Published in “Proceedings of FHWA/NCEER Workshop on the National Representation of Seismic Ground Motion for New and Existing Highway Facilities,” NCEER Technical Report 97-0010, pp. 39-73, 1997.
Arthur Frankel, Stephen Harmsen,
Charles Mueller, Theodore Barnhard,
E.V. Leyendecker, David Perkins,
Stanley Hanson, Nancy Dickman,
Margaret Hopper
U.S. Geological Survey
MS 966, Box 25046
Denver Federal Center
Denver, CO 80225
afrankel@usgs.gov
(303) 273-8556
We have recently completed new probabilistic seismic hazard maps for the contiguous United States. In June 1996, these U.S. Geological Survey (USGS) national seismic hazard maps were placed on our Internet World Wide Website (http://eqhazmaps.usgs.gov/). The color maps can be viewed on the Web or downloaded to the user's computer for printing. The hazard maps depict probabilistic values of peak horizontal ground acceleration (PGA) and spectral accelerations (SA) at 0.2, 0.3, and 1.0 sec periods (5% of critical damping) with 10%, 5%, and 2% probabilities of exceedance (PE) in 50 years. These PE's correspond to return times of approximately 500, 1000, and 2500 years, respectively. Our website also has text files with the gridded values of PGA and SA at the 150,000 sites used to make the maps. We have recently completed calculations for SA values at 0.1, 0.5, and 2.0 sec. A partial set of 4.0 sec values has also been prepared (see below).
The methodology used for the maps was presented,
discussed, and substantially modified during six regional workshops convened
by the USGS from June 1994-June 1995. This process was part of Project 97
with the Building Seismic Safety Council (BSSC) to produce seismic hazard
and design maps for the 1997 Edition of the NEHRP Recommended Provisions for
Seismic Regulations for New Buildings, which is prepared by BSSC and published
by FEMA. Many of the associated products of the maps (e.g., de-aggregation)
were suggested at a users' needs workshop convened by BSSC and the Applied
Technology Council.
This paper briefly summarizes the methodology used to make the maps and presents analyses of the results. For more detail on the methodology see Frankel et al. (1996). An important aspect of the methodology is the use of alternative models of seismicity, fault recurrence, and ground-motion relations in a logic tree formalism. We divided the contiguous U.S. into a central and eastern U.S. (CEUS) portion and a western U.S. (WUS) portion, based on the difference in ground-motion attenuation (see later section on attenuation). The boundary we chose between these attenuation regions is shown in Figure 1, along with the historic seismicity.
We applied three basic organizing principles in the making of the new maps, for both the CEUS and the WUS.
(1) We used the spatially-smoothed historic seismicity
(Figure 1) as one component of the hazard calculation (see Frankel, 1995).
This assumes that future damaging earthquakes will occur near areas which
have had small earthquakes (M>3 or M>4) in the historic past. Analysis of historic seismicity indicates
that this is usually the case. Previously-published methods of using historic
seismicity directly to determine hazard are Jacob et al. (1994) and EPRI (1986).
(2) We used large background source zones based on broad geologic criteria to quantify hazard in areas with little or no historic seismicity but with the potential for damaging earthquakes.
(3) We determined the hazard from specific fault sources, most of which are in the WUS. A major advance in the new maps is the use of geologic slip rates to determine fault recurrence rates. We have used slip rates from about 450 faults (Figure 2) or fault segments in the new maps.
A site spacing of 0.1 degrees in latitude and longitude was used for the WUS and 0.2 degrees for the CEUS (finer spacing of 0.05 degrees was used for the California maps). This resulted in hazard calculations at about 65,000 sites for the WUS runs and 35,000 sites for the CEUS runs. After interpolation for the CEUS, a grid of hazard curves with 0.1 degree spacing was obtained for the entire conterminous U.S. This grid consisted of hazard curves for about 150,000 sites.
