Content uploaded by S.Mostafa Mousavi
Author content
All content in this area was uploaded by S.Mostafa Mousavi on Feb 23, 2018
Content may be subject to copyright.
Evaluating the 2016 One-Year Seismic Hazard
Model for the Central and Eastern United States
Using Instrumental Ground-Motion Data
by S. Mostafa Mousavi and Gregory C. Beroza
ABSTRACT
Hazard curves in probabilistic seismic hazard assessment
(PSHA) models are used to quantify seismic hazard by providing
the annual rates of exceedance, the reciprocal of the return
period, as a function of ground-motion levels. Beginning in
2016, the U.S. Geological Survey (USGS) started to produce
one-year PSHA models for the central and eastern United States
(CEUS) to account for the elevated seismicity in this region due
to the wastewater injection. These models have much shorter
return periods (99.5 years) compared to previous models (e.g.,
2475 years for the 2014 model) and consider recent levels of
induced seismicity in their construction. The nonstationarity
in the level and location of wastewater injection, however, should
lead to a change in the rate of induced seismicity, which makes
any time-independent forecast challenging. We assess the 2016
seismic hazard model by comparing the model forecast with the
observed ground motions during a one-year period. For this test,
we use more than 18,000 instrumental strong-motion records
observed during 2016 by 189 stations in the CEUS. We test
the full model by considering the hazard curves in peak accel-
eration and spectral response acceleration for 1 and 5 Hz over
the entire CEUS. Our results indicate that the observed hazard is
generally consistent with that forecast by the model for peak
ground acceleration (PGA) and 1 Hz (except at 5%g)and
5 Hz spectral accelerations. Although we find that the hazard
model is consistent with observed ground motions, this does not
necessarily validate the theories and assumptions used in the
model development. Our results show that for mapped hazard
level (1% probability of exceedance in one year) and using only
one year of observation, the power of a statistical test will not be
very high unless the actual hazard is grossly larger (>6times) or
smaller (<40%) than the forecast hazard. In other words, the
data are still unlikely to reveal the inconsistency between the
observed and forecasted hazards for one-year models with high
confidence, due to the low amount of data at CEUS.
INTRODUCTION
A probabilistic seismic hazard assessment (PSHA) model pro-
vides forecasts of locations, magnitudes, and rate of future
earthquakes and ground-motion exceedances in a specific
region (Cornell, 1968;McGuire, 1976). PSHA models are
widely used for establishing seismic building codes, risk assess-
ments, and other public policy applications (Petersen et al.,
2015); however, the difficulty of testing these models using
observed data has led to questions about the credibility of
PSHA forecasts (e.g., Stein et al., 2011,2012;Hanks et al.,
2012;Stirling, 2012;Frankel, 2013;Iervolino, 2013;Mulargia
et al., 2017).
There have been efforts to evaluate PSHA models using the
observations at different regions, including southern California
(Ward, 1995), Mexico City (Ordaz and Reyes, 1999), New
Zealand (Stirling and Petersen, 2006;Stirling and Gerstenberger,
2010), United States (Stirling and Petersen, 2006;Mak and
Schorlemmer, 2016), Italy (Albarello and D'Amico, 2008;Muc-
ciarelli et al.,2008;Nekrasova et al.,2014;Albarello et al., 2015;
Stein et al.,2015), Japan (Fujiwara et al.,2009;Miyazawa and
Mori, 2009;Brooks et al.,2016), Spain (Mezcua et al.,2013), as
well as France and Turkey (Tasan et al., 2014).
In 2016 and 2017, the U.S. Geological Survey (USGS)
produced a one-year PSHA model for the central and eastern
United States (CEUS; Petersen et al., 2016a,b,2017) to ac-
count for the elevated seismicity in this region attributed to the
wastewater injection. The 2016 model indicated a greater than
1% chance of occurrence of damaging ground shaking (∼0:12
peak ground acceleration [PGA]) near some areas of active-
induced seismicity in 2016 (3- to 10-fold higher than the 2014
model). The one-year models have much shorter return periods
(99.5 years) compared to the previous models (e.g., 2475 years
for the 2014 model) and consider both induced and natural
seismicity in their construction under the assumption of sta-
tionarity for a short time interval; however, the nonstationarity
in wastewater injection should lead to changes in the rate of
induced seismicity (Langenbruch and Zoback, 2016), which
makes any time-independent forecast challenging.
