International Journal of Geosciences, 2010, 32-37
doi:10.4236/ijg.2010.11004 Published Online May 2010 (http://www.SciRP.org/journal/ijg)
The Analysis of Accelerograms for the Earthquake
Resistant Design of Structures
Victor Corchete
Higher Polytechnic School, University of Almeria, Almeria, Spain
Received February 25, 2010; revised March 26, 2010; accepted April 20, 2010
Abstract
In this paper, the analysis of ground motions (displacements, velocities and accelerations) has been per-
formed focused to the seismic design. The relationships between the peak ground acceleration (PGA), the
peak ground velocity (PGV), the peak ground displacement (PGD) and the bracketed duration, with the
earthquake magnitude, are presented and their validity and applicability for seismic design is discussed. Fi-
nally, the dominant periods of the ground motions (displacement, velocity and acceleration) are obtained
from their Fourier Spectrum. Their validity and applicability for the seismic design is discussed also. The
results presented in this paper show that the relationships that exist between the important parameters: PGA,
PGV, PGD and duration; and the earthquake magnitude, allow the prediction of the values for these parame-
ters, in terms of the magnitude for future strong motions. These predictions can be very useful for seismic
design. Particularly, the prediction of the magnitude associated to the critical acceleration, because the earth-
quakes with magnitude greater than this critical magnitude can produce serious damages in a structure (even
its collapsing). The application of the relationships obtained in this paper must be very careful, because these
equations are dependent on the source area, location and type of structure. The dominant periods of the
ground motions (displacement, velocity and acceleration) that are computed and presented in this paper, are
also important parameters for the seismic design, because recent studies have shown that the earthquake
shaking is more destructive on structures having a natural period around some of these dominant periods.
These parameters must also be handled with caution, because they show dependence with the source area,
location and type of structure.
Keywords: Seismic Design, Bracketed Duration, Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak
Ground Displacement (PGD), Dominant Periods
1. Introduction
It is known that earthquakes are responsible of an im-
portant part of the casualties, occurred around the world
due to natural disasters [1]. In addition, earthquakes pro-
duce high economical losses which could be avoided, in
most of the cases, with an adequate seismic design [2].
For this reason, it is the principal importance any study
performed to mitigate the disasters caused by earth-
quakes. For it, the seismic design requires the knowledge
of some parameters that must be included or considered,
for the earthquake resistant design of structures. Ones of
the most important parameters to be considered are: the
peak ground acceleration (PGA), the peak ground veloc-
ity (PGV), the peak ground displacement (PGD) and the
bracketed duration [3]. These parameters are easy to meas-
ure, from the three types of strong-motion record that are
usually available: seismogram (ground display-cement),
velocigram (ground velocity) and accelerogram (ground
acceleration).
The peak ground acceleration (PGA) is the maximum
value of the ground acceleration (positive or negative)
that appears in the accelerogram. The peak ground ve-
locity (PGV) is the maximum value of the ground veloc-
ity (positive or negative) that appears in the velocigram.
The peak ground displacement (PGD) is the maximum
value of the ground displacement (positive or negative)
that appears in the seismogram. The bracketed duration
is the time duration of the ground shaking, defined as the
elapsed time between the first and last acceleration ex-
cursions greater than some reference value (usually taken
as 0.05 g, where g is the gravity acceleration). Figure 1

V. CORCHETE
33
8090 100
-0.2
-0.1
0.0
0.1
0.2
8090 100
-5
0
5
10
8090 100
-400
-200
0
200
cm
Time (s)
Displacement
0.202
7.943
cm/s
Time (s)
Velocity
Duration = 10.86 s
347.69
cm/s2
Time (s)
Acceleration
Figure 1. Ground displacement, velocity and acceleration recorded on the vertical component of the EJON station, for the
event 3 listed in Table 1. The small circles denote the maximum present in the corresponding trace joint to its numerical
value. The dashed lines denote the reference value (0.05 g) selected to determine the bracketed duration. The bracketed dura-
tion is marked in the accelerogram joint to its numerical value.
shows the value of these parameters for a ground motion
recorded on the vertical component [4].
Recent studies have shown that the dominant periods
of the Fourier Spectrum of the ground motion (displace-
ment, velocity and acceleration), are also very important
parameters to be considered in the seismic design, be-
cause the earthquake shaking is more destructive on
structures having a natural period around some of these
dominant periods [5]. Therefore, it is very suitable to
consider also the values of these dominant periods, as
important parameters for the seismic design.
Thus, it would be very desirable to obtain relationships
between the above mentioned parameters (PGA, PGV,
PGD and duration) and the earthquake magnitude, to
predict the possible values that these important parame-
ters can take for future strong motions. This is the goal of
this study, the determination of relationships between
PGA, PGV, PGD and duration with the magnitude. The
validity and applicability of these formulas also will be
discussed. Finally, the dominant periods of the ground
motions considered in this study also will be obtained.