The maps were constructed from the mean hazard curves, that is, the mean probabilities of exceeedance as a function of ground motion or spectral response. Figure 3 shows a set of mean hazard curves used in making the maps. 10% PE in 50 years corresponds to an annual frequency of exceedance of 2.1 x 10-3; 5% PE in 100 years corresponds to 1.03 x 10-3; and 2% PE in 50 years corresponds to 4.04 x10-4 .The sites in this plot with highest hazard are San Francisco and Los Angeles. The lowest hazard site in this plot is St. Paul, Minnesota. This figure shows the general difference in slope of the hazard curves of the CEUS versus the WUS, which is largely caused by the difference in attenuation relations.
The basic procedure for constructing the CEUS portion of the hazard maps is diagrammed in Figure 4. On the left side we considered four alternative models of hazard. Models 1-3 are based on the spatially-smoothed historical seismicity with different magnitude cutoffs and completeness times. Frankel (1995) describes how the hazard is calculated directly from the smoothed historic seismicity. Model 1 is based on mb 3.0 and larger earthquakes since 1924. Model 2 is derived from mb 4.0 and larger earthquakes since 1860. Model 3 is produced from mb 5.0 and larger events since 1700. We primarily used the NCEER catalog of CEUS earthquakes (Seeber and Armbruster, 1991). Model 1 is assigned a weight twice that of the other models. Model 4 uses large background source zones to quantify hazard in areas with little historic seismicity. These background zones consist of an extended margin zone and a stable craton zone (see Frankel et al., 1996; Wheeler, 1995; Johnston et al., 1994). Maximum magnitudes in the calculations differed between these two zones, with a Mmax (M is moment magnitude) of 7.5 in the extended margin and 6.5 in the stable craton, except for Wabash Valley. There are some special cases to this methodology, including an areal source zone for eastern Tennessee. We used a weighting scheme that varies spatially so that the inclusion of the background zones does not lower the hazard estimates in higher-seismicity regions (see Frankel et al., 1996). The results from the models were summed so that the overall earthquake rate was approximately equal to the historic rate.
Model 5 gets full weight and represents the hazard from specific sources. The recurrence rates for these sources was largely determined from paleoseismology. For New Madrid we added the hazard from earthquakes of M8.0 occurring every 1000 years (see Obermeier et al., 1990; Johnston and Schweig, 1996; Johnston, 1996). This is within the magnitude and recurrence range estimated from paleoliquefaction events. Similarly, we used M7.3 events in Charleston, South Carolina with a recurrence time of 650 years (see Amick and Gelinas, 1991). We also added the hazard from the Meers and Cheraw faults based on geological information on their recurrence rates (see Frankel et al., 1996).
Note: the California portion of the hazard maps was produced jointly by us and Mark Petersen, Chris Cramer and Bill Bryant of the California Division of Mines and Geology (see Petersen et al., 1996).
The scheme for mapping hazard in the WUS is shown in Figure 5. On the left side we consider hazard from earthquakes with magnitudes less than or equal to moment magnitude 7.0. For most of the WUS, we used two alternative models: 1) smoothed historical seismicity (weight of 0.67) and 2) large background zones (weight 0.33) based on broad geologic criteria and workshop input. Again, a spatially-varying weighting scheme was used so that including the background zones did not lower the hazard estimates for areas with relatively high seismicity. We also added the hazard from shear zones extending from the northern end of the Death Valley fault (CA) through the Tahoe-Reno NV area through northeast California ending at the latitude of Klamath Falls, OR (see Frankel et al., 1996).
We then added the hazard from about 450 Quaternary faults or fault segments (right side of Figure 5; Figure 2). We considered faults where geologic slip rates have been determined or estimates of recurrence times have been made from trenching studies. We have compiled a table of the parameters used in the hazard calculations, along with references (see our Internet Web site). For California a consensus process of experts was employed to develop fault parameters for the hazard maps (see Working Group on Northern California Earthquake Potential, 1996; McCrory, 1996; Petersen et al., 1996, and references therein).
