Proceedings of the 9th International Conference on Structural Dynamics, EURODYN... Porto, Portugal, 30 June - 2 July 2014

Transcription

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)
ISSN: 2311-9020; ISBN: 978-972-752-165-4
Ground motion prediction equations for Vrancea intermediate-depth earthquakes
S. Demetriu1, R.Vacareanu2, D. Lungu2, F. Pavel2, C. Arion2, M. Iancovici1, A. Aldea2, C.Neagu2
Department of Mechanics of Structures, Technical University of Civil Engineering, Bd. Lacul Tei no. 124, 020396 Bucharest,
Romania
2
Department of Reinforced Concrete Structures, Technical University of Civil Engineering, Bd. Lacul Tei no. 124, 020396
Bucharest, Romania
email: [email protected], [email protected], [email protected], [email protected], [email protected],
[email protected], [email protected], [email protected]
1
ABSTRACT: Vrancea intermediate-depth seismic source dominates the seismic hazard in more than two thirds of the Romanian
territory and in Bucharest as well, and it is likely to produce large magnitude earthquakes (MW > 7.0) several times per century.
The paper presents the new ground motion prediction equations (GMPEs) for peak ground acceleration and response spectral
accelerations developed for Vrancea intermediate-depth seismic source. The strong ground motion database comprises 465
horizontal components recorded from Vrancea source in earthquakes with moment magnitude in between 5.2 and 7.4 and focal
depths ranging from 87 km to 154 km, as well as other 396 horizontal components recorded from subduction intraplate
earthquakes worldwide (Chile, India, Japan, Mexico, New Zeeland) with moment magnitude in between 5.6 and 7.8 and focal
depths ranging from 69 km to 173 km. The database used in this study is several times larger than the previous ones used in the
development of GMPEs for Vrancea intermediate-depth seismic source. The earthquake magnitude, source-to-site-distance and
focal depth are considered in the ground motion prediction model. The GMPEs are developed by multiple regression analysis
using random mixed effects model. The predicted values are geometric means of ground motion intensity parameters. The total,
inter-event and intra-event residuals are analyzed considering several statistical tools and goodness-of-fit parameters. Finally, a
comparison is made between the predicted values of ground motion intensity parameters obtained using previous GMPEs
developed or recommended for Vrancea subcrustal source and the values obtained using the new attenuation relationship.
KEY WORDS: Vrancea seismic source; Ground motion prediction equation; Strong ground motion database; Seismic hazard.
1
INTRODUCTION
A comprehensive description regarding the characteristics
(focal depth range, area of seismic source, magnitude range,
etc.) of the Vrancea subcrustal seismic source can be found in
[14], [15] and [7]. A more complex shape of this seismic
source was defined by the National Institute for Earth Physics
for the SHARE project [35]. On average, this seismic source
produced 3 to 5 earthquakes of MW > 6.5 each century [7]. In
the 20th century earthquakes with magnitudes MW > 6.7,
occurred in October 1908 (MW = 7.1, h = 125 km), November
1940 (MW = 7.7, h = 150 km), March 1977 (MW = 7.4, h = 94
km), August 1986 (MW = 7.1, h = 131 km) and May 1990 (MW
= 6.9, h = 91 km), respectively. Several possible geodynamic
models for the Vrancea subcrustal seismic source are
presented in [24], [31], [18], [19], [20] or [7].
