Attenuation modeling of recent earthquakes in Turkey

Abstract

This paper deals with the derivation of a consistent set of empiricalattenuation relationships for predicting free-field horizontal components ofpeak ground acceleration (PGA) and 5 percent damped pseudoacceleration response spectra (PSA) from 47 strong ground motion recordsrecorded in Turkey. The relationships for Turkey were derived in similarform to those previously developed by Boore et al. (1997) for shallowearthquakes in western North America. The used database was compiledfor earthquakes in Turkey with moment magnitudes (Mw) = 5 thatoccurred between 1976–1999, and consisted of horizontal peak groundacceleration and 5 percent damped response spectra of accelerogramsrecorded on three different site conditions classified as rock, soil and softsoil. The empirical equations for predicting strong ground motion weretypically fit to the strong motion data set by applying nonlinear regressionanalysis according to both random horizontal components and maximumhorizontal components. Comparisons of the results show that groundmotion relations for earthquakes in one region cannot be simply modifiedfor use in engineering analyses in another region. Our results, patternedafter the Boore et al. expressions and dominated by the Kocaeli andDzce events in 1999, appear to underestimate predictions based ontheir curves for up to about 15 km. For larger distances the reverse holds.

Full text

Journal of Seismology 6: 397–409, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands. 397
Attenuation modeling of recent earthquakes in Turkey
Polat Gülkan & Erol Kalkan
Disaster Management Research Center and Dept. of Civil Engineering, Middle East Technical University, Ankara
06531, Turkey
Received 14 May 2001; accepted in revised form 23 December 2001
Key words: attenuation relationship, nonlinear regression analysis, peak ground acceleration, response spectra,
spectral acceleration
Abstract
This paper deals with the derivation of a consistent set of empirical attenuation relationships for predicting free-field
horizontal components of peak ground acceleration (PGA) and 5 percent damped pseudo acceleration response
spectra (PSA) from 47 strong ground motion records recorded in Turkey. The relationships for Turkey were
derived in similar form to those previously developed by Boore et al. (1997) for shallow earthquakes in western
North America. The used database was compiled for earthquakes in Turkey with moment magnitudes (Mw)=5
that occurred between 1976–1999, and consisted of horizontal peak ground acceleration and 5 percent damped
response spectra of accelerograms recorded on three different site conditions classified as rock, soil and soft soil.
The empirical equations for predicting strong ground motion were typically fit to the strong motion data set by
applying nonlinear regression analysis according to both random horizontal components and maximum horizontal
components. Comparisons of the results show that ground motion relations for earthquakes in one region cannot
be simply modified for use in engineering analyses in another region. Our results, patterned after the Boore et al.
expressions and dominated by the Kocaeli and Düzce events in 1999, appear to underestimate predictions based on
their curves for up to about 15 km. For larger distances the reverse holds.
Introduction
Estimation of ground motion, either implicitly through
the use of special earthquake codes or more specific-
ally from site-specific investigations is essential for
the design of engineered structures. The development
of design criteria requires, as a minimum, a strong-
motion attenuation relationship to estimate earthquake
ground motions from specific parameters characteriz-
ing the earthquake source, geologic conditions of the
site, and the length of the propagation path between
the source and the site.
This study describes the best estimates and uncer-
tainties in the ground motion parameters predicted in
a functional form that can be used in probabilistic haz-
ard studies and other earthquake engineering applic-
ations. These models and the values of the predictor
parameters were developed by an extensive analysis of
ground motion data and its relevant information. This
effort was partly motivated by the occurrence of the
1999 Mw= 7.4 Kocaeli and 1999 Mw= 7.1 Düzce
earthquakes. The Kocaeli earthquake was the largest
event that occurred in Turkey within the last 50 years,
and it is the first well-studied and widely recorded
large NAF (North Anatolian Fault) event.
The data includes records from earthquakes of
moment magnitude greater than about 5, and site con-
ditions characterized as soft soil, soil and rock with
closest distance less than about 150 km. This presents
a unique opportunity to study the indigenous atten-
uation characteristics of earthquake ground motions.
Also, the study of the effects of local site on the attenu-
ation of earthquake ground motions becomes possible
since the recording stations are fixed and many stations
have several records.
Finally, this paper describes the procedure for
estimating ground motion at various soil sites by
presenting the tables and equations that describe at-

