Content uploaded by Nicolas Bastias
Author content
All content in this area was uploaded by Nicolas Bastias on Jan 21, 2016
Content may be subject to copyright.
Evaluation of Ground Motion Prediction
Equations (GMPEs) for Chile Subduction
Zone.
Nicolás BASTÍAS a, Gonzalo A. MONTALVA a,1, Felipe LEYTON b, Esteban SAEZ c,
Francisco RUZd and Pedro TRONCOSOa.
a Universidad de Concepción, Concepción, Chile
b Centro Sismológico Nacional, Santiago, Chile
c Pontificia Universidad Católica de Chile, Santiago, Chile
d Ruz y Vukasovic Ingenieros, Santiago, Chile
Abstract. : In this study we present an evaluation of the performance of the latest
ground motion prediction equations for Chilean subduction zone. Ground-motion
prediction equations (GMPEs) for earthquakes that occur in subduction zones are a
key input to seismic hazard analyses and risk mitigation. In this study, we use
recent large subduction events recorded in Chile, including Valparaiso (Mw 7.9),
Maule (Mw 8.8), Iquique (Mw 8.1) and Southern Peru (Mw 8.4). We use shear-
wave velocity profiles that were obtained for several stations through surface wave
dispersion methods using active and passive sources, this represents a significant
contribution to earthquake hazard mitigation in Chile, as this information is useful
for a number of projects that tribute towards that end. All records were processed
following state of the art procedures to obtain comparable signal to noise level and
detrended records, the processing was performed component by component.
Response spectra of the recorded ground motions were compared with those
predicted by BCHydro [1], Ruiz & Saragoni [2], Atkinson & Boore [3][3],
Boroscheck & Contreras [5] and, Zhao et al. [6] ground motion prediction models.
Results show that at low frequencies BCHydro has the best predictive capacity,
while Zhao et al. is the best performing GMPE for high frequencies. Most of the
tested GMPEs underestimate spectral accelerations.
Keywords. Ground Motions, Megathrust Earthquake Intensities, Chile,
Subduction Zone GMPEs, Ground Motion Prediction Equations.
Introduction
Ground motion prediction equations (GMPEs) are a key component and affect
significantly probabilistic seismic hazard analyses (PSHA) outcomes. Therefore,
evaluate the performance of suitable GMPE models in the region will allow appropriate
selection and weighting of them, better seismic hazard analyses and ultimately lower
earthquake related risk. The GMPEs herein analyzed were obtained in subduction
tectonic environments, the GMPEs selected were Atkinson & Boore [3][4], BCHydro
[1], both of which use world data to fit their models, Zhao et al. [6] that was drawn
from Japanese data, and finally, used two models with only Chilean data; Ruiz &
Saragoni [2] and, Boroschek & Contreras [5].
A dataset including Mw from 5 to 8.8 was compiled, including the largest Chilean
strong motion records. This allows developing a robust evaluation of GMPE in the
1Address: Edmundo Larenas 219, Concepción 4030000, Chile | Email: gmontalva@udec.cl |
Phone: (+56) 41 220 4446
Chilean subduction prone region. The records were processed per component and type
of record (i.e. analog or digital) as described in the next section.
The performance of each GMPE is evaluated using the likelihood approach and
average sample log-likelihood (LLH) values by Scherbaum [7] [8]. The first is based in
the statistics of the distributions of the normalized residuals between predicted values
from GMPEs and observations. The second approach [8], calculates the average sample
log-likelihood differences (as estimators for the Kullback-Leibler (KL) differences, that
represented the difference between two probability distributions and , this is a
measure of the loss of information when is used to estimate , in our case
represents the GMPE model and the observed ground motion data. Residuals were
computed for PGA and pseudo-spectral accelerations at 0.1, 0.4, 1.0 and, 2 seconds.
Inslab and interplate events were analyzed dividing the data as two different subsets.
1. Available Data
A key issue to evaluate ground motion prediction equations is the compilation of a
dataset of empirical ground motion records. For this work, ground motions from Chile
have been selected and processed.