The first studies regarding ground motion models for the
prediction of the azimuth-dependent peak ground acceleration
of intermediate-depth Vrancea subcrustal seismic events were
performed in [12] and [23]. The same functional form from
[12] was also used in [13] for the development of an
attenuation relation that is not azimuth-dependent (using all
available recorded data, regardless of their geographic
location). Some additional (azimuth-dependent) ground
motion prediction equations for the Vrancea subcrustal
seismic source and for PGA were also developed in [33] and
[21]. A set of azimuth-dependent ground motion prediction
equations specifically derived for the Vrancea subcrustal
seismic for peak ground acceleration (PGA), peak ground
velocity (PGV), pseudo-spectral acceleration (PSA) and MSK
scale seismic intensity is given in [30]. The characteristics of
the four above-mentioned GMPEs developed for the Vrancea
subcrustal seismic source are given in [5]. Other GMPEs are
recommended for the Vrancea intermediate-depth seismic
source in [4] which deals with attenuation models for the
probabilistic seismic hazard assessment in Europe. The
recommended ground motion prediction equations for
Vrancea are: Youngs et al. (1997) [40], Zhao et al. (2006)
[41], Atkinson and Boore (2003) [1] and Lin and Lee (2008)
[11]. An evaluation of these models is presented in [36] , [37].
The main focus of this paper is the development of a new
ground motion prediction equation GMPE for Vrancea
subcrustal seismic source. The performance of this new
model, which is based on an increased strong ground motion
database, is evaluated using several goodness-of-fit measures
presented in [27], [28] and [4]. The analysis of the inter-event
and intra-event residuals [26], [29], [32] is also performed for
the available dataset of strong ground motions.
2
STRONG GROUND MOTION DATABASE FOR
REGRESSION ANALYSIS
The proposed ground motion model for the prediction of
spectral accelerations is derived from a national database
(strong ground motion records from Vrancea subcrustal
earthquakes) and an international database consisting
altogether of 431 strong ground motions (861 horizontal
components) recorded from 26 intermediate-depth seismic
events with moment magnitudes in the range 5.2 ≤ MW ≤ 7.8
[38]. The strong ground motions from Vrancea earthquakes
were recorded in Romania, Republic of Moldova, Bulgaria
and Serbia.
435
The international strong ground motions were recorded in
intermediate-depth earthquakes in Japan (K-net and Kik-net
data), New Zealand, Mexico, Chile and India. The data come
from nine intermediate-depth Vrancea earthquakes as well as
from seventeen earthquakes produced in other seismic regions
in the world. The range of the focal depth of all earthquakes is
in between 69 km to 173 km. This depth range is typical for
seismic events produced in the Vrancea region, which are the
main focus of this attenuation model.
The main characteristics of the database used for the
derivation of the ground motion prediction model are given in
Table 1. For each seismic event, the date of occurrence, the
moment magnitude, the position of the epicenter, the focal
depth and the number of used strong ground motions are
presented in [38].
Moment magnitude, MW
8.0
No. of
earthquakes
Vrancea +
International
9+
17
No. of
horizontal
components
465 +
396
Epicentral
distance
range, km
2 - 647
The distribution of the earthquake magnitude versus the
epicentral distance for the 26 analyzed seismic events is
shown in Figure 1. More details on the structure and content
of the database used in the multiple regression analysis can be
found in [38].
All the strong ground motions recorded in Vrancea
intermediate depth seismic events were collected for the
BIGSEES national research project [3] from the seismic
networks of INFP (National Institute for Earth Physics),
INCERC (Building Research Institute), GEOTEC (Institute
for Geotechnical and Geophysical Studies) and NCSRR
(National Centre for Seismic Risk Reduction). The positions
of Vrancea epicenters and of the recording stations are given
in Figure 2.
The soil conditions for the seismic stations which have
recorded the strong ground motions are defined according to
EN 1998-1 [6] and are assigned according to [34] (converted
from [22] to [6]).
The vast majority of the strong ground motions were recorded
in soil conditions (classes B, C or D), the exception being
some strong ground motions from Vrancea earthquakes
recorded in the epicentral region in soil class A. These strong
ground motions were also kept in the database due to the lack
of strong ground motions recorded in soil conditions from the
epicentral region of Vrancea intermediate-depth earthquakes.
Although the proposed ground motion prediction model is
derived only for soil conditions, it is the authors' opinion that
the use of the strong ground motions recorded on harder soil
conditions (only in the epicentral region) does not affect the
results for larger epicentral distances. In the case of some
seismic station the exact soil classification could not be
retrieved from the existing database. Nevertheless, the
conditions for these stations were assigned as soil, so these
data were also used in the regressions (these stations are
defined as not classified).