398
tenuation functions and associated measures of uncer-
tainty. One of the major purposes of this paper is to
make comparisons between the direct use of atten-
uation relationships developed elsewhere for Turkey,
and to illuminate the reasons for their differences.
Strong motion database
After carefully searching the strong motion database
of Turkey, a total of 93 records from 47 horizontal
components of 19 earthquakes between 1976–1999
were chosen for the analysis. The strong motion data-
base is given in Table 1, and listing of the earthquakes
and the number of recordings for each of the strong
motion parameters are presented in Table 2. Station
names have not been translated so that independent
checks may be run. Recordings from small earth-
quakes were limited to the closer distances than large
earthquakes depending on the magnitude and the geo-
logy of the recording site to minimize the influence
of regional differences in attenuation and to avoid
the complex propagation effects coming from longer
distances.
In the data set, earthquake size is characterized by
moment magnitude Mw, as described by Hanks and
Kanamori (1979). When original magnitudes were lis-
ted in other scales, conversion was done according
to Wells and Coppersmith (1994). The magnitudes
are restricted to about Mw≥5.0 to emphasize those
ground motions having greatest engineering interests,
and to limit the analysis to the more reliably recor-
ded events. In the regression phase, magnitudes of
earthquakes were locked within ±0.25 band inter-
vals centered at halves or full numbers in order to
eliminate the errors coming from the determination
of these magnitude values. Figure 1 shows the dis-
tribution of these earthquakes in terms of magnitude,
station geology (defined below) and source distance
rcl, defined as the closest horizontal distance between
the recording station and a point on the horizontal
projection of the rupture zone on the earth’s surface.
However, for some of the smaller events, rupture
surfaces have not been defined clearly therefore epi-
central distances are used instead. We believe that use
of epicentral distance does not introduce significant
bias because the dimensions of the rupture area for
small earthquakes are usually much smaller than the
distance to the recording stations. Examination of the
peak ground motion data from the small number of
normal-faulting and reverse faulting earthquakes in the
data set showed that they were not significantly differ-
ent from ground motion characteristics of strike-slip
earthquakes. Therefore, normal, reverse or strike-slip
earthquakes were combined into a single fault cat-
egory. Peak horizontal acceleration (PGA) and pseudo
response spectral acceleration (PSA) are represented
considering both maximum and random horizontal
components. These are explained below.
The data used in the analysis constitutes only main
shocks of 19 earthquakes. They were recorded mostly
in small buildings built as meteorological stations up
to three stories tall because the strong motion stations
in Turkey are co-located with institutional facilities
for ease of access, phone hook-up and security. This
causes modified acceleration records. This is one of
the unavoidable causes of uncertainties in this study,
but there are other attributes that must be mentioned.
The first is our omission of aftershock data. Most
of these come from the two major 1999 events, and
contain free-field data that we did not wish to com-
mingle with the rest of the set. We also omitted the
few records for which the peak acceleration caused by
the main shock is less than about 0.04 g. Our entire,
non-discriminated ensemble is shown in Figure 2.
When we consider the effects of geological con-
ditions on ground motion and response spectra, the
widely accepted method of reflecting these effects
is to classify the recording stations according to the
shear-wave velocity profiles of their substrata. Unfor-
tunately, the actual shear-wave velocity and detailed
site description are not available for most stations in
Turkey. For this reason, we estimated the site classific-
ation by analogy with information in similar geologic
materials. The type of geologic material underlying
each recording site was obtained in a number of ways:
consultation with geologists at Earthquake Research
Division of Ministry of Public Works and Settlement,
various geologic maps, past earthquake reports and
geological references prepared for Turkey. In the light
of this information we divided soil groups for Turkey
into three in ascending order for shear velocity: soft
soil, soil, and rock. The average shear-wave velocities
assigned for these groups are 200, 400 and 700 m/s, re-
spectively. The distribution of the records with respect
to magnitude and distance plotted by type of faulting
isshowninFigure3.