1.1. Ground Motion and Event Characterization
The event information was collected from scientific literature and national/international
seismic agencies. For epicentral locations and depths we used the Centro Sismológico
Nacional (CSN) reports, all events within the dataset are reported by this agency. The
moment magnitudes (Mw) were obtained from the Harvard Centroid Moment Tensor
(CMT, [9]), for events that are not available by CMT we used other magnitude scales
(e.g. Ms) reported by CSN or by International Seismological Centre (ISC), and use
conversion equations by Leyton et al. [10] to convert to Mw.
To define the seismogenesis (i.e., interface, inslab or crustal earthquakes) we first
used the moment tensor reported by the CMT catalog; interface events are associated to
reverse faulting and, inslab events are mostly normal. The above information is
supported also with hypocentral location, it is expected that interface events are located
between the subduction trench and the Chile’s continental coast at ~40-50 km depth, in
the case of inslab are associated to intermediate depths and epicentral location inside
continental Chile.
Closest distance to the fault rupture plane (Rrup) of each event was computed from
finite fault rupture models, compiled by SRCMOD website [11], whenever available.
For events with no published finite fault solution we estimated a rupture plane with the
relationships provided by Strasser et al. [12] that predict the length and width based in
moment magnitude for subduction zone, and located the center of rupture plane in the
centroid reported by CMT. The rupture plane was oriented using the strike and dip
from the CMT catalog.
1.2. Characterization Ground Motion Sites
The main site parameter used by modern GMPEs is Vs30, hence these values and other
geophysical parameters, like predominant frequency (f0), and shear-wave velocity
profile (Vsx) were sought. Efforts to obtain these parameters and characterize the
Chilean GM stations were led by the authors and the Chilean Foundation for
Geotechnical Research (FUCHIGE, [13]); due to space constraints we do not show the
obtained values but they can be accessed freely at [13]. We measured ambient noise
with triaxial geophones, performed active and passive array surveys to invert shear-
wave velocity profiles in more than 20 stations, and referred to the literature ([14]-[17])
for other stations.
For sites without measured Vs30 value, we used their predominant frequency (f0) to
estimate Vs30. The methodology used in this study is discussed in [18], in brief; first, we
computed the S-transform per component and obtained the geometric average of
horizontal components, latter, we smoothed both components, enabling the
computation of the horizontal over vertical spectral ratio. Finally, use the Table 2 of
reference [6] to associate a Vs30 value to each predominant period (T0), here instead of
using one Vs30 value for a range of T0 we linearly interpolate within the range.
1.3. Dataset
The dataset used in this study includes 988 records from 246 earthquakes. Figure 1
shows the relationship between moment magnitude and rupture distance. The dataset
has 725 records from 156 interface events, 19 records from 6 crustal events and 244
records from 84 inslab events. The magnitude range is Mw 5.0-8.8 and, closest distance
range is 25 to 650 kilometers.
Figure 1 Magnitude-distance distribution for Chilean seismic data.
2. Ground Motion Processing
All records have been processed component per component. The pre-processing
sequence is as follows; Analog instruments are instrument corrected [19], then the
record is classified as a late or normal triggered following Pacor et al. [20] proposal,
then spurious spikes are identified [21].
Next in cases were multiple shocks are present on the same record, only the main
shock is kept, including from pre-event noise to coda waves [22], the arrival times of P
and S-waves were picked by visual inspection and, S-waves end time was taken as the
time corresponding to 80% CAV of the record.
To select the low cut-off frequencies, for each component of each record, we
smoothed the S-wave and noise Fourier spectra using Konno-Ohmachi [23] with b-
parameter equal a 20. Then divided the spectrums to obtain Signal Noise Ratio (SNR)
and pick the low cut-off frequency with a SNR greater than 3. The high cut-off
frequencies were selected first to be the Nyquist frequency (as an initial estimation),
and then check for the flat part of spectrum [24], selecting the lower of those.
Finally, the processing is terminated following a methodology adapted from [25],
which consists in a taper the beginning and end of trace (if it is a late triggered record,
only taper end), zero padding, applying a 4-pole Butterworth filter with the corner
frequencies obtained in the previous analysis. Then, we obtain displacements and
correct baseline (fitting a sixth-order polynomial) and last, subtract the second derivate
of polynomial from acceleration, obtaining the corrected traces of acceleration.
3. GMPEs Evaluation: Goodness-of-Fit of GMPEs to Observed Data
To assess the Goodness-of-Fit (GOF) of the different GMPEs to the data, an analysis of
the residuals is necessary. We use two different approaches, study how the observed
data fit the GMPEs using the likelihood (LH) concept as described by [7], and average
sample log-likelihood (LLH) values [8].
