A BASIC INTRODUCTION TO QUANTITATIVE SEISMIC HAZARD ASSESSMENT

Transcription

1 Journal of Earthquake and Tsunami, Vol. 1, No. 2 (2007) c World Scientific Publishing Company A BASIC INTRODUCTION TO QUANTITATIVE SEISMIC HAZARD ASSESSMENT JEROEN TROMP Seismological Laboratory California Institute of Technology Pasadena, CA USA We provide an overview of some of the issues that need to be considered in the context of quantitative seismic hazard assessment. To begin with, one needs to inventory and characterize the major faults that could produce earthquakes that would impact the region of interest. Next, one needs a seismographic network that continually records ground motion throughout the region. Data from this network may be used to assess and locate seismicity, calibrate ground motion simulations, and to conduct seismic earlywarning experiments. To assess the response of engineered structures to strong ground motion, seismographs should also be installed at various locations within such engineered structures, e.g., on bridges, overpasses, dams and in tall buildings. The ultimate goal would be to perform end-to-end simulations, starting with the rupture on an earthquake fault, followed by the propagation of the resulting seismic waves from the fault to an engineered structure of interest, and concluding with an assessment of the response of this structure to the imposed ground motion. To facilitate accurate ground motion and end-to-end simulations, one needs to construct a detailed three-dimensional (3D) seismic model of the region of interest. In particular, one needs to assess the slowest shear-wave speeds within the sediments underlying the metropolitan area. Geological information, and, in particular, seismic reaction and refraction surveys are critical in this regard. In the context of end-to-end simulations, detailed numerical models of engineered structures of interest need to be constructed as well. Data recorded by the seismographic network and in engineered structures after small to moderate earthquakes may be used to assess and calibrate the seismic and engineering models based upon numerical simulations. Once the seismic and engineering models produce synthetic ground motion that match the observed ground motion reasonably well, one can perform simulations of hypothetical large earthquakes to assess anticipated strong ground motion and potential damage. Throughout this article we will use the Los Angeles and Taipei metropolitan areas as examples of how to approach quantitative seismic hazard assessment. 1. Introduction The purpose of this extended abstract for the 2007 Singapore Workshop on Earthquakes and Tsunamis: From Source to Hazard is to summarize some of the basic ingredients that are required to perform quantitative seismic hazard assessment. This summary is largely based upon experiences with such assessments in southern California (Krishnan et al., 2006a, b) and Taipei (Lee et al., 2007b). We will cover the need for an inventory and characterization of the major faults that could produce earthquakes that would produce strong motion in the area of interest, the importance of a seismic network, and the necessity of instrumenting engineered 99

2 100 J. Tromp structures. Data recording, archiving, and distribution is an integral part of seismic hazard assessment, because such data are critical for the characterization of ground motion in the region of interest, and the validation of numerical simulations of 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 the interpretation of surface geology and the acquisition of bore-hole logs and seismic reflection profiles. In particular the geometry and shear-wave speed of the sediments underlying the metropolitan area need to be established, because this is where significant amplification and prolonged shaking will occur. For example, seismic models of southern California were constructed under the auspices of the Southern California Earthquake Center (SCEC; scec.org) by Magistrale et al. (2000) and Süss and Shaw (2003). The former is a largely geologic rule-based model, whereas the latter made extensive use of petroleum industry well-log and reflection data. Once such models have been constructed, small events recorded by the network can be simulated numerically. From a seismological perspective, such simulations may 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 accuracy of these deterministic simulations is approaching a shortest period of 2 s, and in the Taipei metropolitan area 1 s. From an engineering perspective, this implies that such simulations can only be used to assess the response of structures with a comparable or longer dominant period. Buildings with a shorter period response can currently only be modeled empirically, e.g., by subjecting engineered structures to records from actual earthquakes recorded elsewhere. With computational tools in seismology and structural engineering becoming more accurate, reliable, and versatile, it is a natural progression to bring the two together to address the risk posed to engineered structures based upon end-to-end simulations, starting with a kinematic or dynamic rupture scenario, followed by a simulation of seismic wave propagation, and concluding by modeling the resulting 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 the effects 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 the distribution and nature of the geological faults in and near the metropolitan area of interest. Frequently, such faults may be subdivided into two categories: smaller faults located within or bordering the region, and larger faults often located some distance away.

