13th World Conference on Earthquake Engineering
Vancouver, B.C., Canada
August 1-6, 2004
Paper No. 1969
DISPLACEMENT RESPONSE SPECTRA AT LONG PERIODS: AN
APPLICATION TO SEISMIC HAZARD ASSESSMENT IN SOUTHERN
ITALY
Roberto Paolucci1, Ezio Faccioli2 and Julian García-Mayordomo 3
SUMMARY
Motivated by the increasing diffusion of methods based on displacement demand, both for design and
assessment of existing structures, we present here a new contribution that aims at improving the
formulation of displacement response spectra over a wide period range, showing an example of
application to seismic hazard assessment. Based on a previous analysis of selected sets of high quality
digital strong motion data from different regions (Taiwan, Japan, Italy and Greece), we illustrate the
salient features of displacement spectra up to 10 s period, as a function of magnitude, source distance and
site conditions, and interpret them on the basis of simple analytical models of displacement waveforms.
We recall previously derived analytical expressions for the displacement spectra and for the attenuation of
peak ground displacement (dmax) with magnitude and distance, and we show how such expressions, and
those applicable for the long period spectral ordinates, can be implemented in a approach to probabilistic
seismic hazard assessment: by way of illustration, uniform hazard displacement spectra are generated for
Southern Calabria, one of the regions of Italy with highest earthquake hazard exposure.
INTRODUCTION
It is well known that the application seismic design methods based on displacement demand (Priestley
[1]) is affected by the inaccurate definition of spectral response in the long period range (Tolis and
Faccioli [2], Bommer and Elnashai [3]). As a matter of fact, calculating design displacement spectra by
simply multiplying the acceleration spectrum by the factor (Tn/2π)2 may lead to unacceptably large
displacement spectral ordinates, for vibration periods Tn larger than 3 or 4 s. Most of the seismic design
regulations, including recent ones such as the International Building Code (ICC 2000 [4]), ignore this
problem, leading to an indefinite increase of displacement spectral ordinates with period. Hence, the
spectra provided in such regulations are not generally applicable to displacement-based design.
For this reason, in the most recent version of EC8 (CEN 2003 [5]) an independent expression for the
elastic displacement spectrum is provided, for periods larger than 3 s. The EC8 displacement spectral
1
Dept. Structural Engineering, Politecnico of Milano, P.za Leonardo da Vinci, 32 I-20133 Milano, ITALY
Dept. Structural Engineering, Politecnico of Milano, P.za Leonardo da Vinci, 32 I-20133 Milano, ITALY
3
Dept. Geodinámica, Universidad Complutense de Madrid, Avd. Complutense s/n, Madrid, ESPAÑA.
2
shape was originally based on a limited amount of digital strong motion records, essentially from the Kobe
and the Umbria-Marche (Italy) earthquakes (Tolis and Faccioli [2]). However, a very recent study
(Faccioli et al. [6]) using a much wider dataset, with digital records from the 1999 Taiwan (M7.6) and
Greece (M5.9) earthquakes, and from 16 Japanese earthquakes recorded by the K-net, with magnitude in
the range from 5.5 to 6.5, has indicated that the present formulations of elastic displacement spectrum for
design should be probably revised.
Herein, we first summarize the main findings of the study of Faccioli et al [6] (denoted in the following as
FPR04), namely the analytical expressions for the normalized displacement spectral shapes and for the
attenuation of peak ground displacement with magnitude and distance; subsequently, we show an
application of seismic hazard assessment in terms of long period spectral ordinates in the highly seismic
region of Southern Calabria, Italy.
DISPLACEMENT SPECTRAL SHAPES
Effect of magnitude and distance on the observed average spectral shapes
Referring to FPR04 for a thorough analysis of the earthquake records, including the effect of site
conditions, we summarize here the most relevant findings of the analysis of strong motion records in terms
of the influence of magnitude and distance on the 5% damped horizontal spectra. Figure 1 displays the
average displacement spectral shapes, normalized by the 10 s spectral ordinate, for the distance ranges of
10-30 km and 30-50 km.
1.4
Normalized spectral displacement
Normalized spectral displacement
1.4
1.2
1
0.8
0.6
0.4
10-30 km
M = 7.6
6.0 < M < 6.4
5.4 < M < 6.0
0.2
0
1.2
1
0.8
0.6
0.4
30-50 km
M = 7.6
6.0 < M < 6.4
5.4 < M < 6.0
0.2
0
0
2
4
6
Period (s)
8
10
0
2
4
6
8
10
Period (s)
Figure 1. 5% damped horizontal displacement spectra for the indicated magnitude ranges in the distance
intervals 10-30 km (left) and 30-50 km (right), normalized with respect to the 10 s spectral ordinate. Thick
lines represent average values, while thin lines represent average + 1 standard deviation. After FPR04.
