Reply to "Comment on 'Statistical Features of Short‐Period and Long‐Period Near‐
Source Ground Motions' by Masumi Yamada, Anna H. Olsen, and Thomas H. Heaton"by Roberto Paolucci, Carlo Cauzzi, Ezio Faccioli, Marco Stupazzini, and Manuela
Villani
By Masumi Yamada, Anna H. Olsen, and Thomas H. Heaton
The comment by Paolucci and colleagues (Paolucci et al. 2011) states that aprobabilistic seismic hazard analysis (PSHA) can provide “reliable prediction oflong‐period spectral ordinates.” The result of such an analysis would be in contrast
to the more uncertain prediction suggested by our empirical, and proposed
theoretical, distribution of near‐source ground displacements in past, large
magnitude earthquakes (Yamada et al., 2009). After addressing two specificconcerns of Paolucci and colleagues, we use the balance of this reply to discuss theapparent differences between a PSHA and our observations. These two approaches
to understanding the seismic hazard of long‐period ground motions —pastobservations and PSHAs— should be consistent, even though they view the problem
from different perspectives.
Paolucci and colleagues prefer to use elastic spectral displacement as the intensity
measure of long‐period ground motions rather than peak ground displacement(PGD). Spectral displacement and PGD, however, are highly correlated. We calculate
the elastic spectral displacements (Sd) of our original set of recorded groundmotions. We first find Sd for each horizontal component over a range of periods
from 3 to 9 s at a 0.02 s interval, with damping at 5% of critical. At each period, wetake the square root of the sum of the maximum squared Sd of each component.
Then we find the geometric mean over three ranges of periods: 3‐5, 5‐7, and 7‐9 s.
We average the spectral displacements in each range to find a more stable measureof the long‐period spectrum. We also calculate pseudo‐Sd from the spectral
accelerations (Sa) reported in the current Next Generation Attenuation database(see Data and Resources Section).1 Figure 1 shows that the logarithms of PGD and Sd
are highly correlated, with correlation coefficients of 0.9405 (3‐5 s), 0.9707 (5‐7 s),
and 0.9750 (7‐9 s) for the records collected in Yamada et al. (2009). Also, we findsimilar correlations of PGD and pseudo‐Sd from the NGA database. We prefer to use
PGD because it is period independent, physically intuitive, and more concise than afamily of spectral curves. Although the value of PGD is certainly sensitive to theprocessing of a recorded ground motion, our conclusions do not depend on
particular values of PGD.
In our original paper, we showed the distributions of peak ground acceleration(PGA) and PGD from near‐source sites (that is, within 10 km of the surface
1 The NGA project chose to employ the GMRotI50 algorithm (Boore et al., 2006) tocombine horizontal components of ground motion. The NGA Sa are reported at
fewer periods than we calculate within the three ranges. Within each range of
periods, we find the geometric mean of the pseudo‐Sd at the periods given in the
NGA database.
1

projection of the rupture, also known as a Joyner‐Boore distance less than 10 km) oflarge magnitude (between 6.5 and 8) earthquakes recorded in the years 1979
through 2004.2 We now add near‐source records from similar sites since 2004
(Table 1), and Figures 2 and 3 update the PGA and PGD distributions, respectively,
with these records. Our updated PGA and PGD distributions are consistent with the
distributions presented in Yamada et al. (2009). In the years 2005 through 2009,
there was no well‐recorded large earthquake. Thus, we would not expect ourobserved distribution of PGD to change significantly. Figures 2 and 3 also overlay
PGAs and PGDs from the near‐source of past events with magnitudes greater than orequal to 6.5 as reported in the current Next Generation Attenuation database (seeData and Resources Section). The NGA distributions are consistent with ourempirical distributions.
Furthermore, we perform statistical tests on the empirical distributions of PGA and
PGD to determine whether they are consistent with log‐normal or log‐uniform
distributions. We apply Lilliefors tests of the null hypothesis that each observed PGA
dataset is drawn from a log‐normal population distribution (Lilliefors, 1967). The
null hypothesis cannot be rejected for the three PGA datasets (YOH2009: p‐value =0.4617; YOH2009 updated: p‐value = 0.8070; PEER NGA: p‐value = 0.3236); theseobserved PGAs could have been drawn from a log‐normal population distribution.
We apply Chi‐square tests of the null hypothesis that each PGD dataset is drawn
from a truncated, uniform population distribution on a logarithmic scale (see, forexample, Devore (2000) Section 14.1). We limit the range of the log‐uniform
distribution because we select records on a limited range of magnitudes. These
distributions, puniform, are defined as:

1, 1.65  log10 PGD  0.05
puniform  0, otherwisefor our original and updated empirical distributions; and1, 1.35  log10 PGD  0.15
puniform  0, otherwisefor the NGA distribution of PGD. The null hypothesis cannot be rejected for the three
PGD datasets (YOH2009: p‐value = 0.2630; YOH2009 updated: p‐value = 0. 2405;
PEER NGA: p‐value = 0.0799); these observations could have been drawn from atruncated, log‐uniform population distribution. To be clear, these statistical tests do
not demonstrate that the population distributions of PGA and PGD in the near‐

2 In our original paper we incorrectly stated the algorithm we use to calculate PGA(or PGD) for the recorded ground motions. We calculate a peak ground measure by
first finding the maximum squared acceleration (displacement) for each horizontal
component time history. The PGA (PGD) is the square root of the sum of the squared
maxima.
2source of large earthquake are log‐normal and log‐uniform, respectively. Rather, theavailable observations are consistent with these population distributions.
There is no question that seismic hazards exist throughout the world. However thequestion of how to conceptualize and quantify these hazards remains. How do we asa seismological and earthquake engineering community understand the likelihoodand intensity of future ground motions? There should be several, distinct
approaches to quantifying seismic hazard, because, if the approaches provide
consistent results, the community can have greater confidence in our understandingof seismic hazard. If these various approaches provide inconsistent results, then wemust identify the source of the inconsistencies and work to improve ourunderstanding.
Returning to the present discussion of future long‐period ground motions, we seek
to determine whether different techniques of quantifying this seismic hazard areconsistent. We begin with an example from recent work of the Tall Buildings
Initiative of the Pacific Earthquake Engineering Research Center (PEER). Theirstudy analyzes the performance—both structural and economic—of forty‐ or forty‐
two‐story buildings designed according to three procedures (PEER, 2010). To thisend, the researchers use five sets of fifteen ground motions to represent five levelsof seismic hazard for a site in downtown Los Angeles (see Data and Resources
Section). The hazard levels are defined by return periods of 4,975, 2,475 (themaximum considered earthquake, MCE), 475 (the design basis earthquake, DBE), 43,
and 25 years. The ground motions representing these hazard levels result fromselecting recorded or simulated ground motions and then scaling them according to
the technique of spectrum matching (Jones and Zareian, 2010). Figure 3 shows the
PGDs that represent the 4,975‐ and 2,475‐year hazard levels compared with theempirical distributions of near‐source displacements. According to the Tall
Buildings Initiative, the 4,975‐year hazard level represents “extremely rare shaking… which is well beyond the ground motion level generally considered in the building
industry” (PEER, 2010). However, when we compare the PGDs representing the4,975‐ and 2,475‐year hazards to our set of observed PGDs, these “rare” groundmotions are smaller than the largest recorded observations. In fact, the geometricmean PGD within the 4,975‐year hazard level (1.00 m) is much smaller than themost extreme observed PGD (2.99 m). Given the considerable number of identified
faults with the capacity to generate large earthquakes—and an unknown number ofunidentified faults—in the Los Angeles basin and proximate areas (Dolan et al.,1995), why are 1‐in‐4,975‐year ground motions for a site in downtown Los Angeles
no larger than worldwide observations from the last thirty years?
We can also compare the PGDs of the ground motions representing the seismic
hazard at a site in downtown Los Angeles to the PGDs of simulated ground motions
resulting from hypothetical ruptures of the Puente Hills fault system. This fault
system underlies downtown Los Angeles and the areas immediately east, and it has
generated at least four large, blind thrust earthquakes in the past 11,000 years(Dolan et al., 2003). Converting this observation to a recurrence interval suggests

