Equations for the estimation of strong ground motions from
shallow crustal earthquakes using data from Europe and the
Middle East: Horizontal peak ground acceleration and spectral
acceleration
N. N. Ambraseys, J. Douglas
∗
, S. K. Sarma
Department of Civil and Environmental Engineering,
Imperial College London,
South Kensington Campus,
London,
SW7 2AZ,
United Kingdom.
Tel: +44 (0)20 75946059
Fax: +44 (0)20 72252716
Email: n.ambraseys@imperial.ac.uk
and
P. M. Smit currently at:
National Emergency Operations Centre,
CH-8044 Z
¨
urich,
Switzerland.
November 9, 2004
Running title: Equations for estimation of horizontal ground motions
Keywords: Strong ground motion estimation, attenuation relations, Europe, Middle East
Article type: General paper
∗
Now at: ARN/RIS; BRGM; 3 avenue C. Guillemin; BP 6009; 45060 Orl
´
eans Cedex 2; France.
1
Abstract
This article presents equations for the estimation of horizontal strong ground motions caused by shal-
low crustal earthquakes with magnitudes M
w
≥ 5 and distance to the surface projection of the fault
less than 100 km. These equations were derived by weighted regression analysis, used to remove ob-
served magnitude-dependent variance, on a set of 595 strong-motion records recorded in Europe and the
Middle East. Coefficients are included to model the effect of local site effects and faulting mechanism
on the observed ground motions. The equations include coefficients to model the observed magnitude-
dependent decay rate. The main findings of this study are that: short-period ground motions from small
and moderate magnitude earthquakes decay faster than the commonly assumed 1/r , the average effect of
differing faulting mechanisms is not large and corresponds to factors between 0.8 (normal and odd) and
1.3 (thrust) with respect to strike-slip motions and that the average long-period amplification caused by
soft soil deposits is about 2.6 over those on rock sites. Disappointingly the standard deviations associated
with the derived equations are not significantly lower than those found in previous studies.
1 Introduction
This paper is the latest in a series of studies on the estimation of strong ground motions for engineering
design using the strong-motion archive at Imperial College London. Previous studies include: Ambraseys
& Bommer (1991), Ambraseys et al. (1996), Ambraseys & Simpson (1996) and Ambraseys & Douglas
(2003). There are a number of reasons for this new study. Firstly, the amount of strong-motion data
available for this study is much greater than was available for previous studies; this enables more robust
estimation of the regression coefficients. This new data has been collected in the framework of three
projects by Imperial College and European partners which sought to improve the dissemination of high-
quality strong-motion data (Ambraseys et al., 2000, 2002, 2004a), see Ambraseys et al. (2004c) and
Ambraseys et al. (2004b) for details. Also during these projects many of the associated parameters of
the strong-motion data contained within the databank were reassessed. This reassessment should lead to
an improvement in the reliability of the obtained equations. Previous equations have been derived using
a limited quantity of data from the near source of large earthquakes. There is evidence that this has lead
to equations that overpredict near-source ground motions for large earthquakes (Ambraseys & Douglas,
2003). In addition previous equations did not consider the effect of source mechanism on ground motions
although this has been shown to be an important factor (e.g. Bommer et al., 2003).
Only data from Europe and the Middle East has been used because it is felt that the data in the Im-
perial College London strong-motion archive is reasonably complete for moderate and large earthquakes
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that occurred in this region. Also this data has been carefully reviewed and the associated parameters
appraised and reassessed during the three recent projects mentioned above. In addition, Douglas (2004b)
has shown, using a method based on analysis of variance, that there seems to be a significant difference
in ground motions between California and Europe; those in California seem to be slightly higher than
those in Europe for the same magnitude and distance. Consequently, it has been decided to exclude
data from California and elsewhere although it would increase the quantity of high-quality near-source
data available. Chen & Atkinson (2002) investigate the apparent source spectra in a number of regions,
including California and Turkey, and conclude that they are similar. In view of this, data from different
parts of the world could be used to validate the equations by examining residuals but this has not been
attempted here.
It is not expected that the standard deviations of the equations presented here will be significantly
less than those derived in previous studies because not many new independent variables are introduced
but the median ground motions given a particular magnitude and distance are likely to be better defined
because the equations are based on more and higher quality data than previous equations.
2 Data used
The choice of which records to include and which to exclude from the regression analysis is one of
the most important decisions in deriving ground motion estimation equations. There is a balance to
be struck between being not restrictive enough in the data used leading to unreliable coefficients and
hence predictions due to errors and uncertainties in the independent and dependent parameters and too
restrictive, which leads to a too small set of data and hence non-robust coefficients. An example of
this is the problem of a lack of local site information. Ideally all stations would have a published local
shear-wave velocity profile so the shear-wave velocity could be used directly in the equations. However,
to restrict data selection to only stations with shear-wave velocity profiles would lead to a small, poorly
distributed set of data and consequently the equations could be unreliable.
