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

Arthur Frankel U.S. Geological Survey, Denver

INTRODUCTION

With the increasing use of probabilistic seismic hazard assessment (PSHA) in building codes, bridge design, loss studies, setting of insurance premiums, etc., it is evident that an improved understanding of this method and its implications would be helpful to nonpractitioners. In this article I explain one result of PSHA that has caused confusion: how seismic hazard at low probability levels can be similar, for some ground-motion parameters, in the vicinity of the New Madrid seismic zone in the central U.S. to the hazard in parts of California, despite the different earthquake recurrence rates in the two areas. The short answer is that one also has to consider the ground shaking generated by each earthquake, which is expected to be larger for central U.S. earthquakes of a given magnitude than California earthquakes of the same magnitude. The similarity in seismic hazard between the New Madrid area and California was questioned by Stein et al. (2003) and justified in a reply by Frankel (2003).

Probabilistic seismic hazard assessment provides estimates of the probability of having ground shaking larger than a certain amount (see Cornell, 1968). This is described in a seismic hazard curve, the essential product of PSHA. The probabilities can be expressed as annual probabilities or as probabilities over a specified number of years. Historically, probabilities have often been expressed in terms of 50 years, which is frequently quoted as the effective lifetime of a typical building. The term "seismic hazard" is used here in two senses: (1) to describe the annual probability of having a ground motion larger than a specified value or (2) to describe the ground motions with a specified probability of being exceeded. The following arguments apply to both uses of the t e r m .

PSHA EXAMPLES FOR CALIFORNIA AND NEW MADRID

Hazard from a Single Source To see how seismic hazard can be similar between New Madrid and California, consider the simplest example of haz-

ard from a single fault that generates earthquakes of a single magnitude. I compare hazard for a site in San Francisco 15 km from the San Andreas Fault (Figure 1) and a site near the Arkansas-Tennessee border 15 km from the narrow zone of seismicity (M < 4) that likely indicates the location of the fault that generated some of the M > 7 earthquakes in the New Madrid zone (Figure 1), such as those that occurred in 1811-1812. The conclusions in this paper would also be found for sites at other distances from these faults.

The annual probability P (U_> U 0) that ground motions U at the site will be equal to or greater than some specified value U 0 is the product

,,,(u__ Uo (1)

where P(E) is the annual probability of the earthquake occur- ring and P(U_> U01E) is the probability of having shaking U 0 or greater at the site if that earthquake occurs. Here U is peak ground acceleration (PGA) or another measure such as response spectral acceleration (S.A.) at a certain frequency. I'll use PGA and S.A. at 1 and 5 Hz in this article. Note that 1 and 5 Hz S.A. values are used in the International Building Code. One and 5 Hz are the nominal natural frequencies for frame buildings with ten and two stories, respectively.

The second factor on the right-hand side of Equation 1 depends on the ground motion expected for an earthquake with a given magnitude M and distance D from the site. This is often expressed in an "attenuation relation" or, more accu- rately, a "ground-motion prediction relation." It is critical to recognize that there is variability in ground motions for a given magnitude and distance. This can be caused by varia- tions of rupture direction, focal mechanism, stress release, path effects, site conditions, etc. Typically, the ground motion for any M,D is observed to follow a log-normal probability distribution (e.g., Youngs et al., 1995), such as shown in Figure 2. This distribution is characterized by a median value, which is the ground motion that is exceeded in half the observations, and the standard deviation. The second factor on the right-hand side of Equation 1 is the area under the dis-

Seismological Research Letters September/October2004 Volume 75, Number5 575

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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.

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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 U 0. So, if U o

equals the median value, the probability of having ground motion U 0 or greater equals 0.5. For very low values of U 0 this probability approaches 1, and for very high U 0 this probability approaches 0.

Figure 2 shows the construction of a hazard curve for the site near the San Andreas Fault. Two segments of the San Andreas Fault most affect San Francisco: the Peninsular and North Coast segments. Here I use recurrence times and magnitudes developed in the recent report by the Working Group on California Earthquake Probabilities (2003, which I designate as WG02). The mean recurrence time for scenarios involving one or both of these segments is about 180 years (WG02), with a range of moment magnitudes M from 7.2 to 7.9. For scenarios involving M 7.7-7.9 on these segments, the average recurrence time is 240 years (WG02). I choose a magnitude of 7.8 for this example, equal to the magnitude of the 1906 earthquake on this portion of the San Andreas Fault (WG02), and an average recurrence time of 200 years.

