterpretation of surface geology and the acquisition of bore-hole logs and seismicreflection profiles. In particular the geometry and shear-wave speed of the sedimentsunderlying the metropolitan area need to be established, because this is wheresignificant amplification and prolonged shaking will occur. For example, seismicmodels of southern California were constructed under the auspices of the South-ern California Earthquake Center (SCEC; scec.org) by Magistrale et al. (2000)and Suss and Shaw (2003). The former is a largely geologic ‘rule-based’ model,whereas the latter made extensive use of petroleum industry well-log and reflectiondata.

Once such models have been constructed, small events recorded by the networkcan be simulated numerically. From a seismological perspective, such simulationsmay be performed deterministically based upon finite-difference techniques (e.g.,Wald and Graves, 1998; Olsen, 2000), finite-element methods (e.g., Bao et al., 1998;Akcelik et al., 2003), and spectral element methods (e.g., Komatitsch and Tromp,1999; Komatitsch et al., 2004). In the Los Angeles metropolitan area the accuracyof these deterministic simulations is approaching a shortest period of 2 s, and inthe Taipei metropolitan area ∼1 s. From an engineering perspective, this impliesthat such simulations can only be used to assess the response of structures with acomparable or longer dominant period. Buildings with a shorter period responsecan currently only be modeled empirically, e.g., by subjecting engineered structuresto records from actual earthquakes recorded elsewhere.

With computational tools in seismology and structural engineering becomingmore accurate, reliable, and versatile, it is a natural progression to bring the twotogether to address the risk posed to engineered structures based upon ‘end-to-end’simulations, starting with a kinematic or dynamic rupture scenario, followed bya simulation of seismic wave propagation, and concluding by modeling the result-ing building response. Such simulations have just recently become feasible (e.g.,Krishnan et al., 2006a, b). Current limitations are that soil-structure interactions(Fenves and Serino, 1990; Trifunac et al., 2001) are frequently ignored, and theeffects of the shallow geotechnical layer are not incorporated.

2. Geological Fault Inventory and Characterization

A critical ingredient for accurate quantitative hazard assessment is knowledge of thedistribution and nature of the geological faults in and near the metropolitan areaof interest. Frequently, such faults may be subdivided into two categories: smallerfaults located within or bordering the region, and larger faults often located somedistance away.

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A Basic Introduction to Quantitative Seismic Hazard Assessment 101

Fig. 1. Broadband Southern California Seismic Network (SCSN) stations (dark gray triangles)and major faults in southern California. The light gray dot denotes the city of Pasadena, CA,which is to the North of downtown Los Angeles. (Courtesy Carl Tape.)

For example, as shown in Fig. 1, in the greater Los Angeles metropolitan areathere are numerous faults in the first category, e.g., the Hollywood, Raymond,Santa Monica, Whittier, Sierra Madre, Palos Verdes, and Newport-Inglewood faults.These faults are all capable of supporting earthquakes with magnitudes as large asapproximately seven. Faults in the second category are the San Andreas, San Jac-into and Elsinore faults, which are all capable of supporting earthquakes approach-ing magnitude eight, and, in the case of the San Andreas fault, beyond.

As a second example, in the Taipei Metropolitan area, shown in Fig. 2, theTaipei sedimentary basin is bordered by two main faults, the Taipei fault to theSouth and the San Chiao fault to the northwest, and dissected by the Kanchiafault (Lin, 2005). These faults are all capable of supporting sizeable earthquakes.In Taipei the main threat for large events comes from plate-boundary earthquakesassociated with the collision between the Philippine Sea Plate, which is believed toterminate deep below the Taipei basin, and the Eurasian Plate.