Recent PSHA tests for the United States have focused on
the long-term National Seismic Hazard models (Petersen et al.,
2014). Both Stirling and Petersen (2006) and Mak and Schor-
lemmer (2016) used microseismic intensity data to evaluate
long-term forecasts over the CEUS. Stirling and Petersen
doi: 10.1785/0220170226 Seismological Research Letters Volume XX, Number XX –2018 1
SRL Early Edition
(2006) used a site-specific approach, whereas Mak and Schor-
lemmer (2016) used an aggregated approach that evaluates the
model as a whole. Brooks et al. (2017) and White et al. (2017)
recently compared the hazard from the 2016 one-year model
and observed shaking in Oklahoma and its surrounding.
Brooks et al. (2017) used “Did You Feel It?”(DYFI) data
for 2016 and compared the fraction of sites at which the maxi-
mum ground motion exceeded the values on the seismic hazard
map (intensities associated with a fixed probability of exceed-
ance, one point in the hazard curves of the model) with the
fraction that has been forecasted by the model. The reported
shaking was used to test how well the hazard map performs
without adjustments for site conditions or clustering. On
the other hand, White et al. (2017) used the DYFI and instru-
mental (PGA) data for 2014–2015 and compared them with
the 2016 one-year hazard model for the same region, adjusting
for the declustering and site condition.
In this study, we assess the 2016 one-year probabilistic seis-
mic hazard model fully (PGA, 1 and 5 Hz spectral accelerations
and for wider range of annual rate of exceedances) by compar-
ing the model’s forecast with instrumental ground-motion data
recorded during the one-year forecast period (2016) over entire
CEUS. We test the final model and its constituent submodels
by considering the hazard curves in peak acceleration and in
spectral acceleration at response periods of 1.0 and 0.2 s. The
goal is to evaluate the final output of the 2016 model as it is
presented (mean hazard curve). Exploring and understanding
the uncertainties of the model’s components and their impact
on the final output is not straightforward (e.g., Beauval and
Scotti, 2004;Tasan et al., 2014;Mousavi et al., 2018), especially
in the case of one-year models that comprise two submodels.
Both the quantity and quality of observations affect the per-
formance of the test. To compensate for the relatively low-ob-
served seismicity in CEUS, we use an aggregated approach to
include more data and increase the statistical power of the test.
To insure high-quality data, we use instrumental ground mo-
tions and pay particular attention to completeness, correlation,
and clustering of data. We also estimate the statistical power of
a test using 2016 instrumental data.
MODEL AND OBSERVATION
The 2016 model incorporates two equally weighted submodels
(the informed model and the adaptive model) that include
alternative earthquake inputs for catalog duration, smoothing
parameters, maximum magnitudes, and ground-motion models
(Petersen et al., 2016a). In the informed submodel, earthquakes
are classified as induced or natural, whereas there is no distinc-
tion in the adaptive submodel. The final results are presented
in forms of peak ground acceleration (PGA) and spectral re-
sponse acceleration at 1 Hz (1 s) and 5 Hz (0.2 s) for a uniform
rock site condition (VS30 760 m=s). The model primarily
considers the seismicity rates of 2014 and 2015 as input data
(Petersen et al., 2016b).
To evaluate a model, we need a dataset that has not been
used directly in deriving it. In this study, we use a database of
instrumental ground motions compiled from Mw≥3events
that occurred from 1 January 2016 to 31 December 2016
in the CEUS (Gupta et al., 2017) to test the forecast. Figure 1
presents the distribution of recorded ground motions used in
this study. The stations recording these ground motions were
equipped with accelerometers, seismometers, or both. For sta-
tions having both accelerometer and seismometer instruments,
just the accelerometer data are used. For stations without
accelerometers, high-gain seismograms with sampling rates of
40 Hz and higher were collected and, after removing the trends
and mean, instrument responses were deconvolved to obtain
horizontal acceleration seismograms. The data were band-
passed filtered between 0.3 and 20 Hz, and only high-quality
traces (signal-to-noise ratio ≥2) were retained to compute the
RotD50 median ground-motion spectral amplitudes (Boore,
2010) and measured PGA and response spectral values (1 and
5 Hz). Most of the stations in the CEUS are on soft sediments
(VS30 <760 m=s), and out of 18,000 records only ∼1100
▴Figure 1. Magnitudes and distances of the considered ground
motions.
0 20 40 60 80 100 120 140 160 180 200
Distance (km)
10–5
10–4
10–3
10–2
10–1
PGA (%g)
Shahjouei and Pezeshk (2016)
Atkinson (2015)
▴Figure 2. Observed peak ground acceleration (PGA) values for
all events (and magnitude range) in the dataset and the median
estimated accelerations using the ground-motion prediction
equation (GMPE) of Atkinson (2015) (magenta) and Shahjouei
and Pezashk (2016) (cyan).
