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An Assessment of the Relevance of Parameters Used for Ground Motion Frequency Content Characterization with Application to Vrancea Subcrustal Earthquakes

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The paper presents new results from a detailed study, involving an analysis of several deterministic and stochastic indices computed for over 100 tri-axial accelerograms recorded during four strong Vrancea seismic events with moment magnitude, Mw, larger than 6. The study aims to better reveal the spectral characteristics of the analyzed ground motions. Various analytical estimators of the predominant period, such as those based on power spectral density, Fourier amplitude spectrum, response spectra etc. are computed and compared. Additionally, a number of bandwidth measures are used in the assessment. The variability of the analyzed period-type parameters from one event to another is pointed out, as well as, when relevant, their spatial variability. Observations are correlated with available information on local site conditions, geology etc., in order to investigate the influence of different factors on the frequency content of the analyzed motions.
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An Assessment of the Relevance of Parameters Used
for Ground Motion Frequency Content Characterization
with Application to Vrancea Subcrustal Earthquakes
Iolanda-Gabriela Craifaleanu
Technical University of Civil Engineering Bucharest, Romania &
National R&D Institute, URBAN-INCERC, INCERC Bucharest Branch, Romania
SUMMARY:
The paper presents new results from a detailed study, involving an analysis of several deterministic and
stochastic indices computed for over 100 tri-axial accelerograms recorded during four strong Vrancea seismic
events with moment magnitude, Mw, larger than 6. The study aims to better reveal the spectral characteristics of
the analyzed ground motions. Various analytical estimators of the predominant period, such as those based on
power spectral density, Fourier amplitude spectrum, response spectra etc. are computed and compared.
Additionally, a number of bandwidth measures are used in the assessment. The variability of the analyzed
period-type parameters from one event to another is pointed out, as well as, when relevant, their spatial
variability. Observations are correlated with available information on local site conditions, geology etc., in order
to investigate the influence of different factors on the frequency content of the analyzed motions.
Keywords: frequency content, Vrancea earthquakes, predominant period
1. INTRODUCTION
The characterization of the frequency content of ground motions by a single synthetic parameter
provides a straightforward criterion for their classification. During the last decades, several proposals
have been made to this end. However, the relevance of proposed parameters depends on different
factors and, at present, a unique solution has not yet been found.
The study presented in this paper continues a research initiated by Lungu et al. in the early nineties
(Lungu et al, 1992, Dubină and Lungu, 2003). The aim of the study is to investigate the relevance of
the analyzed estimators for describing the ground motions frequency content. A set of improved
ground motion digitisations is used, together with newly developed software. The first results,
concerning correlations existing between various parameters, have been discussed in (Craifaleanu,
2011a, 2011b). Some new findings are presented in the following, including observations concerning
the spatial distribution of the most significant parameters for each event. Considerations are made, as
well, on the relevance of computed parameters for different types of ground motions and different
geological site conditions.
2. PREREQUISITES OF THE STUDY
2.1. Parameters used in the study for assessing the frequency content of ground motions
A relatively large number of parameters are used in the literature to characterize the frequency content
of earthquake ground motions. New and improved expressions of the scalar definitions of the
frequency content, expressed as period values, were proposed in the last few years by different authors
(Rathje, Abrahamson and Bray, 1998; Rathje, Faraj, Russell and Bray, 2004; Bommer, Hancock and
Alarcon, 2006; Ruiz-Garcia and Miranda, 2005). A number of bandwidth measures and related
parameters are used as well (JCSS, 2001).
For the study, three categories of parameters were computed: (a) parameters based on power spectral
density and on the Fourier spectrum, (b) parameters based on response spectra and (c) parameters
based on peak ground motion values.
(a) Parameters based on power spectral density and on Fourier amplitude spectrum
1. The frequencies f1, f2 and f3, corresponding to the first three peaks, in order of their amplitude,
of the PSD (JCSS, 2001). In the paper, T1(PSD) = 1/f1 is used.
2. The f10, f50 and f90 fractile frequencies below which 10%, 50% and 90%, respectively, of the
total cumulative power of PSD occur (JCSS, 2001).
3. The central frequency, (Vanmarcke, 1976)
4. The mean frequency,
ω
(Thrainsson, Kiremidjan and Winterstein, 2000), with its inverse, the
mean period, denoted in the following by Tmean.
5. The shape factor, q (Vanmarcke, 1976)
6. The ε frequency bandwidth parameter (Cartwright and Longuet-Higgins, 1956)
7. The ξ frequency bandwidth parameter (Boore, 2003)
8. The mean square period, Tms (Rathje, Abrahamson and Bray, 1998).
(b) Parameters based on response spectra
1. The predominant period based on acceleration spectrum, TgSA (Rathje, Abrahamson and Bray,
1998), defined as the period at which the maximum ordinate of an acceleration response
spectrum computed for 5% damping occurs.
