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Impact of using updated seismic information on seismic hazard in western Canada K. Goda, H.P. Hong, and G.M. Atkinson
Abstract: This study provides a preliminary assessment of the impact of new seismological information on the existing seismic hazard model, as implemented in the 2005 National building code of Canada (NBCC); this seismic hazard model was actually developed in the early 1990s, and thus there is significant new information available in the literature since then. A reassessment of seismic hazard is carried out by updating magnitude-recurrence relations based on the earthquake catalog up to the end of 2006, including conversion of all earthquake magnitudes to a homogenous moment magnitude scale. The recent ground-motion prediction equations, which update the knowledge base used in the 2005 NBCC, are also used. Focusing on Vancouver and Victoria, sensitivity analyses are carried out to investigate both individual and combined impacts of these updates on the uniform hazard spectra. The proposed model can be used as a guide to the direction in which future seismic hazard models for western Canada may move. Key words: probabilistic seismic hazard analysis, uniform hazard spectra, western Canada. Re´sume´ : Cette e´tude fournit une premie`re e´valuation de l’impact de nouvelles informations sismologiques dans le mode`le existant de risques sismiques tel qu’implante´ dans le Code national du baˆtiment du Canada (CNBC). Ce mode`le de risques sismiques a e´te´ de´veloppe´ au de´but des anne´es 1990; beaucoup de nouvelles informations sont donc disponibles. Le risque sismique est re´e´value´ par une mise a` jour des relations magnitude-re´currence en se basant sur le catalogue des se´ismes jusqu’a` la fin de 2006, incluant la conversion de toutes les magnitudes de se´ismes en une e´chelle homoge`ne de magnitude de moment. Les e´quations re´centes de pre´vision du mouvement du sol, qui mettent a` jour la base de connaissances utilise´e dans le CNBC 2005, sont e´galement utilise´es. Des analyses de sensibilite´ cible´s sur Vancouver et Victoria ont e´te´ re´alise´es afin d’examiner les impacts individuels et combine´s de ces mises a` jour sur les spectres de risques uniformes. Le mode`le propose´ peut eˆtre utilise´ comme guide des directions possibles des futurs mode`les de risques sismiques pour l’Ouest canadien. Mots-cle´s : analyse probabiliste des risques sismiques, spectres de dangers uniformes, Ouest canadien. [Traduit par la Re´daction]
1. Introduction Seismic hazard assessments are usually based on the probabilistic seismic hazard analysis (PSHA) (Cornell 1968; McGuire 2004). Results of the assessments are most often presented in terms of the uniform hazard (response) spectra (UHS), which plot the expected response spectra values for a given probability of exceedance (or return period) in terms of the natural vibration period, Tn. A national seismic-hazard model for Canada including estimates of the 5%-damped horizontal component pseudo-spectral acceleration (PSA) Received 4 July 2008. Revision accepted 24 November 2009. Published on the NRC Research Press Web site at cjce.nrc.ca on 14 April 2010. K. Goda and G.M. Atkinson. Department of Earth Sciences, The University of Western Ontario, London, ON N6A 5B7, Canada. H.P. Hong.1 Department of Civil and Environmental Engineering, The University of Western Ontario, London, ON N6A 5B9, Canada. Written discussion of this article is welcomed and will be received by the Editor until 31 August 2010. 1Corresponding 2Halchuk,
author (e-mail:
[email protected]). S. 2007. Personal communication.
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for a 2% probability of exceedence in 50 years (i.e., 2475year return period), developed by the Geological Survey of Canada (GSC) (Adams and Halchuk 2003), forms the basis for the seismic provisions of the 2005 National building code of Canada (NBCC). The GSC seismic hazard model (hereafter referred to as the GSC model), as described by Adams and Halchuk (2003), contains information on seismicity and ground motions on a regional level across Canada, which was the state-of-the-art at the time it was developed (early 1990s). However, significant new information is available in the literature that warrants a reevaluation; in particular, improvements can be readily made with regard to the earthquake catalog, magnitude-recurrence relations for different types of earthquakes, ground-motion prediction equations (GMPE), use of an extended source model rather than a point source model, and adoption of mean estimates versus median estimates. In this study, we examine the impact of the most significant aspects of the GSC model that could be improved. More specifically, the earthquake catalog used in the GSC model is complete only up to 1991; currently, the Seismic Hazard Earthquake Epicenter File (SHEEF) catalog up to the end of 2006 is available.2 It is noted that magnitudes reported in the SHEEF catalog are based on a number of magnitude scales, while the moment magnitude, Mw, is the
doi:10.1139/L09-170
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parameter used in developing GMPEs. The conversions of magnitude amongst various scales in the catalog were not carried out for the GSC model, though it is recognized that the use of mixed magnitude scales in PSHA could result in biased assessments of magnitude-recurrence relations. There are currently a number of magnitude conversion equations that can be applied to convert earthquake catalogs to a uniform moment magnitude standard (Ristau et al. 2003, 2005; Atkinson and McCartney 2005). The GMPEs used in the GSC model for western Canada are those given by Boore et al. (1997) and Youngs et al. (1997). The availability of extensive databases for strong ground-motion records has prompted the development of new GMPEs over the last 10 years (Atkinson and Boore 2003; Kanno et al. 2006; Hong and Goda 2007; Boore and Atkinson 2008). These new GMPEs have significant implications for seismic hazard estimates in western Canada. Furthermore, all GMPEs used for western Canada employ distance measures based on an extended source model (i.e., closest horizontal distance to surface projection of a fault on the Earth or Joyner-Boore distance, rjb, and closest distance to a rupture plane, rrup), rather than those based on a point source model (i.e., epicentral distance, repi, and hypocentral distance, rhypo). However, the GSC model does not make such a distinction, which can lead to biased estimates (Scherbaum et al. 2004). Finally, the GSC model provides ‘‘median’’ estimates of seismic hazard; the discussions on the adoption of ‘‘median’’ versus ‘‘mean’’, which are valuable and philosophically challenging (Abrahamson and Bommer 2005; McGuire et al. 2005), are outside the scope of this study. The use of ‘‘mean-hazard’’ ground-motion estimates is of advantage because the exceedance probability is defined for the ‘‘mean ground-motion’’ motions, which cannot be inferred directly if the ‘‘median’’ is used. One more note related to the modeling of the Cascadia subduction events is in order. The GSC model treated these events as a deterministic scenario event with Mw equal to 8.2 and a specified rupture front location. However, Hyndman and Wang (1995) and Satake et al. (1996) suggested that the magnitude of such events can be as large as 9.0, and Mazzotti and Adams (2004) indicated that they occur quasiperiodically. This warrants the consideration of the probabilistic characteristics in recurrence, magnitude, and rupture