2 Seismological Research Letters Volume XX, Number XX –2018
SRL Early Edition
have been recorded on very dense-soil or soft-rock sites. Hence,
observed ground-motion amplitudes were corrected to a nomi-
nal site condition of VS30 760 m=s(the site condition
considered in the 2016 model), using the approximate VS30
values of Wald and Allen (2007) and the site amplification
model of Seyhan and Stewart (2014).
In our analyses, we use data only from stations that com-
pletely reported all expected ground motion during 2016 that
was sufficiently high to be recorded by sensors. We checked the
completeness of data during the operational time of each
station using the catalog (Incorporated Research Institutions
for Seismology) of seismicity in 2016 and a ground-motion
prediction equation (GMPE). Atkinson (2015) proposed one
of the GMPEs that is used most commonly for small-to-
moderate events in CEUS. Gupta et al. (2017) studied this
GMPE using ground-motion data and concluded that,
although the Atkinson’s equation provides a good fit at hypo-
central distances of less than 60 km, a scaled version of a
GMPE proposed by Shahjouei and Pezeshk (2016) better
captures the geometric spreading of ground motions at larger
distances for both induced and tectonic events (Fig. 2). Hence
in this study, we use a scaled version of the GMPE proposed by
Shahjouei and Pezeshk (2016) for all ground-motion estima-
tion. The final dataset includes just stations that recorded all
ground motions corresponding to the predicted PGA larger
than 0:001g. Our analysis indicates 189 out of 197 stations are
complete, resulting in a final database of more than 18,000
strong-motion records. The spatial distribution of earthquakes
and stations in the final dataset is presented in Figure 3.
METHODOLOGY
Iervolino (2013) showed that for a meaningful test of seismic
hazard forecast at a site, one needs a time span of continuous
observation equal to 10 times the return period, assuming 10
observations are sufficient to get a good estimate of the return
frequency. Hence, in practice it is impossible to evaluate a
probabilistic seismic hazard forecast with observations (Beauval
et al., 2008). For this reason, site-specific approaches for testing
seismic hazard models (e.g., Ordaz and Reyes, 1999;Stirling
and Petersen, 2006;Stirling and Gerstenberger, 2010;Mezcua
et al., 2013) do not provide a powerful means of validation
(Mak et al., 2014).
An approach to overcome this shortage is to aggregate all
data available at different sites and test the performance of the
model for a region as a whole to increase the power of the test at
the cost of losing spatial resolution (e.g., Albarello and D'Amico,
2008;Tasan et al.,2014;Albarello et al., 2015;Mak and Schor-
lemmer, 2016). In our study, we follow this approach to com-
pensate for the problem of having a too-short observation time
window by aggregating all data and sampling in space.
In the aggregated approach, hazard curves are constructed
by summation of individual forecast or observed hazard curves
over multiple sites. Following Albarello and D'Amico (2008),
Tasan et al. (2014),andMak and Schorlemmer (2016),weex-
press aggregated hazard curves as the number of sites with ex-
ceedances (i.e., sites with at least one exceedance during the
observation period), instead of the number of ground-motion
exceedances, to eliminate the potential effect of aftershocks
and small earthquakes that are not included in the 2016 model.
This is in line with the PSHA results that usually are presented
as the probability that an acceleration level will be exceeded “at
least once”over a time window; however, this approach follows
this assumption that the ground-motion exceedances at different
sites generated by one earthquake are stochastically independent,
and that data are uncorrelated. This assumption can be valid for
stations that are sufficiently apart. The choice of minimum in-
tersite distance for defining independent sites depends on the
ground-motion distance-decay rate and maximum earthquake
size in the population. Albarello and D'Amico (2008) used
50 km minimum intersite distance for Italy, Tasan et al. (2014)
used 10 km, and Mak and Schorlemmer (2016) used 50 km for
CEUS. In this study, we use 45 km, based on the decay of the
PGA values by distance (Fig. 2).
To account for the data correlation in our statistical com-
parison, we follow the approach used by Mak and Schorlemmer
(2016) and suppressed the correlation by discarding sites that
are too close to each other. In this procedure, a set of sites with
intersite distances of at least 45 km is selected in a random
process. To account for different combinations of independent
sites in the analysis, we repeated this process 500 times to gen-
erate 500 realizations of a set of independent sites. The number
of sites in each set ranges from 71 to 78 stations. The spatial
distribution of the independent sites for two different sets is
presented in Figure 4. The difference is mainly in Oklahoma
and the New Madrid Seismic Zone where denser seismic net-
works exist. The independency of sites was further constrained
by excluding multiple exceedances due to one earthquake.