399
Table 1. Records used in the development of the attenuation equations for peak horizontal acceleration and spectral accelerations
Date Earthquake MWrcl (km) Recording station Station Station Peak Hor. Acc. (mg)
coordinates site class N-S E-W
19.08.1976 DEN˙
IZL˙
I 5.3 15.20 Denizli: Meteoroloji ˙
Istasyonu 37.8140N- 29.1120E Soil 348.53 290.36
05.10.1977 ÇERKE ¸S 5.4 46.00 Çerke¸s: Meteoroloji ˙
Istasyonu 40.8800N- 32.9100E Soft Soil 36.03 38.94
16.12.1977 ˙
IZM˙
IR 5.5 1.20 ˙
Izmir: Meteoroloji ˙
Istasyonu 38.4000N- 27.1900E Soft Soil 391.41 125.40
18.07.1979 DURSUNBEY 5.3 10.30 Dursunbey: Kandilli Gözlem ˙
Istasyonu 39.6700N- 28.5300E Rock 232.29 288.25
05.07.1983 B˙
IGA 6.0 57.70 Edincik: Kandilli Gözlem ˙
Istasyonu 40.3600N- 27.8900E Rock 53.44 46.51
05.07.1983 B˙
IGA 6.1 48.70 Gönen: Meteoroloji ˙
Istasyonu 40.0800N- 27.6800E Soft Soil 50.11 46.77
05.07.1983 B˙
IGA 6.2 75.00 Tekirda˘
g: Meteoroloji ˙
Istasyonu 40.9600N- 27.5300E Rock 29.89 34.91
30.10.1983 HORASAN- 6.5 25.00 Horasan: Meteoroloji ˙
Istasyonu 40.0400N- 42.1700E Soft Soil 150.26 173.30
NARMAN
29.03.1984 BALIKES˙
IR 4.5 2.40 Balıkesir: Meteoroloji ˙
Istasyonu 39.6600N- 27.8600E Soft Soil 223.89 128.97
12.08.1985 K˙
I˘
GI 4.9 80.77 Ki˘
gı: Meteoroloji ˙
Istasyonu 39.3400N- 40.2800E Soil 163.06 89.09
05.05.1986 MALATYA 6.0 29.63 Gölba¸sı: Devlet Hastanesi 37.7810N- 37.6410E Rock 114.70 76.04
06.06.1986 SÜRGÜ 6.0 34.70 Gölba¸sı: Devlet Hastanesi 37.7810N- 37.6410E Rock 68.54 34.43
(MALATYA)
20.04.1988 MURAD˙
IYE 5.0 37.30 Muradiye: Meteoroloji ˙
Istasyonu 39.0300N- 43.7000E Rock 49.50 51.18
13.03.1992 ERZ˙
INCAN 6.9 65.00 Refahiye: Kaymakamlık Binası 39.9010N- 38.7690E Soft Soil 67.21 85.93
13.03.1992 ERZ˙
INCAN 6.9 5.00 Erzincan: Meteoroloji ˙
Istasyonu 39.7520N- 39.4870E Soil 404.97 470.92
06.11.1992 ˙
IZM˙
IR 6.1 41.00 Ku¸sadası: Meteoroloji ˙
Istasyonu 37.8610N- 27.2660E Soft Soil 83.49 71.80
24.05.1994 G˙
IR˙
IT 5.4 20.10 Foça: Gümrük Müdürlü ˘
gü 38.6400N- 26.7700E Rock 36.06 49.80
13.11.1994 KÖYCE ˘
G˙
IZ 5.2 17.41 Köyce ˘
giz: Meteoroloji ˙
Istasyonu 36.9700N- 28.6940E Soft Soil 72.79 96.51
01.10.1995 D˙
INAR 6.4 3.00 Dinar: Meteoroloji ˙
Istasyonu 38.0600N – 30.1500E Soft Soil 288.30 269.95
01.10.1995 D˙
INAR 6.4 46.20 Çardak: Sa˘
glık Oca˘
gı 37.8250N- 29.6680E Soil 65.07 61.30
27.06.1998 ADANA- 6.3 80.10 Mersin: Meteoroloji ˙
Istasyonu 36.8300N- 34.6500E Soft Soil 119.29 132.12
CEYHAN
27.06.1998 ADANA- 6.3 28.00 Ceyhan: PTT Müd. 37.0500N 35.8100E Soft Soil 223.42 273.55