3 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 area there 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 as approximately seven. Faults in the second category are the San Andreas, San Jacinto and Elsinore faults, which are all capable of supporting earthquakes approaching 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, the Taipei sedimentary basin is bordered by two main faults, the Taipei fault to the South and the San Chiao fault to the northwest, and dissected by the Kanchia fault (Lin, 2005). These faults are all capable of supporting sizeable earthquakes. In Taipei the main threat for large events comes from plate-boundary earthquakes associated with the collision between the Philippine Sea Plate, which is believed to terminate deep below the Taipei basin, and the Eurasian Plate. The nature of strong ground motion induced by a moderate earthquake from a nearby fault is noticeably different from the kind of ground motion produced

4 102 J. Tromp Fig. 2. Seismographic stations and major faults in the Taipei Metropolitan Area. The various networks are identified by the legend to the right; these include stations from the Broadband Array in 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 Sinica in Taiwain. (Courtesy Shiann-Jong Lee.) by a large earthquake on a distant fault. Nearby smaller earthquakes can produce intense higher frequency ground motion (frequencies of 0.5 Hz and higher) affecting smaller structures, where as distant large events tend to produce dramatic longer period 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 that are potentially capable of producing strong ground motion in the region of interest. Once this fault inventory is complete, one needs to characterize the kinds of earthquakes one may expect on these faults, e.g., vertical strike-slip motion, as on the 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 expression may 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 impact on the kind of ground motion one might expect. For example, the manner in which a fault ruptures, e.g., bi- or uni-laterally, can have a significant impact on the peak ground velocities and accelerations one can expect at any given location, as will be further discussed in Sec. 8. For this reason one needs to conduct a wide range of

5 A Basic Introduction to Quantitative Seismic Hazard Assessment 103 scenario earthquake simulations to ascertain the range of ground motion that one can conceivably expect at a particular location. 3. Instrumentation To characterize ground motion in the area of interest and to facilitate quantitative modeling of such motion, a network of broadband and strong-motion seismometers is critical. Ideally, such instruments are installed on the ground and in boreholes, as well as in key engineered structures such as bridges, dams, major overpasses, and tall buildings Seismic network A permanent network of seismometers that continuously records ground motion is a critical ingredient for quantitative seismic hazard assessment. Such a network can be used to locate and characterize seismicity, calibrate ground motion simulations, and to conduct seismic early-warning experiments. Figures 1 and 2 show the broadband stations that continuously record ground motion in the greater Los Angeles and Taipei areas, respectively. The data recorded by the Southern California Seismic Network (SCSN) are freely available via website, and the data recorded by the Broadband Array in Taiwan for Seismology (BATS) are available via Figure 3 illustrates the distribution of magnitude 3 and greater earthquakes recorded by the SCSN between 1985 and The SCSN is currently operating a near real-time system for the determination of earthquake centroid-moment tensors based upon the method developed and implemented by Liu et al. (2004). The June 28, 1992, magnitude 7.3 Landers, January 17, 1994, magnitude 6.7 Northridge, and October 16, 1999, magnitude 7.1 Hector Mine earthquakes are the three largest events during this twenty year period. Note that numerous sizeable aftershocks are associated with these main shocks. Note also the absence of events larger than magnitude 3 along much of the San Andreas fault. Besides recording and distributing data, locating seismicity, and providing station response information, there are numerous opportunities for education & outreach. For example, the ShakeMap website, shakemap/provides near real-time maps of ground motion and shaking intensity following significant earthquakes, and the Shake-Movie website allows near-real time visualization of earthquakes in southern California by the media and the general public Building instrumentation The ultimate goal of quantitative seismic hazard assessment should involve a selfconsistent accounting of all aspects of the problem, starting with the rupture on