The nature of strong ground motion induced by a moderate earthquake froma nearby fault is noticeably different from the kind of ground motion produced

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Fig. 2. Seismographic stations and major faults in the Taipei Metropolitan Area. The variousnetworks are identified by the legend to the right; these include stations from the Broadband Arrayin Taiwan for Seismology (BATS), stations from the Central Weather Bureau Seismic Network(CWBSN), and stations operated by the Institute of Earth Sciences (IES) of the Academia Sinicain Taiwain. (Courtesy Shiann-Jong Lee.)

by a large earthquake on a distant fault. Nearby smaller earthquakes can produceintense higher frequency ground motion (frequencies of 0.5Hz and higher) affectingsmaller structures, where as distant large events tend to produce dramatic longerperiod ground motion (periods longer than 2 s) mostly affecting taller buildings.

So the first order of business is to establish the nearby and distant faults thatare potentially capable of producing strong ground motion in the region of inter-est. Once this fault inventory is complete, one needs to characterize the kinds ofearthquakes one may expect on these faults, e.g., vertical strike-slip motion, as onthe San Andreas fault, or thrusting, as on the Sierra Madre fault. In this context,paleo-seismological studies play a central role, e.g., faults with a surface expressionmay be trenched in order to determine the nature and history of slip (e.g., Sieh,1978a,b). It is important to realize that the nature of rupture has a profound impacton the kind of ground motion one might expect. For example, the manner in whicha fault ruptures, e.g., bi- or uni-laterally, can have a significant impact on the peakground velocities and accelerations one can expect at any given location, as will befurther discussed in Sec. 8. For this reason one needs to conduct a wide range of

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scenario earthquake simulations to ascertain the range of ground motion that onecan conceivably expect at a particular location.

3. Instrumentation

To characterize ground motion in the area of interest and to facilitate quantitativemodeling of such motion, a network of broadband and strong-motion seismometersis critical. Ideally, such instruments are installed on the ground and in boreholes, aswell as in key engineered structures such as bridges, dams, major overpasses, andtall buildings.

3.1. Seismic network

A permanent network of seismometers that continuously records ground motion is acritical ingredient for quantitative seismic hazard assessment. Such a network can beused to locate and characterize seismicity, calibrate ground motion simulations, andto conduct seismic early-warning experiments. Figures 1 and 2 show the broadbandstations that continuously record ground motion in the greater Los Angeles andTaipei areas, respectively. The data recorded by the Southern California SeismicNetwork (SCSN) are freely available via website, http://scsn.org, and the datarecorded by the Broadband Array in Taiwan for Seismology (BATS) are availablevia http://bats.earth.sinica.edu.tw.

Figure 3 illustrates the distribution of magnitude 3 and greater earthquakesrecorded by the SCSN between 1985 and 2005. The SCSN is currently operating anear real-time system for the determination of earthquake centroid-moment tensorsbased upon the method developed and implemented by Liu et al. (2004). The June28, 1992, magnitude 7.3 Landers, January 17, 1994, magnitude 6.7 Northridge, andOctober 16, 1999, magnitude 7.1 Hector Mine earthquakes are the three largestevents during this twenty year period. Note that numerous sizeable aftershocks areassociated with these main shocks. Note also the absence of events larger thanmagnitude 3 along much of the San Andreas fault.

Besides recording and distributing data, locating seismicity, and providing sta-tion response information, there are numerous opportunities for education & out-reach. For example, the ShakeMap website, http://earthquake.usgs.gov/eqcenter/shakemap/provides near real-time maps of ground motion and shakingintensity following significant earthquakes, and the Shake-Movie websitehttp://shakemovie.caltech.edu allows near-real time visualization of earthquakesin southern California by the media and the general public.