½1
FY ðyÞ ¼ 1
ns X zone; i¼1
Z UXEU;i
front location of the Cascadia subduction events for assessing a UHS. In this study, an updated seismic hazard model for western Canada is developed by incorporating the following improvements: (1) use of a uniform moment magnitude scale for the earthquake catalog, (2) reevaluation of the magnitude-recurrence relations for different types of earthquake, (3) use of recently developed GMPEs, and (4) use of an extended source model rather than a point source model, and (5) consideration of probabilistic scenarios for the Cascadia subduction events. The updated model could be of benefit to the NBCC committees and seismic risk management agencies. The updates should be viewed as complementary to the existing GSC model, and the use of ‘‘mean’’ seismic hazard estimates reported hereafter reflects the authors’ preference. It should be noted that this study is not a comprehensive reevaluation of seismic hazard in western Canada. There are significant aspects of the GSC model that we have not reevaluated herein. In particular, the seismic source zones and their boundaries as defined in the GSC model are retained, with no evaluation as to what improvements could be made in this regard. Rather, we focus on the most clear and significant updates that can be made at present as a guide to the direction in which future more detailed re-evaluations may move. We emphasize that these estimates are provisional guides, rather than specific recommendations.
2. Updated seismic hazard model 2.1 Approach The most popular PSHA procedure for characterizing seismic hazard is the Cornell–McGuire method (Cornell 1968; McGuire 2004). The Cornell–McGuire method, which is adopted by Adams and Halchuk (2003), is considered in the present study. It combines the earthquake occurrence model, seismic source-zone model, magnitude-recurrence relation, and GMPE through the total probability theorem to assess seismic hazard at sites of interest, as explained in the following. Consider that the seismic ground-motion measure, Y, represents the peak ground acceleration (PGA) and (or) the PSA. The cumulative distribution function (CDF) of Y, FY(y), can be expressed as
Z lMmin ;i ½1 FYjM;R;i ðyÞ fM;R;i ðm; rÞdmdr fXEU;i ðxEU ÞdxEU Ui
where the summation considers earthquakes originating from ns seismic source zones; lMmin,i is the occurrence rate of seismic events with magnitudes greater than or equal to Mmin; for the i-th source zone, fM,R,i(m) denotes the joint probability density function (PDF) of the earthquake magnitude measure M and the distance measure R, and Ui denotes the domain of M and R for the i-th source zone; FY|M,R,i(y) is the CDF of Y conditioned on M, R, and the i-th source zone; XEU,i represents the epistemic random variables for the i-th source zone whose joint PDF is given by fXEU,i(xEU); and UXEU,i denotes the domain of XEU for the i-th source
zone. Equation [1] can be evaluated numerically by using a simulation-based approach (Hong et al. 2006). The simulation-based approach, which is illustrated in Fig. 1, facilitates the incorporation of time-dependent earthquake occurrence modeling, synthetic earthquake catalog, and extended source model, and the flexible treatment of epistemic uncertainty. Individual model components shown in the figure are discussed in the following subsections. Although the classification of uncertainty is irrelevant in estimating ‘‘mean’’ seismic hazard using eq. [1], in this study a distinction between ‘‘aleatory uncertainty’’ and Published by NRC Research Press
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Fig. 1. Illustration of probabilistic seismic-hazard analysis.
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Fig. 2. Magnitude-recurrence relation for the Cascade Mountain R (CASR) seismic-source zone.
‘‘epistemic uncertainty’’ is made to follow current mainstream practice. The former represents intrinsic physical variability, whereas the latter is related to the uncertainty concerning the correctness of alternative models. 2.2 Seismic source zones and magnitude-recurrence relations Historical seismic events observed in western Canada are used to define seismic source zones that reflect the geological and seismological features of the considered regions. Within each source zone, the spatial distribution of seismic events is assumed to be random and the same magnituderecurrence relation and GMPE are used. The GSC sourcezone model was developed based on the SHEEF catalog up to 1991 (Adams and Halchuk 2003), and two alternative source-zone models were considered: the historical (H) model and the regional (R) model. These two models are adopted in this study for simplicity. It should be pointed out that these source-zone models are not exhaustive, and a more comprehensive or site-specific study should consider other alternatives. In this study, the combination of the H and R models is considered by assigning relative weights to the models. This differs from the Adams and Halchuk’s ‘‘robust’’ approach, which adopted the higher of the two seismic hazard estimates from the H and R models. The magnitude-recurrence relation characterizes the frequency of earthquake occurrence of different magnitudes, and it is often modeled by the truncated exponential distribution with both minimum and maximum earthquake magnitudes, Mmin and Mmax. For a given seismic source zone, the annual occurrence rate of earthquakes with magnitudes greater than or equal to Mmin, lMmin, is given by ½2
lMmin ¼ N0
exp ðbMmin Þ exp ðbMmax Þ 1 exp ðbMmax Þ
Fig. 3. Fault geometry for an extended earthquake source model.