CEYHAN
17.08.1999 KOCAEL˙
I 7.4 55.00 Bursa: Sivil Sav. Müd. 40.1830N- 29.1310E Soft Soil 54.32 45.81
17.08.1999 KOCAEL˙
I 7.4 81.00 Çekmece: Nükleer Santral Bn. 40.9700N- 28.7000E Soil 118.03 89.61
17.08.1999 KOCAEL˙
I 7.4 11.00 Düzce: Meteoroloji ˙
Istasyonu 40.8500N- 31.1700E Soft Soil 314.88 373.76
17.08.1999 KOCAEL˙
I 7.4 116.00 Ere ˘
gli: Kaymakamlık Bn. 40.9800N- 27.7900E Soil 90.36 101.36
17.08.1999 KOCAEL˙
I 7.4 15.00 Gebze: Tübitak Marmara Ara¸s. Mer. 40.8200N- 29.4400E Rock 264.82 141.45
17.08.1999 KOCAEL˙
I 7.4 32.00 Göynük: Devlet Hastanesi 40.3850N- 30.7340E Rock 137.69 117.9
17.08.1999 KOCAEL˙
I 7.4 49.00 ˙
Istanbul: Bayındırlık ve ˙
Iskan Müd. 41.0580N- 29.0130E Rock 60.67 42.66
17.08.1999 KOCAEL˙
I 7.4 8.00 ˙
Izmit: Meteoroloji ˙
Istasyonu 40.7900N- 29.9600E Rock 171.17 224.91
17.08.1999 KOCAEL˙
I 7.4 30.00 ˙
Iznik: Karayolları ¸Sefli˘
gi 40.4370N- 29.6910E Soft Soil 91.89 123.32
17.08.1999 KOCAEL˙
I 7.4 140.00 Kütahya: Sivil Savunma Müd. 39.4190N- 29.9970E Soil 50.05 59.66
17.08.1999 KOCAEL˙
I 7.4 3.20 Sakarya: Bayındırlık ve ˙
Iskan Müd. 40.7370N- 30.3840E Rock 407.04 –
17.08.1999 KOCAEL˙
I 7.4 150.00 Tekirda˘
g: Hükümet Kona˘
gı 40.9790N- 27.5150E Rock 129.79 128.33
17.08.1999 KOCAEL˙
I 7.4 17.00 Darıca: Arçelik Arge Bn. 40.82360N- 29.3607E Soil 211.37 133.68
17.08.1999 KOCAEL˙
I 7.4 82.50 Ambarlı: Termik Santral 40.9809N- 28.6926E Soft Soil 252.56 186.04
17.08.1999 KOCAEL˙
I 7.4 116.00 M. Ere˘
glisi: Bota¸s Gas Terminali 40.9919N- 27.9795E Soil 98.88 87.10
17.08.1999 KOCAEL˙
I 7.4 72.00 Ye¸silköy: Havalimanı 40.9823N- 28.8199E Soil 90.21 84.47
17.08.1999 KOCAEL˙
I 7.4 63.00 4. Levent: Yapı Kredi Plaza 41.0811N- 20.0111E Rock 41.08 35.52
17.08.1999 KOCAEL˙
I 7.4 3.28 Yarımca: Petkim Tesisleri 40.7639N–29.7620E Soil 230.22 322.20
17.08.1999 KOCAEL˙
I 7.4 63.00 Fatih: Fatih Türbesi 41.0196N–28.9500E Soft Soil 189.39 161.87
17.08.1999 KOCAEL˙
I 7.4 43.00 Heybeliada: Sanatoryum 40.8688N- 29.0875E Rock 56.15 110.23
17.08.1999 KOCAEL˙
I 7.4 71.00 Bursa: Tofa¸s Fab. 40.2605N- 29.0680E Soft Soil 100.89 100.04
17.08.1999 KOCAEL˙
I 7.4 81.00 Çekmece: Nükleer Santral Bn. 40.9700N- 28.7000E Soil 177.31 132.08
12.11.1999 DÜZCE 7.1 20.41 Bolu: Bayındırlık ve ˙
Iskan Müd. 40.7450N- 31.6100E Soft Soil 739.56 805.88
12.11.1999 DÜZCE 7.1 8.23 Düzce: Meteoroloji ˙
Istasyonu 40.8500N- 31.1700E Soft Soil 407.69 513.78
12.11.1999 DÜZCE 7.1 30.90 Mudurnu: Kaymakamlık Binası 40.4630N- 31.1820E Soft Soil 120.99 58.34

