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How Can Seismic Hazard Around the New Madrid Seismic Zone Be Similar to That in California ?

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How Can Seismic Hazard Around the New Madrid Seismic Zone Be Similar to That in California ? How Can Seismic Hazard around the New Madrid Seismic Zone Be Similar to That in California ? Arthur Frankel U.S. Geological Survey, Denver INTRODUCTION ard from a single fault that generates earthquakes of a single magnitude. I compare hazard for a site in San Francisco With the increasing use of probabilistic seismic hazard assess- 15 km from the San Andreas Fault (Figure 1) and a site near ment (PSHA) in building codes, bridge design, loss studies, the Arkansas-Tennessee border 15 km from the narrow zone setting of insurance premiums, etc., it is evident that an of seismicity (M < 4) that likely indicates the location of the improved understanding of this method and its implications fault that generated some of the M > 7 earthquakes in the would be helpful to nonpractitioners. In this article I explain New Madrid zone (Figure 1), such as those that occurred in one result of PSHA that has caused confusion: how seismic 1811-1812. The conclusions in this paper would also be hazard at low probability levels can be similar, for some found for sites at other distances from these faults. ground-motion parameters, in the vicinity of the New The annual probability P (U_> U 0) that ground motions Madrid seismic zone in the central U.S. to the hazard in parts U at the site will be equal to or greater than some specified of California, despite the different earthquake recurrence value U 0 is the product rates in the two areas. The short answer is that one also has to consider the ground shaking generated by each earthquake, (1) which is expected to be larger for central U.S. earthquakes of ,,,(u__ Uo a given magnitude than California earthquakes of the same magnitude. The similarity in seismic hazard between the New where P(E) is the annual probability of the earthquake occur- Madrid area and California was questioned by Stein et al. ring and P(U_> U01E) is the probability of having shaking U 0 (2003) and justified in a reply by Frankel (2003). or greater at the site if that earthquake occurs. Here U is peak Probabilistic seismic hazard assessment provides esti- ground acceleration (PGA) or another measure such as mates of the probability of having ground shaking larger than response spectral acceleration (S.A.) at a certain frequency. I'll a certain amount (see Cornell, 1968). This is described in a use PGA and S.A. at 1 and 5 Hz in this article. Note that 1 seismic hazard curve, the essential product of PSHA. The and 5 Hz S.A. values are used in the International Building probabilities can be expressed as annual probabilities or as Code. One and 5 Hz are the nominal natural frequencies for probabilities over a specified number of years. Historically, frame buildings with ten and two stories, respectively. probabilities have often been expressed in terms of 50 years, The second factor on the right-hand side of Equation 1 which is frequently quoted as the effective lifetime of a typical depends on the ground motion expected for an earthquake building. The term "seismic hazard" is used here in two with a given magnitude M and distance D from the site. This senses: (1) to describe the annual probability of having a is often expressed in an "attenuation relation" or, more accu- ground motion larger than a specified value or (2) to describe rately, a "ground-motion prediction relation." It is critical to the ground motions with a specified probability of being recognize that there is variability in ground motions for a exceeded. The following arguments apply to both uses of the given magnitude and distance. This can be caused by varia- term. tions of rupture direction, focal mechanism, stress release, path effects, site conditions, etc. Typically, the ground PSHA EXAMPLES FOR CALIFORNIAAND NEW motion for any M,D is observed to follow a log-normal prob- MADRID ability distribution (e.g., Youngs et al., 1995), such as shown in Figure 2. This distribution is characterized by a median Hazard from a Single Source value, which is the ground motion that is exceeded in half the To see how seismic hazard can be similar between New observations, and the standard deviation. The second factor Madrid and California, consider the simplest example of haz- on the right-hand side of Equation 1 is the area under the dis- Seismological Research Letters September/October2004 Volume75, Number5 575 -122.6" -122.4" -122.2" -122" -90.4" -90.2" -90" -89.8" -89.6" I I I 36.2" I I 