where b and N0 are the magnitude-recurrence parameters, and the GSC model adopts Mmin equal to 4.75. The SHEEF catalog reports seismic events with mixed magnitude scales, such as the local magnitude ML, bodywave magnitude mb, coda duration magnitude Mc, and surface magnitude Ms. Using the inconsistent magnitude scales in developing magnitude-recurrence relations is likely to result in biased assessments of magnitude-recurrence parameters b and N0 and increased uncertainty (Atkinson and McCartney 2005). A reassessment of magnitude-recurrence parameters is thus warranted by using the modified SHEEF catalog with all earthquake magnitudes converted to Mw. This conversion is carried out by using the reported Mw values where available (see Atkinson (2005) and Atkinson and McCartney (2005)). For events with no reported Mw values, we use empirical magnitude conversion equations to estimate Mw. The used conversion equations are given as follows for the continental events and for the offshore events, respectively: ½3a
Mw ¼ ML M w ¼ M L þ 0:6
ð3 < M L < 6Þ
for ML (Ristau et al. 2003, 2005; Atkinson and McCartney 2005) ½3b
Mw ¼ mb þ 0:46
ð4 < mb < 7Þ
for mb (Braunmiller and Nabelek 2002) ½3c
Mw ¼ 0:96Mc þ 0:19
for Mc (Dewberry and Crosson 1995) and ½3d
Mw ¼ 0:64Ms þ 2:18
ðMs 6:1Þ
for Ms (Braunmiller et al. 2005). The magnitude-recurrence parameters b and N0 for each source zone are determined from the earthquake catalog by using the maximum likelihood method (Weichert 1980). The time period over which the catalog is complete varies with magnitude; therefore, we adopt the completeness intervals given by Adams and Halchuk (2003). As an illustration, the magnitude-recurrence relation for the Cascade Mountain R (CASR) source zone (see Adams and Halchuk 2003) is Published by NRC Research Press
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Can. J. Civ. Eng. Vol. 37, 2010 Table 1. Modified magnitude-recurrence parameters for seismic source zones in western Canada. Source zone* H model: CASH H model: PUG H model: JDF H model: NJFP H model: GEO{ H model: SCM R model: CASR R model: GSP R model: JDFN R model: JDFF
Mw-ML conversion equation Mw = ML Mw = ML + 0.6 Mw = ML Mw = ML Mw = ML + 0.6 Mw = ML + 0.6 — Mw = ML Mw = ML + 0.6 Mw = ML Mw = ML + 0.6 Mw = ML Mw = ML Mw = ML + 0.6
Mmin{ 3.25 3.25 3.25 3.25 3.25 3.75 — 3.25 3.25 3.25 3.25 3.25 3.25 3.25
Mmax{ 7.25 7.25 7.25 7.75 7.75 7.25 — 7.25 7.25 7.75 7.75 7.25 7.25 7.25
b 1.849 1.876 0.992 1.327 1.743 1.318 2.250 1.923 1.785 1.694 1.779 1.018 0.919 1.797
N0 653 2379 18.4 26.0 366 46.3 85.0 276 432 571 2404 20.2 3.63 185
*For the definition of the source zones, see Adams and Halchuk (2003). { Events within Mmin and Mmax are used to estimate the magnitude-recurrence parameters. { The parameters for the GEO are adopted from those by Adams and Halchuk (2003) because of the very limited number of earthquakes in the source zone.
Table 2. Summary of probabilistic information for fault geometry parameters. Fault geometry parameter Fault width (km): log10W Fault length (km): log10L Focal depth (km): H
Probability distribution Normal Normal Truncated normal
Dip (8): d Strike (8): f
Truncated normal Uniform
Mean and standard deviation 0.32Mw - 1.01 and 0.15* 0.59Mw - 2.44 and 0.16* Shallow events: 0.61Mw+7.08 and 4.55{ Deep events: 50 and 25 65 and 20{ —
Lower and upper bounds — — 3 and 25{ 35 and 100 40 and 90{ 0 and 360
*Wells and Coppersmith (1994). { Scherbaum et al. (2004).
Table 3. Model coefficients for the mean and coefficient of variation of distance gap data (eqs. [4] and [5]) for shallow and deep events. Mean (eq. [4]) Distance gap data Shallow events: repi–rjb (R = repi) Shallow events: rhypo–rrup (R = rhypo) Deep events: rhypo–rrup (R = rhypo)
a1 0.458 0.363 0.103
a2 –0.0549 –0.0437 –0.0120
a3 1.046 0.978 1.278
a4 –0.0361 –0.0256 –0.0518
a5 –1.297 –1.213 –1.201
a6 –0.138 –0.149 –0.170
a7 0.105 0.104 0.109
Coefficient of variation (eq. [5]) Distance gap data Shallow events: repi–rjb (R = repi) Shallow events: rhypo–rrup (R = rhypo) Deep events: rhypo–rrup (R = rhypo)
b1 0.227 0.181 –0.078
b2 –0.0448 –0.0560 –0.0237
determined by considering a magnitude bin size equal to 0.5 and Mmax equal to 7.75; the results are illustrated in Fig. 2 together with those of Adams and Halchuk (2003) and Atkinson and McCartney (2005) for the same source zone. In this study, two curves are developed based on different assumptions in converting events with ML to Mw: Mw = ML (generally applies to continental events) and Mw = ML + 0.6 (generally applies to offshore events). Note that data points for the two cases, shown in Fig. 2 with a circle and a square, coincide in the range of Mw greater than 6.0. The CASR magnitude-recurrence relation fits the data well for the entire magnitude range, if seismic events are converted to Mw using Mw = ML + 0.6. The obtained magnitude-recurrence
b3 1.921 1.239 1.394
b4 –0.0566 –0.1013 –0.0644
b5 –2.109 –1.561 –0.889
b6 0.331 0.275 0.242
relations are close to those suggested by Atkinson and McCartney (2005). Note also that the CASR magnitude-recurrence relations given by Adams and Halchuk (2003) show significantly different slopes for smaller and larger magnitude ranges. The difference can be attributed to the use of mixed magnitude scales in the earthquake catalog (Atkinson and McCartney 2005). For other source zones in western Canada, the same analysis is carried out, and the obtained parameters b and N0 are listed in Table 1 and used for the sensitivity analysis in Sect. 3. 2.3 Extended earthquake source model Historical seismicity compiled in the SHEEF catalog corPublished by NRC Research Press
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Fig. 4. Probability distribution of distance gap data conditioned on the distance measure ranging from 0 to 10 km for shallow events with Mw = 6.0 and 7.0: (a) repi–rjb; (b) rhypo–rrup