The site-specific hazard curves in the one-year models are
presented as the annual rate of exceedance for different ground-
motion levels (e.g., PGA). For each set of independent sites, the
aggregate observed hazard is simply constructed by counting
the number of ground motions that exceeded different ground-
motion levels l
EQ-TARGET;temp:intralink-;df1;323;289Hobs X
M
i
1∃j:oij ≥l;1
in which Mis the number of stations in each independent set,
oij is the value of ground-motion jat site i,lrepresents the
ground-motion levels given by the hazard model, and 1(…)
is the indicator function that takes the value one when the
statement inside the bracket is true or zeros otherwise.
The expected number of sites with exceedance and the
corresponding aggregated forecast hazard is given by the
Poisson binomial distributed variable
EQ-TARGET;temp:intralink-;df2;323;143Hfor X
M
i
Bp;2
in which Bpare independent Bernoulli distributed variables,
each having a different probability of success p.pis calculated
Seismological Research Letters Volume XX, Number XX –2018 3
SRL Early Edition
based on the Poisson distribution that is assumed in the
model
EQ-TARGET;temp:intralink-;df3;40;104
pobserving at l east one exceedance at
site iduring time interval t1−e−λi;3
in which λiis the annual rate of exceedance at site iobtained
from the PSHA model. To calculate the probability of observing
at least one exceedance at site iduring the observational period ti,
we compute the distribution function using Monte Carlo sim-
ulations similar to Tasa n et al. (2014), as illustrated in Figure 5.
▴Figure 3. (a) Locations of seismic stations used in this study, color coded based on their VS30; and (b) spatial distribution of earthquakes.
4 Seismological Research Letters Volume XX, Number XX –2018
SRL Early Edition
▴Figure 4. Spatial distribution of independent stations in (a,b) two different sets.
Seismological Research Letters Volume XX, Number XX –2018 5
SRL Early Edition
RESULTS
In this study, we used 5000 runs to sample the probability
distribution that describes the expected number of sites with
exceedance. A stability test (not shown in article) showed that
5000 runs are large enough to get stable results. To compare
the observed and forecast number of sites with exceedance, we
use the 5%–95% forecast interval expressed by the 5% and 95%
quantiles of the probability distribution. The forecast would be
inaccurate if the observed hazard falls systematically outside
this interval.
The variation of aggregated observed and forecast hazards
as a function of the ground-motion level for a few sample sets
of independent sites is given in Figure 6. The observed hazard
during 2016 mostly falls within the forecast hazard interval at
all ground-motion levels for PGA and spectral accelerations
(Fig. 6a–c). The aggregated hazard from the informed submo-
dels tends to be lower than the adaptive one, whereas the
hazard from the final model lies between the submodels. The
observed hazards for PGA and spectral accelerations (1 and
5 Hz) are mostly within the forecast intervals for the final
model and adaptive submodel.
Figure 6shows that the aggregated hazard obtained from
different sets of independent stations can be different, as
should be expected. For this reason, we present the observed
and forecast hazards at a few fixed ground-motion levels for
500 sets of independent stations obtained from Monte Carlo
sampling in Figure 7. A similar overall trend can be seen from
the Monte Carlo samples in which the observed hazard mostly
falls within the forecast intervals for PGA and 5 Hz, indicating
a good agreement between the observed and forecast hazards;
however, at 1 Hz, the observed hazard decreases. This migra-
tion of hazard level is partially (for >0:01g) captured by the
forecasts at 1 Hz (which is lower than the forecast PGA). The
GMPEs could cause the overestimation of the 1-Hz spectral
acceleration at lower ground-motion levels (Delavaud et al.,
2012). A similar pattern was observed for 1-Hz spectral accel-
eration in the 2014 model (Mak and Schorlemmer, 2016).
When comparing two quantities, the result of a statistical
test could be due to chance, and the chance increases if two
quantities are not significantly different with respect to the avail-
able data (Mak and Schorlemmer, 2016). One can quantitatively
estimate the resolving power of a PSHA test by calculating its
statistical power given the available data (Mak et al.,2014). The
▴Figure 5. The Monte Carlo sampling process for calculating Poisson binomial distribution at individual ground-motion level l. (a) Con-
structing the Poisson probability distribution using the annual rate of exceedance (λ) from the site-dependent model at each run to
estimate the number of exceedances (Nexc ) at each site, (b) sampling of the distribution and calculating number of sites with at least
one exceedance (Nsites) for each run, and (c) constructing the probability distribution for the number of sites with at least one exceed-
ance. Red circles on the final probability distribution (c) represent 5% and 95% quantiles.
6 Seismological Research Letters Volume XX, Number XX –2018
SRL Early Edition
▴Figure 6. The forecast and observed number of sites with exceedance for five random sets of independent sites for (a) PGA, and
(b) spectral acceleration (SA) at 1 Hz and (c) SA at 5 Hz.