436
7.0
6.5
6.0
5.5
Table 1. Characteristics of the database of strong ground
motions [38].
Database
7.5
5.0
0
250
500
Epicentral distance, km
750
Figure 1. Distribution of the earthquake magnitude versus the
epicentral distance.
Figure 2. Positions of Vrancea epicenters (circles) and of the
recording stations (red triangles).
3
FUNCTIONAL FORM AND REGRESSION MODEL
The following functional form of the GMPE is selected for the
regression analysis [38]:
ln y ij T   c1 T   c 2 T M W ,i  6 
 c3 T M W ,i  62  c 4 T  ln Rij  C5 T Rij 
(1)
 c6 T hi   i   ij
where i is the earthquake index, j is the recording station’s
index, yij is the geometrical mean of the two horizontal
components of either PGA (in cm/s2) or 5% damped response
spectral acceleration (in cm/s2) for a spectral period T, MW is
the moment magnitude (use MW = 7.6 for events of MW > 7.6
for spectral periods up to 1.0 s and use MW = 8.0 for events of
MW > 8.0 for spectral periods in excess of 1.0 s), R is the
source to site (hypocentral) distance in kilometers, h is the
focal depth in kilometers and ck (k = 1 to 6) are coefficients
determined from the data set by regression analysis at each
spectral period.
The range of the total standard deviation from 0.711 to
0.923 and the contributions of intra- and inter-event standard
deviations to the total variability of the model are rather
balanced.
The regression coefficients and the residual terms are
obtained with the maximum likelihood method [8], [9]. The
magnitude effect on the predicted values of ground motion
parameters is considered through c1 to c3 coefficients. The
influences of the geometrical spreading and of the anelastic
attenuation are accounted for in relation (1) through c4 (set to 1.000) and c5 coefficients. The depth effect is included by the
coefficient c6.
4
c5
0.00138
0.00095
0.00193
0.00267
0.00269
0.00289
0.00276
0.00271
0.00275
0.00271
0.00247
0.00287
0.00312
0.00329
0.00329
0.00324
0.00312
0.00275
0.00236
0.00198
c6
0.00484
0.00447
0.00474
0.00571
0.00561
0.00518
0.00381
0.00308
0.00273
0.00242
0.00097
0.00036
0.00073
0.00039
0.00002
0.00115
0.00175
0.00218
0.00290
0.00313
Table 3. Standard deviations of the proposed GMPE [38].
T, s
σT
τ
σ
0.0
0.738
0.550
0.491
0.1
0.923
0.692
0.611
0.2
0.874
0.658
0.575
0.3
0.818
0.617
0.536
0.4
0.823
0.592
0.572
0.5
0.790
0.513
0.601
0.6
0.793
0.502
0.614
0.7
0.773
0.488
0.599
0.8
0.755
0.461
0.597
0.9
0.729
0.414
0.600
1.0
0.729
0.414
0.600
1.2
0.719
0.377
0.612
1.4
0.711
0.366
0.610
1.6
0.728
0.401
0.608
1.8
0.732
0.410
0.607
2.0
0.730
0.410
0.605
2.5
0.735
0.402
0.615
3.0
0.750
0.433
0.613
3.5
0.751
0.436
0.612
4.0
0.752
0.463
0.593
300
400
50%
16%
84%
Rec
350
300
250
200
150
50%
16%
84%
Rec
250
SA1.0 s, cm/s2
c3
-0.4758
-0.3798
-0.5250
-0.6167
-0.6987
-0.7008
-0.6845
-0.7029
-0.6726
-0.6653
-0.6684
-0.6193
-0.5977
-0.5812
-0.5865
-0.5638
-0.5870
-0.6053
-0.6290
-0.6607
200
150
100
100
50
50
0
0
0
100
200
300
0
Epicentral distance d, km
500
450
400
350
300
250
200
150
100
50
0
100
200
300
400
50%
16%
84%
Rec
50%
16%
84%
Rec
350
300
SA1.0 s, cm/s2
c2
1.4863
1.2914
1.5016
1.7468
1.9355
2.0346
2.0695
2.1370
2.1907