3.2. Building instrumentation

The ultimate goal of quantitative seismic hazard assessment should involve a self-consistent accounting of all aspects of the problem, starting with the rupture on

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Fig. 3. All magnitude 3 and larger earthquakes recorded by the SCSN between 1985 and 2005.The size of the symbols increases with magnitude, and the color of the symbols denotes depth, asshown to the right. (Courtesy Carl Tape.)

an earthquake fault, followed by the propagation of the resulting seismic wavesradiated from the fault to an engineered structure of interest, and concluding withan assessment of the response of this structure to the imposed ground motion. Tocalibrate such ‘end-to-end’ simulations one needs to collect data both from free-fieldseismometers as well as instruments located in engineered structures such as dams,overpasses, and skyscrapers. With this goal in mind, the Advanced National SeismicNetworks (ANSS, http://anss.org) includes a number of urban seismic networks. Asexamples of instrumented buildings, the nine-story Millikan Library on the campusof the California Institute of Technology has 36 strong-motion sensors, and theseventeen-story Factor Building at the University of California-Los Angeles has72 instruments. Data from both buildings are freely available via the SouthernCalifornia Earthquake Data Center (SCEDC, www.data.scec.org).

4. 3D Model Construction

From a numerical modeling perspective, the most important ingredient for suc-cessful simulations of strong ground motion is a detailed three-dimensional (3D)seismic model of the region of interest. Such a model must include variations incompressional- and shear-wave speeds and density. The geometry of the sedimen-tary basins and the shear-wave speeds within those basins control amplification

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and the duration of shaking. The construction of a detailed 3D model of the areaof interest ideally involves the acquisition of extensive seismic reflection and/orrefraction profiles, borehole sonic logs, and constraints based upon surface geology.

The creation of a high-resolution wave-speed model for southern Californiahas been a primary focus of the Southern California Earthquake Center (SCEC,http://scec.org). Figure 4 shows the prominent Los Angeles and Ventura sedimen-tary basins in the southern California model of Suss and Shaw (2003), which isbased on more than 85,000 direct measurements from boreholes and seismic reflec-tion profiles. The LA basin is 9 km deep, and the Ventura basin is 15 km deep.These pockets of slow shear-wave speed sediments tend to trap seismic energy andsignificantly prolong the duration of seismic shaking. Cross-sections through theSuss and Shaw (2003) model are shown in Fig. 5. These clearly highlight the slowwave-speed Los Angeles and Ventura basins, the significant topography associatedwith the San Gabriel mountains, and the dramatic variations in the thickness ofthe crust as prescribed by the Moho map determined by Zhu and Kanamori (2000).

Compared to the Los Angeles basin, the Taipei basin, shown in Fig. 6, is small,about 20 km× 20 km at the surface, and shallow, with a depth of less than 1000m.The basin is surrounded by varied topography, including mountains, tableland,

Fig. 4. 3D southern California sedimentary basin model. Shown is the depth to the basement ofthe sediments in 1000 m contour intervals. The greatest depth of the Los Angeles basin is 9 km,and that of the Ventura basin 15 km. (Courtesy Andreas Plesch.)

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Fig. 5. Cross-sections through the southern California model shown in Fig. 4. Note the slowwave-speed Los Angeles and Ventura basins, the topography associated with the San Gabrielmountains (exaggerated by a factor of five), and the variations in crustal thickness denoted by thetop of the dark blue upper mantle. (Courtesy Carl Tape.)

Fig. 6. (Left) Map view of the Taipei basin. The depth of the basement is represented by graycolors. It’s deepest part is ∼700m, i.e., more than ten times shallower than the Los Angeles basinshown in Fig. 1. The red line shows the JhongShan freeway across the basin. The world’s currenttallest building, Taipei 101, is marked in the shallow eastern basin. (Right) Perspective view ofthe two major discontinuities in the Taipei basin. The first is the SongShan formation and thesecond is the basin basement. Surface topography around the basin is shown at the top of thefigure. (Courtesy Shiann-Jong Lee.)

and a volcano group, collectively producing changes in elevation varying betweensea level and about 1120m. There are two major discontinuities in the basin: theSongShan formation and the basin basement (Fig. 6(b)). The SongShan formationis a shallow, low shear-wave speed sedimentary layer with a depth less than ∼120m.The basin is surrounded by Tertiary basement with a deepest extent of about 700–1000 m, and is bordered to the northwest by the San Chiao fault. Taipei city’s

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high-rise buildings, including the world’s current tallest building Taipei 101 in theshallow eastern part of the basin, make the heavily populated region particularlyvulnerable to earthquakes.