3that the Puente Hills fault system generates a magnitude 7.2 to 7.5 earthquake withan average recurrence of 2,800 years. Graves and Somerville (2005) simulated
broadband ground motions throughout the Los Angeles basin from a hypothetical M
7.15 rupture of this fault (see Data and Resources Section). Figure 3 compares the
PGDs at 648 sites for five scenario ruptures with the PGDs of the PSHA describedabove. The Graves and Somerville simulations of a roughly 2,800‐year event
produce numerous PGDs in excess of the PGDs representing the 4,975‐year hazard
level. Granted, the hazard analysis is site‐specific, and the Graves and Somervilleground motions are for sites throughout the Los Angeles basin. However, is ourknowledge of future ground motions at sites in downtown Los Angeles so certainthat it precludes the possibility of displacements at least as large as the largest
displacements in these simulations?
Accurately characterizing the hazard of long period ground motions is important forassessing the performance of long period structures and, in particular, for designingtall buildings in areas of high seismicity. In a recent study, Jones and Zareian (2010)
applied the seventy‐five, spectrum matched ground motions just mentioned toforty‐story building models of a buckling‐restrained braced frame, designed
according to three procedures: the 2006 International Building Code (abbreviated
CBD, following Jones and Zareian); the Los Angeles Tall Buildings Structural Design
Council Alternative Procedures for Tall Buildings (PBD); and the PEER Tall
Buildings Initiative Guidelines (PBD+). Jones and Zareian found that one of the2,475‐year hazard ground motions caused an inter‐story drift ratio (IDR) greaterthan 3%—which they deem the collapse prevention limit—in the PBD building
model. For the same building, three of the 4,975‐year hazard ground motions
induced responses in excess of this limit. For the CBD building model, one 4,975‐
year hazard ground motion induced a response greater than this limit. None of the2,475‐ or 4,975‐year hazard ground motions caused the PBD+ building model toexceed the collapse prevention limit. We assume that the ground motions causing
the largest building responses have the largest PGDs within each hazard level.
Therefore, ground motions with PGDs of roughly 1.3 m or greater can cause forty‐
story building models of buckling‐restrained braced frames, designed with current
techniques, to develop IDRs larger than 3%, the value associated with collapse
prevention.
Jones and Zareian (2010) also applied two sets of nine near‐fault ground motions
from the Graves and Somerville (2005) Puente Hills simulations. Of these eighteen
ground motions: 28% caused the CBD model to exceed the collapse prevention limit;
33% caused the PBD model to exceed this limit; and 50% caused the PBD+ model toexceed this limit. Certainly, non‐linear time history analyses of forty‐story buildings
with different lateral force‐resisting systems—or analyses of tall buildings withmore or fewer stories—will find different cutoffs for ground motions that cause
buildings to exceed their collapse prevention limits. Nonetheless, PGDs of 1‐2 mshould be of concern when assessing tall buildings. A recent PSHA for a site in
downtown Los Angeles at this level of ground displacement seems to beinconsistent with the past thirty years of recorded ground motions and inconsistent4with realistic simulations of ruptures on a well‐studied fault system. If these hazard
assessments are too low, then the calculated probabilities of unsafe building
responses are also too low.
There are well‐known concerns with each model of a PSHA (that is, the definition of
the earthquake sources, magnitude‐frequency relationships, and ground motion
prediction equations). Quantifying the uncertainties associated with each model isrobust for near‐source short‐period ground motions because there is sufficientavailable data from past events to establish that the distribution is approximately
log‐normal and independent of the fault slip. Data on near‐source long‐period
ground motions from large‐slip earthquakes are not so readily available, although
the occurrence of just a small number of large urban earthquakes could dramaticallychange that.