2. Analogously, the predominant period based on velocity spectrum, TgSV (Miranda, 1993a;
Ruiz-Garcia and Miranda, 2005) and the predominant period based on input energy spectrum,
TgSEI (Miranda, 1993b).
3. The characteristic period, *
1
T, defined as the period at the transition between the
constant-acceleration and the constant-velocity segments of a 5% damped elastic spectrum,
and given by
(
)
( )
max
max
*
12
a
v
S
S
T
π
= (2.1)
where (Sv)max and (Sa)max are the maximum ordinates of the pseudo-velocity and
pseudo-acceleration response spectra, computed for 5% damping.
An alternate definition of the characteristic period, proposed by Lungu et al. in 1997 (cited in
Dubină and Lungu, 2003), is used in this paper, i.e.:
EPAEPVTC
π
2= (2.2)
with
5.2),( max0.4sonaveragedv
SEPV = (2.3)
5.2),( max0.4sonaverageda
SEPA = (2.4)
In Eqns. (3.3) and (3.4), (Sv, averaged on 0.4s)max and (Sa, averaged on 0.4s)max are the maximum values of
velocity and acceleration response spectra, respectively, averaged on a 0.4 s period mobile
window.
Ruiz-Garcia and Miranda (2005) have proposed modified definitions of the spectral moments,
computed from the squared values of the velocity spectra, for elastic SDOF systems with damping
ratios of 5%. Based on the above definitions, they computed a modified spectral characteristic period,
=
==
n
i
iv
n
i
ivic TSTSTT
1
2
,
1
2
,
* (2.5)
and a modified central period
=
==
n
i
iv
n
i
ivicen TSTSTT
1
2
,
1
2
,
2* (2.6)
where n is the number of periods in the velocity spectra, Sv is the spectral velocity and T is the period
interval on the spectrum abscissa. Analogously to the Vanmarcke shape factor, q, the cited authors
also computed a frequency bandwidth parameter, , also based on modified spectral moments.
Smaller values of this parameters are associated with narrow band signals (e.g. 5.0
<
is considered a
narrow band ground motion).
To avoid confusion with Vanmarcke’s parameter, the modified shape factor of Ruiz-Garcia and
Miranda is denoted, in this paper, by q*
. For the same reason and also due to its analogy to Tmean, the
modified spectral characteristic period, *
c
T, is denoted by *
mean
T.
(c) Parameters based on peak ground motion values
A single parameter is considered in this category, i.e. the characteristic period of the ground motion,
computed based on an empirical relationship, suggested by Heidebrecht in 1987 (cited in Fajfar, Vidic
and Fischinger, 1990):
PGV
T3.4
3.4 = (2.7)
In the above equation, PGV is the peak ground velocity and PGA is the peak ground acceleration. This
period was used to define the lower bound of the medium period region, i.e. the period range where
the smoothed pseudo-velocity spectrum reaches its maximum values.
2.2. Ground motion database
The study was performed by using ground motions recorded during the four strong subcrustal seismic
events with moment magnitude, Mw, larger than 6, generated by the Vrancea seismogenic source
during the past 35 years. The seismic events considered in the analysis were: March 4, 1977 (moment
magnitude Mw = 7.4, focal depth h = 94 km), August 30, 1986 (Mw = 7.1, h = 131 km), May 30, 1990
(Mw = 6.9, h = 91 km) and May 31, 1990 (Mw = 6.4, h = 87 km).
A database of 313 ground motions, recorded during the four above-mentioned earthquakes, was used
(Fig. 2.1).
The records were classified according to their frequency bandwidth, by using the criteria in Table 2.1,
which are to some extent similar to those used by Lungu et al. in (Dubina and Lungu, 2003). All the
criteria in a row needed to be satisfied for a record to be classified as “narrow bandwidth” or “broad
bandwidth”.
3
101
122
87
2
70
85
61
1
31 37 26
March 4, 1977
(Mw=7.4)
Aug.30, 1986
(Mw=7.1)
May 30, 1990
(Mw=6.9)
May 31,1990
(Mw=6.4)
Number of records
Total
H
V
Figure 2.1. Number of ground motion records used in the study
Table 2.1. Criteria used in the study for the classification of ground motion records according to their bandwidth
Bandwidth ε f50 TC
Narrow
0.95
2.0Hz
0.95s
Intermediate all other records
Broad
0.85
3.0Hz
0.75s
By using the criteria in Table 2.1, from the total of 218 horizontal ground motion records, 21 were
identified as narrow band records, 151 as intermediate band records and 46 as broad band records.
2.3. Peculiarities of Vrancea earthquakes related to the determination of the predominant
period of ground motions
According to the literature (Sandi et al., 2004; Sandi and Borcia, 2011), the radiation directivity is
differentiated between the four seismic events considered in the study. While, for the 1977 and 1986
earthquakes, radiation was quite similar, i.e. approximately NE-SW, for the May 30, 1990 and May
31, 1990 earthquakes, N-S and S-E directivity was observed, respectively.