For this example, I use the Sadigh et al. (1997) ground- motion prediction relation to calculate a median PGA of 0.38 g from a M 7.8 strike-slip earthquake at 15 km horizontal distance from the fault. I assume a minimum fault depth of 0 km. I consider other attenuation relations later in the paper. I use the Sadigh et al. (1997) value for a "rock" site condition, which for California conforms to a "firm-rock" site condition with shear-wave velocity of about 600-800 m/s averaged over the top 30 m (Vs30; Boore and Joyner, 1997). I apply the standard deviation of 0.38 in natural log units that is cited in Sadigh et al. (1997) for this magnitude. This describes the width of the ground-motion distribution and quantifies the variability.

At low ground motions the hazard curve is nearly horizontal (Figure 2). It intersects the vertical axis at the annual probability of 1/200, or 1 over the average recurrence time. This is due to the second term on the right-hand side of Equation 1 being nearly 1 at low ground-motion values, so that P(U_> U 0) is approximately the probability of the earthquake.

Consider three points on the hazard curve (Figure 2), moving from low to high ground motions. The probability of exceeding 0.2 g equals the earthquake recurrence probability of 1/200 multiplied by the area under the distribution for values greater than 0.2 g, which is 0.96. The hazard curve starts to curve downward as the ground motion approaches the median ground motion of 0.38 g expected for M 7.8 at 15 km. At the median ground motion of 0.38 g, the hazard curve is at half the value of the annual probability of the earthquake, since the second factor on the right-hand side of Equation 1 equals 0.5 at the median ground motion.

The above calculation illustrates an important link between probabilistic and deterministic (scenario) ground motions. If you want to know the annual probability of having a ground motion equal to or greater than the median ground motion when an earthquake actually occurs, multiply 0.5 by the annual probability of the earthquake.

Moving to higher ground motions, the hazard curve falls off with a rate related to the variability of the ground-motion distribution. The area under the distribution for values greater than 0.6 g equals 0.11. Thus the probability of exceeding 0.6 g equals 1/200 • 0.11, or about 1/1,800.

Figure 3 shows hazard curves derived for this site in San Francisco for San Andreas Fault hazard, using four different attenuation relations: Sadigh et al. (1997), Abrahamson and Silva (1997), Boore et al. (1997), and Campbell and Bozo- rgnia (2003), all derived from data from western North American earthquakes. These attenuation relations were used in the 2002 national seismic hazard maps (Frankel et al.,

2002). The median PGA values for M 7.8 at 15 km horizontal distance vary from 0.30-0.38 g (Table 1), depending on the attenuation relation, causing the horizontal shift in the hazard curves. I have used the same variability of 0.38 natural-log units for each attenuation relation. Of course, ifI considered different earthquake recurrence times, this would shift the hazard curves vertically in the plot.

Hazard curves derived for the site near the New Madrid source are also shown in Figure 3. Again I consider a single source. I use a recurrence time of 500 years for the characteristic source for large New Madrid earthquakes. This was derived from the paleoliquefaction studies of Tuttle et al.

(2002). They dated prehistoric sand blows and found two previous sequences of large earthquakes that produced lique- faction similar to the 1811-1812 earthquakes. These prehistoric earthquakes occurred around A.D. 900 and 1450. Including the 1811-1812 sequence yields an average recurrence time of about 500 years (Cramer, 2001). It has been noted that the rate of these large earthquakes as documented by paleoliquefaction is higher than that derived from extrap- olating the observed rate of recent earthquakes from M 3-5 using the Gutenberg-Richter relation (Cramer, 2001). Thus the large New Madrid earthquakes represent characteristic earthquakes (e.g., Schwartz and Coppersmith, 1984).

Ground-motion prediction relations for the central and eastern U.S. (CEUS) have been developed from models of the earthquake source and measured values of crustal propagation parameters. In this paper, I use the results from a recent expert-opinion study sponsored by the Electric Power Research Institute (EPRI, 2003). In this study, a panel of ground-motion experts evaluated 13 different attenuation relations for the CEUS. The USGS was not involved in this study, although the Frankel et al. (1996) relation was among those considered. The EPRI study grouped the relations into four types: single-corner frequency models, two-corner frequency models, hybrid models which convert western U.S. (WUS) attenuation relations into CEUS ones using source parameter and Q adjustments, and finite-fault rupture models. Each of the attenuation relations in a group was assigned a weight, and a set of composite attenuation relations were then developed for each group. Weights were also assigned to the results of the four groups. For each group, a median ground-motion relation and 5th and 95th percentile ground-