For faults with known segmentation (e.g. San Andreas, Wasatch faults) we used a characteristic model where the recurrence times are determined for single-segment rupture. For the San Andreas and Hayward faults we also used multiple-segment rupture scenarios. Most of the faults have not been sufficiently studied to know their rupture segmentation. For these faults, we use two alternatives to calculate recurrence times and magnitudes: 1) characteristic rupture of the entire fault length and 2) Gutenberg-Richter recurrence relation with a minimum magnitude of 6.5 and a maximum magnitude corresponding to rupture of the entire fault. The recurrence times for both recurrence models were determined from the geologic slip rates.
We considered two alternative scenarios for great earthquakes on the Cascadia subduction zone. For both scenarios we assumed that the recurrence time of rupture at any point along the subduction zone was 500 years. This time is in or near most of the average intervals estimated from coastal and offshore evidence (see, e.g., Atwater and Hemphill-Haley, 1996). The first scenario (weight 0.67) is for the rupture zones of moment magnitude 8.3 earthquakes to fill the entire subduction zone every 500 years. The second scenario (weight 0.33) we used is a moment magnitude 9.0 earthquake rupturing the entire Cascadia subduction zone every 500 years, on average.
Whenever possible we used more than one ground-motion attenuation relation in the hazard maps. Figure 6 lists the various relations used in the maps. Different attenuation relations were used in the CEUS than the WUS. Special attenuation relations were required for Cascadia subduction zone earthquakes and deep, intra-slab events beneath Puget Sound. When multiple relationships were used, they were assigned equal weights. The WUS relations were determined empirically from strong-motion data, while the CEUS relations were derived from random vibration theory and path properties determined from small earthquakes.
The reference site condition for the maps was a firm-rock site with an average shear-wave velocity of 760 m/sec in the top 30m. This corresponds to the boundary between NEHRP B and C sites (see Martin and Dobry, 1994). This is a typical rock site for the western U.S. The Toro et al. (1997) attenuation relations for hard-rock sites in the CEUS were adjusted to the B-C site by using amplification factors derived from a hypothesized velocity profile (see Frankel et al., 1996).
We calculated uniform hazard spectra (UHS) at the 150,000 sites used in the maps, for spectral accelerations at periods of 0.1, 0.2, 0.3, 0.5, 1.0 and 2.0 sec. Figure 8 shows the uniform hazard spectra for several cities, for 10% and 2% PE's in 50 years. For 10% PE in 50 years, San Francisco and Los Angeles have the highest hazard spectra of this set, Seattle and Salt Lake City are about equal, and Memphis is lower at all periods. The UHS for the WUS cities decreases as the period shortens from 0.2 to 0.1 sec. The UHS for CEUS cities usually increase from 0.2 to 0.1 sec. This has been noted in previous studies and is caused by the lower attenuation in the CEUS relative to the WUS.
For 2% PE in 50 years, the UHS for Salt Lake City is somewhat higher than that for Los Angeles, because of the effect of the Wasatch fault, which has recurrence times of 1500-2500 years for each segment and is located adjacent to Salt Lake City. At 0.1 sec, the UHS for Memphis is comparable to those of San Francisco, Salt Lake City, Los Angeles and Seattle.
We mapped the ratios of the spectral accelerations at various periods in the UHS for 2% PE in 50 years. The map of the ratio of the 0.1 sec to 0.2 sec SA is shown in Figure 9. This ratio is generally higher in the CEUS than the WUS, because of the lower attenuation of high frequency seismic energy in the CEUS along the path and under the site. For the CEUS, this ratio is higher at sites near clusters of historic seismicity (compare Figures 2 and 9). Figure 10 depicts the map of the ratio of 0.2 sec to 1.0 sec SA. For this ratio, there is no systematic difference between the CEUS and the WUS. Higher values of 0.2 to 1.0 sec SA ratio correlate with clusters of seismicity in the CEUS. Sites near clusters of seismicity in the CEUS have UHS that are enriched in short-period (· 0.2 sec) levels, because the hazard at these sites is dominated by smaller (M<6.5), close-in (< 100 km) earthquakes with large amounts of high-frequency energy relative to their low-frequency energy. We will discuss this further in the description of de-aggregation below.