Seismological Research Letters Volume XX, Number XX –2018 7
SRL Early Edition
▴Figure 7. Observed and forecast aggregated hazards for 500 Monte Carlo samples (sets of independent sites) at six different accel-
eration levels for (a) PGA, and (b) SA at 1 Hz and (c) SA at 5 Hz.
8 Seismological Research Letters Volume XX, Number XX –2018
SRL Early Edition
statistical power is defined as the probability that a testcan reveal
the misfits between two quantities knowing that they are
different.
Figure 8shows the statistical power of the test for one
Monte Carlo sample. Assuming that the actual hazard
(Hact)isKtimes larger the forecast (Hfor), we calculate
pHK
act >q1−α (for upper one-tail test) and
pHK
act <qα (for lower one-tail test), in which qis the quan-
tile function of the forecast hazard, and αis the probability of
having an incorrect rejection of the null hypothesis (i.e., the
probability of committing a type I error). The αvalues of 0.1,
0.05, or 0.01 are widely used. In this study, we use α0:05.
The statistical power for the upper one-tail test represents
the probability for the test to reveal an underestimated hazard
forecast, whereas the power for the lower one-tail test addresses
the probability for the test to reveal an overestimated hazard
forecast. Figure 8shows that if the forecast is wrong (by a factor
of K) how likely the test will be able to reject it. A useful test
should have a high power (probability) of revealing inconsis-
tencies between the actual hazard and the forecast.
Figure 8shows that for the annual rate of exceedance of 2,
if the actual hazard (in terms of occurrence rate) is <0:9or
>1:45 times of the forecast hazard, the test will have a >90%
chance of rejecting the hazard model. Up to a one-year return
period, the lowest power at this return period (associated with
Hact 1:3Hfor) is still higher than 50%. The statistical power
decreases as the return period increases (annual rates get
smaller). We obtained very similar results using α0:01
and 0.1.
To check the possible influence of aftershocks on test re-
sults, we repeated the test for a declustered PGA dataset. We
use a declustered USGS catalog of seismicity (used in the 2017
one-year model) to identify acceleration records associated
with mainshocks. A total of 3190 strong-motion records on
92 stations from 122 mainshocks were identified in the dataset.
Results of the test and its statistical power are presented in
Figures 9and 10, respectively. The results are very similar to
the results without declustering, indicating no influence of
aftershocks on test results. However, considering the whole
dataset (without declustering) can result in a slightly higher
statistical power for smaller return periods.
CONCLUSIONS
We evaluated the one-year seismic hazard model of 2016 for
the CEUS using instrumental ground-motion data. We tested
the final model and its constituent submodels for PGA and
spectral accelerations at 1 and 5 Hz. Our results agree with
other studies (Brooks et al., 2017;White et al., 2017) and in-
dicate that the observed hazard generally agrees with model
forecasts for peak acceleration and spectral acceleration at 1 Hz
(except at 5%g) and 5 Hz. Although the test has relatively high
power for revealing differences between the observation and
forecast for most of the scenarios, its power is low for the re-
turn periods greater than 5 years (annual rates of exceedance
smaller than 0.2) using only one year of data. The aggregated
methods, such as used in this study, provide direct evidence to
evaluate a model as a whole but do not necessarily evaluate the
components of assumptions of the model (e.g., Schorlemmer
et al., 2007).
One-year hazard maps have shorter return periods to
represent the short-term seismic hazard than typical PSHA
maps; however, we find that, even for this hazard level (1%
probability of exceedance in one year), the power of the test
will not be very high unless the actual hazard is grossly larger
(>6times) or smaller (<40%) than the forecasted hazard. In
other words, the tests are unlikely to reveal an inconsistency
between the observed and forecast hazards with high confi-
dence at this hazard level. Therefore, for the one-year forecasts
(short-term seismic hazard prediction), the amount of data in
CEUS is still too small for almost any reasonable observation
to differ from the forecast in a statistical sense, even if the fore-
cast is moderately wrong (by a factor of smaller than 6). This is
not a problem of the test itself; rather, it is about a consequence
of the limited data for the region. We conclude that the seismic
hazard maps produced remain difficult to validate against data.
DATA AND RESOURCES
The hazard models are from https://earthquake.usgs.gov/
hazards/hazmaps/ (last accessed August 2017). Ground-
motion data were collected from Incorporated Research Insti-
tutions for Seismology (IRIS) Data Services (DS; http://ds.iris.
edu/ds/nodes/dmc/, last accessed May 2017). The facilities of
IRIS-DS, and specifically the IRIS Data Management Center,
were used for access to waveform, metadata, or products
required in this study. The IRIS-DS is funded through the
National Science Foundation (NSF) and specifically the GEO
Directorate through the Instrumentation and Facilities
Program of the NSF. S. M. Hoover, from the U.S. Geological
▴Figure 8. The statistical power of the test under different hy-
potheses (represented by the ratio of the true to the forecast rate,
K) for the test assuming α0:05 (the probability of committing a
type I error); contour intervals are 10%.