400
Figure 1. The distribution of records in the database in terms of magnitude, distance and local geological conditions.

401
Table 2. Earthquakes used in the analysis
Number of recordings
Date Earthquake Fault type MwSoft soil Soil rock
19.08.1976 DEN˙
IZL˙
INormal5.3 2
05.10.1977 ÇERKE ¸S Strike-Slip 5.4 2
16.12.1977 ˙
IZM˙
IR Normal 5.5 2
18.07.1979 DURSUNBEY Strike-Slip 5.3 2
05.07.1983 B˙
IGA Reverse 6.0 2 4
30.10.1983 HORASAN-NARMAN Strike-Slip 6.5 2
29.03.1984 BALIKES˙
IR Strike-Slip 4.5 2
12.08.1985 K˙
I˘
GI Strike-Slip 4.9 2
05.05.1986 MALATYA Strike-Slip 6.0 2
06.06.1986 SÜRGÜ (MALATYA) Strike-Slip 6.0 2
20.04.1988 MURAD˙
IYE Strike-Slip 5.0 2
13.03.1992 ERZ˙
INCAN Strike-Slip 6.9 2 2
06.11.1992 ˙
IZM˙
IR Normal 6.1 2
24.05.1994 G˙
IR˙
IT Normal 5.4 2
13.11.1994 KÖYCE ˘
G˙
IZ Normal 5.2 2
01.10.1995 D˙
INAR Normal 6.4 2 2
27.06.1998 ADANA-CEYHAN Strike-Slip 6.3 4
17.08.1999 KOCAEL˙
I Strike-Slip 7.4 12 16 15
12.11.1999 DÜZCE Strike-Slip 7.1 6
Total 4 0 24 2 9
Figure 2. Distribution of the larger maximum horizontal acceleration of either component versus distance.

402
Figure 3. The distribution of records in the database in terms of magnitude, distance and type of faulting.

403
Attenuation relationship development
Attenuation relationships were developed by using the
same general form of the equation proposed by Boore
et al. (1997). The ground motion parameter estimation
equation is as follows:
lnY = b1+b
2(M – 6) + b3(M – 6)2
+b
5ln r + bVln (VS/V
A)(1)
r=(r
cl2+h
2)1/2(2)
Here Y is the ground motion parameter (peak hori-
zontal acceleration (PGA) or pseudo spectral acceler-
ation (PSA) in g); M is (moment) magnitude; rcl is
closest horizontal distance from the station to a site
of interest in km; VSis the shear wave velocity for
the station in m/s; b1,b
2,b
3,b
5,h,b
V,andV
Aare
the parameters to be determined. Here h is a fictitious
depth, and VAa fictitious velocity that are determined
by regression. The coefficients in the equations for
predicting ground motion were determined by using
nonlinear regression analysis. Nonlinear regression is
a method of finding a nonlinear model of the rela-
tionship between the dependent variable and a set of
independent variables. Unlike traditional linear regres-
sion, which is restricted to estimating linear models,
nonlinear regression can estimate models with arbit-
rary relationships between independentand dependent
variables. This is accomplished using iterative estim-
ation algorithms. The nonlinear regression procedure
on the database was performed using SPSS statistical
analysis software program (Ver.9.00, 1998). This ex-
ercise was performed separately on PGA and on PSA
data at each oscillator period considered (total of 46
periods from 0.1 to 2.0 s.).
The procedure that we have used to develop the
attenuation curves consists of two stages (Joyner and
Boore, 1993). In the first, attenuation relationships
were developed for PGA and spectral acceleration val-
ues by selecting the acceleration values in the database
as maximum horizontal components of each record-
ing station. Then, a nonlinear regression analysis was
performed. In the next stage, random horizontal com-
ponents were selected for the acceleration values in
the database and regression analyses were applied.
The results were compared for PGA, 0.3 s and 1.0
s PSA cases, and it was concluded that selection of
maximum, rather than of random, horizontal compon-
ents did not yield improvedestimates and smaller error
terms. This issue is taken up again in the section on
comparisons of our results with other relations.
Figure 4. Curves of peak acceleration versus distance for magnitude
5.5, 6.5 and 7.5 earthquakes at rock sites.
Figure 5. Curves of peak acceleration versus distance for magnitude
5.5, 6.5 and 7.5 earthquakes at soil sites.