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A Figure 3. Hazard curves at the San Francisco site (solid lines) for M 7.8 earthquakes on the San Andreas Fault and at the New Madrid site (dashed lines) for New Madrid characteristic earthquakes, for peak ground acceleration (PGA). Each curve is derived from a separate attenuation relation. Nearest horizontal distance to fault is 15 km in both cases. (A) Using a M 7.7 characteristic source for New Madrid and (B) using a M 7.2 characteristic source. Note the higher ground-motion values of the New Madrid curves for 2% probability of exceedance (P.E.) in 50 years for the M 7.7 and M 7.2 cases. In all figures shown in this paper, the San Francisco hazard is calculated for a typical western U.S. firm-rock condition, whereas the New Madrid hazard curves are for a hard-rock site condition (see text). The curves are labeled by attenuation relation. For San Francisco, B = Boom et al. (1997), C = Campbell and Bozorgnia (2003), A = Abrahamson and Silva (1997), S = Sadigh et al. (1997). For New Madrid the curves are labeled by numbers corresponding to those of the EPRI (2003) attenuation relations (see text).

motion relations were produced for each ground-motion parameter.

For the New Madrid example, I use the four median ground-motion relations derived by the EPRI (2003) study. These relations are for hard-rock sites, generally characterized

TABLE 1 Median Ground Motions Predicted for M 7.8 San Andreas

Fault Earthquake for Closest Horizontal Distance of 15 km, for a Firm-rock Site Condition*

Sadigh Abrahamson Boore Campbelland et al. and Silva et al. Bozorgnia

(1997) (1997) (1997) (2003)

PGA 0.38 g 0.34 g 0.30 g 0.35 g

5 Hz S.A. 0.88 g 0.80 g 0.53 g 0.72 g

1 Hz S.A. 0.41 g 0.34 g 0.38 g 0.39 g

*Using minimum rupture depth of 0 km for Sadigh et al. (1997) and Abrahamson and Silva (1997) and 3 km for Campbell and Bozorgnia (2003). A Vs30 of 620 m/s was used for Boore et al. (1997) and generic-rock site condition for Campbell and Bozorgnia (2003).

by a shear-wave velocity of about 2.8 km/sec at the surface. This is substantially different from the firm-rock, western U.S. site condition that is used for the California hazard calculations here. For PGA, 5 Hz and 1 Hz spectral accelerations, the ground motions would be higher at firm-rock sites than hard-rock sites, because of the lower shear-wave velocity at the firm-rock sites. Lower (2 at shallow depths under firm- rock sites will reduce this amplification at higher frequencies.

Since firm-rock sites amplify PGA, 5 Hz and 1 Hz spectral accelerations above those that would be observed at hard- rock sites for the same input motions, I think it is fair to say that by comparing hard-rock CEUS hazard curves with firm- rock WUS ones, I am underestimating the relative hazard at CEUS sites for these ground-motion parameters. The conversion of hard-rock ground motions to firm-rock sites is dis- cussed in a later section.

The moment magnitudes M of the largest events in the 1811-1812 New Madrid sequence have been estimated by three studies that used intensity observations from these events and correlated them with intensity observations from more recent earthquakes that had determinations of magnitudes from seismograms. Johnston (1996) concluded that the 16 December 1811 event had M 8.1 and the 7 February 1812 event had M 8.0, by comparing isoseismal areas with those from other stable-continental-region (SCR) earthquakes and adjusting for the attenuation in central and eastern North America, which is even lower than the SCR average attenuation. Hough et al. (2000) re-evaluated the intensity data and adjusted for bias caused by sampling in river valleys with high site response. They found an M of 7.4-7.5 for the 7 February 1812 event. Most recently, Bakun and Hopper (2004) used the intensity observations as point data to determine magnitude. They determined a preferred magnitude of 7.8 for the 7 February 1812 event. So the preferred magnitude estimates by these three studies for the largest events in 1811-1812 range from M 7.4-8.1.

For the 2002 version of the national seismic hazard maps, a workshop was held in June 2000 that gathered opin- ions from 56 experts on inputs for the central and eastern

578 Seismological Research Letters Volume 75, Number 5 September/October 2004

U.S. This workshop found a general consensus of M 7.5-8.0 for the largest New Madrid earthquakes (Wheeler and Per- kins, 2000). The largest magnitudes of the A.D. 900 and 1450 earthquake sequences appear to be similar to those in 1811-1812, based on the areal extent of the paleoliquefaction and sand dike sizes (Tuttle et al., 2002). I designate these magnitudes of the characteristic large earthquakes as Mchar.