5. Seismic Model Validation

Once detailed 3D models of the region of interest have been constructed, as in Figs. 1and 2 for the Los Angeles and Taipei metropolitan areas, numerical simulations ofseismic wave propagation may be performed based upon various numerical methods.Studies of this kind have been conducted based upon finite-difference techniques(e.g., Wald and Graves, 1998; Olsen, 2000; Lee et al., 2007a), finite-element methods(e.g., Bao et al., 1998; Akcelik et al., 2003), and spectral-element methods (e.g.,Komatitsch and Tromp, 1999; Komatitsch et al., 2004; Lee et al., 2007b). Thesesimulations generally involve hundreds of millions of integrations points, tens ofgigabytes of distributed memory, and are therefore typically performed on parallelcomputers based upon message-passing techniques (e.g., Gropp et al., 1996).

Figure 7 shows a comparison between data recorded after the February 22, 2003,magnitude 5.2 Big Bear main shock and synthetic seismograms calculated for theSuss and Shaw (2003) model shown in Figs. 4 and 5 based upon the spectral-elementmethod (Komatitsch et al., 2004). The spectral-element mesh contains a total of45.4 million grid points and the calculations require 14 gigabytes of distributedmemory. The data and synthetics are low-pass filtered with a corner at 6 s.

Figure 8 shows an example of a spectral-element mesh used to simulate seismicwave propagation in the Taipei basin. The mesh covers an area of 101.9 km×87.5 kmand extends vertically from an elevation of 2.89 km to a depth of 100km. The meshincorporates the steep topography around the city of Taipei, the geometry of theshallow sedimentary basin, topography on the boundary between the crust and themantle (the Moho), and a background 3D tomographic model for northern Taiwan.The slowest compressional wave speed in the basin is 350m/s, and the slowestshear-wave speed is 200m/s.

Figure 9 shows the results of a spectral-element simulation of the October 23,2004, magnitude 3.8 Taipei earthquake (Lee et al., 2007b). The calculation wasperformed in parallel by decomposing the area of interest in 324 mesh slices, involved297 million integration points, required 116 GB of distributed memory, and requiredapproximately 9.5 h of wall-clock time to obtain 30 s long seismograms. The velocitywaveforms are band-pass filtered between 0.1 and 1.25Hz.

6. 3D Engineered Structures

From the perspective of quantitative seismic hazard assessment, the ultimate goal isto integrate simulations of rupture and the resulting seismic wave propagation withthe analysis of engineered structures in one single ‘end-to-end’ simulation. Krishnanet al. (2006a,b) took a step in this direction by simulating the damage in two

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Fig. 7. Transverse component data (black) and spectral-element synthetics (dark gray) atselected stations of the Southern California Seismic Network (SCSN, http://scsn.org) for theFebruary 22, 2003, magnitude 5.2 Big Bear earthquake. The location and mechanism of thisearthquake are denoted by the beach ball. Both the synthetics and the data are low-pass filteredwith a corner at 6 s. (Courtesy Qinya Liu).

18-story steel moment-frame buildings in southern California from two hypotheticallarge earthquakes on the San Andreas Fault.

The base building is an existing 18-story steel moment-frame building located onCanoga Avenue in Woodland Hills, CA, that suffered significant damage during theJanuary 17, 1994, Northridge earthquake (Fig. 10). The second building is similarto the base building, but the structural system has been redesigned according tothe current southern California building code, UBC97. These 1997 code regulationsspecify larger design forces and call for greater redundancy in the lateral force-resisting system. This results in a greater number of bays of moment frames. Asa result, the dynamic properties of the two buildings are significantly different. Ingeneral, the redesigned building is expected to perform better than the existingbuilding in the event of an earthquake.