6 104 J. Tromp Fig. 3. All magnitude 3 and larger earthquakes recorded by the SCSN between 1985 and The size of the symbols increases with magnitude, and the color of the symbols denotes depth, as shown to the right. (Courtesy Carl Tape.) an earthquake fault, followed by the propagation of the resulting seismic waves radiated from the fault to an engineered structure of interest, and concluding with an assessment of the response of this structure to the imposed ground motion. To calibrate such end-to-end simulations one needs to collect data both from free-field seismometers as well as instruments located in engineered structures such as dams, overpasses, and skyscrapers. With this goal in mind, the Advanced National Seismic Networks (ANSS, includes a number of urban seismic networks. As examples of instrumented buildings, the nine-story Millikan Library on the campus of the California Institute of Technology has 36 strong-motion sensors, and the seventeen-story Factor Building at the University of California-Los Angeles has 72 instruments. Data from both buildings are freely available via the Southern California Earthquake Data Center (SCEDC, D Model Construction From a numerical modeling perspective, the most important ingredient for successful simulations of strong ground motion is a detailed three-dimensional (3D) seismic model of the region of interest. Such a model must include variations in compressional- and shear-wave speeds and density. The geometry of the sedimentary basins and the shear-wave speeds within those basins control amplification

7 A Basic Introduction to Quantitative Seismic Hazard Assessment 105 and the duration of shaking. The construction of a detailed 3D model of the area of interest ideally involves the acquisition of extensive seismic reflection and/or refraction profiles, borehole sonic logs, and constraints based upon surface geology. The creation of a high-resolution wave-speed model for southern California has been a primary focus of the Southern California Earthquake Center (SCEC, Figure 4 shows the prominent Los Angeles and Ventura sedimentary basins in the southern California model of Süss and Shaw (2003), which is based on more than 85,000 direct measurements from boreholes and seismic reflection 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 and significantly prolong the duration of seismic shaking. Cross-sections through the Süss and Shaw (2003) model are shown in Fig. 5. These clearly highlight the slow wave-speed Los Angeles and Ventura basins, the significant topography associated with the San Gabriel mountains, and the dramatic variations in the thickness of the 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 1000 m. 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 of the 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.)

8 106 J. Tromp Fig. 5. Cross-sections through the southern California model shown in Fig. 4. Note the slow wave-speed Los Angeles and Ventura basins, the topography associated with the San Gabriel mountains (exaggerated by a factor of five), and the variations in crustal thickness denoted by the top 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 gray colors. It s deepest part is 700 m, i.e., more than ten times shallower than the Los Angeles basin shown in Fig. 1. The red line shows the JhongShan freeway across the basin. The world s current tallest building, Taipei 101, is marked in the shallow eastern basin. (Right) Perspective view of the two major discontinuities in the Taipei basin. The first is the SongShan formation and the second is the basin basement. Surface topography around the basin is shown at the top of the figure. (Courtesy Shiann-Jong Lee.) and a volcano group, collectively producing changes in elevation varying between sea level and about 1120 m. There are two major discontinuities in the basin: the SongShan formation and the basin basement (Fig. 6(b)). The SongShan formation is a shallow, low shear-wave speed sedimentary layer with a depth less than 120 m. The basin is surrounded by Tertiary basement with a deepest extent of about m, and is bordered to the northwest by the San Chiao fault. Taipei city s

9 A Basic Introduction to Quantitative Seismic Hazard Assessment 107 high-rise buildings, including the world s current tallest building Taipei 101 in the shallow eastern part of the basin, make the heavily populated region particularly vulnerable to earthquakes. 5. Seismic Model Validation Once detailed 3D models of the region of interest have been constructed, as in Figs. 1 and 2 for the Los Angeles and Taipei metropolitan areas, numerical simulations of seismic 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). These simulations generally involve hundreds of millions of integrations points, tens of gigabytes of distributed memory, and are therefore typically performed on parallel computers 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 the Süss and Shaw (2003) model shown in Figs. 4 and 5 based upon the spectral-element method (Komatitsch et al., 2004). The spectral-element mesh contains a total of 45.4 million grid points and the calculations require 14 gigabytes of distributed memory. 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 seismic wave propagation in the Taipei basin. The mesh covers an area of 101.9km 87.5km and extends vertically from an elevation of 2.89 km to a depth of 100 km. The mesh incorporates the steep topography around the city of Taipei, the geometry of the shallow sedimentary basin, topography on the boundary between the crust and the mantle (the Moho), and a background 3D tomographic model for northern Taiwan. The slowest compressional wave speed in the basin is 350 m/s, and the slowest shear-wave speed is 200 m/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 was performed in parallel by decomposing the area of interest in 324 mesh slices, involved 297 million integration points, required 116 GB of distributed memory, and required approximately 9.5 h of wall-clock time to obtain 30 s long seismograms. The velocity waveforms are band-pass filtered between 0.1 and 1.25 Hz. 6. 3D Engineered Structures From the perspective of quantitative seismic hazard assessment, the ultimate goal is to integrate simulations of rupture and the resulting seismic wave propagation with the analysis of engineered structures in one single end-to-end simulation. Krishnan et al. (2006a,b) took a step in this direction by simulating the damage in two