Estimating the probability of near‐source shaking is further complicated by the factthat there are numerous examples of very damaging earthquakes caused by either
unknown or low slip‐rate faults. For example, the 1994 Northridge (Mw 6.7) and2008 Iwate‐Miyagi Nairiku (Mw 6.9; Toda et al., 2010) earthquakes ruptured
previously unidentified faults. In a seismically active region, not identifying a fault
has less severe consequences for short‐period ground motion prediction ascompared to long‐period. Since PGA saturates with magnitude, identifying a “new”
fault would not significantly change the expectation of a reasonably large PGA. If amajor fault is not included in a PSHA, there may be an unaccounted potential for alarger PGD than otherwise expected.
Second, magnitude‐frequency relationships are not well‐constrained at large
magnitudes because of the paucity of data. A PSHA might extrapolate the Gutenberg‐
Richter relationship from frequent events, or place an upper bound on thisrelationship, or define a characteristic earthquake (Kramer, 1996, Section 4.4.1.2).
These various approaches reflect our incomplete knowledge of the recurrence oflarge earthquakes. Propagating this uncertainty to the prediction of future groundmotions should result in greater uncertainties for long‐period—but not necessarily
for short‐period—ground motions. Further, there have been observations of large
slips (and thus large magnitudes) in areas previously believed to have only amoderate seismic hazard. The 1976 earthquake in Tangshan, China (Allen et al.,1984) and the 1995 Kobe earthquake on Awaji Island (Toda et al., 1996) are
examples of this.
Third, there is not a lot of data to define robust ground motion prediction equationsin the near‐source of large earthquakes. We collect 174 near‐source records frompast large earthquakes (146 in Yamada et al. (2009) and 28 additional records here).
In the current Next Generation Attenuation database there are 129 such records,
accounting for only 3.6% of the total database. Ground motion prediction equations
rely on the character of empirical data from larger distances and smaller
magnitudes to inform the predictions of ground motions in the near‐source of large
magnitude earthquakes. These assumptions may not be consistent with scaling5relations for fault slip derived from teleseismic observations of many large
earthquakes.
Not only are the large uncertainties in future long‐period ground motions the resultof a relatively short instrumental record, these large uncertainties result from ourlimited theoretical knowledge of earthquake sources. As shown in our original
paper, magnitude and PGD are correlated in the near source (also see Aagaard andHeaton, 2004). However, the physical quantity measured by magnitude is the
product of crustal rigidity, the rupture area, and the average slip. If we seek apredictive theory for PGD in the near source, we must anticipate the distribution ofslip on a fault (and thus average slip) and anticipate the rupture area. Compilationsof source models (for example, the Finite‐Source Rupture Model Database (Mai2010)) demonstrate that slip can have a considerable spatial variability and that slip
is difficult to reliably estimate, as evidenced by many plausible slip distributions
inferred from the same past event. Theories of slip initiation and termination are
still open to debate, thus making any theoretical prediction of rupture area quite
uncertain. We believe the best current “theory” applicable to the prediction of PGD
in the near‐source are the scaling relations we employed in our original paper.
At present, predictions of future long‐period ground motions from probabilistic
seismic hazard analyses appear inconsistent with—specifically, smaller than—pastobservations and plausible rupture simulations. Perhaps current PSHAs do notproperly account for the inherent uncertainties in predicting near‐source grounddisplacements. These uncertainties exist because near‐source ground displacements
at the surface are strongly correlated with the amplitude of slip on nearby patchesof fault rupture, and anticipating fault slip is highly uncertain given our current
knowledge. Until we have enough data or a reliable theory, any prediction of long‐
period ground motion in the near‐source of large earthquakes will remain highly
uncertain.