responds to locations of epicenters of seismic events; consequently, the developed seismic source-zone model is also related to the spatial distribution of epicenters. However, all current GMPEs for western North America are developed by adopting distance measures based on an extended source model, such as rjb and rrup, rather than those based on a point source model, such as repi and rhypo (see Fig. 3 for schematic illustration of different distance measures associated with a fault plane). The distance measure used to develop the GMPEs should be applied in PSHA, as the use of inconsistent distance measures results in biased (underestimated) seismic hazard assessments (Scherbaum et al. 2004). An efficient and practical way to achieve this is by developing equations that relate rjb and (or) rrup to repi and rhypo, respectively, and then using a point source model in PSHA. Equations relating different distance measures are developed as follows. Fault geometry is simulated for each generated seismic event by following the simulation procedure suggested by Scherbaum et al. (2004), and the simulated fault geometry is used to calculate different distance measures for a site of interest. The considered fault model is illustrated in Fig. 3, and the following fault model parameters are treated as random variables: fault width W (km), fault length L (km), focal depth H (km), dip angle d, and strike angle f. Their probabilistic information employed in this study is summarized in Table 2. The focal depth of shallow events is modeled according to Scherbaum et al. (2004), whereas that of deep events is modeled as a normal variate with mean equal to 50 km and standard deviation equal to 25 km, truncated at the lower and upper bounds of 35 and
½4
100 km, respectively (see Table 2). The statistical information is considered suitable for earthquakes in western Canada (note: we examined the focal depth distribution of seismic events included in the SHEEF catalog; however, we were unable to conclude that the assumed depth information is consistent with the actual focal-depth distribution owing to the poor quality of depth information). Based on simulation results, conversion equations from repi to rjb or from rhypo to rrup, which are needed in PSHA and are not available in the literature, are developed by characterizing the probability distribution and the mean and the coefficient of variation (cov) of the simulated distance gap data repi–rjb or rhypo– rrup, as a function of a distance measure repi or rhypo. Note that Scherbaum et al. (2004) modeled the distance gap repi– rjb conditioned on rjb, as a gamma variate. A detailed statistical analysis is carried out for the assessment,; as an illustration, the probability mass functions of repi–rjb and rhypo–rrup conditioned on repi and rhypo ranging from 0 to 10 km for shallow events are shown in Fig. 4, together with fitted gamma distributions based on the maximum likelihood method. The results shown in Fig. 4 indicate that repi–rjb and rhypo–rrup can be modeled as a gamma variate. This conclusion is valid for values of repi and rhypo greater than 10 km as well as for deep events. Moreover, the mean and cov of the distance gap data (i.e., repi–rjb or rhypo–rrup) are functions of the selected distance measure (i.e., repi or rhypo) and Mw. To develop prediction equations for the mean and cov of repi–rjb conditioned on repi or of rhypo–rrup conditioned on rhypo, nonlinear least-squares fitting is performed by using the following functional forms:
mGap ¼ 1 exp ½ða1 þ a2 Mw ÞRa3 þa4 Mw exp ða5 þ a6 Mw þ a7 Mw2 Þ
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Fig. 5. Statistics of distance gap data rhypo–rrup for shallow events: (a) Mean; (b) Coefficient of variation.
Fig. 6. Ground-motion prediction equations for the reference ground condition (Vs30 = 555 (m/s)): (a) Shallow crustal earthquakes (Mw = 7.0); (b) In-slab subduction earthquakes (H = 50 (km) and Mw = 7.5); (c) Interface subduction earthquakes (H = 20 (km) and Mw = 8.5).
for the mean of the distance gap data, and ½5
nGap ¼ ½1 þ ðb1 þ b2 Mw Þexpðb3 Rb4 Þexpðb5 þ b6 Mw Þ
for the cov of the distance gap data, where R represents repi or rhypo and ai, (i = 1,. . .,7), and bi, (i = 1,. . .,6), are the model coefficients. For shallow and deep events, the obtained coefficients for the mean and cov of the distance gap data are summarized in Table 3, and for shallow events, the adequacy of the fit is illustrated in Fig. 5. The developed equations for the statistics of the distance gap data along with the assumption that the distance gap data is a gamma variate can be used to convert probabilistically one distance measure (i.e., repi or rhypo) to another (i.e., rjb or rrup) in PSHA. Published by NRC Research Press
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Table 4. Scenario events for the interface Cascadia subduction earthquakes. Scenario Case 1 Case 2 Case 3 Case 4 Case 5
Inter-arrival time model EXP(600){ LN(500/600, 0.25/0.5, 308){ LN(500/600, 0.25/0.5, 308) LN(500/600, 0.25/0.5, 308) LN(500/600, 0.25/0.5, 308)
Magnitude 8.2 8.2 N(8.5, 0.5, 8.0, 9.0)§ N(8.5, 0.5, 8.0, 9.0) N(8.5, 0.5, 8.0, 9.0)
Ground-motion prediction equation* YCSH97 (1.0) YCSH97 (1.0) YCSH97 (1.0) AB03 (1.0) [YCSH97 (0.2), GSWY02 (0.2), AB03 (0.4), AM09 (0.2)]
*The number inside the brackets represents the assigned weight, and if a single GMPE is used, the GSC approach to capture epistemic uncertainty is considered (see Sect. 3.4). { EXP(m) indicates that the inter-arrival time is modeled by the exponential distribution with the mean recurrence period of m years. { LN(m, n, tE) indicates that the inter-arrival time is modeled by the truncated lognormal distribution with the mean recurrence period of m years, the coefficient of variation of n, and the elapsed time of tE years since the last occurrence. § N(m, s, Mmin, Mmax) indicates that the characteristic magnitude is modeled by the truncated normal distribution with the mean of m, the standard deviation of s, and the lower and upper bounds of Mmin and Mmax.