By investigating the influence of local site conditions on the frequency content of ground motions, it
was shown that, for a large proportion of the area affected by Vrancea earthquakes, it is difficult to
identify the depth of base rock, due to the particular geological conditions (Sandi et al., 2004a). The
reason is the absence of an interface where an obvious contrast can be identified in the shear wave
propagation velocity, i.e. a significant increase with depth of this parameter.
Based on parametric studies performed on the transfer function of superficial soil deposits for two
characteristic sites, the cited reference concludes that sites can be classified according to two distinct
situations:
a) a strong increase of shear wave propagation velocity at shallow depths;
b) a gradual increase with depth of the shear wave propagation velocities, proportional with
the number of soil layers taken into account in the analysis.
In the first case, local site conditions have a significant influence, and a stability tendency of the
predominant periods of ground motions is observed. In the second case, a tendency of variability of
the frequency content is found, and it is considered that the determinant influences are, most probably,
those of the focal mechanism and of the radiation / long distance attenuation characteristics.
A typical site from the first category is that of the “Cernavodă Municipality” seismic station, located
in the south-eastern part of Romania, while one of the most important sites in the second category is
the site of INCERC, in Bucharest, where the narrowest frequency band motions were recorded, during
the strong Vrancea earthquakes of March 4, 1977 and of August 30, 1986.
A research based on a different approach, performed by Lungu et al. (Dubină and Lungu, 2003) has
obtained, for the same site of INCERC, results that generally confirm the above observations. The
shear wave propagation velocities and soil layer characteristics were measured in a 128 meters-deep
borehole. By using this data, the fundamental period for the site was determined and compared with
predominant periods computed based on the power spectral density and the autocorrelation function,
for the local records of the March 4, 1977 and August 30, 1986. The predominant periods of vibration
computed for the two earthquakes were, for the NS components, 1.6 s and 1.4 s, respectively. Similar
values were obtained, based on borehole data, only by considering the entire soil profile (128 m).
3. CORRELATION STUDIES
Detailed results of correlation analyses performed for the parameters described in Section 2.1 have
been presented in (Craifaleanu, 2011a; b). Some results are briefly summarized below.
Table 3.1 shows the correlation coefficients, R2, computed for the horizontal components of the
ground motions in the database. It was assumed that the relationship between two parameters is given
by a linear function, of the form y = a · x + b.
Table 3.1. Correlation coefficients (R2) between the analyzed ground motion frequency content and bandwidth
parameters (assumed relationship: y=a·x+b). Horizontal components for all seismic events
Tms T1(PSD)
Tmean
Tcen TgSA TgSV TgSEI
TC Tmean
*
Tcen
*
T4.3 q q* ε ξ
Tms 1.000
0.531
0.763
0.570
0.441
0.285
0.417
0.831
0.330
0.235
0.759
0.515
0.574
0.445
0.551
T1(PSD)
0.531
1.000
0.384
0.261
0.227
0.189
0.358
0.468
0.242
0.182
0.378
0.324
0.375
0.161
0.201
Tmean
0.763
0.384
1.000
0.921
0.543
0.127
0.204
0.512
0.111
0.066
0.559
0.272
0.267
0.481
0.588
Tcen 0.570
0.261
0.921
1.000
0.443
0.071
0.126
0.341
0.048
0.023
0.410
0.098
0.149
0.420
0.491
TgSA 0.441
0.227
0.543
0.443
1.000
0.030
0.064
0.276
0.023
0.007
0.307
0.196
0.108
0.356
0.435
TgSV 0.285
0.189
0.127
0.071
0.030
1.000
0.417
0.366
0.627
0.574
0.266
0.253
0.565
0.127
0.133
TgSEI 0.417
0.358
0.204
0.126
0.064
0.417
1.000
0.426
0.403
0.338
0.318
0.258
0.474
0.111
0.127
TC 0.831
0.468
0.512
0.341
0.276
0.366
0.426
1.000
0.401
0.290
0.715
0.442
0.673
0.274
0.371
Tmean
*
0.330
0.242
0.111
0.048
0.023
0.627
0.403
0.401
1.000
0.975
0.356
0.229
0.769
0.053
0.072
Tcen
* 0.235
0.182
0.066
0.023
0.007
0.574
0.338
0.290
0.975
1.000
0.276
0.160
0.626
0.028
0.040
T4.3 0.759
0.378
0.559
0.410
0.307
0.266
0.318
0.715
0.356
0.276
1.000
0.379
0.519
0.310
0.372
As it can be observed from Table 3.1, in most cases (56%) correlation coefficients for the period-type
parameters are in the intermediate range (0.1…0.5, values shown in italic font). In 31% of the cases
the correlation coefficients exceed 0.5 (values shown in bold font), while in about 13% of the analyzed
cases a weak correlation was obtained, with R2 values less than 0.1 (values shown in normal font).