All spectra tend to increase up to an apparent “corner period” beyond which the ordinates remain roughly
constant for M 7.6, while for the other magnitude classes they tend to decrease gently towards the peak
ground displacement value. The influence of magnitude on such corner period is not evident for M<6.5:
although there is a slight tendency of a shift towards longer periods for increasing magnitudes, the corner
period in this magnitude range lies typically between 1 and 2 s. For the Chi-Chi earthquake the normalized
average spectral shape is quite different, with a corner period between 6 and 7 s.
The effect of distance on the normalized spectral shape is small, at least up to 50 km from the source, due
to the predominantly geometrical attenuation effect. However, for M<6.5 the corner period moderately
increases with distance, likely due to the increasing influence of surface waves in the recorded motions. In
a previous study using the European strong-motion data set, Bommer and Elnashai [3] found that the
influence of distance on displacement spectral shape, up to 3 s period, is negligible for practical purposes.
Analytical models
The previous displacement spectral shapes can be reasonably well interpreted through simple pulseshaped waveforms. These are typical of near-field ground motion from large earthquakes, where the
component in the direction of fault slip is generally characterized by a “fling-step” displacement pulse,
and the fault-normal component by a narrow-band directivity pulse, the period of which increases with
magnitude (Somerville [7]).
While most of the near-field Chi-Chi records present a fling-step pulse such as shown in the left side of
Figure 2, the displacement histories from the moderate magnitude earthquakes considered in this study are
generally more complicated. However, in several cases, especially in the rock or stiff soil records at 10 to
30 km distance, the displacement waveform is dominated by a single pulse, such as shown in the right
side of Figure 2.
TCU129.ew
Syntagma-3rd.l
1000
2
100
2
0
s/
m
c
0
s/
m
c
-1000
-100
10
50
s/
m
c
0
0
s/
m
c
-50
-10
100
1
0
m
c
0
m
c
-100
0
10
20
30
40
Time (s)
50
-1
60
0
5% Spectral displacement
1
2
3
4 5 6
Time (s)
7
8
9 10
5% Spectral displacement
100
3
2
50
m
c
m
c
0
0
2
4
6
Period (s)
8
10
1
0
0
2
4
6
Period (s)
8
10
Figure 2. Examples of digital records from our data set showing a permanent offset (left) and a prevailing
narrow band displacement pulse (right). The TCU129 record, from the 1999 Chi-Chi earthquake, was
baseline corrected. The Syntagma record, from the 1999 Athens earthquake, was high-pass filtered at 0.1
Hz, after baseline correction. In the lower part of the figure, the 5% displacement response spectra of these
records are shown. After FPR04.
This has suggested to interpret the observed records through simple pulse-shaped waveforms such as
shown in Figure 3. The waveform on the left of Figure 3, defined by two branches of a parabola, can be
used for “fling-step” pulses such as those recorded during the Taiwan Chi-Chi earthquake, while that on
the right turns out to be appropriate for narrow-band displacement pulses from moderate magnitude
earthquakes (5.4<M<6.5), up to an epicentral distance of 30 km. The analytical expressions of the
displacement response spectra for the two pulses can be found in FPR04, while the normalized spectrum
for the narrow-band pulse is depicted in Figure 4.
dmax
dmax
displacement
displacement
t0
t
2t0
t0
t
2t0
Figure 3. Pulse-shaped displacement waveforms.
Note that both waveforms of Figure 3 are defined by only two parameters, i.e., the half-duration t0 of the
pulse and the peak value dmax. We summarize in the following the most relevant aspects for the estimation
of such parameters, based on the source magnitude and distance; more details are found in FPR04.
1.6
2 ⎛ Tn
⎜
( 2π ) ⎜⎝ t0
⎞⎛
⎛ t0
⎟⎟⎜⎜1 − cos 2π1.4
⎜⎜
⎠⎝
⎝ Tn
damping 0%
damping 5%
⎞⎞
⎟⎟ ⎟⎟
⎠⎠
1.2
D/Dmax
1
0.8
1 ⎛ Tn
⎜
( 2π ) ⎜⎝ t0
0.6
⎞⎛
⎛t
⎟⎟⎜⎜ sin 2π ⎜⎜ 0
⎠⎝
⎝ Tn
⎞⎞
⎟⎟ ⎟⎟
⎠⎠
0.4
1 ⎛ Tn
⎜
( 2π ) ⎜⎝ t0
0.2
0
0
2
⎞⎛⎜
⎛t
⎟⎟ 5 − 4 cos 2π ⎜⎜ 0
⎠⎜⎝
⎝ Tn
4
6
⎞ ⎞⎟
⎟⎟
⎠ ⎟⎠
8
10
Tn/t0
Figure 4. Displacement spectrum for the impulsive signal defined by Equation 3. Thick line: undamped
spectrum of equation 4a to 4c. Dashed line: 5% damped spectrum (calculated by numerical integration).