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Fig. 8. Northern Taiwan spectral-element mesh. The size of the model is 01.9 km × 87.5 kmhorizontally and +2.89 km to −100 km vertically. The 3D P wave-speed variations are representedby the rainbow color scale. The Taipei basin is located in the middle part of the model, and ischaracterized by relatively low wave speeds compared to the surrounding areas. Notice how themodel domain is ‘sliced’ for parallel computing purposes, such that the spectral elements containedin the slice in the lower left corner of the model go to CPU 0, the elements in the neighboringslice to the right go to CPU 1, etc. (Courtesy Shiann-Jong Lee).

The nonlinear time-history analyses of the building models are carried outusing the finite-element program FRAME3D (Krishnan (2003a); see www.frame3d.caltech.edu for details). The particular 3D elements used by the program to modelbeams, columns, and joints in buildings have been shown to simulate damage accu-rately and efficiently (Krishnan, 2003b). Material nonlinearity resulting in flex-ural yielding, strain hardening, and ultimately rupturing of steel at the ends ofbeams and columns, and shear yielding in the joints is included (Krishnan andHall, 2006a,b).

7. Engineered Structure Validation

Like the simulations of seismic waves generated by small to moderate earthquakesrecorded by the seismic network, the engineering simulations should be validated.For example, Krishnan et al. (2006a,b) used data from a seismograph located on thetop floor of an 18-story office building that was heavily damaged during the 1994Northridge earthquake to calibrate and validate the structural engineering analysis.

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Fig. 9. Comparison between synthetic waveforms and strong motion records of the October 23,2004, magnitude 3.8 Taipei earthquake (mechanism denoted by the beach ball). The velocitywaveforms are band-pass filtered between 0.1 and 1.25 Hz. Observations are denoted by blacklines, and synthetics are denoted by dark gray (N component), orange (E component), and green(Z component) lines. (Courtesy Shiann-Jong Lee).

To facilitate such calibrations and validations, a significant variety of structuresshould be equipped with seismometers, and the data recorded by such urban seis-mic arrays should be made readily available to the seismological and engineeringcommunities.

8. Rupture Scenarios

Once the seismological and engineering models have been extensively tested againstdata for small to moderate earthquakes, one can numerically simulate the impact

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Fig. 10. Structural models of the two buildings considered by Krishnan et al. (2006a,b).(a) Isometric view of the existing building (designed using the 1982 Uniform Building Code).(b) Isometric view of the new building (redesigned using the 1997 Uniform Building Code). (c) Planview of a typical floor of the existing building showing the location of columns and moment-frame(MF) beams. (d) Plan view of a typical floor of the redesigned (new) building showing the loca-tion of columns and moment-frame beams. Note the greater number of moment-frame bays in theredesigned building. (Courtesy Swami Krishnan).

of hypothetical large earthquakes on engineered structures. Figure 11 shows thedomain of such scenario simulations considered by Krishnan et al. (2006a) forsouthern California. In one scenario a magnitude 7.9 rupture initiates in Park-field to the North and progresses in a southeasterly direction over a distance ofapproximately 290 km. In the other scenario the same magnitude earthquake rup-tures in the opposite direction, starting in the South and terminating at Parkfield.Both scenarios are based upon the slip determined for the November 3, 2002, mag-nitude 7.9 Denali, Alaska, vertical strike-slip earthquake (Tsuboi et al., 2003). Themaximum depth of this rupture is about 20 km. The surface slip grows slowly to

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Fig. 11. Geographical scope of the simulation (The color scheme reflects topography, with graydenoting low elevation and light gray denoting mountains). The solid black triangles represent the636 sites at which seismograms are computed and buildings are analyzed. The white box is thesurface projection of the January 17, 1994, Northridge earthquake fault. The dark gray line inthe inset is the trace of the hypothetical 290 km rupture of the San Andreas fault that is theprimary focus of this study. The area enclosed by the blue polygon denotes the region covered bythe 636 sites. (Courtesy Swami Krishnan).