We have also calculated spectral response values for 4.0 sec period. Since many of the attenuation relations in Figure 6 do not go up to 4.0 sec period, we could only use one relation for the CEUS (Frankel et al., 1996) and one for the WUS (Sadigh et al., 1997). We are not aware of any attenuation relations for 4.0 sec for subduction zone earthquakes and intra-slab events for rock sites. Therefore, we did not include these sources in our calculations for 4.0 sec. We also re-did our calculations for 2.0 sec period with the same two attenuation relations as for the 4.0 sec values, so that we could fairly compare the two periods. Figure 11 shows a map of the ratio of 2 sec to 4 sec spectral accelerations. The most obvious feature in this map is the 1000 km radius disk centered on New Madrid, MO. This highlights the dominance of M8.0 earthquakes at New Madrid in the hazard at these long periods for most of the CEUS. The 1000 km limit is an artifact of the maximum distance we used in the hazard calculation. The dominance of the New Madrid events with M8.0 causes an enrichment in 4 sec amplitude relative to the 2 sec levels in a broad region within 1000 km of New Madrid. Designers of long-period structures in the CEUS should be aware of the importance of New Madrid M8.0 earthquakes to the long-period hazard estimates.
We have de-aggregated the hazard to examine the contribution
to hazard as a function of magnitude and distance. These plots can be useful
for specifying design earthquakes from a probabilistic analysis. We show some
de-aggregation plots for New York City and Chicago in Figure 12. The height
of each bar on these plots represents the percent contribution of that magnitude
and distance bin to the annual rate of exceeding the ground motion corresponding
to the specified probability level (e.g., 10% PE in 50 years). The total probabilistic
hazard (annual frequency of exceedance) is the sum over all of these magnitude,
distance bins. The de-aggregation results are often described in terms of
the mean magnitude 
and mean distance 
(pronounced
M bar and D bar). It has been suggested that 
and
be used to
specify a design earthquake. Modal magnitude and distance have also been proposed
as design input.
The de-aggregation plot for New York City (Figure 12)
for 0.3 sec SA shows that most of the hazard is from close-in (< 100 km
distance) smaller earthquakes (M< 6.5). 
is 6.0 and 
is 47 km for
this period and PE. For 1.0 sec SA, more distant and larger events are important
to the hazard estimate and 
and
are larger
than for the 0.3 sec SA. In general, as the period of the SA is increased,
larger, more distant earthquakes have more contribution to the hazard at a
site.
The de-aggregation plots for Chicago (Figure 12) show two overall peaks: one for nearby
smaller earthquakes and one for M8.0
earthquakes in New Madrid at about 550 km distance. The New Madrid events
clearly dominate the hazard at 1.0 sec SA for Chicago. The height of the bins
for the New Madrid earthquakes could be reduced somewhat if we assumed some uncertainty in the magnitudes
of these large events, but the total contribution of these earthquakes to
the hazard would remain the same. 
and
for 1.0 sec
SA (2% PE in 50 years) are 7.2 and 360 km, respectively, and are averages
between the peak for close-in events and the peak for the New Madrid earthquakes.
For 0.2 sec SA (2% PE in 50 years), the hazard at Chicago is dominated by
close-in smaller earthquakes, with the New Madrid events having a smaller
relative contribution than at 1.0 sec. As the probability is increased to
10% PE in 50 years, the New Madrid events become more important to the hazard
at 0.2 sec. As the PE is raised, the probabilistic ground motions decrease,
and more distant events contribute more to the hazard at most locations.