After FPR04.
Evaluation of t0
A simple way of estimating the t0 parameter of the previous pulses is to take it equal to one-half the
duration τ of the largest velocity pulse of recorded ground motion. In the absence of more general studies,
we used the relationship recently proposed by Somerville [8] that correlates τ with magnitude for faultnormal forward rupture directivity pulses. On rock, the Somerville relationship reads
log10 τ = - 3.17 + 0.5 MW.
(1)
Estimating t0=τ/2 through (1) resulted in a satisfactory agreement of the analytical spectral shapes with
the observed ones for the different magnitude ranges considered, as shown in Figures 5 and 6.
Evaluation of dmax
Existing attenuation relationships for dmax (Gregor and Bolt [9] for California; Tromans and Bommer [10]
for Europe) are mainly based on analog records and suffer from the well-known instrumental limitations
and long-period noise at periods larger than about 3s. Consistently with the framework of this study, we
preferred to check if a simple theoretical estimate of dmax as a function of magnitude and distance could fit
reasonably well the data. Based on simple analytical derivations from the Brune [11] source model, we
obtained the following simple form of the attenuation relation for dmax:
log10 d max = −4.3 + M W − log10 r
(2)
where r = hypocentral distance. Incorporating in this attenuation relation the specific features of near-field
motion, such as rupture directivity, azimuth, and static components of displacement (Somerville [7]),
would require investigations that are beyond the scope of this work.
Details on the derivation of (2), as well as the comparison with observed values of peak ground
displacement, are reported in FPR04.
Normalized spectral displacement
Chi-Chi (MW=7.6)
1
0.8
0.6
0.4
Average observed
(Taiwan 0-30 km)
impulsive signal (1),
t0=2 s, 5% damping
0.2
0
0
2
4
6
8
10
Period (s)
Figure 5. Comparison of the 5% damped normalized displacement spectrum of the displacement pulse (1)
with the average displacement spectra of the Taiwan (Chi-Chi) records in the distance range 0-30 km. The
impulsive signal is defined by the parameter t0=2s, corresponding to τ = 4s for a M 7.6 earthquake,
according to Somerville (2003). From FPR04.
5.4 < M W < 6.0
(b)
2
Normalized spectral displacement
Normalized sp ectral displacement
(a)
Average observed
(K-Net + Europ. data)
impulsive signal (3),
t0=0.25 s, 5% damping
1.5
1
0.5
0
0
2
4
6
Period (s)
8
10
6.0 < M W < 6.5
2
Average observed
(K-Net)
impulsive signal (3),
t0=0.44 s, 5% damping
1.5
1
0.5
0
0
2
4
6
8
10
Period (s)
Figure 6. Comparison of the 5% damping normalized displacement spectrum of the impulsive signal (3)
with the average displacement spectra of observed records in the distance range 10-30 km: (a) magnitude
range 5.4≤MW≤6 and earthquakes from K-Net and European data, and (b) magnitude range 6≤MW≤6.5
and earthquakes from K-Net. According to Equation 5, for the first magnitude range the impulsive signal
is defined by the parameter t0=0.25s, corresponding to an M=5.7 earthquake, while for the second one
t0=0.45s, corresponding to an M=6.25 earthquake. From FPR04.
APPLICATION TO SEISMIC HAZARD ASSESSMENT IN THE CALABRIAN ARC AREA,
SOUTHERN ITALY
To illustrate the potential for applications of the previous expressions for long period spectral ordinates to
seismic hazard assessment (SHA), we have selected one of the highest seismicity regions of Southern
Italy, namely the Calabrian Arc.
Seismicity and tectonics of the Calabrian Arc area
The Calabrian Arc constitutes the southern segment of the Apennines orogenesis in continental Italy is
characterized by substantial seismic activity. In the last 800 years, 16 earthquakes have hit this region with
MCS epicentral intensities from IX to XI. According to most credited intensity – magnitude correlations
(Camassi and Stucchi [12]) five of these earthquakes have reached magnitudes equal or bigger than 7.0
(Figure 7). In southern Calabria the most important events struck respectively the Gioia Tauro and Upper
Mesima basins on 5 and 7 February 1783, with an estimated MS of 7.3 and 7.0. Also on 8 September 1905
and 28 December 1908 two offshore events struck respectively the Eufemia Gulf and the Messina Straits
areas, with an estimated MS magnitudes of 7.5 and 7.3 (recently revised to 7.1).