404
Table 3. Attenuation relationships of horizontal PGA and response spectral accelerations
(5% damping)
ln(YO = b1 + b2 (M–6) + b3 (M–6)2+b5lnr+b
Vln (VS/VAwith r = (rcl 2+h2)1/2
Period,sb1b2b3b5b
VVAhσln(Y)
0 (PGA) –0.682 0.253 0.036 –0.562 –0.297 1381 4.48 0.562
0.10 –0.139 0.200 –0.003 –0.553 –0.167 1063 3.76 0.621
0.11 0.031 0.235 –0.007 –0.573 –0.181 1413 3.89 0.618
0.12 0.123 0.228 –0.031 –0.586 –0.208 1501 4.72 0.615
0.13 0.138 0.216 –0.007 –0.590 –0.237 1591 5.46 0.634
0.14 0.100 0.186 0.014 –0.585 –0.249 1833 4.98 0.635
0.15 0.090 0.210 –0.013 –0.549 –0.196 1810 2.77 0.620
0.16 –0.128 0.214 0.007 –0.519 –0.224 2193 1.32 0.627
0.17 –0.107 0.187 0.037 –0.535 –0.243 2433 1.67 0.621
0.18 0.045 0.168 0.043 –0.556 –0.256 2041 2.44 0.599
0.19 0.053 0.180 0.063 –0.570 –0.288 2086 2.97 0.601
0.20 0.127 0.192 0.065 –0.597 –0.303 2238 3.48 0.611
0.22 –0.081 0.214 0.006 –0.532 –0.319 2198 1.98 0.584
0.24 –0.167 0.265 –0.035 –0.531 –0.382 2198 2.55 0.569
0.26 –0.129 0.345 –0.039 –0.552 –0.395 2160 3.45 0.549
0.28 0.140 0.428 –0.096 –0.616 –0.369 2179 4.95 0.530
0.30 0.296 0.471 –0.140 –0.642 –0.346 2149 6.11 0.540
0.32 0.454 0.476 –0.168 –0.653 –0.290 2144 7.38 0.555
0.34 0.422 0.471 –0.152 –0.651 –0.300 2083 8.30 0.562
0.36 0.554 0.509 –0.114 –0.692 –0.287 2043 9.18 0.563
0.38 0.254 0.499 –0.105 –0.645 –0.341 2009 9.92 0.562
0.40 0.231 0.497 –0.105 –0.647 –0.333 1968 9.92 0.604
0.42 0.120 0.518 –0.135 –0.612 –0.313 1905 9.09 0.634
0.44 0.035 0.544 –0.142 –0.583 –0.286 1899 9.25 0.627
0.46 –0.077 0.580 –0.147 –0.563 –0.285 1863 8.98 0.642
0.48 –0.154 0.611 –0.154 –0.552 –0.293 1801 8.96 0.653
0.50 –0.078 0.638 –0.161 –0.565 –0.259 1768 9.06 0.679
0.55 –0.169 0.707 –0.179 –0.539 –0.216 1724 8.29 0.710
0.60 –0.387 0.698 –0.187 –0.506 –0.259 1629 8.24 0.707
0.65 –0.583 0.689 –0.159 –0.500 –0.304 1607 7.64 0.736
0.70 –0.681 0.698 –0.143 –0.517 –0.360 1530 7.76 0.743
0.75 –0.717 0.730 –0.143 –0.516 –0.331 1492 7.12 0.740
0.80 –0.763 0.757 –0.113 –0.525 –0.302 1491 6.98 0.742
0.85 –0.778 0.810 –0.123 –0.529 –0.283 1438 6.57 0.758
0.90 –0.837 0.856 –0.130 –0.512 –0.252 1446 7.25 0.754
0.95 –0.957 0.870 –0.127 –0.472 –0.163 1384 7.24 0.752
1.00 –1.112 0.904 –0.169 –0.443 –0.200 1391 6.63 0.756
1.10 –1.459 0.898 –0.147 –0.414 –0.252 1380 6.21 0.792
1.20 –1.437 0.962 –0.156 –0.463 –0.267 1415 7.17 0.802
1.30 –1.321 1.000 –0.147 –0.517 –0.219 1429 7.66 0.796
1.40 –1.212 1.000 –0.088 –0.584 –0.178 1454 9.10 0.790
1.50 –1.340 0.997 –0.055 –0.582 –0.165 1490 9.86 0.788
1.60 –1.353 0.999 –0.056 –0.590 –0.135 1513 9.94 0.787
1.70 –1.420 0.996 –0.052 –0.582 –0.097 1569 9.55 0.789
1.80 –1.465 0.995 –0.053 –0.581 –0.058 1653 9.35 0.827
1.90 –1.500 0.999 –0.051 –0.592 –0.047 1707 9.49 0.864
2.00 –1.452 1.020 –0.079 –0.612 –0.019 1787 9.78 0.895