As mentioned above, data from all seismically active parts of Europe and the Middle East has been
considered whereas data from outside this region has been excluded from consideration. One justifica-
tion for combining data from different regions of Europe and the Middle East is that Douglas (2004a)
has shown, through a method based on analysis of variance, that recorded strong ground motion in the
Caucasus region, central Italy, Friuli, Greece and south Iceland shows little evidence for regional dif-
ferences although this is based on a limited amount of data with low engineering significance. Whereas
Douglas (2004b) does find some evidence for regional differences in ground motions between Europe
and California.
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2.1 Magnitude
The magnitude scale used here is moment magnitude (M
w
), defined by Kanamori (1977) as: M
w
=
2/3 log M
0
− 6 where M
0
is the seismic moment in Nm. Only earthquakes with available estimates of
M
0
were used. Empirical conversion formulae from other magnitude scales, e.g. M
s
or M
L
, to M
w
were
not used because this conversion can increase the uncertainty in the magnitude estimates. The choice of
M
w
means that only strong-motion records from moderate and large earthquakes can be used because
M
w
is not routinely calculated for small earthquakes. Therefore, in order to have a good distribution of
records at all magnitudes, only records from earthquakes with M
w
≥ 5 were chosen. This also excludes
records from small earthquakes that are unlikely to be of engineering significance.
2.2 Source-to-site distance
The distance to the surface projection of the fault (Joyner & Boore, 1981), d
f
, (also known as fault dis-
tance or Joyner-Boore distance) is used as the distance metric for this study. For earthquakes where the
location of the causative fault has not been reported, mainly earthquakes with M
w
≤ 6, epicentral dis-
tance, d
e
is used instead. For small earthquakes d
e
and d
f
are similar because of the small rupture planes
of such earthquakes. Distance to the surface projection of the fault is used because it does not require an
estimate of the depth of the earthquake, which can be associated with large error, unlike distance to the
rupture or seismogenic distance (e.g. Campbell & Bozorgnia, 2003). Also it has been found (Douglas,
2001) that distance to the rupture does not lead to a reduction in the standard deviation associated with
ground motion prediction equations. Records from distances greater than 100 km have been excluded
for a number of reasons. Firstly, this excludes records that are likely to be of low engineering signifi-
cance due to their large source-to-site distances. Secondly, it reduces the bias that could be introduced
by including records from distances greater than the distance to the first non-triggering station. Thirdly,
it reduces the effect of differences in the anelastic decay in different regions of Europe and the Middle
East. Lastly it means that the distribution of records with respect to magnitude and distance is reasonably
uniform and reduces the correlation between magnitude and distance, which can cause problems in the
regression stage.
2.3 Faulting mechanism
Only earthquakes with a published focal mechanism solution in terms of the trends and plunges of the
T, B and P axes have been included. In some previous studies, earthquakes have been classified us-
ing knowledge of regional tectonics or by assuming that aftershocks have the same mechanism as the
mainshock. These assumptions will sometimes lead to incorrectly classifying earthquakes. For example,
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Ouyed et al. (1983) compute well-constrained focal mechanisms for 81 aftershocks of the thrust faulting
10th October 1980 El Asnam (Algeria) earthquake using an array of 28 portable seismic stations. They
find that aftershocks mainly displayed thrust mechanisms but a significant proportion showed strike-
slip mechanisms and two aftershocks even had normal faulting. Lyon-Caen et al. (1988) compute focal
mechanisms of 133 aftershocks of the normal faulting 13th September 1986 Kalamata (Greece) earth-
quake using records from 16 temporary stations. They find that although most aftershocks displayed
normal mechanisms, some showed strike-slip faulting and some aftershocks in the footwall had reverse
mechanisms. Consequently, if records from aftershocks with no published focal mechanisms, but which
are assumed to have the same mechanism as the main shock, are used, this can increase the uncertainty
in the computation of style-of-faulting coefficients (Bommer et al., 2003).
The method of Frohlich & Apperson (1992) has been used to classify earthquakes by style of faulting.
In this scheme, earthquakes with plunges of their T axis greater than 50
◦
are classified as thrust, those
with plunges of their B axis or P axis greater than 60
◦
are classified as strike-slip or normal and all
other earthquakes are classified as odd. Bommer et al. (2003) have investigated the different published
schemes for classifying earthquakes with respect to mechanism and have found that the method proposed
by Frohlich & Apperson (1992) does not suffer from the ambiguities of methods based on the rake angle
because it does not require knowledge of which plane is the main plane and which the auxiliary. Bommer
et al. (2003) also show that the method of Frohlich & Apperson (1992) classifies earthquakes similarly
to that adopted by Boore et al. (1997), i.e. classifying earthquakes with rake angles within 30
◦
of the
horizontal as strike-slip and other earthquakes into the correct dip-slip category.
Note that in this article the classification ‘thrust’ is used, following its use by Frohlich & Apperson
(1992), rather than the more commonly-used word ‘reverse’.
2.4 Building type
In parts of Europe and the Middle East (e.g. Greece) it is common to install strong-motion instruments
in the ground floors or basements of relatively large buildings. There is evidence that such buildings
can influence the measured ground motions and therefore in other parts of the world with much strong-
motion data, such as California, records from such buildings are excluded from analysis. Since good-
quality data, with all the required independent variables, from Europe and the Middle East is already
limited it was decided not to reject records from stations within the ground floors or basements of large
buildings.
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