Table 1 shows the GMPEs used in this study, Ruiz & Saragoni [2] was excluded of
the final analysis because the model does not have a published standard deviation and
uses Ms instead of the accepted Mw [26], making the comparison impossible with this
scheme.
Table 1. Summary table of GMPEs for subduction zone relevant in Chile
GMPE Region[a] Intensity
Measures N° records /
N° events[e] Mag Distance[f] Site
Characterization
AB03[3] AL, CS, CH,
JA, ME, PE PGA,
PSA Iter = 349/49
Itra = 761/30 Mw Rrup 4 discrete class
(NEHRP B, C, D, E)
RS05[2] CH PGA Iter=49/8
Itra=19/7 Ms Rhyp Hard rock and
rock/hard soil[c]
ZH06[6] JA PGA, SA Iter=1508
Itra=1725 Mw Rrup 5 discrete class (hard
rock + 4 soil class)
BC12[5][b] CH PGA,
PSA Iter=117/13 Mw Rrup 2 discrete class (rock
and soil)[d]
BCHy10[1] JA, TW, CD,
ME, PE, CH,
AL, SI. PGA, SA Iter=1378/46
Itra=3946/76 Mw Rrup (iter) /
Rhyp (itra) Continuous (Vs30)
[a]
AL=Alaska, SI=Salomon Island, CH=Chile, CS=Cascadia, JA=Japan, ME=Mexico, PE=Peru, TW=Taiwan
[b]
Only predicts interface event
[c]
Hard rock is defined by V
s30
≥1500 (m/s) and rock/hard soil by 360≤V
s30
≤1500 (m/s).
[d]
Rock are defined by V
s30
≥900 (m/s) and in other cases the sites are classified as soil.
[e]
Iter, interplate events. Itra, intraplate/inslab events
[f]
R
rup
, closest distance to the fault plane. R
hyp
, hypocentral distance.
The normalized residuals are defined as the log of the observed seismic intensity
(IMobs) minus the log of the predicted seismic intensity (IMGMPE) divided by the total
standard deviation of model in natural log units (Eq. 1).
=()()
(1)
The evaluation was made with native periods of each GMPE (i.e. no interpolation
was performed). The residuals were computed for PGA and pseudo-spectral
accelerations of 0.1, 0.4, 1.0 and 2 seconds. The objective of this methodology is to
characterize the GOF of each GMPE to three parameters of central tendency (i.e. mean,
median, and standard deviation of the normalized residual distribution), and LH values.
If the data is unbiased, the normalized residuals would be distributed with zero mean
and unit variance. The classes which define the GOF of each GMPE to the observed
data are defined in [7] and consist in four levels of predictive capability; class A is for
models with high predictive capability, class B with intermediate capability, class C
with low and D with unacceptable predictive capability.
Moreover, we computed the average sample LLH values according the
methodology proposed by Scherbaum [8]. For in depth statistical methodologies see
references [7] and [8].
The analysis of GOF was segregated by interface and inslab events. Figure 3 and
Table 2 show the result of the analyses for interface events, while Figure 2 and Table 3
show the results for the inslab events. Median LH values close to 0.5 imply good
agreement between observed and predicted surface intensities. For the LLH values,
lower values imply a better prediction capacity of each model, in this case values lower
than 1.9 are considered as acceptable. Note that for the inslab events the BC12 GMPE
could not be assessed as they do not provide a model for these events.
Figure 2. GOF analysis of GMPE for pseudo spectral acceleration at 0.01 (PGA) s and 1 s, considering only
inslab events. First and third column are distributions of normalized total residuals, the solid red line is the
normal distribution fitted to normalized total residuals, the green dashed lines are the associated standard
normal distribution. Second and last column are associated likelihood values (LH).