10 108 J. Tromp Fig. 7. Transverse component data (black) and spectral-element synthetics (dark gray) at selected stations of the Southern California Seismic Network (SCSN, for the February 22, 2003, magnitude 5.2 Big Bear earthquake. The location and mechanism of this earthquake are denoted by the beach ball. Both the synthetics and the data are low-pass filtered with a corner at 6 s. (Courtesy Qinya Liu). 18-story steel moment-frame buildings in southern California from two hypothetical large earthquakes on the San Andreas Fault. The base building is an existing 18-story steel moment-frame building located on Canoga Avenue in Woodland Hills, CA, that suffered significant damage during the January 17, 1994, Northridge earthquake (Fig. 10). The second building is similar to the base building, but the structural system has been redesigned according to the current southern California building code, UBC97. These 1997 code regulations specify larger design forces and call for greater redundancy in the lateral forceresisting system. This results in a greater number of bays of moment frames. As a result, the dynamic properties of the two buildings are significantly different. In general, the redesigned building is expected to perform better than the existing building in the event of an earthquake.

11 A Basic Introduction to Quantitative Seismic Hazard Assessment 109 Fig. 8. Northern Taiwan spectral-element mesh. The size of the model is 01.9km 87.5km horizontally and km to 100 km vertically. The 3D P wave-speed variations are represented by the rainbow color scale. The Taipei basin is located in the middle part of the model, and is characterized by relatively low wave speeds compared to the surrounding areas. Notice how the model domain is sliced for parallel computing purposes, such that the spectral elements contained in the slice in the lower left corner of the model go to CPU 0, the elements in the neighboring slice to the right go to CPU 1, etc. (Courtesy Shiann-Jong Lee). The nonlinear time-history analyses of the building models are carried out using the finite-element program FRAME3D (Krishnan (2003a); see caltech.edu for details). The particular 3D elements used by the program to model beams, columns, and joints in buildings have been shown to simulate damage accurately and efficiently (Krishnan, 2003b). Material nonlinearity resulting in flexural yielding, strain hardening, and ultimately rupturing of steel at the ends of beams and columns, and shear yielding in the joints is included (Krishnan and Hall, 2006a,b). 7. Engineered Structure Validation Like the simulations of seismic waves generated by small to moderate earthquakes recorded by the seismic network, the engineering simulations should be validated. For example, Krishnan et al. (2006a,b) used data from a seismographlocated on the top floor of an 18-story office building that was heavily damaged during the 1994 Northridge earthquake to calibrate and validate the structural engineering analysis.

12 110 J. Tromp 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 velocity waveforms are band-pass filtered between 0.1 and 1.25 Hz. Observations are denoted by black lines, 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 structures should be equipped with seismometers, and the data recorded by such urban seismic arrays should be made readily available to the seismological and engineering communities. 8. Rupture Scenarios Once the seismological and engineering models have been extensively tested against data for small to moderate earthquakes, one can numerically simulate the impact

13 A Basic Introduction to Quantitative Seismic Hazard Assessment 111 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) Plan view 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 location of columns and moment-frame beams. Note the greater number of moment-frame bays in the redesigned building. (Courtesy Swami Krishnan). of hypothetical large earthquakes on engineered structures. Figure 11 shows the domain of such scenario simulations considered by Krishnan et al. (2006a) for southern California. In one scenario a magnitude 7.9 rupture initiates in Parkfield to the North and progresses in a southeasterly direction over a distance of approximately 290 km. In the other scenario the same magnitude earthquake ruptures 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, magnitude 7.9 Denali, Alaska, vertical strike-slip earthquake (Tsuboi et al., 2003). The maximum depth of this rupture is about 20 km. The surface slip grows slowly to