2.4 Ground-motion prediction equations Two GMPEs were adopted in the GSC model for western Canada: the BJF97 relation (Boore et al. 1997) for shallow crustal earthquakes and the YCSH97 relation (Youngs et al. 1997) for both deep in-slab and shallow interface subduction earthquakes (see Adams and Halchuk (2003) for details). Several more recent GMPEs that can be used for PSHA in western Canada have been developed based on a larger set of strong ground-motion records (Atkinson and Boore 2003; Atkinson 2005; Hong and Goda 2007; Boore and Atkinson 2008). The GMPEs that are developed for other regions, such as the one given by Kanno et al. (2006), could also be considered, particularly for in-slab subduction earthquakes in the Cascadia region. In the present study, multiple GMPEs for each earthquake type are considered and weighted. That is, in place of the BJF97 relation and the YCSH97 relation, the following GMPEs are considered: the A05 relation (Atkinson 2005), the HG07 relation (Hong and Goda 2007), and the BA08 relation (Boore and Atkinson 2008) for shallow crustal earthquakes; the AB03 relation (Atkinson and Boore 2003) and the KNMFF06 relation (Kanno et al. 2006) for deep in-slab subduction earthquakes; and the GSWY02 relation (Gregor et al. 2002), the AB03 relation, and the AM09 relation (Atkinson and Macias 2009) for interface subduction earthquakes. The reference site condition used with these relations is the NEHRP site class C (i.e., average shearwave velocity in the uppermost 30 m Vs30 equal to 555 m/ s). The use of a limited set of GMPEs is intended to illustrate the effects of using recent GMPEs on seismic hazard estimates. In adopting these GMPEs, several comments are warranted. For the A05, GSWY02, and AM09 relations, the soil amplification factors given by Boore and Atkinson (2008) are used to adjust peak ground motions and response spectra for different soil conditions. For the HG07 relation, an anelastic term is included for rjb greater than 100 km (Adams and Halchuk 2003). The AB03 relation is applied with the coefficient developed for the Cascadia region (Atkinson and Boore 2003). It is noted that there is an erratum to the AB03 relation that affects interface events (Atkinson and Boore 2008). However, the use of the Cascadia modification factors in this study implicitly corrects the underlying database error in the AB03 relation, since the Cascadia data used in deriving those factors (i.e., the Cape Mendocino records) do not have any database errors. The KNMFF06 relation, which was developed based on the peak square root of
the sum of squares of two horizontal components in the time domain, is applied together with empirical factors that convert from the peak square root response to the geometric mean response. The conversion factors were developed using Japanese ground-motion data (Goda and Atkinson 2009) and range from 1.2 to 1.3 for the PGA and the PSA at the vibration periods between 0.1 and 3.0 s. A beneficial feature of new GMPEs is that they allow one to carry out seismic hazard assessments for various soil conditions. The GMPEs used in this study are shown in Fig. 6; the BJF97 and YCSH97 relations are also included for comparison. Inspection of Fig. 6a indicates that for shallow crustal earthquakes the BJF97, HG07, and BA08 relations are similar, whereas the A05 relation lies above the other three relations. For Mw > 7.0, the BA08 relation lies below the BJF97 and HG07 relations, since the BA08 relation incorporates the saturation effects for magnitude scaling, whereas the other two relations do not. Inspection of Fig. 6b shows that GMPEs for deep in-slab earthquakes (Mw = 7.5) vary significantly. This is due to the differences in the employed datasets and functional forms. For example, the AB03 relation has a steeper slope than the YCSH97 and KNMFF06 relations, which results in significantly different predicted ground-motion levels. The comparison shown in Fig. 6c indicates that GMPEs for interface subduction earthquakes (Mw = 8.5) differ significantly in the predicted ground-motion levels as well as the slope of GMPEs in terms of distance. In summary, for the sets of GMPEs under consideration, pronounced differences among GMPEs are observed especially for in-slab and interface subduction earthquakes. Such differences partly arise from competing assumptions about GMPEs and considered records. Thus, they need to be incorporated in PSHA as an important component of epistemic uncertainty. In this study, we have used the expediency of representing this epistemic uncertainty by selecting a few alternative equations. This is not necessarily the best approach, and a future study should address the more fundamental question as to how to quantify epistemic uncertainty in selecting GMPEs. Finally, it is emphasized that the sets of GMPEs that are considered in this study are not comprehensive, and more careful reviews are required in determining which GMPEs are indeed adequate for assessing seismic hazard in western Canada, as they have the most significant impact on seismic hazard estimates (as will be highlighted in Sect. 3). For such Published by NRC Research Press