Seismological Research Letters Volume XX, Number XX –2018 9
SRL Early Edition
Survey (USGS) National Seismic Hazard program, provided
individual logic-tree branches of the one-year models. Figures 3
and 4were prepared using Generic Mapping Tools (Wessel
et al., 2013). Computations of statistical power were done us-
ing the package poibin (cran.r-project.org/web/packages/
poibin, last accessed October 2017) of R (www.R-project.org,
last accessed October 2017). The declustred seismicity
catalog was obtained from the USGS National Seismic Hazard
program (https://www.sciencebase.gov/catalog/item/58afd512
e4b01ccd54fb2587, last accessed October 2017). This study
was supported by the Stanford Center for Induced and Trig-
gered Seismicity.
▴Figure 9. Observed and forecast aggregated hazards for 500 Monte Carlo samples (sets of independent sites) at six different accel-
eration levels for declustered PGAs.
10 Seismological Research Letters Volume XX, Number XX –2018
SRL Early Edition
ACKNOWLEDGMENTS
The authors are grateful to S. Mak for help and discussion on
calculating and interpreting the statistical power. The authors
thank Abhineet Gupta and Jack Baker for providing ground-
motion data and ground-motion prediction equations
(GMPEs). The authors would like to thank Mark Petersen,
Jack Baker, and William Ellsworth for discussions and com-
ments during this study. The authors thank Hilal Tasan and
an anonymous reviewer for insightful remarks and comments.
REFERENCES
Albarello, D., and V. D'Amico (2008). Testing probabilistic seismic
hazard estimates by comparison with observations: An example
in Italy, Geophys. J. Int. 175, 1088–1094.
Albarello, D., L. Peruzza, and V. D. Amico (2015). A scoring test on
probabilistic seismic hazard estimates in Italy, Nat. Hazards Earth
Syst. Sci. 15, 171–186.
Atkinson, G. M. (2015). Ground-motion prediction equation for small-
to-moderate events at short hypocentral distances, with application
to induced seismicity hazards, Bull. Seismol. Soc. Am. 105, no. 2A,
981–992.
Beauval, C., and O. Scotti (2004). Quantifying sensitivities of PSHA for
France to earthquake catalog uncertainties, truncation of ground-
motion variability, and magnitude limits, Bull. Seismol. Soc. Am.
94, 1579–1594.
Beauval, C., P.-Y. Bard, S. Hainzl, and P. Guéguen (2008). Can strong-
motion observations be used to constrain probabilistic seismic-haz-
ard estimates? Bull. Seismol. Soc. Am. 98, 509–520.
Brooks, E. M., S. Stein, and B. D. Spencer (2016). Comparing the per-
formance of Japan’s earthquake hazard maps to uniform and ran-
domized maps, Seismol. Res. Lett. 87, no. 1, 90–102, doi: 10.1785/
0220150100.
Brooks, E. M., S. Stein, B. D. Spencer, L. Salditch, M. D. Petersen, and D.
E. McNamara (2017). Assessing earthquake hazard map perfor-
mance for natural and induced seismicity in the central and eastern
United States, Seismol. Res. Lett. 89, no. 1, 118–126, doi: 10.1785/
0220170124.
Boore, D. M. (2010). Orientation-independent, nongeometric-mean
measures of seismic intensity from two horizontal components
of motion, Bull. Seismol. Soc. Am. 100, no. 4, 1830–1835.
Cornell, C. A. (1968). Engineering seismic risk analysis, Bull. Seismol. Soc.
Am. 58, 1583–1606.
Delavaud, E., F. Scherbaum, N. Kuehn, and T. Allen (2012). Testing the
global applicability of ground-motion prediction equations for
active shallow crustal regions, Bull. Seismol. Soc. Am. 102, no. 2,
707–721, doi: 10.1785/0120110113.
Frankel, A. (2013). Comment on “Why earthquake hazard maps often
fail and what to do about it”by S. Stein, R. Geller, and M. Liu,
Tectonophysics 592, 200–206, doi: 10.1016/j.tecto.2012.11.032.
Fujiwara, H., N. Morikawa, Y. Ishikawa, T. Okumura, J. Miyakoshi, N.