2.2422
2.2537
2.3182
2.3958
2.4470
2.4958
2.5124
2.6036
2.6306
2.6152
2.6116
PGA, cm/s2
c1
8.5851
9.1790
9.5719
9.4383
9.2379
9.0571
8.9340
8.7733
8.6120
8.4383
8.3839
8.1855
7.8850
7.7061
7.5257
7.4295
7.0493
6.6822
6.4087
6.1352
The evaluation and validation of the proposed GMPE is
performed in several steps. The first step consists of several
comparisons of the proposed ground motion model with the
observed data from the most instrumented seismic events
produced by the Vrancea subcrustal seismic source. In Figure
3 the proposed model is compared with the spectral
accelerations at T = 0.0 s and 1.0 s obtained from the data
recorded during the Vrancea earthquakes of August 30, 1986
(MW = 7.1), May 30, 1990 (MW = 6.9) and October 27, 2004
(MW = 6.0).
PGA, cm/s2
T, s
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
3.5
4.0
EVALUATION OF PROPOSED GMPE
250
200
150
100
50
0
0
100
200
300
0
100
200
300
250
120
50%
16%
84%
Rec
200
PGA, cm/s2
Table 2. Regression coefficients of the proposed GMPE [38].
150
100
50
50%
16%
84%
Rec
100
SA1.0 s, cm/s2
The independent normally distributed variates i and ij are
the inter-event residuals (error that represents earthquake to
earthquake variability of ground motions) with zero mean and
a standard deviation of  and respectively, the intra-event
residuals (error that represents within earthquake variability of
ground motions) with zero mean and a standard deviation of
. Both intra- and inter-event standard deviations  and  are
period dependent, but are assumed independent of magnitude.
The total standard deviation  of the model’s prediction is
defined as the square root of sum of squares of  and . The
coefficients c1 to c6 and the standard deviations are given in
Table 2 and Table 3 [38].
80
60
40
20
0
0
0
100
200
300
0
100
200
300
Figure 3. Comparison of observed and predicted spectral
accelerations using the proposed GMPE for 3 spectral periods
(T = 0.0 s - left- and T = 1.0 s - right) and for three subcrustal
Vrancea seismic events: August 30, 1986 (MW = 7.1) – top
row-, May 30, 1990 (MW = 6.9) – middle row- and October
27, 2004 (MW = 6.0) – bottom row.
437
It is noticeable from Figure 3 that most of the observed data
for all three periods are distributed between the median
plus/minus one standard deviation.
Figure 4 shows the distribution of the total residuals RES
with epicentral distance for two spectral accelerations at T =
0.0 s and 1.0 s.
spectral periods, it comes out that the homoscedasticity
hypothesis holds true.
2.5
PGA
2.0
1.5
2.5
1.5
Total residuals
1.0
0.5
0.0
-0.5
1.0
Inter-event residuals
2.0
0
250
500
0.5
MW
0.0
5
-0.5
6
7
8
-1.0
750
-1.5
-1.0
-2.0
-1.5
-2.0
-2.5
-2.5
1.5
T = 1.0s
1.0
Inter-event residuals
2.5
0.5
2.0
1.5
Total residuals
0.5
5
6
7
8
-0.5
0.0
-0.5
MW
0.0
1.0
0
250
500
750
-1.0
-1.0
-1.5
-1.5
-2.0
-2.5
Figure 4. Distribution of the total residuals RES
with epicentral distance for two spectral
accelerations at T = 0.0 (top) s and 1.0 s (bottom)
No significant bias in the distribution of the residuals can be
observed from Figure 4. However, the plots reveal a large
amount of variability in the dataset.