405
Figure 6. Curves of peak acceleration versus distance for magnitude
5.5, 6.5 and 7.5 earthquakes at soft soil sites.
The coefficients for estimating the maximum
horizontal-component pseudo-acceleration response
by Equation (1) are given in Table 3. The resulting
parameters can be used to produce attenuation rela-
tionships that predict response spectra over the full
range of magnitudes (Mw5 to 7.5) and distances (rcl)
up to 150 km. The results were used to compute er-
rors for PGA and PSA at individual periods. The
standard deviation of the residuals, σ, expressing the
random variability of ground motions, is an important
input parameter in probabilistic hazard analysis. In this
study, the observed value of σ(ln Y) lies generally
within the range of 0.5 to 0.7. The calculated attenu-
ation relationships for PGA for rock, soil and soft soil
sites are shown in Figures 4 through 6.
Comparison with other ground motion
relationships
The equations developed in this study for ground
motion estimation were compared to those recently
developed by Boore et al. (1997), Campbell (1997),
Sadigh et al. (1997), Spudich et al. (1997) and finally
Ambraseys et al. (1996). The equations of Boore et
al. and Ambraseys et al. divided site classes into four
groups according to shear wave velocities. Campbell’s
equations pertain to alluvium (or firm soil), soft rock
and hard rock. Sadigh et al. and Spudich et al. state
that their equations are applicable for rock and soil
sites.
The attenuation of PGA and PSA at 0.3 and 1.0
sforM
w= 7.4 for rock and soil sites are compared
in Figures 7–9, respectively. The measured database
points from the Kocaeli event are also marked on these
curves to illustrate how well they fit the estimates.
The differences in the curves are judged to be reas-
onable because different databases, regression models
and analysis methods, different definitions for source
to site distance and magnitude parameters among the
relationships are contained in each model.
For some parameters and especially for PGA, there
are numerous published attenuation equations for use
in any particular engineering application. Atkinson
and Boore (1997) showed the differences between at-
tenuation characteristics in western and eastern USA
for stable intraplate and interplate regions. Neverthe-
less, differences among attenuation of strong motions
from one region to another have not been definitely
proven. Because of this reason it is preferableto use at-
tenuation equations that are based on the records taken
from the region in which the estimation equations are
to be applied.
Sensors comprising the national or other strong
motion networks in Turkey are oriented so that their
horizontal axes match the N-S and the E-W directions.
Whereas Figure 2 illustrates the larger of these two
components as a function of distance, it may not rep-
resent the largest horizontal acceleration that occurred
before the cessation of the ground motion. The value
of the absolute maximum acceleration in whichever
direction can be determined by monitoring through
a simple book-keeping procedure for the size of the
resultant horizontal component, and then resolving all
pairs to the direction of that largest component once
it is known. At variance with the customary practice,
we call this component the ‘random’ horizontal com-
ponent. In Figure 10, the difference in the predictive
power of the regression equations derived from both
of these definitions is illustrated for Mw=7.4,and
compared against the Kocaeli measurements. We be-
lieve that both sets yield essentially the same results.
With the differences between the mean or the stand-
ard deviation curves substantially less than the value
of σln (Y) itself, an improvement in accuracy does
not appear to be plausible between the definitions of
maximum horizontal acceleration.