The 2001 Bhuj, India earthquake occurred in an intraplate area, with similarities to the intraplate New Madrid zone. Instrumental determinations of M for the Bhuj earthquakes range from 7.6-7.7. Hough et al. (2002) pointed out the similarity of the intensities with distance between the Bhuj earthquake and those of the 16 December 1811 New Madrid earthquake. Again this supports the magnitude of the New Madrid earthquakes as being in the M 7.5-8.0 range. In the 2002 national seismic hazard maps, a logic tree was used to incorporate the uncertainty in the magnitudes, with branches ranging from M 7.3-8.0 (Frankel et al., 2002). The highest weight was assigned to the branch for M 7.7.

It is well known from instrumental and intensity observations that earthquakes in the CEUS and elsewhere in eastern North America produce higher ground motions at high frequencies (for PGA, and S.A. at about 2 Hz and above) for a given distance than western U.S. earthquakes with the same magnitudes (e.g., Nuttli, 1979; Atkinson, 1993; Atkinson and Silva, 1997). This is partly due to the higher average stress drop of CEUS earthquakes compared to WUS earthquakes and partly due to the higher Q of the CEUS crust, which dissipates energy more slowly with propagation distance than WUS crust (e.g., Evernden, 1967; Frankel et al., 1990; Benz et al., 1997). These properties reflect the differences in source and propagation between intraplate SCR (CEUS) earthquakes and those in or near plate boundaries (wws).

Figure 3A shows the PGA hazard curves derived from the four EPRI relations for a New Madrid characteristic source with a moment magnitude of 7.7 at 15 km distance. The median PGA values from the EPRI (2003) study range from 0.69-0.93 g for the M 7.7 New Madrid scenario (Table 2), much higher than the median values for the M 7.8 San Andreas case at the same distance (0.30-0.38 g). For ease of comparison, I am using the same variability for the New Madrid ground motion as I used for the San Andreas ground motion. At low PGA values the hazard curves are lower than those for the San Andreas Fault because of the longer recurrence time of the New Madrid source (500 years versus 200 years). Because of the higher median ground motions of the M 7.7 New Madrid source compared to those for the M 7.8 San Andreas source, the New Madrid hazard curves exceed the San Andreas ones at higher ground-motion values.

Figure 3 also contains a horizontal line corresponding to a 2% probability of exceedance (EE.) in 50 years, a probability level often used in engineering applications. The 2% P.E. in 50 years corresponds to an annual probability of 4.04 x 10 -4, as will be shown later. The PGA with a 2% P.E.

TABLE 2 Median Values of Ground Motions for New Madrid

Earthquakes Predicted from EPRI (2003) Study for Closest Horizontal Distance of 15 km, for a Hard-rock

Site Condition*

EPRI 1 EPRI 2 EPRI 3 EPRI 4

M 7.7; PGA 0.72 g 0.93 g 0.88 g 0.69 g

M 7.7; 5 Hz S.A. 1.08 g 1.23 g 1.18 g 1.21 g

M 7.7; 1 Hz S.A. 0.42 g 0.25 g 0.40 g 0.37 g

M 7.2; PGA 0.54 g 0.71 g 0.70 g 0.41 g

M 7.2; 5 Hz S.A. 0.79 g 0.88 g 0.91 g 0.72 g

M 7.2; 1 Hz S.A. 0.29 g 0.15 g 0.28 g 0.20 g

*A minimum rupture depth of 5 km was used for EPRI 3, the only EPRI attenuation relation which requires a depth value. I use the rift model for EPRI 4.

in 50 years is found from the intersection of the horizontal line with the hazard curve.

Figure 3A illustrates that the New Madrid source will produce higher ground-motion values for 2% I.E. in 50 years than the San Andreas source. Even when the magnitude of the New Madrid source is reduced to M 7.2 (Figure 3B), the New Madrid hazard curves from three out of four of the EPRI relations have larger PGA values for 2% P.E. in 50 years than the San Andreas curves. The EPRI PGA values for M 7.2 at 15 km distance vary from 0.41-0.71 g, still higher than the median values of 0.30-0.38 g expected for the M 7.8 San Andreas scenario at the same distance.

Hazard from All Sources Of course, considering only a single source is not the whole story. For the San Francisco site, hazard is generated by the Hayward and other faults, as well as by smaller earthquakes not associated with the larger faults. PSHA handles independent, multiple sources by adding the annual frequency of exceedance from each source. PSHA does not assume that each source occurs simultaneously. The total annual rate of exceeding ground motion U 0, Z(U >_ U0), can be found from summing over earthquakes at all relevant magnitudes _/14 and distances D (e.g., Anderson and Trifunac, 1978), such that

M D

-Uo)-Z2;R(M

Here R(M, D) is the annual rate of earthquakes with magnitude M and source-site distance D. P(U>_ UolM, D) is the probability of having ground motions greater than or equal to U 0 if an earthquake of magnitude M at distance D occurs.