In the following a closer look at the inter- and intra-event
residuals [25], [26], [29], [32] is presented. Figure 5 a), b)
displays the variation of the inter-event residuals with the
moment magnitude at two spectral periods T = 0 s; 1.0 s. The
appropriateness of magnitude scaling is tested by examining
the trends of inter-event residuals versus magnitude [26]. The
GMPE’s magnitude scaling at all the spectral periods proves
to be appropriate. The very low values of the slope and of the
offset of the trendlines plotted in Figure 5 a) and b) prove that
there is neither trend nor bias in the inter-event residuals.
Since the same conclusions are reached for all the investigated
438
Figure 5. Distribution of the inter-event residuals with
moment magnitude for two spectral accelerations at T
= 0.0 (top) s and 1.0 s (bottom)
The appropriateness of distance scaling is tested by
examining the trends of intra-event residuals versus distance
[26]. The distance scaling of the proposed GMPE is
investigated in Figure 6 where the intra-event residuals versus
epicentral distances are represented for two spectral periods T,
namely 0 s and 1.0 s. The plots show the variation of all the
intra-event residuals with epicentral distance along with the
linear trendline of the results. The very low values of the slope
and of the offset of the trendlines shown in Figure 6 a) and b)
prove the correctness of the distance scaling for the proposed
GMPE.
The mean, median and standard deviation of the normalised
residuals NRES [27] calculated for the subset of Vrancea
strong ground motions are, respectively MEANNRES = -0.06,
MEDNRES = -0.03 and STDNRES = 0.82. The sampling
errors [39] of the previously mentioned indicators are less
than 1%. If one considers only the ground motions recorded in
Vrancea intermediate depth earthquakes, the total standard
deviation of the model’s prediction decreases overall with
18%. Moreover, the bias introduced by the reduced sampling
is very low, thus providing a high degree of confidence in
using the proposed GMPE for Vrancea intermediate depth
seismic events [38].
2.0
predictions. Moreover, one can notice the low attenuation
with the epicentral distance of the LEA00 attenuation model.
The proposed model gives higher ground motion amplitudes
for T = 1.0 s for earthquakes with MW ≤ 7.0.
PGA
1.5
Intra-event residuals
1.0
0.5
0.0
0
100
200
300
400
500
600
700
-0.5
-1.0
-1.5
-2.0
2.0
T = 1.0s
Intra-event residuals
1.5
1.0
0.5
0.0
0
200
400
600
800
-0.5
-1.0
-1.5
-2.0
Figure 6. Distribution of the intra-event residuals with
epicentral distance for two spectral accelerations at T
= 0.0 (top) s and 1.0 s (bottom)
5
COMPARISON WITH OTHER GMPES
The proposed attenuation model is compared for two generic
earthquakes with other GMPEs from literature in Figure 7
[38]. The reference earthquakes have magnitudes MW =
6.5and MW = 7.5 produced at a depth of 100 km. The
comparisons are performed for two spectral periods T = 0.0 s
and 1.0 s. Our model is assessed against the Lungu et al.
(2000) [13] model (LEA00) and the four GMPEs proposed
within the SHARE project [4]: Youngs et al. (1997) [40] for
soil conditions - YEA97, Atkinson and Boore (2003) [1] for
soil class D - AB03 , Zhao et al. (2006) [41] for soil class III ZEA06 and Lin and Lee (2008) [11] for soil conditions LL08. The comparisons with the LEA00 model are performed
only for T = 0.0 s.
The first obvious conclusion which can be drawn from
Figure 7 is the relatively large scatter in the median
Figure 7. Median amplitudes for two spectral periods (T = 0.0
s and T = 1.0 s) and for seismic events characterized by two
magnitudes (MW = 6.5 and MW = 7.5) with a focal depth of
100 km. The curves correspond to the proposed model and to
5 additional models: LEA00, YEA97, AB03, ZEA06 and
LL08 [38]
It is also worth mentioning the fact that in most of the
analyzed cases, the proposed GMPE has similar median
predictions as the YEA97. One can notice from Figure 7 the
very similar predictions of the median amplitudes of spectral
acceleration at the natural period T = 1.0 s given by both the
YEA97 and proposed GMPEs. The previous remark shows
that the spectral response is less sensitive to local conditions
and, consequently better constrained at higher natural periods.