The mean square period, Tms shows the best correlation (R2 = 0.831) with the characteristic period, TC,
computed with the modified definitions of effective peak ground motion values. Good correlations
(R2
0.76) are also observed with the mean period, Tmean, and with the characteristic period based on
peak ground motion values, T4.3. Lower correlation coefficients (0.570 and 0.531, respectively) result
between Tms and Tcen and between Tms and T1(PSD). The mean square period also shows a good
correlation with the frequency bandwidth indicators, especially q, q* and ξ.
The period corresponding to the maximum PSD value, T1(PSD), is rather poorly correlated with the
other analyzed parameters, except Tms.
A preliminary evaluation made on vertical records has shown a better correlation between T1(PSD) and
TgSV, TgSEI, Tmean
*
and Tcen
*, as compared with the set of horizontal records.
A selection of ground motion records according to the frequency bandwidth criteria in Table 2.1 has
identified, from the total of 218 horizontal components, 21 narrow frequency band motions, recorded
during the earthquakes of March 4, 1977, August 30, 1986 and May 30, 1990. The number of narrow
frequency band records was considered as insufficient to obtain reliable correlation results.
The correlations were also assessed separately for the 1986 and 1990 seismic events. As an alternative
hypothesis, it was assumed that the functional passes through the origin, i.e. y=a·x. Some relevant
results are summarized in Table 3.2.
Table 3.2. Correlations between the mean square period, Tms, and TC, Tmean and T4.3, respectively, for the
horizontal components of the analyzed records. Assumed relationship between two parameters: y=a·x
Aug 30, 1986
May 30, 1990
May 31, 1990
All records,
including those of
March 4, 1977
R2
0.8122 0.8143 0.2084 0.7954
Tms - TC a
0.8006 0.7954 0.8083 0.8017
R2
0.7238 0.7723 0.6978 0.7619
Tms - Tmean
a
1.5409 1.5304 1.4562 1.5328
R2
0.7146 0.6745 0.6137 0.7216
Tms - T4.3 a
1.2008 1.1049 1.1705 1.1508
One can observe that, for all analyzed correlations, the values of both R2 and a coefficients in Table
3.2 vary very little with the considered event, which could be used for the development of empirical
relationships between the above parameters. The only exception is the low R2 (0.2084) resulting for
the Tms - TC correlation, in the case of the May 31, 1990 earthquake. A possible explanation could
reside in the lower magnitude of this earthquake; however, further research is needed in order to
individualize each event.
4. SPATIAL AND TEMPORAL DISTRIBUTION OF PERIOD-TYPE PARAMETERS
The spatial distribution of the analyzed period-type parameters was analyzed, for the considered
seismic events.
Taking into account the promising results obtained for Tms in the correlation studies, the obtained
values were mapped, as shown in Fig. 4.1. Values for both components of ground motions are
displayed, for each seismic station. Due to the gradual development of the seismic networks, or to the
occasional malfunction of some instruments, the set of recording stations differs, to a certain extent,
between the considered earthquakes.
a) Aug 30, 1986 b) May 30, 1990 c) May 31, 1990
Figure 4.1. Maps of the mean square period, Tms, for the 1986 and 1990 earthquakes
As it can be observed on the maps in Fig. 4.1, the variability of Tms values with the seismic event is
different for the recording stations. While in the stations located in the north-eastern and south-eastern
parts of the country the variability is small, there are stations near to the Carpathian Arc bend and in
Bucharest, which exhibit larger Tms values for one or two of the three considered events.
Similar observations were made by examining the maps for T1(PSD) displayed in Figs. 4.2 and 4.3. As in
the case of Tms, the stations located in the north-eastern and south-eastern parts of the country appear to
have a smaller variability the values with the event, while other stations exhibit large T1(PSD) values for
one or two of the three considered events and much smaller values for the other event(s). To this
second category belong most of the records obtained on August 30, 1986 at the stations located in
Bucharest and its surroundings (the group of stations in the south-west of the analyzed zone), at some
stations near the Carpathian Arc bend (Muntele Roşu (MLR), Râmnicu Sărat (RMS1) and Focşani
(FOC3) in 1986, Surduc (SDR), RMS1 and Vrâncioaia (VRI) on May 30, 1990, IstriŃa (ISR) on May
31, 1990) and at station Shabla in Bulgaria, for the earthquake of May 30, 1990. Practically all the
records in the second category are narrowband motions, according to the criteria in Table 2.1.
a) Aug 30, 1986 b) May 30, 1990 c) May 31, 1990
Figure 4.2. Maps of the period corresponding to maximum PSD, T1(PSD), for the 1986 and 1990 earthquakes
The above observations are also illustrated by the maps of T1(PSD) for Bucharest, in Fig. 4.3. As it can
be seen from this figure, large values of T1(PSD) are characteristic for the 1986 earthquake, for one or
both components of the ground motions. The situation is radically different for the other two events,
with a single exception, that of the EW component at the MTR1 station, on May 31, 1990. This record
does not meet all conditions in Table 2.1 for a narrowband motion; however, it has a q value of 0.95.
a) Aug 30, 1986 b) May 30, 1990 c) May 31, 1990
Figure 4.3. Bucharest: maps of the period corresponding to maximum PSD, T1(PSD), for the 1986 and 1990
earthquakes
The explanation of the strong contrast observed in Bucharest between the frequency content of the
1986 records and that of the 1990 records could possibly reside in the different characteristics
(directivity of radiation / attenuation) of the analyzed earthquakes, discussed in Section 2.3 of the
paper.