2. Methodology and Background
It is known that the maximum acceleration A (cm/s2) of
the ground motion produced by an earthquake, is related
to the intensity of this earthquake, by means of a linear
equation [3]. On the other hand, also it is known that the
intensity of an earthquake is also related to the magnitude
M (mb) of this earthquake, by means of a linear equation
[6]. Therefore, a linear relationship must exist between
maximum acceleration A (cm/s2) and magnitude M (mb).
This relation is given by
11
2
10 b)mb(Ma))s/cm(A(Log  (1)
where (a1, b1) are constants to be determined. Logically,
the existence of the relationship (1) implies that a similar
relationship must exist for the maximum velocity and the
maximum displacement [7]. These linear relationships
are given by
2210 b)mb(Ma))s/cm(V(Log  (2)
3310 b)mb(Ma))cm(D(Log 

(3)
where V is the maximum velocity, D is the maximum
displacement and (a2, b2, a3, b3) are constants to be de-
termined. Respect to the bracketed duration, also exits a
relationship between this parameter and the magnitude,
but this relation is not linear. Nevertheless, this relation-
ship can be written in linear form by means of the for-
mula [3]

34 V. CORCHETE
44 b)c)mb(Mtanh(a)s(Duration  (4)
where (a4, b4, c) are constants to be determined.
Equations (1) to (4) are the relationships that exist
between the above mentioned important parameters
(PGA, PGV, PGD and duration) and the earthquake
magnitude. These linear equations allow the prediction
of the values for these parameters, in terms of the mag-
nitude for future strong motions [8]. The application of
Equations (1) to (4) must be very careful, because the
constants (a1, b1, a2, b2, a3, b3, a4, b4, c) of these equations
are determined for a location (station) and a source area
(a small area in which the epicenters can be grouped),
i.e., the values for these constants can be different for
different locations and/or different source areas (there are
a dependence with the propagation path). Moreover, for
the same location and source area, the values of these
constants can depend on the type of soil (over which the
structure is built), the type of structure (masonry struc-
ture, timber structure, iron structure, concrete structure,
building, bridge, nuclear power plant, etc.), the founda-
tions of the structure or the type of connection between
structure and foundations [1,9]. Thus, Equations (1) to (4)
must be handled with caution.
3. Data
In this kind of studies, the primary data are seismograms,
velocigrams and accelerograms. Nevertheless, in some
cases only the accelerograms are available, then seismo-
grams and velocigrams must be computed from the ac-
celerograms by integration, using the Fast Fourier Trans-
form (FFT) and its properties, applied to the Fourier
Spectrum of the corresponding accelerogram [9,10]. In
this study, only seismograms have been available, ve-
locigrams and accelerograms have been computed from
these seismograms by derivation, using the FFT and its
properties, applied to the Fourier Spectrum of the corre-
sponding seismogram [10].
The seismograms used in this study correspond to 22
earthquakes (Table 1), which occurred on the neighbor-
ing of the Iberian Peninsula. These earthquakes have
been registered by the broadband station EJON located
on Iberia (latitude 42.4487 ºN, longitude 2.8886 ºE), with
a sampling ratio of 100 samples per second (100 sps).
The instrumental response (Figure 2) has been taken into
account to avoid the time lag introduced by the seismo-
graph system and all distortions produced by the instru-
ment [11]. This correction recovers the true amplitude
and phase of the ground motion, allowing the analysis of
the true ground motion. For this reason, all the traces
considered in this study were corrected for instrument
response.
The traces used in this study correspond to events
grouped in the same source area, to ensure that the
propagation path be the same for all events, because the
constants (a1, b1, a2, b2, a3, b3, a4, b4, c), of Equations (1)
to (4), are propagation-path dependent as it was men-
tioned in the previous section of this paper. A source
area is defined as a location in which the seismic events
have occurred with similar epicenter coordinates [12].
The maximum coordinate difference considered to group
events has been equal to 0.2 degrees in latitude and lon-
gitude.
Table 1. Near events recorded at EJON station (latitude 42.4487 ºN, longitude 2.8886 ºE).