Data and Resources
The Pacific Earthquake Engineering Research Center’s Next Generation Attenuation
database flatfile can be downloaded at http://peer.berkeley.edu/nga/. We use
public version 7.3 in this work (accessed 12 June 2010). The strong motion data forthe 2007 Noto‐hanto, 2007 Chuetsu‐oki, 2008 Iwate‐Miyagi Nairiku, and 2009
Suruga‐wan earthquakes were recorded by the K‐NET and KiK‐net seismic
networks, operated by the National Research Institute for Earth Science andDisaster Prevention in Japan (www.kyoshin.bosai.go.jp; last accessed September2010). The dataset of the 2008 Wenchuan earthquake was recorded by the National
Strong Motion Observation Network System of China, managed by the National
Strong Motion Observation Center and local strong motion observation centers(www.csmnc.net/selnewxjx1.asp?id=749; last accessed September 2010).

6

Farzin Zareian, in personal communication of June 2010, provided the seventy‐fiveground motions used in the PEER study of downtown Los Angeles. In a personalcommunication of March 2007, Robert Graves provided the ground motion time
histories described in Graves and Somerville (2005).

References:
Aagaard, B. and T. Heaton (2004). Near‐source ground motions from simulations ofsustained intersonic and supersonic fault ruptures, Bull. Seismol. Soc. Am. 94,
no.6, 2064‐2078.
Allen, C. R., A. R. Gillespie, HAN Yuan, K. E. Sieh, ZHANG Buchun, and ZHU Chengnan(1984, June) Red River and associated faults, Yunnan Province, China:
Quaternary geology, slip rates, and seismic hazard, Geological Society ofAmerica Bulletin 95, 686‐700.
Aoi, S.,B. Enescu, W. Suzuki, Y Asano, K. Obara, T. Kunugi, and K. Shiomi (2010).
Stress transfer in the Tokai subduction zone from the 2009 Suruga Bay
earthquake in Japan, Nature Geoscience, 3, 496‐500.
Aoi, S., H. Sekiguchi, N. Morikawa, and T. Kunugi (2008). Source process of the 2007
Niigata‐ken Chuetsu‐oki earthquake derived from near‐fault strong motion
data, Earth, planets and space 60, no.11, 1131‐1135.
Boore, D.,J. Watson‐Lamprey, N. Abrahamson (2006) Orientation‐independentmeasures of ground motion, Bull. Seismol. Soc. Am. 96, no.4A, 1502‐1511.
Devore, Jay L. (2000) Probability and Statistics for Engineering and the Sciences. 5th
ed. Pacific Grove, CA: Duxbury.
Dolan, J., K. Sieh, T. Rockwell, R. Yeats, J. Shaw, J. Suppe, G. Huftile, and E. Gath (1995).
Prospects for larger or more frequent earthquakes in the Los Angeles
metropolitan region, Science 267, no.5195, 199‐205.
Dolan, J., S. Christofferson, J. Shaw (2003). Recognition of paleoearthquakes on the
Puente Hills blind thrust fault, California, Science 300, no.5616, 115‐118.
Graves, R. and P. Somerville (2005). Broadband ground motion simulations for
scenario ruptures of the Puente Hills fault, Proceedings of the 8th National
Conference on Earthquake Engineering, San Francisco, California, USA, paper
no. 1052.
Jones, P. and F. Zareian (2010). Seismic response of a forty‐story buckling restrainedbraced frame designed for the Los Angeles region, Proceedings of the 2010
Annual Meeting of the Los Angeles Tall Building Design Council, May, 2010,
Los Angeles, CA, 86‐93.

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Koketsu, K., Y. Yokota, H. Ghasemi, K. Hikima, H. Miyake, and Z. Wang (2010). Source
process and ground motions of the 2008 Wenchuan Earthquake. In“Investigation report of the May 12th 2008, Wenchuan earthquake, China,
Grant‐in‐Aid for Special Purposes of 2008, Ministry of Education, Culture,
Sports, Science and Technology (MEXT). No. 20900002.” http://shake.iis.u‐
tokyo.ac.jp/wenchuan/
Kramer, Steven L. (1996) Geotechnical Earthquake Engineering. Upper Saddle River,
New Jersey: Prentice Hall.
Kurahashi, S., K. Masaki, and K. Irikura (2008). Source model of the 2007 Noto‐
Hanto earthquake (Mw 6.7) for estimating broad‐band strong ground motion.
Earth, planets and space 60, no.2, 89‐94.
Lilliefors, Hubert. W. (1967) On the Kolmogorov‐Smirnov Test for Normality with
Mean and Variance Unknown, Journal of the American Statistical Association
62, no. 318, 399‐402.
Mai, P. M. (2010). Finite‐Source Rupture Model Database (SRCMOD).
http://www.seismo.ethz.ch/srcmod/Homepage.html. Accessed 2 July 2010.
Paolucci, R., C. Cauzzi, E. Faccioli, M. Stupazzini, and M. Villani (2011). Comment on“Statistical features of short‐period and long‐period near‐source groundmotions” by Masumi Yamada, Anna H. Olsen, and Thomas H. Heaton, Bull.
Seismol. Soc. Am.
PEER (2010) Implications of performance‐based seismic design of tall buildings,
Proceedings of the 2010 Annual Meeting of the Los Angeles Tall Building
Design Council, May, 2010, Los Angeles, CA, 1‐2.
Suzuki, W., S. Aoi, and H. Sekiguchi (2010). Rupture Process of the 2008 Iwate‐
Miyagi Nairiku, Japan, Earthquake Derived from Near‐Source Strong‐Motion
Records, Bull. Seismol. Soc. Am. 100, no.1 , 256‐266.
Toda S., T Maruyama, M. Yoshimi, H. Kaneda, Y. Awata, T. Yoshioka, and R. Ando(2010). Surface rupture associated with the 2008 Iwate‐Miyagi Nairiku,
Japan, earthquake and its implications to the rupture process and evaluationof active faults, Zisin : Journal of the Seismological Society of Japan 62, no.4,
153‐178 (in Japanese with English abstract).
Toda, Shinji, Ryuta Hataya, Shintaro Abe, and Katsuyoshi Miyakoshi (1996). The
1995 Kobe earthquake and problems of evaluation of active faults in Japan.
Engineering Geology 43, 151‐167.
Yamada, M., A. Olsen, and T. Heaton (2009) Statistical Features of Short‐ and Long‐
Period Near‐Source Ground Motions, Bull. Seismol. Soc. Am. 99, no.6, 3264–
3274.