One problem with using 
and
to specify
a design earthquake is that for sites with bi-modal de-aggregations (e.g.,
Chicago for 0.2 sec SA with 10%PE in 50 years and 1.0 sec SA with 2%PE in
50 years), 
>and
produce an
average result that has no physical meaning for design purposes. For such
de-aggregations, it is better to have two design earthquakes corresponding
to the two peaks in the de-aggregation plot.>
We have calculated 
and 
for all the
sites used to make the hazard maps. Figure 13 contains the maps for the CEUS
of 
and
for various
periods, for 2% PE in 50 years. At
shorter periods (· 0.3 sec), the 
map looks much
like a map of seismicity (Figure 1) with small 
values for
sites near clusters of seismicity. This 
map also has
similarities to the maps of the ratio of 0.1 to 0.2 sec SA (Figure 9) and
0.2 sec to 1.0 sec SA (Figure 10) from the uniform hazard spectra. These ratios
are higher in areas of smaller 
, indicating enrichment in high-frequency energy in
the UHS for sites close to clusters of historic seismicity.
generally increases with increasing period of
ground motion (Figure 13). At 1.0 sec, the 
for much of
the CEUS is similar to the distance to New Madrid, indicating the dominance
of New Madrid events to the long-period hazard. The 
plots show
increasing 
values for
increasing periods. 
also increases
to about M8.0 as one gets closer
to New Madrid.
Figure 14 displays the de-aggregation plots for Los Angeles and Seattle for 1.0 sec spectral acceleration with 10% PE in 50 years. For Los Angeles (near City Hall), the hazard is dominated by close-in faults such as the Elysian Park blind thrust, the Whittier fault, the Palos Verde fault and the Sierra Madre fault. The San Andreas fault(M7.8) at a nearest distance of 55 km is a smaller, but still significant contributor to the hazard at this period and PE. For Seattle, much of the hazard is from close-in faults such as the Seattle fault. The intra-slab seismicity constitutes about 18% of the hazard. The de-aggregation plot also shows that the great Cascadia subduction earthquakes (M8.3 and 9.0) are a significant portion of the hazard at 1.0 sec to Seattle.
Maps of 
and
for the WUS
for 1.0 sec SA and 2% PE in 50 years are exhibited in Figures 15a and b. For
most of the WUS, 
is between
6.0 and 7.0. Higher values of 
are found for
regions of active faulting. Along the San Andreas fault, 
is higher (7.5-8.0),
reflecting the dominance of the hazard from large earthquakes along this fault.
Along the coast of the Pacific Northwest, 
is between
8.3 and 9.0, indicating the importance of the great Cascadia subduction earthquakes.
The 
map illustrates
that 
in the WUS
basically represents the distance to the nearest fault with significant hazard.
Small values of 
occur for sites
along the major faults.
Tables of the de-aggregation results are available on our website (http://eqhazmaps.usgs.gov/) for about 100 cities in the U.S. A map is displayed on our website showing these cities. The user clicks on a city and the de-aggregation tables are displayed for that city for PGA and 0.2, 0.3, and 1.0 sec SA for 2% PE in 50 years.
We have estimated the uncertainty of the hazard curves for about 35 cities in the CEUS and are beginning uncertainty studies for WUS cities. We used a Monte Carlo simulation method, where we varied different parameters to generate a set of hazard curves for each city. Figure 16 lists the various parameters sampled in the simulations. We used 500 simulations for each city. The earthquake catalog was randomly re-sampled to produce multiple, alternative catalogs for the simulations. Different seismicity models, spatial-smoothing parameters, maximum magnitudes, and b-values were sampled in the simulations. In addition the recurrence times and magnitudes of large events in New Madrid and Charleston were varied. We used a logic tree to determine the values for each simulation. We also considered the epistemic uncertainty in ground-motion attenuation relations, which captures the difference between the attenuation relations proposed by various authors.
Figure 17 displays the 15th, 50th, 85th, and mean hazard curves determined for New York City for 0.2 sec spectral acceleration. We also show the "preferred-value" hazard curve used in the hazard maps, based on preferred parameters and mean hazard values of a sub-set of alternatives. The preferred-value hazard curve is very similar to the mean hazard curve derived from the Monte Carlo simulations.
A map of uncertainties is shown in Figure 18 for selected cities in the CEUS. The diameter of the circle is proportional to the ratio of the 85th to 15th fractile result for the 0.2 sec spectral acceleration at 10% PE in 50 years. This ratio varies from about 2.5 to about 15. In general the uncertainty is larger for cities where there is little or no historic seismicity, such as Houston or Orlando. For these locations there is larger uncertainty because, although these areas have not had damaging earthquakes in the historic record, we do not know if they have the potential for damaging earthquakes.