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determination and selection, it is important to achieve good balance and consistency between the past and current practices and the proposed future practices so that drastic changes of seismic hazard estimates (using newer GMPEs) do not cause unduly low seismic safety margins to structures and infrastructure that are designed according to updated seismic hazard estimates. It is also important to address what is the best way of modeling epistemic uncertainty in GMPEs, as this may not be entirely captured simply by using a range of alternative equations. 2.5 Interface Cascadia subduction earthquake The GSC model treats the interface Cascadia subduction earthquakes as a deterministic scenario event, and the seismic hazard due to such events was combined with those based on the H and R models through the ‘‘robust’’ approach by taking the largest of the seismic hazard estimates. Consequently, the Cascadia hazard did not affect final seismic hazard estimates at most sites in western Canada. However, strictly speaking, they should be integrated directly in the H and R models for PSHA, since the Cascadia hazard is additive to those due to crustal earthquakes and in-slab earthquakes. It has been observed that earthquakes from identified faults and subduction zones often show quasi-periodic recurrence (Matthews et al. 2002; Mazzotti and Adams 2004). If such quasi-periodic recurrence is modeled by a renewal process with an assigned probability distribution for the inter-arrival time, time-dependent characteristics of the Cascadia subduction events can be incorporated in PSHA using a simulation-based approach. The elapsed time since the last major earthquake needs to be considered for the renewal model. For the inter-arrival time distribution, the lognormal distribution, which provides reasonable behavior with mathematical simplicity, and the inverse Gaussian distribution, which mimics physical process of loading and unloading stress along rupture plane (Matthews et al. 2002), can be considered, as well as the exponential distribution (i.e., homogeneous Poisson process). Another important aspect in characterizing the Cascadia subduction events is to define their magnitudes and occurrence locations. These might be related to their occurrence times, but they are treated separately herein because of the limited knowledge. By comparison, the GSC model considered a deterministic scenario event of Mw equal to 8.2 and depth equal to 25 km with a specified fault rupture front. For the United States seismic-hazard map projects (Petersen et al. 2002), several scenarios for the Cascadia events were considered by varying Mw (i.e., Mw equal to 8.3 and 9.0) and locations of the rupture front within the transition zone, where the event with Mw = 8.3 was considered to float along the entire rupture front that could extend more than 1000 km. Other hypotheses, such as a bi-modal occurrence process with different characteristic magnitudes (Mazzotti and Adams 2004), could be used. Based on the above discussion, several possible scenario events for the interface Cascadia subduction events are constructed and listed in Table 4 for sensitivity analysis. 2.6 Simulation algorithm A simulation approach (Hong et al. 2006) is employed to carry out PSHA. The approach was validated by checking
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that the values of seismic hazard estimate for a number of sites across Canada based on simulation match the results published by the GSC to within a few percentage, when the same input models and assumptions were used (Goda and Hong 2009). Note that the GSC computations are based on an entirely different algorithm, the FRISK88 program of Risk Engineering, Inc. Three layers of epistemic uncertainty are considered: seismic source-zone models, magnitude-recurrence parameters, and applicable GMPEs. This treatment was limited, as alternative models considered are not exhaustive. For the Cascadia subduction events, time-dependent models and multiple scenario events are taken into account. To reduce computation time and to incorporate an extended source model, the developed conversion equations for different distance measures based on the location of epicenter and (or) hypocenter can be used.
3. Sensitivity analysis This section presents PSHA results in the form of UHS for Vancouver [49.28N, 123.28W] and Victoria [48.58N, 123.38W], using the results based on the GSC model (i.e., robust approach) as a reference. The sensitivity analysis addresses the use of mean or median seismic hazard estimates, the effects of the updated magnitude-recurrence relations, the effects of an extended source model, the effects of using newly available GMPEs, the impact of the Cascadia subduction events, and their combined influence on the PSHA results. For the assessment, seismic events with magnitudes greater than or equal to 4.75 (i.e., Mmin = 4.75) within a radius of 200 km from the site are included. The reference soil condition represented by Vs30 equal to 555 m/s is considered. Simulation is carried out to produce a 5-million-year catalog of the annual maximum ground motion. In the updated seismic hazard model, an equal weight is assigned to the H and R models. In Sects. 3.1 to 3.4, the Cascadia subduction events are not included to facilitate the direct comparison between the GSC model and the updated model. 3.1 Mean and median seismic hazard estimates It must be emphasized that for the reasons mentioned previously, the present study reports ‘‘mean’’ seismic hazard estimates, unless otherwise indicated, whereas those given by Adams and Halchuk (2003) are ‘‘median’’ estimates. To investigate the difference between the mean and median UHS, PSHA is carried out by considering the same information as contained in the GSC model (i.e., source zones, magnitude-recurrence parameters, and GMPEs); the obtained mean UHS for the return periods of 475 and 2475 years (i.e., 10% and 2% probabilities of exceedance in 50 years, respectively) are shown in Fig. 7. The results based on the GSC model (Adams and Halchuk 2003) are also shown in the figures. Figure 7 indicates that for all cases, mean seismic hazard estimates are greater than median seismic hazard estimates by a factor of 1.11–1.47, depending on details of the considered seismic hazard models as well as probability levels of interest. The differences are mainly attributed to epistemic uncertainty associated with GMPEs specified in the GSC model. Published by NRC Research Press
Goda et al. Fig. 7. Mean and median uniform hazard (response) spectra (UHS) based on the Geological Survey of Canada (GSC) model and mean UHS based on the modified magnitude-recurrence relations for the return periods of 475 and 2475 years: (a) Vancouver; (b) Victoria.