7.4m and drops drastically towards the end of the rupture. The peak slip at depthis about 12m. At 636 sites within the greater Los Angeles area the two buildingsshown in Figure 10 are subjected to these scenario ground motion.

Using the spectral-element method developed by Komatitsch and Tromp (1999)and implemented for southern California by Komatitsch et al. (2004), seismogramsare computed at each of the 636 analysis sites shown in Fig. 11, lowpass filtered witha corner at 2 s. Figure 12 compares the peak ground displacements, velocities andaccelerations associated with the two hypothetical San Andreas Fault earthquakes(Krishnan et al., 2006a,b). These two simulations make it abundantly clear that it isinsufficient to determine seismic risk solely based upon the distance to major faultsand the potential size of earthquakes on these faults: one also needs to characterizethe kind of earthquake, in particular its directivity.

In the north-to-south scenario, summarized in Figs. 12(a–c) for all three compo-nents, regions that are closest to the fault trace experience the strongest shaking.Strong directivity dictated by the big bend in the San Andreas Fault leads tolarge peak velocities (2 m/s) and displacements (2 m) in the San Fernando Valley.Going south from the San Gabriel mountains and the Hollywood hills into the

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Fig. 12. Peak ground velocities (PGVs) associated with two hypothetical magnitude 7.9 earth-quakes on the San Andreas fault (Krishnan et al., 2006a,b) (Fig. 11). Top row: PGV on theeast-west (a), north-south (b), and vertical (c) components for a North-to-South rupture scenario.Bottom row: PGV on the east-west (d), north-south (e), and vertical (f) components for a South-to-North rupture scenario. The simulations are based upon the spectral-element method (e.g.,Komatitsch & Tromp, 1999; Komatitsch et al., 2004) and are altered with a corner period of 2 s.(Courtesy Swami Krishnan).

Los Angeles basin, the peak velocities and displacements reduce to about 1m/sand 1 m, respectively, although the Baldwin Park/La Puente region in the SanGabriel Valley, which is quite close to the location of rupture termination, expe-riences shaking with a peak velocity up to 1.2m/s and a peak displacement upto 1.1m.

It is interesting to ask what would happen if the earthquake ruptured in theopposite direction, i.e., from south-to-north rather than from north-to-south. Shownin Figs. 12(d–f) are the peak velocities of the ground-motion time histories lowpassfiltered with a corner period of 2 s. Although the San Fernando valley still experi-ences the most shaking, ground motion in Santa Monica and to some extent BaldwinPark is comparable in magnitude. The peak velocities are of the order of 0.6m/s inthe San Fernando valley, 0.5m/s in Santa Monica and El Segundo, and 0.3m/s inthe remaining parts of Los Angeles and Orange Counties. The corresponding peakdisplacements are in the range of 0.5–0.6m in the San Fernando valley, 0.4–0.5m inSanta Monica and El Segundo, and 0.3–0.4m in the remaining parts of Los Angelesand Orange Counties.

Similar numerical simulations of hypothetical major earthquakes on the SanAndreas fault are the SCEC sponsored TeraShake simulations, which use the finite-difference method to simulate wave propagation on the DataStar supercomputer atthe San Diego Supercomputing Center (http://sceclib.sdsc.edu/TeraShake).

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9. End-to-End Simulations

Once detailed 3D models of the geographic region and the engineered structures ofinterest have been constructed and validated, one can attempt to perform ‘end-to-end’ simulations, starting with a kinematic or dynamic rupture simulation, followedby a simulation of the resulting seismic wave propagation, and ending with anassessment of the response of the engineered structure. Ideally, such simulationsshould be accomplished as part of a single simulation, incorporating the shallowgeotechnical layer and feedback between the response of the structure and the soil.At the moment the seismic and engineering simulations are performed consecutively,without interaction and feedback between the two.