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Tables:
Table 1. Earthquakes since 2004 that provided near‐source records from large earthquakes. *Earthquake
2007 Noto‐hanto
2007 Chuetsu‐oki
2008 Wenchuan
2008 Iwate‐Miyagi Nairiku
2009 Suruga‐wan

Mw†
6.7
6.6
7.9
6.9
6.4

N
3
10
6
7
2

Focal Depth†
8.0
12.0
19.0
7.8
26.8

Fault Model
Kurahashi et al. 2008
Aoi et al. 2008
Koketsu et al. 2010
Suzuki et al. 2010
Aoi et al. 2010

* Near‐source records are within 10 km of the surface projection of the rupture; large earthquakes arethose with magnitudes greater than or equal to 6.4.
The magnitude and focal depth for the Suruga‐wan earthquake is from the United States Geological
Survey; the magnitudes and focal depths for all other earthquakes are from the Harvard CMT model.
This table augments table 1 in Yamada et al. (2009). (See the Data and Resources Section for
descriptions of the data sources.)†

Figure captions:Figure 1. Peak ground displacement (PGD) versus spectral displacement (Sd) for three ranges of long‐
period (T) Sd: T = 3‐5 s (left); T = 5‐7 s (middle); and T = 7‐9 s (right). Circles represent data from the
NGA database, and crosses represent data from Yamada et al. (2009). For periods of 3‐5s, the slope of
PGD versus Sd is closest to one. For periods of 7‐9 s, the correlation coefficient, R, between the logarithmsof PGD and Sd is largest.

Figure 2. Distributions of recorded peak ground accelerations (PGA). The YOH2009 distribution was
published in Yamada et al. (2009). The “YOH2009 updated” distribution adds records since 2004 to theoriginal distribution. The PEER NGA distribution uses data from the current NGA database. The three
PGA distributions are consistent with a log‐normal distribution. There has been no well‐recorded large
earthquake since 2004, which we expect would change the PGD distribution in Figure 3 but not the PGA
distributions here.

Figure 3. Distributions of recorded peak ground displacement (PGD) at top and box‐and‐whisker plots
for sites in the Los Angeles area at bottom. The “YOH2009,” “YOH2009 updated,” and “PEER NGA”

9

distributions represent the same datasets described in the caption for Figure 2. The three PGD
distributions at the top of this figure are consistent with a truncated log‐uniform distribution. In thebottom plot, we locate the quartiles of three additional datasets. A probabilistic seismic hazard analysis
for a site in downtown Los Angeles used fifteen ground motions to represent the 4,975‐year hazard andan additional fifteen motions to represent the 2,475‐year hazard. Graves and Somerville (2005)
simulated five M 7.15 ruptures on the Puente Hills fault system and generated ground motions at 648
sites in the Los Angeles region (Figures:
10

1

10

1

10

10

0

-1

10

10

0

-1

R = 0.941
10

-1

10

0

S (T = 3-5 s) [m]
d

10

10

0

-1

R = 0.971

-2

10 -2
10

PEER NGA
YOH2009

PGD [m]10

1

PEER NGA
YOH2009

PGD [m]PGD [m]PEER NGA
YOH200910

1

10

R = 0.975

-2

10

-2

10

-1

10

0

S (T = 5-7 s) [m]dFigure 1

10

10

1

10

-2

10

-2

10

-1

10

0

S (T = 7-9 s) [m]
d

10

1

30
YOH2009
YOH2009 updated
PEER NGA

25

Count

20
15
10
5
0

1

10

100

PGA [m/s2]
Figure 2

11

1000

20

Count

15

YOH2009
YOH2009 updated
PEER NGA

10

5

0
0.01

0.1

1

10

1

10

PGD [m]4975-yr2475-yr
M 7.150.01

0.1

PGD [m]Figure 312