The variability of T1(PSD) with seismic event is summarized in Fig. 4.4. Blue circles denote the August
30, 1986 earthquake, magenta circles, the May 30, 1990 earthquake, and green circles, the May 31,
1990 earthquake. Values for both components are displayed for each station.
As it can be observed, for the stations located in the south-eastern part of Romania, the variation of
T1(PSD) with the seismic event is small. Among these stations, it can be mentioned the “Cernavoda
Municipality” seismic station (CVD1 and CVD2), mentioned in Section 2 of the paper, as well as the
neighboring stations, Feteşti (FET1), Baia (BAA) and Tulcea (TLC1). Taking into account the
geology of the concerned area (Dobrogea), the above results could confirm the hypotheses concerning
the predominant influence, for these sites, of local soil conditions. A small variability of T1(PSD) values
can be also observed for other stations, for instance in Bârlad (BIR1 and BIR2). Additional research is
needed to further refine the identification of the site categories discussed in Section 2.
a) All seismic stations b) Stations in Bucharest
Figure 4.4. Bucharest: maps of the period corresponding to maximum PSD, T1(PSD) , for the 1986 and 1990
earthquakes
5. CONCLUSIONS
The capacity of eleven different scalar period-type parameters, used in the literature to describe the
frequency content of ground motions, was assessed comparatively, by using a database of over 300
records obtained from the four strong earthquakes with moment magnitude, Mw, larger than 6, that
occurred in the Vrancea region in the past 35 years. Additionally, information provided by four
spectral bandwidth measures was used. Correlations between the considered parameters were
determined for the entire ground motion set, as well as for subsets created by type of component
(horizontal or vertical), event or frequency bandwidth. The study presented in the paper is part of a
larger research, previous results being described in (Craifaleanu, 2011a; b).
Good and remarkably stable correlations were obtained between the mean square period, Tms (Rathje et
al., 1998) and the characteristic period, TC, computed with modified definitions of effective peak
ground motion values (Lungu et al., 1997), the mean period, Tmean, and the characteristic period based
on peak ground motion values, T4.3 (Heidebrecht, 1987), respectively.
Based on the analysis of the spatial and temporal distributions of period-type parameters, it was
concluded that the variability of these parameters with the seismic event differs substantially among
the analyzed seismic stations. The first conclusions appear to confirm the hypothesis of Sandi et al.
(2004) concerning the types of sites in Romania for which the influence of local site conditions on the
frequency content of the ground motions prevails over other factors, as directivity, attenuation or focal
mechanism.
ACKNOWLEDGEMENTS
The author would like to thank Dr. Ioan Sorin Borcia from URBAN-INCERC, INCERC Bucharest Branch, for
providing the TC values used in the study.
The work reported in this paper was partly sponsored by the Romanian National Authority for Scientific
Research, ANCS.
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90/15.10.2001.
... This parameter was extensively used in the studies dedicated to the microzonation of Bucharest, and also in the development of the macrozonation maps in the Romanian seismic design code (Dubina and Lungu 2003). The second parameter, T 1(PSD) , has a particular relevance for narrowband motions, as are the majority of the records obtained in Bucharest during the strong earthquakes of 1977 and 1986 (Craifaleanu 2011(Craifaleanu , 2012. ...
... While T C varies significantly within the area of the city, T 1(PSD) has much more stable values. Given the different frequency bandwidths of the ground motions used in the analysis, i.e. narrowband for most of the 1986 records and for the 1977 record and broadband for the 1990 records (Craifaleanu 2011(Craifaleanu , 2012, a better relevance of T 1(PSD) for the first category of motions was observed. ...
Chapter
With a population of over 2 million inhabitants, Bucharest is considered as one of the world’s 10 most vulnerable cities to earthquakes. Several destructive earthquakes, occurring from the Vrancea seismogenic source, have hit the city in the past. According to previous studies, the particular local near surface geology of the city seems to play an important role in the site amplification phenomena recorded during strong earthquakes. In the paper, the frequency content of ground motions recorded in Bucharest during the strong Vrancea earthquakes of the last four decades is assessed analytically, based on parameters used in literature, and results are mapped and interpreted in correlation with the information obtained by in situ measurements. Conclusions are drawn, with reference to the combined effects of seismic source and of local site conditions in the analyzed area.