Figure 13 summarizes the response of the two 18-story buildings displayed inFig. 10 at the 636 sites shown in Fig. 11. The results corresponding to a north-to-south rupture of the San Andreas fault are summarized in Figs. 13(a) and 13(b) forthe existing 18-story steel building (Fig. 10(a)). Figure 13(a) shows the percentageof connections where fracture occurred in the existing building. At least 25% ofthe connections in this building fracture when it is located in the San Fernandovalley. Note that the scale saturates at 25% and that this number is exceeded atmany locations. About 10% of the connections fracture in the building when it islocated in downtown Los Angeles and the mid-Wilshire district (Beverly, Hills),whereas the numbers are about 20% when it is located in Santa Monica, westLos Angeles, Inglewood, Alhambra, Baldwin Park, La Puente, Downey, Norwalk,Brea, Fullerton, Anaheim, and Seal Beach. Figure 13(b) shows the peak interstory

Fig. 13. Percentage of connections in the existing building (Fig. 10(a)) where fractures occur(left column) and the peak interstory drift in the existing (middle column) and redesigned (rightcolumn) building (Fig. 10(b)) due to two hypothetical magnitude 7.9 earthquakes on the SanAndreas fault (Krishnan et al., 2006a, b) (Fig. 11). Top row: North-to-South rupture scenario.Bottom row: South-to-North rupture scenario. (Courtesy Swami Krishnan).

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drift that occurs in the existing building. Consistent with the extent of observedfractures, the peak drifts in the existing building exceed 0.10 when it is locatedin the San Fernando valley, Baldwin Park and neighboring cities, Santa Monica,west Los Angeles and neighboring cities, Norwalk and neighboring cities, and SealBeach and neighboring cities, which is well into the postulated collapse regime.Note that the scale saturates at 0.10 and that the drifts far exceed this numberin many locations in these regions. When the building is located in downtown LosAngeles and the mid-Wilshire district, the building would barely satisfy the collapseprevention criteria set by the Federal Emergency Management Agency (FEMA),with peak drifts of about 0.05.

Figure 13(c) shows the peak interstory drift that occurs in the redesigned 18-story steel building (Fig. 10(b)) during the north-to-south rupture scenario. Theperformance of this building is noticeably better than the existing building for theentire region. However, note that the new building has significant drifts indicativeof serious damage when located in the San Fernando valley or the Baldwin Parkarea. When located in coastal cities (such as Santa Monica or Seal Beach), theWilshire corridor (west Los Angeles, Beverly Hills), the neighborhoods of Downeyand Norwalk, or the rapidly developing Orange County cities of Anaheim and SantaAna, it exhibits peak drifts of about 0.05, once again barely satisfying the FEMAcollapse prevention criteria. In downtown Los Angeles it does not undergo muchdamage in this scenario. Thus, even though this building has been designed accord-ing to the latest code, it suffers damage that would necessitate closure for sometime after the earthquake in most areas, but this should be expected because this isa large earthquake and building codes are written to limit the loss of life and ensurecollapse prevention for such large earthquakes, but not necessarily limit damage.

The reduced peak ground velocities during the south-to-north rupture scenario(Figs. 12(d–f)) is reflected in the corresponding results of the building analysesshown in Figs. 13(d–f). Figure 13(d) shows the percentage of connections wherefracture occurs in the existing building model. Fracture occurs in 3–7% of theconnections in this building when it is located in the San Fernando valley. About4–5% of the connections fracture in the building model when it is located in SantaMonica or El Segundo. In most other areas, there is little or no risk associated withmoment-frame connection fractures. Figure 13(e) shows the peak interstory driftthat occurs in the existing building. Peak interstory drifts beyond 0.06 are indicativeof severe damage, whereas drifts below 0.01 are indicative of minimal damage notrequiring any significant repairs. Peak drifts are in the neighborhood of 0.03 in theSan Fernando valley, Santa Monica, El Segundo, and Baldwin Park. Peak drifts inmost other areas are less than 0.02. As for the north-to-south rupture scenario, thepeak interstory drifts in the middle third and bottom third of the existing buildingare greater than in the top third, which indicates that the damage is localized inthe lower floors.