The relation of these large seismic events with known faults is to date not univocal, similar to other parts
of continental Italy (Valensise and Pantosti [13]). Specifically, the 5th February 1783 earthquake in
southern Calabria has been associated to two faults with very different geometry and location (Valensise
and D’Addezio [14]; Galli and Bosi [15]).
SZ#64
Surface Wave Magnitude
4.0
5.0
6.0
7.0
4,400,000
to
to
to
to
5.0
6.0
7.0
7.5
SZ#65
SZ#67
SZ#66
4,300,000
SZ#68
SZ#70
SZ#69
SZ#74
4,200,000
SZ#72
SZ#71
SZ#73
450,000
550,000
650,000
Figure 7. Seismicity of the Calabrian Arc according to the NT catalogue (Camassi and Stucchi [12]).
Seismogenic sources 64 to 74 are also depicted (after Scandone et al. [16]). The square outlines the area
were seismic hazard calculations and mapping was performed (see section 4). UTM coordinates related to
zone 33 are used.
Seismic hazard assessment in the long period range
Seismic source zones (SZ) from 64 to 74 of the widely used GNDT model for Italy (Scandone et al. [16])
were taken into account, as indicated in Figure 6. Due to the purpose of our study, we did not make a
specific investigation to calibrate the seismicity parameters of the region, such as Gutenberg-Richter bvalue, maximum and minimum magnitudes (Mmax and Mmin, respectively) and the annual occurrence rates;
rather, we borrowed them published studies ( Romeo and Pugliese [17]), see Table 1.
Ground motion hazard in terms of displacement spectral ordinates for several return periods was
calculated for each point of a 10x10 grid with origin at 37.5ºN latitude and 15ºE longitude. The grid step
is approximately 20 km (0.2º). We represent ground motion by means of uniform-hazard spectra for
several selected towns: Messina, Reggio Calabria, Siderno, Gioia Tauro, Vibo Valentia, Sant'Andrea,
Catanzaro and Rosarno. A detailed presentation of the method and of the results may be found in GarcíaMayordomo et al. [18]. Hazard calculations were carried out making use of the CRISIS99 v.18 computer
program developed in the UNAM (México) (Ordaz et al. [19]), considering a Poisson recurrence model
for seismic events.
Table 1. Seismic parameters of seismogenic zones 64 to 74 (after Romeo and Pugliese [18]).
SZ #
b
64
65
66
67
68
69
70
71
72
73
74
0.53
0.62
0.68
0.69
0.59
0.59
0.76
0.73
0.69
1.33
0.85
Annual rate of exceedance
(Mmin = 4.7)
0.00990
0.01534
0.06301
0.02740
0.02164
0.06094
0.01599
0.06263
0.01892
0.02020
0.08766
Mmax
6.6
6.4
7.3
6.4
6.7
7.5
5.6
7.3
5.9
5.1
5.1
The following can be singled out as the most relevant features of the proposed procedure:
• Use of (2) for the attenuation of dmax with magnitude and distance. To account for data variability and
introduce such relation in a probabilistic approach, we have estimated from the available records a
standard deviation σ=0.21 of the lognormal distribution of dmax.
• By combining equations (2) and (1), together with the analytical expression for the spectral ordinates
depicted in Figure 4 for the narrow-band pulse case, one can obtain an attenuation relation for the
spectral ordinates of each structural period of interest, referring to a structural damping ξ=0%.
• The influence of damping at long periods is limited, as may be seen from Figure 4. To produce the
results for a structural damping ξ=5%, we multiplied the 0% ordinates by the ratio of the two curves
in Figure 4.
• The results refer to generic stiff soil conditions.
We have compared in Figure 8 the displacement spectral ordinates obtained by our approach for M=6.5
and epicentral distance R=10 km and 30 km, with those provided by the attenuation relation of Bommer
and Elnashai [3] (BE99), defined up to 3 s. A conventional focal depth of 10 km has been assumed, since
our attenuation relation for dmax is defined in terms of hypocentral distance. Our ordinates generally
exceed those of BE99, but the difference is more relevant in terms of dmax, where our results are
significantly higher than those of BE99. This difference can be understood considering that BE99 have
worked with a much larger dataset, but mainly consisting analog data: the high-pass filtering applied by
these authors at long periods may have significantly depleted the signal in the very long period range.