... Single scalar parameters are often defined using the maximum or average acceleration or Fourier spectra values in a specific range of frequencies. Mean period (T m ), an average spectral period (T avg ) have found their application for three reasons, namely: (i) simplicity of using these parameters in interpreting the results as evaluating the possibility of resonance phenomenon [3] and description of ground motion records which makes it easier to compare and evaluate ground motion characteristics [4], (ii) meaningful relationship of these parameters with the seismic response of structures [5][6][7], (iii) the scalar single frequency content parameters provide a suitable platform for earthquake ground-motions clustering [1,8]. ...
Article
Most of the empirical models that have been proposed to estimate the frequency variation of earthquakes were based on shallow earthquake data, so the need to examine the accuracy of these relationships and provide a new relationship for intermediate-depth earthquakes is obvious. As a new attempt, the interpretation of the difference in the behaviour of the frequency content indicators with distance and magnitude for shallow and intermediatedepth earthquakes as a function of the difference in attenuation properties is discussed. The ground motion database of this study consists of 243 horizontal components of events recorded at Vrancea, Romania and Makran, Iran. The focal depth of selected events was reported between 82 and 131 km. Two scalar parameters, the average spectral period (Tavg) and the mean period (Tm), have been used as frequency content indicators. In addition to examining the accuracy of previous models, a new predictive relationship has been proposed for the two selected scalar quantities as a function of moment magnitude, hypocentral distance and site conditions. Findings provide evidence that the empirical models proposed in the past could not provide accurate estimates of the frequency content of intermediate-depth events. In contrast, the quality of assessments has significantly improved based on the new model of this study.
... It is seen that the two parameters describe not only the energy distribution of earthquake ground motion but also the spectral properties. It is recognized that various characteristic periods, which are usually single scalar parameters, were used to characterize the frequency content of strong ground motion before [Rathje et al., 1998;Rathje et al., 2004;Rathje and Antonakos, 2011;Zhao and Tong, 2009;Craifaleanu, 2012;Yaghmaei-Sabegh, 2017]. While single scalar parameters were proved to be useful for the narrow-band ground motions, but remained challenges in efficiently characterizing the wide-band ground motions. ...
Article
Classification of earthquake ground-motion records is carried out in this article using K-means cluster technique. Two kinds of cluster attributes are introduced, which are augmented by the frequency band of energy concentration and by the magnitude distance of earthquake ground motions. The effectiveness of cluster analysis is testified through the investigation of 7692 earthquake ground-motion records. It is revealed that the clustered ground-motion records show significant group discrepancies in spectral properties. A new seismic response spectrum is then suggested taking account of the influences of magnitude, propagation distance, and site class. An optimization criterion is introduced to identify the characteristic period of the suggested seismic response spectrum, through a comparative study between the mean response spectrum of the clustered ground-motion accelerations and the seismic response spectrum in provisions. It provides a comprehensive argument for characterizing the spectral properties of ground motions not only with respect to specific site but also with respect to specific magnitude and propagation distance. Numerical investigations indicate that the cluster analysis technique has the benefit of dealing with massive ground-motion records, whereby the suggested seismic response spectrum and associated characteristic periods are applicable of integrated design of seismic structures.
... Simple representation may make the comparisons of ground-motion characteristics easier (Stewart et al. 2001). It also allows choosing a straightforward criterion for classification of motions (Craifaleanu 2012). Another reason for the large use of frequency content indicators is their simplicity. ...
Article
Full-text available
This paper presents a new clustering procedure based on K-means and self-organizing map (SOM) network algorithms for classification of earthquake ground-motion records. Six scalar indicators are used in data analysis for describing the frequency content features of earthquake ground motions, named as the average spectral period (Tavg), the mean period (Tm), the smoothed spectral predominant period (T0), the characteristic period (T4.3), the predominant period based on velocity spectrum (TgSv), and the shape factor (Ω). Different clustering validity indexes were applied to determine the best estimates of the number of clusters on real and synthetic data. Results showed the high performance of proposed procedure to reveal salient features of complex seismic data. The comparison between the results of clustering analyses recommend the smoothed spectral predominant period as an effective indicator to describe ground-motion classes. The results also showed that K-means algorithm has better performance than SOM algorithm in identification and classification procedure of ground-motion records.
... Simple representation of frequency content may make the comparisons of ground-motions' characteristics easier (Stewart et al. 2001). It also allows a straightforward criterion for classification of earthquake ground-motions (Craifaleanu 2012). Another reason for the large use of frequency content indicators is their simplicity. ...
Article
This paper presents the development of new and simple empirical models for frequency content prediction of ground-motion records to resolve the assumed limitations on the useable magnitude range of previous studies. Three period values are used in the analysis for describing the frequency content of earthquake ground-motions named as the average spectral period (T avg), the mean period (T m), and the smoothed spectral predominant period (T 0). The proposed models could predict these scalar indicators as function of magnitude, closest site-to-source distance and local site condition. Three site classes as rock, stiff soil, and soft soil has been considered in the analysis. The results of the proposed relationships have been compared with those of other published models. It has been found that the resulting regression equations can be used to predict scalar frequency content estimators over a wide range of magnitudes including magnitudes below 5.5.