14 112 J. Tromp Fig. 11. Geographical scope of the simulation (The color scheme reflects topography, with gray denoting low elevation and light gray denoting mountains). The solid black triangles represent the 636 sites at which seismograms are computed and buildings are analyzed. The white box is the surface projection of the January 17, 1994, Northridge earthquake fault. The dark gray line in the inset is the trace of the hypothetical 290 km rupture of the San Andreas fault that is the primary focus of this study. The area enclosed by the blue polygon denotes the region covered by the 636 sites. (Courtesy Swami Krishnan). 7.4 m and drops drastically towards the end of the rupture. The peak slip at depth is about 12 m. At 636 sites within the greater Los Angeles area the two buildings shown 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), seismograms are computed at each of the 636 analysis sites shown in Fig. 11, lowpass filtered with a corner at 2 s. Figure 12 compares the peak ground displacements, velocities and accelerations associated with the two hypothetical San Andreas Fault earthquakes (Krishnan et al., 2006a,b). These two simulations make it abundantly clear that it is insufficient to determine seismic risk solely based upon the distance to major faults and the potential size of earthquakes on these faults: one also needs to characterize the kind of earthquake, in particular its directivity. In the north-to-south scenario, summarized in Figs. 12(a c) for all three components, 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 to large 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

15 A Basic Introduction to Quantitative Seismic Hazard Assessment 113 Fig. 12. Peak ground velocities (PGVs) associated with two hypothetical magnitude 7.9 earthquakes on the San Andreas fault (Krishnan et al., 2006a,b) (Fig. 11). Top row: PGV on the east-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 Southto-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 1 m/s and 1 m, respectively, although the Baldwin Park/La Puente region in the San Gabriel Valley, which is quite close to the location of rupture termination, experiences shaking with a peak velocity up to 1.2 m/s and a peak displacement up to 1.1 m. It is interesting to ask what would happen if the earthquake ruptured in the opposite direction, i.e., from south-to-north rather than from north-to-south. Shown in Figs. 12(d f) are the peak velocities of the ground-motion time histories lowpass filtered with a corner period of 2 s. Although the San Fernando valley still experiences the most shaking, ground motion in Santa Monica and to some extent Baldwin Park is comparable in magnitude. The peak velocities are of the order of 0.6 m/s in the San Fernando valley, 0.5 m/s in Santa Monica and El Segundo, and 0.3 m/s in the remaining parts of Los Angeles and Orange Counties. The corresponding peak displacements are in the range of m in the San Fernando valley, m in Santa Monica and El Segundo, and m in the remaining parts of Los Angeles and Orange Counties. Similar numerical simulations of hypothetical major earthquakes on the San Andreas fault are the SCEC sponsored TeraShake simulations, which use the finitedifference method to simulate wave propagation on the DataStar supercomputer at the San Diego Supercomputing Center (

16 114 J. Tromp 9. End-to-End Simulations Once detailed 3D models of the geographic region and the engineered structures of interest have been constructed and validated, one can attempt to perform end-toend simulations, starting with a kinematic or dynamic rupture simulation, followed by a simulation of the resulting seismic wave propagation, and ending with an assessment of the response of the engineered structure. Ideally, such simulations should be accomplished as part of a single simulation, incorporating the shallow geotechnical layer and feedback between the response of the structure and the soil. At the moment the seismic and engineeringsimulations are performed consecutively, without interaction and feedback between the two. Figure 13 summarizes the response of the two 18-story buildings displayed in Fig. 10 at the 636 sites shown in Fig. 11. The results corresponding to a north-tosouth rupture of the San Andreas fault are summarized in Figs. 13(a) and 13(b) for the existing 18-story steel building (Fig. 10(a)). Figure 13(a) shows the percentage of connections where fracture occurred in the existing building. At least 25% of the connections in this building fracture when it is located in the San Fernando valley. Note that the scale saturates at 25% and that this number is exceeded at many locations. About 10% of the connections fracture in the building when it is located in downtown Los Angeles and the mid-wilshire district (Beverly, Hills), whereas the numbers are about 20% when it is located in Santa Monica, west Los 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 (right column) building (Fig. 10(b)) due to two hypothetical magnitude 7.9 earthquakes on the San Andreas 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).