1 I / 36.2" 38,2" ssour - 7"t. I" 38" 38. ~ 35.8" 35.8" 37.8" 37,8" tl~ Arkan#sas ~ t 35.6" 35.6" 37.6" 37.6" "~ 35.4" 35,4" 37.4" ~.4"- 15 k 1 35.2" I f 35.2" -122.6" -122.4" -122.2" -122" -90.4" -90.2" -90" -89,8" -89.6" A ML ~-4.0 ~5,4 mblg ~-4.0 ~ 4.8 i Figure 1. Maps of the San Francisco Bay area (left) and New Madrid area (right), with filled circles indicating the sites considered. Solid lines indicate major faults in the San Francisco Bay area and the likely source of some of the characteristic earthquakes in New Madrid, based on the trend of microseismicity. For the San Francisco area, stars are earthquakes with M L >_ 4.0, 1933-2000. For New Madrid, stars are earthquakes with mbLg >_ 4.0, 1933-2000. Aftershocks were removed from both catalogs. Sizes of stars are keyed to magnitude. e-(b 121 _Q ,,_._ Peak Acceleration (g) Peak Acceleration (g) Peak Acceleration (g) ~10 "3 g 10 4 0,10 1.00 PGA (g) i Figure 2. Construction of a hazard curve from a single source, in this case M 7.8 earthquakes on the San Andreas Fault, with return time of 200 years. PGA is peak ground acceleration (same as "peak acceleration" in upper plots). Hazard curve is for a site 15 km from fault. At top are plots showing the area under the log-normal distribution for PGA values greater than 0.2 g, 0.38 g, and 0.6 g. The median PGA is 0.38 g. The hazard curve values are calculated using Equation 1. The probability densities are plotted as a function of log ground motion. 576 Seismological Research Letters Volume 75, Number5 September/October2004 tribution for values greater than ground motion U0. So, if U o Moving to higher ground motions, the hazard curve falls equals the median value, the probability of having ground off with a rate related to the variability of the ground-motion motion U0 or greater equals 0.5. For very low values of U0 distribution. The area under the distribution for values this probability approaches 1, and for very high U0 this prob- greater than 0.6 g equals 0.11. Thus the probability of ability approaches 0. exceeding 0.6 g equals 1/200 • 0.11, or about 1/1,800. Figure 2 shows the construction of a hazard curve for the Figure 3 shows hazard curves derived for this site in San site near the San Andreas Fault. Two segments of the San Francisco for San Andreas Fault hazard, using four different Andreas Fault most affect San Francisco: the Peninsular and attenuation relations: Sadigh et al. (1997), Abrahamson and North Coast segments. Here I use recurrence times and mag- Silva (1997), Boore et al. (1997), and Campbell and Bozo- nitudes developed in the recent report by the Working Group rgnia (2003), all derived from data from western North on California Earthquake Probabilities (2003, which I desig- American earthquakes. These attenuation relations were used nate as WG02). The mean recurrence time for scenarios in the 2002 national seismic hazard maps (Frankel et al., involving one or both of these segments is about 180 years 2002). The median PGA values for M 7.8 at 15 km horizon- (WG02), with a range of moment magnitudes M from 7.2 to tal distance vary from 0.30-0.38 g (Table 1), depending on 7.9. For scenarios involving M 7.7-7.9 on these segments, the attenuation relation, causing the horizontal shift in the the average recurrence time is 240 years (WG02). I choose a hazard curves. I have used the same variability of 0.38 natu- magnitude of 7.8 for this example, equal to the magnitude of ral-log units for each attenuation relation. Of course, ifI con- the 1906 earthquake on this portion of the San Andreas Fault sidered different earthquake recurrence times, this would (WG02), and an average recurrence time of 200 years. shift the hazard curves vertically in the plot. For this example, I use the Sadigh et al. (1997) ground- Hazard curves derived for the site near the New Madrid motion prediction relation to calculate a median PGA of source are also shown in Figure 3. Again I consider a single 0.38 g from a M 7.8 strike-slip earthquake at 15 km horizon- source. I use a recurrence time of 500 years for the character- tal distance from the fault. I assume a minimum fault depth istic source for large New Madrid earthquakes. This was of 0 km. I consider other attenuation relations later in the derived from the paleoliquefaction studies of Tuttle et al. paper. I use the Sadigh et al. (1997) value for a "rock" site (2002). They dated prehistoric sand blows and found two condition, which for California conforms to a "firm-rock" previous sequences of large earthquakes that produced lique- site condition with shear-wave velocity of about faction similar to the 1811-1812 earthquakes.
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