3.2 Effects of the modified magnitude-recurrence relations To investigate the effects of the modified magnitude-recurrence relations on UHS, PSHA is carried out by using the modified magnitude-recurrence parameters shown in Table 1 and calculated in Sect. 2.2 while holding all other parameters at the values used in the GSC model. To take into account the range of possibilities for the ML–Mw conversion equations (i.e., equations for ‘‘offshore’’ events and ‘‘continental’’ events), two sets of the modified magnitude-recurrence rela-
571 Fig. 8. Mean uniform hazard (response) spectra (UHS) based on the newly selected sets of ground-motion prediction equations (GMPEs) and the mean and median UHS based on the Geological Survey of Canada (GSC) model for the return periods of 475 and 2475 years: (a) Vancouver; (b) Victoria.
tions, each with the same weight, are considered for the ‘‘CASH’’, ‘‘JDF’’, ‘‘SCM’’, and ‘‘CASR’’ source zones. The UHS based on the modified parameters are shown in Fig. 7 for Vancouver and Victoria. The results indicate that the use of the modified relations leads to an increase in UHS by a factor of about 1.0–1.1 (on average, a factor of 1.05). 3.3 Effects of an extended source model To investigate the effects of using an extended source Published by NRC Research Press
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Can. J. Civ. Eng. Vol. 37, 2010 Table 5. Mean uniform hazard (response) spectra (UHS) for Vancouver and Victoria for the return period of 2475 years considering the Cascadia scenario events. Updated model{
GSC model* Site Vancouver
Victoria
Scenario case Case 0{ Case 1 Case 2 Case 3 Case 4 Case 5 Case 0 Case 1 Case 2 Case 3 Case 4 Case 5
PGA (g) 0.676 0.681 0.680 0.687 0.678 0.677 0.842 0.866 0.863 0.878 0.846 0.849
PSA (g) at Tn = 0.2 (s) 1.354 1.370 1.369 1.388 1.369 1.366 1.693 1.749 1.746 1.785 1.718 1.728
PSA (g) at Tn = 1.0 (s) 0.438 0.456 0.454 0.471 0.533 0.476 0.534 0.579 0.577 0.599 0.645 0.596
PGA (g) 0.484 0.497 0.494 0.503 0.489 0.487 0.610 0.649 0.643 0.657 0.619 0.622
PSA (g) at Tn = 0.2 (s) 1.118 1.146 1.142 1.167 1.143 1.135 1.414 1.495 1.491 1.528 1.459 1.464
PSA (g) at Tn = 1.0 (s) 0.362 0.388 0.385 0.403 0.478 0.409 0.460 0.527 0.517 0.545 0.600 0.541
*The ‘‘GSC model’’ indicates that seismic hazard assessments for the rest of areas are based on the GSC model. { The ‘‘updated model’’ indicates that seismic hazard assessments for the rest of areas are based on the updated model. { Case 0 indicates that the Cascadia subduction events are not included in assessing seismic hazard.
model on UHS, PSHA is carried out by taking fault geometry for each simulated seismic event into account. For this investigation, three cases are considered: ‘‘GSC approximation’’ adopts repi & rjb and rhypo & rrup and the deterministic depth of 50 km for deep earthquakes, noting that depth is not a parameter for shallow crustal earthquakes as the GMPEs for these events are based on rjb (note: the BJF97 relation adopts a fictitious depth h along with rjb, where h is determined through regression analysis (i.e., regression coefficient)); ‘‘exact distance’’ generates an extended fault geometry for each event and calculates the required distance measures exactly; and ‘‘distance conversion’’ adopts the conversion equations between various distance measures. The UHS for the return periods of 475 and 2475 years based on ‘‘GSC approximation’’, ‘‘exact distance’’, and ‘‘distance conversion’’ are calculated for Vancouver and Victoria. The obtained results indicate that the UHS based on ‘‘GSC approximation’’ are smaller than those based on ‘‘exact distance’’ and ‘‘distance conversion’’, which is expected, since repi ‡ rjb and rhypo ‡ rrup. The ratios of the UHS based on ‘‘GSC approximation’’ to those based on ‘‘exact distance’’ or ’’distance conversion’’ are about 1.1– 1.3 (on average, a factor of 1.18). The UHS based on ‘‘exact distance’’ and ‘‘distance conversion’’ match closely, which validates the accuracy and usefulness of the developed distance conversion equations. 3.4 Effects of ground-motion prediction equations The PSHA is carried out to investigate the sensitivity of UHS to the adopted GMPEs. The preliminary results indicate that for shallow crustal earthquakes, the impact of using the BJF97, HG07, or BA08 relation on UHS is not significant, whereas the A05 relation increases UHS at short periods. For in-slab subduction earthquakes, the impact of using the YCSH97 or AB03 relation is significant. Based on the preliminary analysis results, a set of GMPEs is selected: for shallow crustal earthquakes, the A05, HG07, and BA08 relations are adopted with an equal weight of 1/3, and for in-slab subduction earthquakes, the YCSH97, AB03,
and KNMFF06 relations are adopted with weights of 0.25, 0.50, and 0.25, respectively. For in-slab subduction earthquakes, a greater weight is given to the AB03 relation, since this relation is based on a more extensive strong groundmotion database than the YCSH97 relation, and is calibrated for the Cascadia region. The UHS based on the newly selected sets of GMPEs are shown in Fig. 8 and are compared with those based on the GSC model. It is observed that the ratios of mean UHS based on the new GMPE sets to mean UHS based on the GSC model range from 0.54 to 0.80 (on average about 0.64) and the ratios of mean UHS based on the new GMPE sets to median UHS based on the GSC model (i.e., seismic hazard estimates used in the 2005 NBCC) range from 0.70 to 1.14 (on average about 0.84), depending on Tn. The results highlight the importance of including multiple GMPEs in PSHA to reflect valid and diverse assumptions on GMPEs. They indicate that a more detailed treatment of epistemic uncertainty for GMPEs is warranted in future studies. 3.5 Effect of the Cascadia subduction events The occurrence of a mega-thrust Cascadia subduction event would be a major potential disaster in southwestern British Columbia. Based on the information discussed in Sect. 2.5 and preliminary investigations, five scenario cases shown in Table 4 are selected. These scenario cases are formed by considering different combinations of timedependent occurrences, magnitudes, and GMPEs. Moreover to incorporate a range of possible scenarios for the fault plane, three rupture front locations (i.e., the rupture front location considered by Adams and Halchuk (2003), and two shifted locations to the westward or eastward direction by about 15 km) with weights of 0.5, 0.25, and 0.25, and four depths of 15, 20, 25, and 30 km with an equal weight of 0.25 are considered. Note that the variations of the fault plane do not affect UHS for Vancouver and Victoria significantly. Case 1 corresponds to the GSC model (yet here the events are treated probabilistically); case 2 incorporates Published by NRC Research Press
Goda et al. Fig. 9. Mean uniform hazard (response) spectra (UHS) based on the updated seismic hazard model and the mean and median UHS based on the Geological Survey of Canada (GSC) model for the return periods of 475 and 2475 years: (a) Vancouver; (b) Victoria.