Seismic hazard maps
Seismic hazard maps were produced for a reference return period of 475 years and a representative
number of vibration periods up to 10 s, using the FPR04 and BE99 attenuation functions, respectively.
Two examples of maps are depicted in Figures 9 and 10, for the 3s and 10s vibration periods, respectively.
Note that throughout our study we have approached the 10 s spectral ordinate with dmax. Both approaches
predict the maximum spectral displacement around 3 s, and yield similar results for low vibration periods,
although the BE99 relation in general gives lower values than the FPR04. The most relevant differences
occur in the very long period range: as already pointed out, our results are more than twice larger than
those obtained by the BE99 attenuation relation for dmax. (Figure 10). It is also observed that the FPR04
relation attenuates slower than the BE99 and therefore yields a smoother spatial distribution of the
spectral values.
Finally, we plot in Figure 11 the uniform hazard spectra for Rosarno Calabro, that turned out to be the
most hazardous site considered in the area. Again, the results yielded by both attenuation relations are
similar for periods up to 3 s, but in terms of dmax differences are quite significant.
14.0
M S=6.5
Spectral Displacement (cm)
12.0
10 km
10.0
FPR04
h=10km
ξ=5
BE99,
Stiff
8.0
6.0
FPR04,
30 km
4.0
BE99,
2.0
0.0
0
1
2
3
4
5
Period
6
7
8
9
10
Figure 8. Comparison between BE99 and FPR04 spectral displacement attenuation relationships for 10
and 30 km epicentral distances and 5% damping ratio. A hypocentral depth of 10 km and stiff soil
conditions are assumed in the FPR04 approach. Predicted peak ground displacement (dmax) are depicted at
10 s vibration period.
CONCLUSIONS
We have shown that the average spectral shapes from a significant set of digital strong motion records can
be reasonably approximated with simple analytical models, and also that their basic features depend on
the moment magnitude and distance, consistently with standard seismic source models. Furthermore, by
the same models, we found that the observed variation of peak ground displacement with magnitude and
distance can be predicted reasonably well through simple physical considerations.
T=3 s.
T=3 s.
SD (cm)
15.00
12.00
12.00
16.6
14.5
9.00
9.00
6.00
6.00
3.00
3.00
0.00
0.00
FPR0
BE9
Figure 9. Seismic hazard maps for a 475 year return period in terms of the spectral displacement
ordinate at Tn=3 s. making use of the BE99 and FPR04 attenuation relationships. Stiff soil conditions.
T=10
T=10
PG
(cm)
SD (cm)
5.00
12.00
14.0
9.00
4.00
5.7
3.00
6.00
2.00
3.00
1.00
0.00
0.00
FPR0
BE9
Figure 10. Seismic hazard maps for a 475 year return period in terms of spectral displacement
ordinates at T=10 s., which in the BE99 case is represented by dmax. Stiff soil conditions.
Comparison at Rosarno, the most hazardous town Tr=475 yr.
20
Spectral Displacement
BE99
FPR04
MaxDisp FPR04
MaxDisp BE99
ξ=5%
18
16
14
12
10
8
6
4
2
0
0
1
2
3
4
5
Period
6
7
8
9
10
Figure 11. Uniform hazard displacement spectra for a 475 return period at the town of Rosarno, obtained
using the FPR04 and BE99 attenuation relations. 5% damping and stiff soil conditions are assumed. Peak
ground displacement predictions from BE99 and FPR04 approaches are also represented.
The analytical expressions obtained in a previous article (Faccioli et al. [6]) have been incorporated in a
procedure for seismic hazard assessment at long periods. A sample area of high seismic hazard in
Southern Italy has been selected and spectral displacement hazard maps have been produced, using both
the FPR04 procedure for attenuating spectral displacements, and the BE99 attenuation relation.
Comparison of the results obtained by the BE99 and FPR04 relations show that, while there is a
reasonable agreement of results up to 3 s, where the highest spectral values are obtained, there is a major
discrepancy in terms of predicted peak ground displacement.
This clearly points on the need of improving our knowledge of long period spectral ordinates, that is
severely affected by the relative scarcity and heterogeneity of good quality digital records for a wide
variety of magnitude, distances and site conditions. Furthermore, several relevant issues related to long
period ground motion need further investigation, such as modeling the directivity effects on spectra in the
near-field, the dependence on the style of faulting and the role of site effects for very soft soil conditions.
We hope that the results of this study may stimulate research on these topics.
ACKNOWLEDGEMENTS
This work has been supported by the European Commission Contract no. HPRN-CT-1999-00035 (Safety
assessment for earthquake risk reduction).
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