Event (nº) Date (d-m-y) Time (h-m-s)Latitude (ºN)Longitude (ºE) Magnitude (mb)
1 27 05 2003 17 11 32.5 36.802 3.610 6.1
2 28 05 2003 11 26 31.6 37.135 3.393 4.5
3 28 05 2003 19 05 22.2 36.932 3.737 4.9
4 31 05 2003 11 44 46.3 37.048 3.780 4.6
5 01 06 2003 02 54 21.0 36.990 3.983 4.6
6 02 06 2003 08 20 24.2 37.017 3.185 4.5
7 03 06 2003 23 17 46.2 37.208 3.710 4.4
8 06 06 2003 03 13 47.0 37.072 3.733 4.4
9 15 06 2003 01 06 10.8 36.893 3.348 4.1
10 17 06 2003 07 52 55.1 37.113 3.838 4.5
11 18 06 2003 19 36 13.1 36.970 3.682 4.5
12 21 06 2003 11 01 27.5 37.038 3.467 4.1
13 05 07 2003 20 03 35.9 37.212 3.470 4.2
14 06 07 2003 02 56 9.2 37.012 3.758 4.4
15 06 07 2003 08 50 20.6 36.998 3.513 4.3
16 14 07 2003 22 52 26.4 36.925 3.308 4.2
17 17 07 2003 21 07 50.3 36.645 3.493 4.4
18 18 07 2003 08 14 53.5 37.202 3.725 4.4
19 07 08 2003 08 23 11.7 37.103 3.722 4.5
20 11 08 2003 20 03 47.2 36.923 3.328 4.6
21 03 09 2003 14 04 49.8 37.155 3.600 4.6
22 12 10 2003 07 08 45.0 37.045 3.418 4.4

V. CORCHETE
35
0.001 0.010.1110100
0.001
0.01
0.1
1
10
0.001 0.010.1110100
-360
-270
-180
-90
0
90
180
Normalized Amplitude
Frequency (Hz)
Phase (degrees)
Frequency (Hz)
Figure 2. Frequency response of the broadband seismograph (100 sps).
4. Application and Results
The values of the constants (a1, b1, a2, b2, a3, b3, a4, b4, c)
have been determined for the location and source area
considered in this study, from the seismograms corre-
sponding to the events listed Table 1 recorded at the
EJON station (velocigrams and accelerograms has been
computed by derivation), by a linear fit as it is shown in
Figures 3-6. These constants could be different for dif-
ferent locations and/or different source areas. Also, these
constants could be different for the same location and
source area, if the type of soil over which the structure is
built, the type of structure, the foundations of the struc-
ture or the type of connection between structure and
foundations; are different [1]. For this reason, Equations
(1) to (4), which predict the values of the parameters
(PGA, PGV, PGD and duration) with the earthquake
magnitude, must be handled with caution, because these
predictions could be false when the conditions previously
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Log10(Amax(cm/s2))
Magnitude (mb)
Log10(Amax(cm/s2)) = 0.814*M(mb)  1.744
AC = 0.5 g
Figure 3. Relationship between PGA and magnitude com-
puted for the accelerograms corresponding to the events
listed in Table 1. The continuous line denotes the linear fit
performed between PGA and magnitude. The dashed line
denotes the value of the critical acceleration assumed in this
study as 0.5 g.
3.03.54.04.55.05.56.06.57.07.58.08.59.0
-1.5
-1.0
-0.5
0. 0
0. 5
1. 0
1. 5
2. 0
2. 5
3. 0
3. 5
4. 0
4. 5
Log10(Vmax(cm/s))
Magnitude (m
b
)
Log10(Vmax(cm/s)) = 0.999*M(mb)  4.411
Figure 4. Relationship between PGV and magnitude com-
puted for the velocigrams corresponding to the events listed
in Table 1. The continuous line denotes the linear fit per-
formed between PGV and magnitude.
3.03.54.04.55.05.56.06.57.07.58.08.59.0
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.
0
Log10(Dmax(cm))
Magnitude (mb)
Log10(Dmax(cm)) = 1.001*M(mb)  5.898
Figure 5. Relationship between PGD and magnitude com-
puted for the seismograms corresponding to the events
listed in Table 1. The continuous line denotes the linear fit
performed between PGD and magnitude.

36 V. CORCHETE
-1.2-1.0-0.8-0.6-0.4-0.20.0 0.2 0.4 0.6 0.8 1.0 1.2
0
5
10
15
20
25
30
35
40
45
50
Duration (s)
Tanh (Magnitude (mb)  5.5)
Duration (s) = 21.44*tanh (M(mb)  5.5)  20.67
Figure 6. Relationship between bracketed duration and ma-
gnitude computed for the accelerograms corresponding to
the events listed in Table 1. The continuous line denotes the
linear fit performed between duration and magnitude.
mentioned be not satisfied. For different source areas,
locations and structures, the values of the constants (a1,
b1, a2, b2, a3, b3, a4, b4, c) must be recomputed to ensure
the validity and applicability of the predictions given by
Equations (1) to (4).