Conference Paper
A parametric study on the seismic response of base isolated steel-moment resisting frame buildings is presented. Taking into account the inelastic behavior of isolation system and superstructure, a number of special steel moment-resisting frames with different heights are considered. The models are designed according to ASCE07-10 for high seismic risk and developed using Opensees. Near-fault and far-fault earthquake ground motions are selected and arranged into different categories according to the frequency content features of records which are quantified in terms of peak ground acceleration to peak ground velocity ratio, AP/VP. The variation of story drift, floor acceleration and isolator displacement under different earthquakes is computed to study the effects of the AP/VP ratio on the response of base isolated steel frames. The nonlinear response-time history analyses show that the isolator displacement and story drift is significantly influenced by the AP/VP ratio of ground motions. Also, inelastic behavior was observed in base isolated steel frames under near-fault excitations with a low value of AP/VP ratio.
Conference Paper
Full-text available
The paper presents findings from some recent studies performed by the author on Vrancea earthquakes. By using a large database of accelerograms recorded during the strong events (moment magnitude Mw > 6) in 1977, 1986 and 1990, a detailed analysis was conducted in order to identify the best parameters to express essential characteristics of ground motions, as frequency bandwidth and predominant period. Sixteen parameters in the literature were computed and correlations between them were investigated. In another stage of the research, the Park-Ang damage index and two derivate indices were used to express the damage potential of the analyzed ground motions. Damage spectra, as well as uniform damage spectra of the yield strength capacity were computed, and their spatial distribution was represented. Based on values obtained by averaging spectral ordinates on characteristic period intervals, and taking into account actual damage reported following the considered events, conclusions were drawn on the damage potential of the analyzed Vrancea earthquakes.
Article
The paper presents the results of a study performed on a large ground motion database, containing records obtained during the three strongest earthquakes that occurred during the past four decades in the Vrancea seismogenic zone. In order to express strength demands imposed by these earthquakes, constant-ductility nonlinear acceleration spectra were computed for two sets of seismic records, selected as representative for narrow frequency band and broad frequency band ground motions, respectively. The spectra, determined for various types of bilinear hysteretic models, were normalized with respect to peak ground acceleration and mean values, as well as coefficients of variation, were computed for each analysis case. The sensitivity of spectral values to the variation of strength hardening and stiffness degradation parameters was determined, with reference to the elastic-perfectly plastic model. Conclusions were drawn, separately for the two distinct types of ground motion frequency content, on the significance of the considered hysteretic model parameters for the assessment of seismic strength demands.
Article
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Analyse de l'atténuation pour les séismes récents à profondeur intermédiaire de Vrancea. On présente les résultats de l'analyse de l'atténuation, effectuée pour les séismes de Vrancea (Roumanie), de 1977.03.04 (M GR = 7.2), 1986.08.30 (M GR = 7.0), 1990.05.30 (M GR = 6.7) et 1990.05.31 (M GR = 6.1). Les données d'entrée ont été de nature instrumentale. L'analyse de l'atténuation a été effectuée d'une manière approfondie, allant jusqu'à la considération des caractéristiques directionnelles et spectrales. On a défini les paramètres du mouvement du terrain utilisés alternativement. On présente les techniques d'analyse utilisées. On présente, comme élément de référence, les résultats obtenus auparavant, en 1995. On présente ensuite les nouveaux résultats, ayant comme point de départ une base de données plus complète. Ils concernent différentes fonctions de régression, les résultats du développement Fourier par rapport à l'angle azimutal, et des valeurs de l'écart moyen quadratique pour les différents paramètres. Ensuite on discute les résultats et on en déduit des conclusions concernant les aspects méthodologiques et les caractéristiques des séismes de Vrancea.
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In recent years, the utilization of time histories of earthquake ground motion has grown considerably in the design and analysis of civil structures. It is very unlikely, however, that recordings of earthquake ground motion will be available for all sites and conditions of interest. Hence, there is a need for efficient methods for the simulation and spatial interpolation of earthquake ground motion. In addition to providing estimates of the ground motion at a site using data from adjacent recording stations, spatially interpolated ground motions can also be used in design and analysis of long-span structures, such as bridges and pipelines, where differential movement is important. The objective of this research is to develop a methodology for rapid generation of horizontal earthquake ground motion at any site for a given region, based on readily available source, path and site characteristics, or (sparse) recordings. The research includes two main topics: (i) the simulation of earthquake ground motion at a given site, and (ii) the spatial interpolation of earthquake ground motion. In topic (i), models are developed to simulate acceleration time histories using the inverse discrete Fourier transform. The Fourier phase differences, defined as the difference in phase angle between adjacent frequency components, are simulated conditional on the Fourier amplitude. Uniformly processed recordings from recent California earthquakes are used to validate the simulation models, as well as to develop prediction formulas for the model parameters. The models developed in this research provide rapid simulation of earthquake ground motion over a wide range of magnitudes and distances, but they are not intended to replace more robust geophysical models. In topic (ii), a model is developed in which Fourier amplitudes and Fourier phase angles are interpolated separately. A simple dispersion relationship is included in the phase angle interpolation. The accuracy of the interpolation model is assessed using data from the SMART-1 array in Taiwan. The interpolation model provides an effective method to estimate ground motion at a site using recordings from stations located up to several kilometers away. Reliable estimates of differential ground motion are restricted to relatively limited ranges of frequencies and inter-station spacings.