0 0.5 1
0
50
100 Class D
Median: 0.15
-5 0 5
0
0.2
0.4
0.6
Mean: 1.35 | std: 1.31
Freq
AB03 0.01sec
0 0.5 1
0
50
100
150 Class D
Median: 0.13
-5 0 5
0
0.2
0.4
0.6
Mean: 1.38 | std: 1.51
AB03 1 sec
0 0.5 1
0
20
40 Class B
Median: 0.47
-5 0 5
0
0.2
0.4
0.6
Mean: 0.32 | std: 0.98
Freq
ZH06 0.01sec
0 0.5 1
0
50
100 Class D
Median: 0.31
-5 0 5
0
0.2
0.4
0.6
Mean: -1.01 | std: 1.27
ZH06 1 se c
0 0.5 1
0
20
40
LH
Class C
Median: 0.44
-5 0 5
0
0.2
0.4
0.6
Mean: 0.63 | std: 0.95
Zt
Freq
BCHy10 0.01sec
0 0.5 1
0
20
40
LH
Class B
Median: 0.44
-5 0 5
0
0.2
0.4
0.6
Mean: -0.41 | std: 1.22
Zt
BCHy10 1 se c
Figure 3. GOF analysis of GMPE for pseudo spectral acceleration at 0.01 (PGA) s and 1 s, considering only
interface events. First and third column are distributions of normalized total residuals, the solid red line is the
normal distribution fitted to normalized total residuals, the green dashed lines are the associated standard
normal distribution. Second and last column are associated likelihood values (LH).
Table 2. Classes and average sample LLH values of GMPEs used in analysis for interface events.
Class (LLH Value)
GMPE Sa @ 0.01 s
/ PGA
Sa @ 0.1 s Sa @ 0.4 s Sa @ 1 s Sa @ 2 s
AB03 D (10.3485) D (10.6382) D (8.2502) D (3.5442) C (2.1331)
ZH06 A (1.6493) A (1.7635) C (2.0175) D (2.4347) D (2.5057)
BCHy10 D (2.5594) D (2.8881) D (2.6357) B (1.8701) B (1.8415)
BC12 C (1.9526) C (1.7696) C (2.2563) D (3.0964) D (3.5439)
Table 3. Classes and average sample LLH values of GMPEs used in analysis for inslab events.
Class (LLH Value)
GMPE Sa @ 0.01 s
/ PGA
Sa @ 0.1 s Sa @ 0.4 s Sa @ 1 s Sa @ 2 s
AB03 D (3.1745) D (4.5309) D (5.8017) D (3.7637) D (2.5492)
ZH06 B (1.5474) D (2.0568) D (2.4405) D (2.7359) D (2.7763)
BCHy10
C (1.8807)
D (2.2213)
A (1.8468)
B (2.1353)
B (2.0818)
0 0.5 1
0
200
400
600 Class D
Median: 0
-5 0 5
0
0.2
0.4
0.6
Mean: 2.83 | std: 2.41
Freq
AB03 0.01sec
0 0.5 1
0
100
200
300 Class D
Median: 0.19
-5 0 5
0
0.2
0.4
0.6
Mean: 1.23 | std: 1.44
AB03 1 sec
0 0.5 1
0
50
100 Class A
Median: 0.45
-5 0 5
0
0.2
0.4
0.6
Mean: 0.02 | std: 1.11
Freq
ZH06 0.01sec
0 0.5 1
0
100
200
300 Class D
Median: 0.27
-5 0 5
0
0.2
0.4
0.6
Mean: -0.97 | std: 1.11
ZH06 1 se c
0 0.5 1
0
100
200 Class D
Median: 0.28
-5 0 5
0
0.2
0.4
0.6
Mean: 1.02 | std: 1.09
Freq
BCHy10 0.01sec
0 0.5 1
0
50
100
150 Class B
Median: 0.47
-5 0 5
0
0.2
0.4
0.6
Mean: 0 | std: 1.13
BCHy10 1 se c
0 0.5 1
0
100
200
LH
Class C
Median: 0.31
-5 0 5
0
0.2
0.4
0.6
Mean: -0.33 | std: 1.48
Zt
Freq
BC12 0.01sec
0 0.5 1
0
200
400
LH
Class D
Median: 0.17
-5 0 5
0
0.2
0.4
0.6
Mean: -1.06 | std: 1.6
Zt
BC12 1 sec
4. Conclusions
A rigorous assessment of different GMPEs developed for subduction environments was
performed. The data used to compare these GMPEs was also rigorously processed; it
includes analog and digital records from 1985 to 2014, for inslab and interface events.
These interface events include the largest ground motions recorded in Chile.