The predictions given by Equations (1) to (4) can be
very useful for seismic design. Particularly, Equation (1)
can be very useful because it allows the knowledge of
the maximum acceleration that can occur for any earth-
quake, including earthquakes with high magnitudes
which have not occurred up to now. With Equation (1), it
can be known in which magnitude the critical accelera-
tion is reached (Figure 3). The critical acceleration is
defined as the maximum acceleration that a structure
(building, bridge, nuclear power plant, etc.) can bear
without damages [1]. For each structure, this critical
value of the acceleration exists. The structure can bear
serious damages or collapse, if this value of the accelera-
tion is overcame [2]. Thus, an important application of
Equation (1) is to know the magnitude associated to the
critical acceleration, because earthquakes with magni-
tude greater than this magnitude can produce serious
damages in that structure (even its collapsing).
Finally, the dominant periods of the ground motions
(displacement, velocity and acceleration) considered in
this study, have been obtained from their Fourier Spec-
trum, as it is shown in Figure 7. These dominant periods
are parameters that can be very useful for seismic design,
because recent studies have shown that the earthquake
shaking is more destructive on structures having a natu-
ral period around some of these dominant periods [5].
These parameters also show dependence with the source
area, location and type of structure. For it, they must be
recomputed for different source area, location and type
of structure; to ensure their validity and applicability.
5. Conclusions
Equations (1) to (4) obtained and discussed in this paper,
are the relationships that exist between the important
parameters: PGA, PGV, PGD and duration; and the
earthquake magnitude. These linear equations allow the
prediction of the values for these parameters, in terms of
the magnitude for future strong motions. The application
of Equations (1) to (4) must be very careful, because the
constants (a1, b1, a2, b2, a3, b3, a4, b4, c) of these equations
are dependent on the source area, location and type of
structure. The predictions given by Equations (1) to (4)
can be very useful for seismic design. Particularly, the
prediction given by Equation (1), because it can provide
the magnitude associated to the critical acceleration. The
knowledge of this critical magnitude is very important in
seismic design, because earthquakes with magnitude
greater than this magnitude can produce serious damages
in a structure (even its collapsing).
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.00
0.01
0.02
0.03
0.04
0.00.20.40.60.81.0
0.0
0.1
0.2
0.3
0.4
0.00.20.40.60.81.
0
1
2
3
4
5
6
7
8
9
10
11
0
Displa cement
Amplitude (cm s)
Period (s)
Veloci ty
Amplitude (cm)
Period (s)
T = 1.466 s
T = 0.320 sT = 0.096 s
Accelera tio n
Amplitude (cm/s)
Period (s)
Figure 7. Amplitude Spectrum corresponding to the ground motion (displacement, velocity and acceleration) of the event 1
listed in Table 1, recorded on the vertical component of the EJON station.

V. CORCHETE
37
The dominant periods of the ground motions (dis-
placement, velocity and acceleration) also have been
computed and presented in this paper. These dominant
periods are parameters that can be very useful for seismic
design, because recent studies have shown that the
earthquake shaking is more destructive on structures
having a natural period around some of these dominant
periods. Nevertheless, these parameters must be handled
with caution because they also show dependence with
the source area, location and type of structure.
6. Acknowledgements
The author is grateful to Instituto Geográfico Nacional
(Madrid, Spain), who has provided the seismic data used
in this study.
7. References
[1] S. K. Duggal, “Earthquake Resistant Design of Struc-
tures,” Oxford University Press, India, 2009.
[2] H. K. Gupta, “Response Spectrum Method in Seismic
Analysis and Design of Structures,” CRC Press, Boca
Raton, Florida, 1992.
[3] K. E. Bullen and A. B. Bolt, “An Introduction to the The-
ory of Seismology,” Cambridge University Press, Camb-
ridge, 1993.
[4] M. O. Erdik and M. N. Toksöz, “Strong Ground Motion
Seismology (NATO Science Series C),” Springer, New
York, 1987.
[5] K. Adalier and O. Aydingun, “Structural Engineering
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[6] B. F. Howell, “An Introduction to Seismological Research.
History and Development,” Cambridge University Press,
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[7] H. Doyle, “Seismology,” Wiley, New York, 1995.
[8] B. A. Bolt, “Seismic Strong Motion Synthetics,” Acade-
mic Press, Orlando, 1987.
[9] W. Lee, H. Kanamori, P. Jennings and C. Kisslinger,
“International Handbook of Earthquake and Engineering
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[10] M. Bath, “Spectral Analysis in Geophysics,” Elsevier Sc-
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[11] O. Kulhánek, “Anatomy of Seismograms,” Elsevier Scie-
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[12] V. Corchete, M. Chourak and H. M. Hussein, “Shear Wa-
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