Nojima, and Y. Fukushima (2009). Statistical comparison of national
probabilistic seismic hazard maps and frequency of recorded JMA
seismic intensities from the K-NET strong-motion observation net-
work in Japan during 1997–2006, Seismol. Res. Lett. 80, 458–464.
Gupta, A., J. W. Baker, and W. L. Ellsworth (2017). Assessing ground-
motion amplitudes and attenuation for small-to-moderate induced
and tectonic earthquakes in the central and eastern United States,
Seismol. Res. Lett. 88, 1379–1389, doi: 10.1785/0220160199.
Hanks, T. C., G. C. Beroza , and S. Toda (2012). Have recent earthquakes
exposed flaws in or misunderstandings of probabilistic seismic haz-
ard analysis? Seismol. Res. Lett. 83, no. 5, 759–764, doi: 10.1785/
0220120043.
Iervolino, I. (2013). Probabilities and fallacies: Why hazard maps cannot
be validated by individual earthquakes, Earthq. Spectra 29, no. 3,
1125–1136.
Langenbruch, C., and M. D. Zoback (2016). How will induced seismicity
in Oklahoma respond to decreased saltwater injection rates? Sci.
Adv. 2, e1601542, doi: 10.1126/sciadv.1601542.
Mak, S., and D. Schorlemmer (2016). A comparison between the forecast
by the United States national seismic hazard maps with recent
ground-motion records, Bull. Seismol. Soc. Am. 106, 1817–1831,
doi: 10.1785/0120150323.
Mak, S., R. A. Clements, and D. Schorlemmer (2014). The statistical
power of testing probabilistic seismic-hazard assessments, Seismol.
Res. Lett. 85, no. 4, 781–783, doi: 10.1785/0220140012.
McGuire, R. K. (1976). FORTRAN computer program for seismic risk
analysis, U.S. Geol. Surv. Open-File Rept. 76-67.
Mezcua, J., J. Rueda, and R. M. G. Blanco (2013). Observed and calculated
intensities as a test of a probabilistic seismic-hazard analysis of Spain,
Seismol. Res. Lett. 84, no. 5, 772–780, doi: 10.1785/0220130020.
Miyazawa, M., and J. Mori (2009). Test of seismic hazard map from 500
years of recorded intensity data in Japan, Bull. Seismol. Soc. Am. 99,
no. 6, 3140–3149, doi: 10.1785/0120080262.
Mousavi, S. M., G. C. Beroza, and S. M. Hoover (2018). Variabilities in
probabilistic seismic hazard maps for natural and induced seismicity
in the central and eastern United States, The Leading Edge 37,
no. 2, 141a1–141a9, doi: 10.1190/tle37020810.1.
Mucciarelli, M., D. Albarello, and V. D'Amico (2008). Comparison of
probabilistic seismic hazard estimates in Italy, Bull. Seismol. Soc.
Am. 98, 2652–2664.
Mulargia, F., P. B. Stark, and R. J. Geller (2017). Why is probabilistic seismic
hazard analysis (PSHA) still used? Phys. Earth Planet. Int. 264, 63–75.
Nekrasova, A., V. Kossobokov, A. Peresan, and A. Magrin (2014). The
comparison of the NDSHA, PSHA seismic hazard maps and real
seismicity for the Italian territory, Nat. Hazards 70, 629–641, doi:
10.1007/s11069-013-0832-6.
Ordaz, M., and C. Reyes (1999). Earthquake hazard in Mexico City: Ob-
servations versus computations, Bull. Seismol. Soc. Am. 89, no. 5,
1379–1383.
Petersen, M. D., M. P. Moschetti, P. M. Powers, C. S. Mueller, K. M.
Haller, A. D. Frankel, Y. Zeng, S. Rezaeian, S. C. Harmsen, O.
S. Boyd, et al. (2014). Documentation for the 2014 update of
the United States national seismic hazard maps, U.S. Geol. Surv.
Open-File Rept. 2014-1091, 243 pp., doi: 10.3133/ofr20141091.
▴Figure 10. The statistical power of the test using declustered
data. Kis the ratio of the true to the forecast rate and contour
intervals are 10%.
Seismological Research Letters Volume XX, Number XX –2018 11
SRL Early Edition
Petersen, M. D., M. P. Moschetti, P. M. Powers, C. S. Mueller, K. M.
Haller, A. D. Frankel, Y. Zeng, S. Rezaeian, S. C. Harmsen, O.
S. Boyd, et al. (2015). The 2014 United States national seismic
hazard model, Earthq. Spectra 31, no. S1, S1–S30, doi: 10.1193/
120814EQS210M.
Petersen, M. D., C. S. Mueller, M. P. Moschetti, S. M. Hoover, A. L.
Llenos, W. L. Ellsworth, A. J. Michael, J. L. Rubinstein, A. F.