Of the initial set of selected GMPEs to be analyzed, RS05 [2] had to be excluded
from the analyses as the lack of standard deviation of the models does not allow the
comparison used in this work.
Our results indicate that BCHydro [1] has similar behavior to Zhao et al. [6] for
interface (or interplate) events. For short periods, ZH06 et al. shows the best fit to the
data (LLH<1.8), and for the longer periods (Sa at 1 and 2 seconds) BCHydro is the best
fit(LLH<1.9). BC12 shows less accuracy (class C in Scherbaum’s [7] methodology,
average LLH of 2.5) and obtains “low capability” level in some periods (PGA, 0.1, and
0.4 s), with good LLH value for Sa at 0.1 secs. AB03 obtain “unacceptable capability”
(class D along with high LLH values) for all periods except in pseudo spectral
acceleration at 2 seconds.
Inslab ground motion intensities show a similar behavior to those of interface.
Again BChydro and ZH06 are the best performing GMPEs for the Chilean data. For
these events BCHydro performs better for Sa at 0.4, 1, and 2 seconds, while ZH06 does
better at PGA and 0.1 secs. As mentioned above, the BC12 could not be used. AB03
did not fit well this data either.
Contrary to the expected, BC12 did not perform better than the other models. Good
behavior was expected because the model was fitted to Chilean data, much of the same
data that was used to tests all GMPEs. Improvements in the statistical processing of the
data, will likely lead to lower standard deviation estimations of this model and thus an
overall improvement of its performance.
As shown in Figures 2 and 3, the analyzed GMPEs have predominantly positive
residuals, underestimating pseudo accelerations at the periods under consideration. An
exception to this trend is the BC12 GMPE which overestimates Sa values at all periods.
Acknowledgements
This work was partially funded by FONDECYT 11121404, is part of an ongoing effort
by GEM-SARA (Global Earthquake Model - Seismic Risk in South America) topic 6
workgroup, and FUCHIGE foundation. The data of shear wave profiles of Chilean
stations are available at FUCHIGE´s website.
References
[1] N. Abrahamson, N. Gregor, and K. Addo. BC Hydro Ground Motion Prediction Equations For
Subduction Earthquakes, Earthquake Spectra (2015). In press.
[2] S. Ruiz and G. Saragoni. Attenuation equations for subduction-zone earthquakes in Chile considering
two seismogenic mechanisms and site effects. IX Jornadas Chilenas de Sismología e Ingeniería
Antisísmica (2005), Concepción, Chile.
[3] G. M. Atkinson and D. M. Boore. Empirical ground-motion relations for subduction-zone earthquakes
and their application to Cascadia and other regions, Bull. Seismol. Soc. Am. (2003). 93, 1703–1729.
[4] G. M. Atkinson and D. M. Boore. Erratum to empirical ground-motion relations for subduction-zone
earthquakes and their application to Cascadia and other regions, Bull. Seismol. Soc. Am. (2008). 98,
2567–2569.
[5] R. Boroschek and V. Contreras. Strong ground motion from the 2010 Mw 8.8 Maule Chile earthquake
and attenuation relations for Chilean subduction zone interface earthquakes. International Symposium
on Engineering Lessons Learned from the 2011 Great East Japan Earthquake (2012), March 1-4,
Tokyo, Japan.
[6] J. X. Zhao, J. Zhang, A. Asano, Y. Ohno, T. Oouchi, T. Takahashi, H. Ogawa, K. Irikura, H. K. Thio, P.
G. Somerville, and Y. Fukushima. Attenuation relations of strong ground motion in Japan using site
classification based on predominant period,. Bulletin of the Seismological Society of America (2006) 96,
898–913.
[7] F. Scherbaum, F. Cotton, and P. Smit. On the use of response spectral-reference data for the selection of
ground-motion models for seismic hazard analysis: the case of rock motion, Bulletin of the
Seismological Society of America (2004) 94(6), 2164-2185.
[8] F. Scherbaum, E. Delavaud, and C. Riggelsen. Model Selection in Seismic Hazard Analysis: An
Information-Theoretic Perspective, Bulletin of the Seismological Society of America (2009). 99(6),
3234-3247.