17 A Basic Introduction to Quantitative Seismic Hazard Assessment 115 drift that occurs in the existing building. Consistent with the extent of observed fractures, the peak drifts in the existing building exceed 0.10 when it is located in the San Fernando valley, Baldwin Park and neighboring cities, Santa Monica, west Los Angeles and neighboring cities, Norwalk and neighboring cities, and Seal Beach 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 number in many locations in these regions. When the building is located in downtown Los Angeles and the mid-wilshire district, the building would barely satisfy the collapse prevention criteria set by the Federal Emergency Management Agency (FEMA), with peak drifts of about 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. The performance of this building is noticeably better than the existing building for the entire region. However, note that the new building has significant drifts indicative of serious damage when located in the San Fernando valley or the Baldwin Park area. When located in coastal cities (such as Santa Monica or Seal Beach), the Wilshire corridor (west Los Angeles, Beverly Hills), the neighborhoods of Downey and Norwalk, or the rapidly developing Orange County cities of Anaheim and Santa Ana, it exhibits peak drifts of about 0.05, once again barely satisfying the FEMA collapse prevention criteria. In downtown Los Angeles it does not undergo much damage in this scenario. Thus, even though this building has been designed according to the latest code, it suffers damage that would necessitate closure for some time after the earthquake in most areas, but this should be expected because this is a large earthquake and building codes are written to limit the loss of life and ensure collapse 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 analyses shown in Figs. 13(d f). Figure 13(d) shows the percentage of connections where fracture occurs in the existing building model. Fracture occurs in 3 7% of the connections in this building when it is located in the San Fernando valley. About 4 5% of the connections fracture in the building model when it is located in Santa Monica or El Segundo. In most other areas, there is little or no risk associated with moment-frame connection fractures. Figure 13(e) shows the peak interstory drift that occurs in the existing building. Peak interstory drifts beyond 0.06 are indicative of severe damage, whereas drifts below 0.01 are indicative of minimal damage not requiring any significant repairs. Peak drifts are in the neighborhood of 0.03 in the San Fernando valley, Santa Monica, El Segundo, and Baldwin Park. Peak drifts in most other areas are less than As for the north-to-south rupture scenario, the peak interstory drifts in the middle third and bottom third of the existing building are greater than in the top third, which indicates that the damage is localized in the lower floors. The performance of the newly designed 18-story steel building is slightly better than the existing building for the entire region. Figure 13(f) shows the peak

18 116 J. Tromp interstory drift that occurs in the building. Peak drifts are in the neighborhood of when the building model is located in the San Fernando valley, Santa Monica, El Segundo, and Baldwin Park. Building peak drifts in most other areas are in the neighborhood of A significant limitation of the Krishnan et al. (2006a) study is that soil-structure interaction (SSI) (e.g., Stewart et al., 1998)is not included in the analyses.dynamic nonlinear SSI is not a well-understood phenomenon, because of the lack of recorded data and the difficulty in designing accurate numerical tools to study it. One of the few real-world examples of extensive SSI research is a 14-story reinforced concrete storage building in Hollywood constructed in 1925 (Fenves and Serino, 1990; Trifunac et al., 2001). These studies indicate that the change in various structuralresponse parameters in this building during the October 1, 1987, magnitude 5.9 Whittier Narrows earthquake due to SSI could have been up to 20%. SSI is an active 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 be addressed in the context of quantitative seismic hazard analysis. Using examples from the Los Angeles and Taipei Metropolitan Areas, we have emphasized the need to instrumentation, data archiving and distribution, 3D model construction, and numerical modeling. Once this infrastructure is in place, quantitative seismic hazard assessment may be performed by considering the implications of various rupture scenarios 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 configurations, constructed with other materials, or having distinct dynamic characteristics could have damage patterns quite different from the results presented here. In addition, there are significant uncertainties in the earthquake source characteristics, including the location of the hypocenter, slip distribution, rupture direction, etc. Future studies striving toward the goal of truly end-to-end simulations must attempt to include the top soil layer in the ground-motion simulations and soilstructure interaction in the structural analysis. The seismic hazard approach outlined in this article, integrating the fields of seismology and structural engineering, can be used to assess specific engineered structures in a quantitative manner. For example, prior to actual construction, a detailed model of a planned structure can be analyzed using simulated seismic waveforms generated by various plausible earthquakes on regional faults, and based on its performance informed decisions can be made to improve its structural design. Similar analyses can be performed to determine the risk posed to an existing structure. Of course in each case the applicability of the band-limited simulated ground motion for the analysis of the particular structure under consideration needs to

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