The attenuation rate with the epicentral distance of the
proposed attenuation model is smaller than that of the models
developed for subduction earthquakes (YEA97, AB03,
ZEA06, LL08) and larger than that of the model developed
using only strong ground motions from Vrancea intermediatedepth earthquakes (LEA00) [38].
Finally, the total standard deviation of the proposed GMPE
is compared in Figure 8 with the standard deviations of the
other four GMPEs: YEA97, AB03, ZEA06 and LL08. The
standard deviation in the case of the YEA97 model is
computed for a MW = 7.0 earthquake. The total standard
deviation of the proposed model is the largest in the period
range up to T = 0.7 s. However, for spectral periods in excess
of 0.7 s, the total standard deviation of the proposed model is
smaller than that of the other considered ground motion
prediction models, except the AB03 model [38].
439
Figure 8. Distribution of the intra-event residuals with
epicentral distance for two spectral accelerations at T
= 0.0 (top) s and 1.0 s (bottom) [38]
6
DISCUSSION
Previous GMPEs developed for Vrancea subcrustal source in
[12], [23], [33] or [21] are azimuth-dependent. Since the new
GMPE proposed in this paper is based on a much larger
database with both domestic and international earthquakes,
the further need for azimuth dependency is investigated. In
this respect, the normalized residuals between the observed
and the predicted ground motion parameters is obtained for
each of the 233 values in the subset of the seismic records
generated by Vrancea intermediate-depth source and the
pattern distribution of the residuals is investigated. The
normalized residuals in each seismic station and for each
Vrancea earthquake are represented on the map and the spatial
distribution of the residuals is investigated. After careful
investigation of the maps one can conclude that there is no
need for further modification of GMPE in order to make it
azimuth-dependent [38]. In Figure 9 the absolute values of
maximum normalized residuals at spectral periods T = 0 s and
T = 1.0 s for the proposed GMPE are represented and one can
notice that there is no significant azimuth dependency of the
residuals. Nevertheless, there is a pattern of the spatial
distribution of the values of the normalized residuals: there is
a slight underestimation of the observed values in the regions
in the front of the Carpathians Mountains (fore-arc region), an
overestimation of the observed values in the regions in the
back of the Carpathians Mountains (back-arc region) and a
transition region in between fore-arc and back-arc [38]. We
are currently investigating this pattern in an ongoing research
project and a GMPE valid for both fore-arc and back-arc
regions is under development.
Another issue to be discussed is the behavior of the
proposed GMPE for values of moment magnitude MW at the
higher end of the scale. A saturation of the values of PGA
along with a trend of predicted values to slightly decrease for
MW > 7.6 was noticed. The decrease of the predicted values
occurs irrespective of the epicentral distance and is produced
440
by the quadratic term in magnitude; the same decrease is
reported in [1]. The GMPE requires the capping of the
maximum magnitude at MW,cap = 7.6 for prediction of PGA
values [38]. Thus estimates of PGA values for seismic events
of MW > 7.6 should be made using MW,cap = 7.6. This
saturation effect does not imply that a maximum moment
magnitude of 7.6 should be assigned in the probabilistic
seismic hazard analysis. Rather, the PGA values for seismic
events of MW > 7.6 should be calculated using the value of
MW,cap = 7.6 in the GMPE. More generally, a capping
magnitude can be derived for any spectral period by
differentiating relation (1) with respect to MW and equating
the result with zero. The analysis reveals that the capping
magnitude is MW,cap = 7.6 for spectral periods up to 1.0 s and
MW,cap = 8.0 for spectral periods in excess of 1.0 s [38].