The performance of the newly designed 18-story steel building is slightly betterthan the existing building for the entire region. Figure 13(f) shows the peak

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interstory drift that occurs in the building. Peak drifts are in the neighborhoodof 0.02–0.03 when the building model is located in the San Fernando valley, SantaMonica, El Segundo, and Baldwin Park. Building peak drifts in most other areasare in the neighborhood of 0.01.

A significant limitation of the Krishnan et al. (2006a) study is that soil-structureinteraction (SSI) (e.g., Stewart et al., 1998) is not included in the analyses. Dynamicnonlinear SSI is not a well-understood phenomenon, because of the lack of recordeddata and the difficulty in designing accurate numerical tools to study it. One ofthe few real-world examples of extensive SSI research is a 14-story reinforced con-crete storage building in Hollywood constructed in 1925 (Fenves and Serino, 1990;Trifunac et al., 2001). These studies indicate that the change in various structural-response parameters in this building during the October 1, 1987, magnitude 5.9Whittier Narrows earthquake due to SSI could have been up to 20%. SSI is anactive area of research and should be incorporated into future studies of this kind.

10. Conclusions

We have attempted to give a basic overview of some of the issues that need to beaddressed in the context of quantitative seismic hazard analysis. Using examplesfrom the Los Angeles and Taipei Metropolitan Areas, we have emphasized the needto instrumentation, data archiving and distribution, 3D model construction, andnumerical modeling. Once this infrastructure is in place, quantitative seismic hazardassessment may be performed by considering the implications of various rupturescenarios on specific engineered structures.

It should be emphasized that the buildings analyzed by Krishnan et al. (2006a,b)are two specific 18-story steel moment-frame structures. Buildings with other con-figurations, constructed with other materials, or having distinct dynamic charac-teristics could have damage patterns quite different from the results presented here.In addition, there are significant uncertainties in the earthquake source character-istics, including the location of the hypocenter, slip distribution, rupture direction,etc. Future studies striving toward the goal of truly end-to-end simulations mustattempt to include the top soil layer in the ground-motion simulations and soil-structure interaction in the structural analysis.

The seismic hazard approach outlined in this article, integrating the fields ofseismology and structural engineering, can be used to assess specific engineeredstructures in a quantitative manner. For example, prior to actual construction, adetailed model of a planned structure can be analyzed using simulated seismic wave-forms generated by various plausible earthquakes on regional faults, and based onits performance informed decisions can be made to improve its structural design.Similar analyses can be performed to determine the risk posed to an existing struc-ture. Of course in each case the applicability of the band-limited simulated groundmotion for the analysis of the particular structure under consideration needs to

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be carefully ascertained. In the future, these kinds of analyses can be extended toinclude economic and financial indicators, and could benefit large cities in layingout emergency-response strategies in the event of a large earthquake, in undertakingappropriate retrofit measures for tall buildings, in formulating zoning regulations,and in developing better guidelines for new construction. Finally, they could provideseismic-risk parameters associated with existing and new construction to insurancecompanies, real estate developers, and individual property owners, so that they canmake appropriate economic decisions.

Acknowledgments

The author wishes to thank Swami Krishnan, Shiann-Jong Lee, Qinya Liu, AndreasPlesch and Carl Tape for contributing figures for this paper. The numerical simu-lations for this paper were performed on Caltech’s GPS Division Dell cluster.

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a basic introduction to quantitative seismic hazard

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