406
Figure 7. Curves of peak acceleration versus distance for magnitude 7.4 earthquake at rock and soil sites.

407
Figure 8. Curves of spectral acceleration at T = 0.3 s versus distance
for a magnitude – 7.4 earthquake at rock and soil sites. Figure 9. Curves of spectral acceleration at T = 1.0 s versus distance
for a magnitude – 7.4 earthquake at rock and soil sites.

408
Figure 10. Differences caused by using the larger of the two hori-
zontal components or the component in the direction of the largest
resultant.
Uncertainty and reliability
Uncertainty is a condition associated with essentially
all aspects of earthquake related science and engin-
eering. The principle sources of uncertainty lie in the
characterization of site geology, calculation of closest
distances, determination of seismic shaking proper-
ties, and in the geotechnical properties of earthquake
motion monitoring sites. The regression analysis is
based on stochastic analysis method, thus the ob-
tained attenuation formula contains unavoidable er-
rors. These uncertainties, for the most part stemming
from the lack of and/or the imperfect reliability of the
specific supporting data available, affect all analytical
methods and procedures applied to the derivation of
all aforementioned parameters.
The attenuation relationships presented in this
study cannot, and do not, eliminate these uncertain-
ties. However through the use of nonlinear regression
analysis, it provides a more sophisticated and direct
approach to address the uncertainties than do tradi-
tional linear analysis procedures. The results we have
presented in tabular and graphical form becomemean-
ingful only in the context of the error distributions that
are associated with each variable. In general, our res-
ults possess larger deviations in comparison with, e.g.,
Boore et al. (1997). This is plausible because of the
smaller number of records from which they have been
derived. In view of the limited number of records util-
ized in this study it may not be appropriate to expect
the distributions to conform to the normal distribution.
We do this only as a vehicle that permits a direct com-
parison to be made between our results and those of
Boore et al. (1997).
Discussion and conclusions
The recommended attenuation relationships presented
in detail in this paper through Table 3 and illustrated
in Figures 4–6 are considered to be appropriate for the
estimation of horizontal components of peak ground
acceleration, and 5 percent damped pseudo accelera-
tion response spectra for earthquakes with magnitude
in the range Mw5to7.5andr
cl<150 km for soft soil,
soil and rock site conditions in active tectonic regions
of Turkey. The database from which these estimates
have been drawn is not pristine. It is handicapped not
only because of the sheer dearth of records but also
because of their poor distribution, arbitrary location,
near-total lack of knowledge of local geology, and
possible interference from the response of buildings
where the sensors have been stationed. We have ex-
cluded aftershock data, and omitted records with peaks
of less than about 0.04 g. It is shown in Table 1 that
more than half of the records have been recovered
from two M 7+ events that occurred in 1999. Inev-
itably, the regression expressions are heavily imbued
with that data proper. A point of generalization is that,
in general, the database causes larger margins of error
in the estimates. This is more noticeable for spectral
accelerations at longer periods.
When we compare our equations with other atten-
uation relationships not developed specifically from
recordings in Turkey, it is concluded that they over-
estimate the peak and spectral acceleration values for
up to about 15–20 km. Trends of our curves are gen-
erally above these curves for larger distances because
for our expressions the fall-off trend is less strong. We
surmise that clipping the minimum peak acceleration
at 0.04 g is the cause of this trend. Among the other
attenuation relationships we have used for comparison
the equations by Ambraseys et al. (1996) for European
earthquakes yields the best match with our equations.
Whether this is caused by the fact that the Ambraseys
study utilized data recorded also in Turkey cannot be
answered except on a conjectural basis. But this com-

409
parison clearly serves as a reminder that there exists
little support for the carefree import of attenuation
curves from other environments for use in important
engineering applications elsewhere.
It is a truism that, as additional strong motion re-
cords, shear wave velocity profiles for recording sites,
and better determined distance data become available
for Turkey, the attenuation relationships derived in this
study can be progressively modified and improved,
and their uncertainties reduced.
Acknowledgements
The authors acknowledgewith gratefulness the help of
Sinan Akkar, Altu˘
g Erberik and Tolga Yılmaz in the
Earthquake Engineering Research Center at Middle
East Technical University (METU/EERC). Sincere
thanks are extended also to Zahide Çolako˘
glu, Tülay
U˘
gra¸s and Ulubey Çeken of the General Directorate of
Disaster Affairs, Earthquake Research Department for
providing references and necessary data.
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