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An important aspect to include in comprehensive characterization of earthquake ground motion is the duration of the shaking, which can be represented either by an interval of time during which the motion fulfils some specified criteria or else the number of effective cycles of motion. Several different definitions have been proposed for measuring both of these parameters and analysis of empirical predictive equations and a large strong-motion dataset show that durations calculated using different definitions are generally poorly correlated. Numbers of cycles of motion calculated using different definitions can show much better correlations in some cases. In nearly all cases the correlations between calculated durations and numbers of cycles are very poor, with the exception of uniform duration and number of cycles obtained using rainflow range counting, both using absolute rather than relative thresholds. The scatter in this correlation can be reduced by adding an appropriate measure of the period content of the motion as an explanatory variable.
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The frequency content of an earthquake ground motion is important because it affects the dynamic response of earth and structural systems. Four scalar parameters that characterize the frequency content of strong ground motions are (1) the mean period (T-m), (2) the average spectral period (T-avg), (3) the smoothed spectral predominant period (T-o), and (4) the predominant spectral period (T-p). T-m and T-avg distinguish the low frequency content of ground motions, while T-o is affected most by the high frequency content. T-p does not adequately describe the frequency content of a strong ground motion and is not recommended. Empirical relationships are developed that predict three parameters (T-m, T-avg, and T-o) as a function of earthquake magnitude, site-to-source distance, site conditions, and rupture directivity. The relationships are developed from a large strong-motion database that includes recorded motions from the recent earthquakes in Turkey and Taiwan. The new relationships update those previously developed by the authors and others. The results indicate that three site classes, which distinguish between rock, shallow soil, and deep soil, provide a better prediction of the frequency content parameters and smaller standard error terms than conventional "rock" and "soil" site classes. Forward directivity significantly increases the frequency content parameters, particularly T-m and T-o, at distances less than 20 kin. Each of the frequency content parameters can be predicted with reasonable accuracy, but T-m is the preferred because it best distinguishes the frequency content of strong ground motions.
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Strength-reduction factors that are used to reduce linear elastic design spectra to account for the hysteretic energy dissipation of the structure are evaluated. The paper presents a summary of results of a statistical analysis of strength-reduction factors computed for single-degree-of-freedom systems undergoing different levels of inelastic deformation when subjected to a relatively large number of recorded earthquake ground motions. Special emphasis is given to the influence of soil conditions. Results indicate that for a given displacement ductility demand, the use of period-independent reduction factors is inadequate. Soil conditions can have an important effect on strength-reduction factors, particularly in the case of soft-soil sites. It is recommended that strength-reduction factors to be used in design be specified as a function of the period and inelastic capacity of the structure, and of at least two types of soil conditions-one for rock and relatively firm sites and another for soft-soil sites. Following these recommendations, simplified expressions to compute strength-reduction factors are proposed.
Article
It is often useful in earthquake engineering practice to characterize the frequency content of an earthquake ground motion with a single parameter. Three simplified frequency content parameters are examined: mean period (T-m), predominant period (T-p), and the smoothed spectral predominant period (T-o). These frequency content parameters are calculated for 306 strong motion recordings from 20 earthquakes in active plate-margin regions. These data are used to develop a model that describes the magnitude, distance, and site dependence of these frequency content parameters, Nonlinear regression analyses are performed to evaluate model coefficients and standard error terms. The results indicate that the traditional T-p parameter has the largest uncertainty in its prediction, and that previous relationships proposed to predict T-p are inconsistent with the current data set. Moreover, T-m is judged to be the best simplified frequency content characterization parameter, and it can be reliably estimated.
Article
The expression I=vgtD0.25 is proposed as an instrumental measure of earthquake ground motion capacity to damage structures with fundamental periods in the medium-period (velocity-controlled) region. Only two of the basic ground motion parameters which can be routinely predicted in the design procedure (peak ground velocity and the duration of strong shaking) are included in the formula. Expressions for determining the bounds of the medium-period region are also proposed as a function of the basic ground motion parameters. A total of 40 records having very different characteristics, including extremely short and long duration, were used in the statistical study. The new intensity parameter has been evaluated by using inelastic and elastic relative displacement and input energy spectra.