time-dependent occurrence characteristics with a deterministic magnitude of 8.2; and cases 3–5 consider both timedependent occurrence modeling and probabilistic magnitudes. Cases 3–5 differ in selecting GMPEs: Case 3 uses the YCSH97 relation, case 4 uses the AB03 relation, and case 5 uses four equations, the YCSH97, GSWY02, AB03, and AM09 relations with assigned weights of 0.2, 0.2, 0.4, and 0.2, respectively. Our rational for assigning a greater weight to the AB03 relation than other relations is that this relation is based on extensive strong ground-motion data and
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is calibrated for the Cascadia region. For cases 1–4, the epistemic uncertainty as in the GSC model is included since a single GMPE is employed, whereas for case 5, the use of the four equations is considered to be adequate to capture epistemic uncertainty associated with the choice of GMPEs for the Cascadia events. For the time-dependent occurrence modeling, the elapsed time since the last major event is considered to be 308 years (Satake et al. 1996). The UHS for the return period of 2475 years are calculated by considering cases 1–5; two sets of results are summarized in Table 5 for Vancouver and Victoria. For seismic sources other than the Cascadia events, the first set considers the GSC model, whereas the second set considers the updated seismic hazard model that incorporates modified magnitude-recurrence relations (Sect. 3.2) and newly selected sets of GMPEs based on an extended source model (Sects. 3.3 and 3.4). Comparison of UHS for different cases indicates that the Cascadia events affect the UHS significantly, particularly at long periods (case 0 versus cases 1– 5), and that at the present time, the use of the exponential distribution or the lognormal distribution does not affect UHS significantly (case 1 versus case 2), although this will not be the case as the elapsed time since the last major event changes. The consideration of probabilistic magnitudes with a higher expected value increases the UHS slightly (case 2 versus case 3), whereas the selection of multiple GMPEs can affect the UHS significantly, depending on Tn. The same conclusions are drawn if the inverse Gaussian distribution instead of the lognormal distribution is considered for the inter-arrival time distribution. If case 5 is taken as a representative scenario case, the ratio of mean UHS with the Cascadia events to those without the Cascadia events is about 1.0–1.03 for the PGA and PSA at short periods and is about 1.1–1.2 for the PSA at long periods. Therefore, it is of importance to take into account the Cascadia subduction events in assessing seismic hazard and risk. 3.6 Overall impact An overall impact of the updated seismic hazard model is assessed by incorporating modified magnitude-recurrence relations, newly selected sets of GMPEs, and the Cascadia subduction events. The obtained mean UHS are shown in Fig. 9 for Vancouver and Victoria and are compared with the mean and median UHS based on the GSC model. The mean UHS based on the updated model lie between the median and mean UHS based on the GSC model. This indicates that the UHS based on the GSC model are reasonable, and that the biases due to the use of mixed magnitude scales in earthquake catalog, the approximation based on a point source model in evaluating the source-to-site distance, and simple multiplicative factors with assigned weights to capture epistemic uncertainty for the choice of adequate GMPEs fortuitously cancel each other out to a significant extent. It is significant to note that although the obtained UHS based on the updated model are similar to those based on the GSC model, the characteristics of seismic events contributing to the considered seismic hazard levels differ. To support this, we carried out seismic hazard deaggregation analysis and noted that for the GSC model, the most significant contributions came from deep in-slab earthquakes for Published by NRC Research Press
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both short and long periods, whereas for the updated model, significant contributions came from shallow crustal earthquakes and the Cascadia subduction earthquakes, in addition to those from in-slab earthquakes. It is thus prudent to consider all three earthquake types as scenario events rather than in-slab subduction earthquakes alone.
4. Conclusions An updated seismic hazard model for western Canada is developed by incorporating new information on earthquake occurrence rates and ground-motion prediction equations (GMPE), and improved computational treatment of some aspects of earthquake source and propagation. The updated model is compared with the model developed by the Geological Survey of Canada (GSC) for the 2005 National building code of Canada (Adams and Halchuk 2003). The proposed model is intended for sensitivity analysis of seismic hazard in western Canada to key model components, which should not be taken as a comprehensive site-specific study. Based on the analysis results focusing on Vancouver and Victoria, the following conclusions are drawn: 1. For the GSC model, the mean uniform hazard spectra (UHS) are greater than the median UHS by a factor of about 1.1–1.5, depending on the vibration period, Tn, site, and considered return period level. 2. The mean UHS based on modified magnitude-recurrence relations are greater than those based on the GSC model by a factor of about 1.0–1.1. 3. The mean UHS based on an extended source model are greater than those based on a point source model by a factor of 1.1–1.3. The developed distance conversion equations can be used to take an extended source representation into account. 4. The mean UHS based on newly selected sets of GMPEs are less than those based on the GSC model by a factor of about 0.6–0.8. 5. The incorporation of the Cascadia subduction events in PSHA increases mean UHS by a factor of about 1.0–1.2, depending on Tn. The impact is especially significant for the PSA at long periods. 6. The ratio of mean UHS based on the updated model to those based on the GSC model ranges from 0.7 to 1.1, depending on Tn, site, and return period level.
Acknowledgments The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. The NSERC postdoctoral fellowship award for the first author is gratefully acknowledged. The authors are thankful to S. Halchuk and J. Adams for providing the SHEEF catalog.
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