Now the Poisson (time-independent) probability P(U_> U 0, t) of exceeding ground motion U 0 in t years is

p ( u > uo, t) = 1 _ ~-x,. (3)


Thus an annual rate of exceedance 2, of 4.04 x 10 -4 corresponds to a 2% probability of exceedance in 50 years, such that P(U_> U 0, 50 years). Note that for annual probabilities much less than 1,

v(u_> Uo,, Z(U_> (4)

I calculated the hazard at the San Francisco site from all the rupture scenarios for all San Francisco Bay area faults specified in the WG02 report, using the recurrence and magnitude information from WG02 for all the faults. In addition, I incorporated the hazard from "background" earthquakes not on specific faults. This follows the procedure used in the 2002 national seismic hazard maps, which is based on the spatially smoothed seismicity (Frankel, 1995; Frankel et al., 2000; Frankel et al., 2002). Here I use a minimum magnitude of M 5.0 in the hazard calculation.

Figure 4A shows how the hazard at the San Francisco site from all sources compares with the hazard from just the single-magnitude San Andreas Fault scenario. At high probabilities and low ground motions, the annual probability of exceedance is much higher when all the sources are considered. Smaller, more frequent earthquakes become very important at the low ground-motion levels, as do earthquakes on more distant faults. At high ground motions, sources such as the Hayward Fault raise the hazard curve above that from just the San Andreas Fault.

For the New Madrid example, I have also included the hazard from smaller earthquakes, as characterized by the spatially smoothed seismicity. This procedure is described in Frankel (1995). I use a minimum m,- of 5 0 in the hazard OLg

calculation. Figure 4B depicts how the addition of these smaller-magnitude sources raises the hazard curve somewhat at lower ground-motion levels but has little effect at the high ground-motion levels.

Hazard curves from all the San Francisco and New Madrid region sources were calculated for each attenuation relation. Figure 5A displays the PGA hazard curves for both sites using all sources, with M~h,~ 7.7 for the New Madrid region. Again, the same ground-motion variability was used for San Francisco and New Madrid calculations. Note that, since the EPRI #4 attenuation relation is intended to apply to earthquakes greater than M __ 6 (EPRI, 2003), I use the other three attenuation relations with equal weights to determine the contribution of the smoothed seismicity when showing the total hazard results for EPRI #4.

At low annual probability levels of less than 0.002, the hazard curves for New Madrid with Mchar 7.7 have larger PGA values than those of the San Francisco site (Figure 5A). The 0.002 annual probability corresponds to 10% P.E. in 50 years (see Equation 3). For 2% P.E. in 50 years, the PGA values for New Madrid (for the Mchar 7.7 case) are substantially higher than those for San Francisco, even without adjusting the hard-rock values of the New Madrid curves to firm-rock site conditions, which would make the difference even larger.

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,A Figure 4. (A) PGA hazard curves at the San Francisco site for the San Andreas single magnitude source (solid line; based on Sadigh et al. [1997] attenuation relation) and from all sources (dashed line; based on EPRI #1 attenuation relation) from the WG02 model, including hazard from other faults and background earthquakes. (B) PGA hazard curves at the New Madrid site for the New Madrid characteristic source (solid line) and from all sources (dashed line), including the background seismicity, using the same attenuation relations as in (A).

At higher annual probability levels above 0.002, the hazard curves for San Francisco show higher PGA values than the New Madrid ones (Figure 5A), reflecting the higher recurrence rates in the San Francisco region.

Even if the Mchar for New Madrid were only 7.2, lower than the moment magnitude inferred for the largest 1811-1812 events by any study of the intensity data, the New Madrid PGA hazard curves are similar to or higher than those for San Francisco for the lower probabilities of exceedance, such as 2% P.E. in 50 years (Figure 5B). Taking the cen- ter of the range of hazard curves would yield similar values of PGA at 2% P.E. in 50 years for New Madrid with Mchar 7.2 and San Francisco.


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& Fioure 5. Comparison of PGA hazard curves from all sources for the San Francisco site (solid lines) and New Madrid site (dashed lines). Each curve is derived from a different attenuation relation. Curves are labeled by attenuation relation, as described in the caption to Figure 3. Note the higher ground motions at 2% P.E. in 50 years for the New Madrid compared to San Francisco for the Mchar 7.7 case. Even the M 7.2 New Madrid case produces similar 2% P.E. in 50-year ground motions as the San Francisco site.