[9] G. Ekström, M. Nettles, and A. M. Dziewonski, The global CMT project 2004-2010: Centroid-moment
tensors for 13,017 earthquakes, Phys. Earth Planet. Inter. (2012), 200-201, 1-9,
doi:10.1016/j.pepi.2012.04.002
[10] F. Leyton, S. Ruiz, and S. Sepulveda. Preliminary Revaluation of Probabilistic Seismic Hazard
Assessment in Chile: from Arica to Taitao Peninsula. Advances in Geosciences (2009), 22, 147-153.
[11] P. M. Mai and K. K. S. Thingbaijam. SRCMOD: An Online Database of Finite‐Fault Rupture Models.
Seismological Research Letters (2014), v. 85, p. 1348-1357. doi: 10.1785/0220140077.
[12] F. O. Strasser, M. C. Arango, and J. J. Bommer Scaling of the Source Dimensions of Interface and
Intraslab Subduction-zone Earthquakes with Moment Magnitude. Seismological Research Letters
(2010), v. 81, p. 941-950, doi:10.1785/gssrl.81.6.941
[13] FUCHIGE. Fundación Chilena de Investigación Geotecnia. Reportes de mediciones geofísicas. [Last
Accessed on 24-01-2015]. Available in: www.fuchige.cl
[14] A. Rodriguez-Marek, J. A. Bay , K. Park , G. A., Montalva, A. Cortez-Flores, J. Wartman , and R.
Boroschek. Engineering analysis of ground motion records from the 2001 Mw8.4 Southern Peru
earthquake, Earthquake Spectra (2010) 26, 499–524
[15] R. Kayen, B. D. Carkin, S. Corbet, C. Pinilla, A. Ng, E. Gorbis, and C. Truong. Seismic Velocity Site
Characterization of Thirty-One Chilean Seismometer Stations by Spectral Analysis of Surface Wave
Dispersion. PEER reports (2014).
[16] R. C. Riddell, M.F Van Sint Jan, S. Midorikawa and J.F. Gajardo. Clasificación geotécnica de los sitios
de estaciones acelerográficas en Chile. Pontificia Universidad Catolica de Chile, Santiago, Chile, 1992.
[17] S. Midorikawa, H. Yamanaka, K. Chimoto, R. Riddell, H. Miura, and Koichiro Saguchi. Evaluation of
Site Effects on Strong‐Motion Records in Concepción during the 2010 Maule, Chile. Earthquake
Bulletin of the Seismological Society of America (2014).
[18] F. Leyton, S. Ruiz and M. Astroza. Correlation between seismic intensity for the Maule 2010
earthquake (Mw 8.8) and microtremors’ HVSR 15WCEE (2012), Lisbon.
[19] M. D. Trifunac. A note on correction of strong-motion accelerograms for instrument response. Bulletin
of the Seismological Society of America (1972) 62:401-409
[20] F. Pacor, R. Paolucci, G. Ameri, M. Massa and R. Puglia. Italian strong motion records in ITACA:
overview and record processing. Bull Earthquake Eng (2011) 9:1741–1759. doi: 10.1007/s10518-011-
9295-x.
[21] D.M. Boore and J.J. Bommer. Processing of strong-motion accelerograms: Needs, options and
consequences, Soil Dynamics and Earthquake Engineering (2005) 25.
[22] T. Kishida, R. E. Kayen, O. Ktenidou, W. J. Silva, R. B. Darragh, and J. Watson-Lamprey. PEER
Arizona Strong-Motion Database and GMPEs Evaluation. PEER reports (2014).
[23] K. Konno and T. Ohmachi. Ground motion characteristics estimated from spectral ratio between
horizontal and vertical components of microtremors. Earthquake Bulletin of the Seismological Society
of America (1998), 88-1, 228-241.
[24] S. Akkar, Ö. Kale, E. Yenier and J. Bommer. The high-frequency limit of usable response spectral
ordinates from filtered analogue and digital strong-motion accelerograms. Earthquake Engng Struct.
Dyn. 2011; 40:1387–1401
[25] D. M. Boore , A. A. Sisi, and S. Akkar. Using pad-stripped acausally filtered strong-motion data, Bull.
Seismol. Soc. Am. (2012)102
[26] J.J. Bommer, J. Douglas, F. Scherbaum, F. Cotton, H. Bungum and D. Fäh. On the selection of ground-
motion prediction equations for seismic hazard analysis. Seismological Research Letters (September
2010), 81(5):783-793