Nevertheless, from our probabilistic seismic hazard analyses
[2], [10], [16], [17], the differences that arise in a probabilistic
seismic hazard analysis performed with and without
magnitude capping amounts 2% at the most for ground motion
amplitudes with mean return periods larger than 1000 years in
the case of MW,cap = 7.6 and vanish for MW,cap = 8.0 [38].
Actually, the capping moment magnitude MW,cap = 8.0
corresponds to the higher end of the scale considered to
provide reliable results in using the proposed GMPE.
Figure 9. Distribution of absolute values of maximum
normalized residuals at T = 0 s (top) and T = 1.0 s
(bottom) for the proposed GMPE) [38]
7
CONCLUSIONS
A new ground motion prediction model for Vrancea
intermediate-depth seismic source is developed in this study.
The database used in the regression analysis is more extended
compared to the previous databases used for the same
purpose. The extension of the database consists in including
all the instrumented Vrancea earthquakes with moment
magnitudes larger than 5.0 and an additional seventeen
foreign intermediate-depth earthquakes. The use of
international earthquake data is a temporary solution for
filling the gaps in the national database. Nevertheless, as more
strong ground motions recorded in Vrancea intermediatedepth earthquakes become available, we will revisit this
analysis. The current extension of the database increased both
the ranges of magnitude and of the source-to-site distance. We
consider that the proposed ground motion prediction model
provides reliable results for a magnitude range MW = 5.0 ÷
8.0, an epicentral distance range from 10 km to 300 km and a
focal depth range from 60 km to 200 km. We acknowledge
that there is some uncertainty related to the upper bound of the
moment magnitude scale, which is poorly constrained by the
data (extending to MW = 7.8). The epicentral distance and the
focal depth ranges may be extrapolated beyond the previously
mentioned limits with some caution. We believe that this new
GMPE might supersede the previous attenuation models
derived for Vrancea intermediate-depth seismic source and
address the limits identified in those models. In addition, the
proposed GMPE covers peak ground acceleration and
response spectral acceleration and a much broader range of
earthquake magnitudes and source-to-site distances. The
regression coefficients of the GMPE and the residual terms
are obtained with the maximum likelihood method [8], [9].
Both intra- and inter-event standard deviations  and  are
period dependent but are independent of magnitude. The total,
inter- and intra-event normalized residuals closely fit a
standard normal distribution of probability.
After careful investigation of the residuals one can conclude
that there is no need for further modification of GMPE in
order to make it azimuth-dependent. The spatial distribution
of the normalized residuals reveals that there is a slight
underestimation of the observed values in the regions in the
front of the Carpathians Mountains (fore-arc region), an
overestimation of the observed values in the regions in the
back of the Carpathians Mountains (back-arc region) and a
transition region in between. A GMPE valid for both fore-arc
and back-arc regions is under development in an ongoing
research project. The predicted values of ground motion
parameters are applicable for average soil conditions (soil
classes B and C in EN 1998-1). The estimates of ground
motion parameters for seismic events with MW > MW,cap
should be made using the impose capping magnitude,
implying that the ground motion parameters’ amplitudes for
seismic events of MW > MW,cap should be calculated using the
value of MW,cap in the proposed GMPE [38].
international cooperation enabled by IPRED Platform. The
authors would also like to acknowledge the permission of the
international journal Earthquakes and Structures for using
some data and results from [38].
ACKNOWLEDGMENTS
[20]
Funding for this research was provided within BIGSEES
Project by the Romanian National Authority for Scientific
Research (ANCS), CNDI – UEFISCDI under the Grant
Number 72/2012. This support is gratefully acknowledged.
The authors would also like to thank Dr. Carlos Gutiérrez
Martínez and Dr. Leonardo Alcántara from CENAPREDUNAM for providing the strong ground motions from
subcrustal earthquakes recorded in Mexico within the
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN... Porto, Portugal, 30 June - 2 July 2014

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