The availability of the new national seismic hazard maps and associated products presents a unique opportunity to better understand the regional factors that control the seismic hazard in the U.S. With the relatively dense spacing of sites, we can map out various parameters in unprecedented detail for such a large area. We will shortly be releasing large paper copies of the maps and GIS export files. We are also preparing new seismic hazard maps for Alaska and Hawaii.
We thank Rob Wesson for his review of the manuscript and his helpful comments. We thank all of the workshop participants and others who provided feedback and input to the national seismic hazard maps.
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Johnston, A.(1996). Seismic moment assessment of stable continental earthquakes, Part 3: 1811-1812 New Madrid, 1886 Charleston, and 1755 Lisbon, Geophys. J. Int., v. 126, pp. 314-344.
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Johnston, A.C. and E.S. Schweig (1996). The enigma of the New Madrid earthquakes of 1811-1812, Annual Review of Earth and Planetary Sciences, v. 24, pp. 339-384.
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McCrory, P.A. (1996). Evaluation of fault hazards, northern coastal California, U.S. Geological Survey, Open-file Report 96-656, 87 pp..
Obermeier, S., R. Jacobson, J. Smoote, R. Weems, G. Gohn. J. Monroe, and D. Powers (1990). Earthquake-induced liquefaction features in the coastal setting of South Carolina and in the fluvial setting of the New Madrid seismic zone, U.S. Geological Survey, Prof. Paper 1504, 44 pp.
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Figure 1. Seismicity map of the United States, showing mb 3 and above earthquakes since 1924 in the CEUS and M 4 and above earthquakes since 1963 in the WUS. Size of stars is scaled to magnitude. Boundary we chose to divide CEUS and WUS attenuation regions is shown as solid line starting in Montana and ending in western Texas.
Figure 2. Quaternary faults used in the national seismic hazard maps.
Figure 3. Mean hazard curves for selected cities.
Figure 4. Methodology used for the central and eastern United States.
Figure 5. Methodology used for the western United States
Figure 6. Attenuation relations used in the national maps.
Figure 7. Seismic hazard maps with 2%PE in 50 years for (a) 0.1 sec, (b) 0.2 sec, (c) 1.0 sec, and (d) 2.0 sec SA.
Figure 8.Uniform hazard spectra for various cities for (a) 10% PE in 50 years and (b) 2% PE in 50 years.
Figure 9. Map of ratio of 0.1 sec to 0.2 sec SA for 2% PE in 50 years
Figure 10. Map of ratio of 0.2 sec to 1.0 sec SA for 2% PE in 50 years.
Figure 11. Map of ratio of 2.0 sec to 4.0 sec SA for 2% PE in 50 years.
Figure 12. De-aggregation plots for New York City and Chicago, for various periods and PE. Height of bars represents percent contribution to hazard (annual rate of exceedance) for that magnitude-distance bin. Magnitude is given as moment magnitude. Shading on bars indicates contribution to hazard as function of the standard deviation of ground motion above or below the median value for that magnitude and distance. Lightest shade (at top of bars) is greater than two standard deviations above the median value, next darkest shade is 1 to 2 standard deviations, then 0 to 1 standard deviation.
Figure 13. 
maps for the
CEUS for various periods (right) with 2% PE in 50 years.
Figure 14. De-aggregation plots for Los Angeles and Seattle.
Figure 15.(a) 
and (b)
maps for the WUS for 1 Hz SA with 2% PE in 50 years.
Figure 16. Table of parameters varied for Monte Carlo simulations used for uncertainty analysis in the CEUS.
Figure 17. Seismic hazard curves for New York City, 5 Hz SA.
Figure 18. Uncertainty estimates for selected cities in the CEUS derived from the Monte Carlo simulations. Diameter of circle is proportional to the ratio between the 85th and 15th fractiles of the 5.0 Hz SA values at 10% PE in 50 years (scale is shown in key to right).