The 5 Hz S.A. values for annual probabilities less than about 6 x 10 4 are about the same for New Madrid (Mchar 7.7) and San Francisco, when including all the sources (Figure 6A). The four median curves for 5 Hz S.A. from the EPRI study actually have a rather narrow spread. The 5 Hz S.A. at 2% P.E. in 50 years is similar for the New Madrid and San Francisco sites, for a New Madrid Mchar of 7.7. The mid- point of the intersections of the four hazard curves with the horizontal line for 2% P.E. in 50 years is about the same for both sites.

The higher ground motions at high frequencies expected for large New Madrid earthquakes relative to large WUS earthquakes cause the 5 Hz S.A. hazard curves at New Madrid and San Francisco to merge at low probability levels (Figure 6A). The median 5 Hz S.A. values (hard-rock sites) from the EPRI study for a New Madrid earthquake with

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A Fioure 8. Comparison of 5 Hz S.A. hazard curves from all sources for the San Francisco site (solid lines) and New Madrid site (dashed lines). Each curve is derived from a different attenuation relation. Curves are labeled by attenuation relation, as described in the caption to Figure 3 (curves for EPRI 2, 3, and 4 are very similar in top panel; curves for EPRI 1 and 2 are very similar in bottom panel). At 2% P.E. in 50 years, the New Madrid and San Francisco hazard curves produce similar values, for New Madrid Mchar 7.7. When the New Madrid Mchar is 7.2, the 2% P.E. in 50-year ground motion is about 70% of that for San Francisco.

Mchar 7.7 (15 km horizontal distance) are 1.08-1.23 g (Table 2), substantially larger than the median 5 Hz S.A. values of 0.53-0.88 g at firm-rock sites for a San Andreas Fault M 7.8 earthquake (15 km horizontal distance) predicted by the four WUS relations (Table 1).

If I use M 7.2 for the New Madrid characteristic source, the 5 Hz S.A. values at 2% EE. in 50 years for New Madrid are about 70% of those for San Francisco (all sources), comparing the midpoints of the intersections of the hazard curves with the horizontal line at 2% EE. in 50 years (Figure 6B). The EPRI median 5 Hz S.A. values for a New Madrid M 7.2 at 15 km distance vary from 0.72-0.91 g (Table 2), values similar to or greater than those expected for the M 7.8 San

Seismological Research Letters September/October2004 Volume75, Number5 581

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,& Figure 7. Comparison of 1 Hz S.A. hazard curves from all sources for the San Francisco site (solid lines) and New Madrid site (dashed lines). Each curve is derived from a different attenuation relation. Curves are labeled by attenuation relation, as described in the caption to Figure 3. At 2% P.E. in 50 years the probabilistic ground motion is lower for the New Madrid case than San Francisco.

Andreas scenario at 15 km (0.53-0.88 g; Table 1). Amplify- ing the New Madrid hard-rock values to a firm-rock site condition would raise them closer to those for San Francisco.

For 1 Hz S.A. with all sources included, the hazard curves for New Madrid are generally below those for San Francisco, for the Mchar 7.7 and 7.2 cases, at all probability levels shown (Figure 7). The median EPRI values for 1 Hz S.A. for M 7.7 (15 km horizontal distance) are 0.25-0.42 g (Table 2). The four WUS attenuation relations predict median 1 Hz S.A. values of 0.34-0.41 g for an M 7.8 earthquake on the San Andreas Fault at the same 15 km distance (Table 1). These median values are similar between the New Madrid and San Andreas scenarios, but the New Madrid hazard curves are lower because of the longer recurrence time for large earthquakes. However, the 1 Hz S.A. values for New

Madrid with M c h a r 7.7 would be similar to the San Francisco at 2% EE. in 50 years, when the New Madrid hard-rock values are adjusted to firm-rock sites (see next section).

The EPRI 1 Hz S.A. values for M 7.2 at 15 km distance span the range from 0.15-0.29 g (Table 2), lower than those predicted for the M 7.8 San Andreas scenario. The New Madrid I Hz S.A. hazard curves using M c h a r 7.2 and all other sources are well below the San Francisco hazard curves (Fig- ure 7B) for all sources, although amplification of the New Madrid hard-rock values will bring them closer to the San Francisco hazard curves.