McGarr, and K. S. Rukstales (2016a). 2016 one-year seismic hazard
forecast for the central and eastern United States from induced and
natural earthquakes, U.S. Geol. Surv. Open-File Rept. 2016-1035,
52 pp., doi: 10.3133/ofr20161035.
Petersen, M. D., C. S. Mueller, M. P. Moschetti, S. M. Hoover, A. L.
Llenos, W. L. Ellsworth, A. J. Michael, J. L. Rubinstein, A. F.
McGarr, and K. S. Rukstales (2016b). Seismic-hazard forecast for
2016 including induced and natural earthquakes in the central
and eastern United States, Seismol. Res. Lett. 87, no. 6, 1327–
1341, doi: 10.1785/0220160072.
Petersen, M. D., C. S. Mueller, M. P. Moschetti, S. M. Hoover, A. M.
Shumway, D. E. McNamara, R. A. Williams, A. L. Llenos, W. L.
Ellsworth, A. J. Michael, et al. (2017). 2017 one-year seismic-hazard
forecast for the central and eastern United States from induced and
natural earthquakes, Seismol. Res. Lett. 88, no. 3, 1–12, doi:
10.1785/0220170005.
Schorlemmer, D., M. Gerstenberger, S. Wiemer, D. D. Jackson, and D. A.
Rhoades (2007). Earthquake likelihood model testing, Seismol. Res.
Lett. 78, no. 1, 17–29, doi: 10.1785/gssrl.78.1.17.
Seyhan, E., and J. P. Stewart (2014). Semi-empirical nonlinear site am-
plification from NGA-West2 data and simulations, Earthq. Spectra
30, no. 3, 1241–1256.
Shahjouei, A., and S. Pezeshk (2016). Alternative hybrid empirical
ground-motion model for central and eastern North America using
hybrid simulations and NGA-West2 models, Bull. Seismol. Soc. Am.
106, no. 2, 734–754.
Stein, S., R. Geller, and M. Liu (2011). Bad assumptions or bad luck:
Why earthquake hazard maps need objective testing? Seismol.
Res. Lett. 82, 623–626.
Stein, S., R. J. Geller, and M. Liu (2012). Why earthquake hazard maps
often fail and what to do about it, Tectonophysics 562/563, 1–25,
doi: 10.1016/j.tecto.2012.06.047.
Stein, S., B. D. Spencer, and E. M. Brooks (2015). Metrics for assessing
earthquake-hazard map performance, Bull. Seismol. Soc. Am. 105,
no. 4, 2160, doi: 10.1785/0120140164.
Stirling, M. W. (2012). Earthquake hazard maps and objective testing:
The hazard mapper’s point of view, Seismol. Res. Lett. 83, 231–232.
Stirling, M., and M. Gerstenberger (2010). Ground motion-based testing
of seismic hazard models in New Zealand, Bull. Seismol. Soc. Am.
100, 1407–1414.
Stirling, M., and M. Petersen (2006). Comparison of the historical record
of earthquake hazard with seismic-hazard models for New Zealand
and the Continental United States, Bull. Seismol. Soc. Am. 96,
1978–1994.
Tasan, H., C. Beauval, A. Helmstetter, A. Sandikkaya, and P. Guéguen
(2014). Testing probabilistic seismic hazard estimates against accel-
erometric data in two countries: France and Turkey, Geophys. J. Int.
198, no. 3, 1554–1571, doi: 10.1093/gji/ggu191.
Wald, D. J., and T. I. Allen (2007). Topographic slope as a proxy for
seismic site conditions and amplification, Bull. Seismol. Soc. Am.
97, no. 5, 1379–1395.
Ward, S. N. (1995). Area-based tests of long-term seismic hazard predic-
tions, Bull. Seismol. Soc. Am. 85, 1285–1298.
Wessel, P.,W. H. F. Smith, R. Scharroo, J. F. Luis, and F. Wobbe (2013).
Generic mapping tools: Improved version released, Eos Trans. AGU
94, no. 45, 409–410, doi: 10.1002/2013EO450001.
White, I. J. O., T. Liu, N. Luco, and A. B. Liel (2017). Considerations
in comparing the U.S. Geological Survey one-year induced-seismic-
ity hazard models with “Did You Feel It?”and instrumental data,
Seismol. Res. Lett. 89, no. 1, 127–137, doi: 10.1785/0220170033.
S. Mostafa Mousavi
Gregory C. Beroza
Department of Geophysics
Stanford University
Stanford, California 94305 U.S.A.
mmousavi@stanford.edu
Published Online 21 February 2018
12 Seismological Research Letters Volume XX, Number XX –2018
SRL Early Edition