CONVERSION OF HARD-ROCK VALUES TO FIRM- ROCK VALUES

Ideally, we would like to compare hazard for sites with identical near-surface shear-wave velocities. Adjustment of the hard-rock values to firm-rock values requires knowledge of the average shear-wave profiles with depth for the two site classes and the relative attenuation at shallow depths under these classes, as quantified by /c (Anderson and Hough, 1984), such that the Fourier spectral amplitude is propor- tional to e - ~ , where f is frequency. Boore and Joyner (1997) determined the average shear-wave velocity profile under WUS "generic rock" (firm-rock) sites, using borehole and refraction measurements. I have estimated the amplification factors for their "generic rock" relative to their "very hard rock" (Vs30 of 2.9 km/s; the "hard rock" described in this paper) by taking the ratio of the Boore and Joyner (1997) amplification factors (without site attenuation) between these two site types and including the difference in/c. Boore and Joyner (1997) found an average/cof0.035 for WUS generic rock sites. Several of the hard-rock CEUS attenuation relations used a/c of 0.006. This results in a total amplification factor for "generic rock" relative to "very hard rock", after the differences in/c are included, of 1.4 at both 5 Hz and 1 Hz. This indicates that the CEUS hard-rock values at 5 Hz and 1 Hz should be multiplied by 1.4 to convert to a WUS firm- rock site condition. I calculated firm-rock to hard-rock amplification for PGA by generating synthetic point-source seismograms using the method of Boore (1983). I used the amplification factors for the two site types given in Boore and Joyner (1997) and the/c values given above. I found an average PGA amplification factor of 1.2 for firm-rock sites relative to hard-rock sites.

In the national seismic hazard maps, adjustments were made to the hard-rock values to equate them to a CEUS site condition with Vs30 of 760 m/s, at the boundary between NEHRP site classes B and C (Frankel et al., 1996). A smaller /c of 0.01 was used for the CEUS BC site than for a typical WUS firm-rock site, based on borehole observations of K" in the eastern U.S. by Fletcher (1995). The hard-rock to firm- rock amplification factors derived were 1.55, 1.76, and 1.33 for PGA, 5 Hz S.A., and 1 Hz S.A., respectively.

The hard-rock to firm-rock conversion factors can also be estimated using the NEHRP amplification factors, which

582 Seismological Research Letters Volume75, Number5 September/October2004

are functions of site classes based on Vs30 and input amplitude (NEHRP Recommended Provisions, BSSC [1998]). The NEHRP amplification factors are consensus values derived by site-response experts from observations and mod- eling. NEHRP site class A represents sites with Vs30 greater than about 1,500 m/s. Taking the ratio of the NEHRP factors between a B-C site (firm rock) and an A site yields 1.25 for 5 Hz S.A. and 1.5 for 1 Hz S.A. These factors were derived from California class A sites, however, which have Vs30 averaging about 1,600 m/s (see Borcherdt, 1994). This likely causes the NEHRP factors to underestimate the amplification of firm-rock sites relative to hard-rock CEUS sites with Vs30 of 2,800 m/s. The coefficients derived by Boore et al. (1997) from analysis of strong-motion data indicate amplification factors of 1.4, 1.3, and 1.7 for PGA, 5 Hz S.A., and 1 Hz S.A, respectively, for sites with Vs30 of 650 m/s, relative to sites with Vs30 of 1,600 m/s.

My major point here is that the work done to date indicates that firm-rock sites amplify PGA, 1 Hz S.A., and 5 Hz S.A relative to hard-rock sites. Certainly, more work needs to be done on the issue of amplification for different rock site conditions. This work should be region-specific, requiring different amplification factors in the WUS than the CEUS.

COMPARISON OF EPRI ATTENUATION RELATIONS WITH THOSE USED IN THE NATIONAL SEISMIC HAZARD MAPS

The EPRI (2003) study represents the latest expert evaluation of CEUS attenuation relations. It is important to compare the CEUS attenuation relations derived in the new EPRI study with those used in the 2002 national seismic hazard maps. Figure 8 compares the four EPRI median relations with the five CEUS attenuation relations used in the 2002 national maps: Frankel et al. (1996), Atkinson and Boore (1995) , Toro et al. (1997), Campbell (2003), and Somerville et al. (2001). This figure compares the median values for an M 7.7 earthquake, using a source depth of 10 km. Note that EPRI relation #4 is equivalent to the Somerville et al. (2001) relation, since this was the only finite-source model available for that category. All of the attenuation relations are for a hard-rock site condition.

For PGA, the attenuation relations used in the national maps encompass a similar range of values at any given distance as those of the EPRI relations. For 5 Hz spectral acceleration the Frankel et al. (1996) relation and the Toro et al. (1997) relation are a bit higher than any of the EPRI relations for distances less than 20 km. The Campbell (2003) relation is somewhat below the lowest of the EPRI relations. The relations used in the national maps have a wider range of values at these close distances than the four EPRI relations. At 1 Hz, two of the five relations used for the national maps are higher than any of the EPRI median relations, for distances less than 50 km and greater than 100 km. It is important to note that the EPRI report also contains attenuation relations for the 5th and 95 th fractiles, in addition to the median relation.

These other fractiles lie below and above the median values plotted in Figure 8.

A reasonable question is: How good are the predictions by the EPRI study and the attenuation relations used in the national maps given the lack of near-source recordings from large CEUS earthquakes? Atkinson and Boore (1998) compared the prediction of several attenuation relations with observations from earthquakes with M 4-7.3 in eastern North America and other intraplate regions. Most of these data are from distances of greater than 100 km. They found that the predictions of the Atkinson and Boore (1995) dou- ble-corner frequency model were similar, on average, to the observations at all frequencies and did not show bias. They reported that the predictions of the Frankel et al. (1996) and Toro et al. (1997) single-corner frequency relations were similar, on average, to the 2-10 Hz data but overestimated the 1 Hz values. Cramer and Kumar (2003) determined PGA and 1 Hz S.A. values for the Bhuj, India earthquake (M 7.6-7.7) using recordings of engineering seismoscopes at epicentral distances of 44-288 km and one accelerograph at 238 km. They found that the median values predicted by the CEUS attenuation relations used in the 2002 national seismic hazard maps generally bounded the observed values. The observed PGA values from the Bhuj earthquake were much higher than those predicted with WUS attenuation relations for a M 7.7 earthquake. These studies lend support to the source models and stress-drop values used to develop the CEUS attenuation relations, providing some confidence in applying these relations to closer distances.

DISCUSSION

All of the examples shown in this paper are based on time- independent models of hazard, which do not depend on the time since the last event. PSHA can also use time-dependent probabilities in Equation 1. Using these time-dependent probabilities can shift the hazard curves vertically on the plots. Time-dependent probabilities for large earthquakes on the San Andreas Fault by WG02 are not much different than the time-independent probabilities. An estimate of the time- dependent probability for New Madrid characteristic earthquakes is only slightly lower (7% over the next 50 years; C.H. Cramer, personal communication, 2002) than the time-independent estimate (10% in 50 years). Here, the time-dependent probability was calculated with a coefficient of variability of 0.5 for the recurrence time, which is typically found for earthquake sequences (see, e.g., WG02).

The exact location of the northeast-striking fault(s) that generated some of the New Madrid earthquakes is not known. In the national seismic hazard maps, three parallel, hypothetical faults were used to describe the uncertainty in the location (Frankel et al., 1996, 2000, 2002), with higher weight given to the central hypothetical fault based on input from the regional experts at the 2000 CEUS workshop (Wheeler and Perkins, 2000). In this article I have chosen the central fault trace used in the national seismic hazard maps,


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,A Figure 8. Comparison of ground motions predicted for a M 7.7 eastern North America earthquake for the four median relations of EPRI (solid lines) and the five attenuation relations used in the 2002 national seismic hazard maps (dashed lines). A source depth of 10 km was used. FEA96: Frankel et aL (1996); AB95: Atkinson and Boore (1995); TEA97: Toro eta/. (1997); C03: Campbell (2003); SOEA01: Somerville et al. (2001). Note that the EPRI #4 and Somerville et a/. (2001) relations are identical.

584 Seismological Research Letters Volume 75, Number 5 September/October 2004

which follows the trend in seismicity (M < 4) that has been located by the local seismic network. Including the two parallel hypothetical faults (with lower weights than the middle one) widens the zone of high hazard but reduces the probabilistic ground motions over the central fault trace.

CONCLUSION

I have demonstrated how probabilistic seismic hazard for New Madrid can be greater than that at San Francisco at low probabilities for PGA and similar at low probabilities for 5 Hz S.A. By low probabilities, I mean annual probabilities less than the reciprocal of the return time of the New Madrid characteristic source, that is, 1/500. This is a consequence of the higher ground motions, for PGA and 5 Hz S.A. (and other high-frequency measures), expected for large New Madrid earthquakes compared to San Andreas earthquakes with similar magnitudes.

Engineering groups and/or regulatory agencies decide on the probability level of ground motions used in the design of structures. This probability level is based on the consequences of structural failure and judgments of the acceptable level of risk. El

ACKNOWLEDGMENTS

Stephen Harmsen provided some of the EPRI (2003) ground-motion values. Reviews by Mark Petersen, Charles Mueller, and Susan Hough helped improve the paper. Mark Petersen, Tianqing Cao, and Mike Blanpied assembled the input files from the WG02 results. I thank Chris Cramer, Dave Boore, Eugene Schweig, Rus Wheeler, and Bill Ellsworth for their useful comments. The California Geolog- ical Survey supplied the California earthquake catalog.

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U.S. Geological Survey MS 966, Box 25046

Denver, CO 80225 alrankel @ usgs.gov


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