Articulo 3C.indd
EARTH SCIENCES
RESEARCH JOURNAL
SEISmOLOgy
Earth Sci. Res. SJ. Vol. 16, No. 2 (December, 2012): 103 - 108
Introduction
Since fractal description was developed for the geometry of natu-
ral objects (mandelbrot B.B., 1982), it has been recognised that many
complex space-time phenomena, such as seismicity, may be described and
interpreted in terms of fractal distributions with power-law scaling (e.g.
Hirata T., 1989; Öncel A.O. et al., 1995; Caneva A., Smirnov V., 2004;
Öncel A.O., Wilson T.H., 2007; Roy S. et al., 2011). However, studies
of possible correlation between seismicity and fault distribution are lim-
ited. Applying seismic hazard assessment to fractal association between
seismotectonic variables requires distinguishing normal and anomalous
correlations between such data sets’ fractal attributes. Since the statisti-
cal behaviour of seismicity may potentially represent sensitive short-term
predictors of major earthquakes, this study’s main aim was to find an em-
pirical relationship between seismic b-values and the fractal distribution of
epicentres for Turkish earthquakes.
Data regarding earthquakes and tectonic zoning
Several earthquake catalogues are available for Turkey from both
national and international sources. Earthquakes occurring between
1970 and 2006 were taken from Öztürk’s catalogue of instrumental data
Statistical correlation between b-value and fractal dimension regarding
Turkish epicentre distribution
Serkan Öztürk
gümüşhane University. Turkey. E-mail: serkanozturk@gumushane.edu.tr
ABSTRACT
This study was aimed at analysing the relationship between seismic b-value and fractal dimension Dc-
value for Turkish epicentres. The earthquake catalogue consisting of 99,737 instrumentally-registered
Turkish events was analysed for the period between 1970 and 2011; Turkey was divided into 55 tec-
tonic zones for making a detailed comparison. The b-values were calculated by the maximum likelihood
method and the Dc-values were obtained with 95% confidence limits by linear regression. The results
showed that higher Dc-values were associated with lower b-values and this could have been an indication
of relatively high stress intensity and stronger epicentre clustering in these regions.
Orthogonal regression was used to estimate a suitable statistical correlation between two seismotec-
tonic parameters; the Dc = 2.44 - 0.30*b relationship was obtained with a strong negative correlation
(r = -0.82) between b-value and Dc-value for Turkish earthquake distribution. This seemed to agree with
other regional results obtained for different parts of Turkey and the rest of the world.
RESUmEN
Este estudio tuvo como objetivo analizar la relación entre el valor b y la dimensión del valor fractal Dc
para los epicentros de Turquia. El catálogo sísmico que consiste en 99.737 eventos registrados instru-
mentalmente fue analizado para el período comprendido entre 1970 y 2011; Turquía se dividió en 55
zonas tectónicas para hacer una comparación detallada. Los valores de b se calcularon por el método de
máxima verosimilitud y la Dc-valores se obtuvieron con límites de confianza del 95% mediante regresión
lineal. Los resultados mostraron que el aumento del valor fractal Dc se asocia con menores valores b y
esto podría haber sido un indicador de intensidad de tensiones relativamente altas y una más fuerte
agrupación de epicentro en estas regiones.
Se utilizó una regresión ortogonal para estimar la correlación estadística adecuada entre dos pará-
metros sismotectónicos la relación de la dimensión fractal Dc = 2,44 a 0,30*b, se obtuvo con una fuerte
correlación negativa (r = -0,82) entre valores b y valores fractales Dc para la distribución de terremotos en
Turquía. Esto parece estar de acuerdo con otros resultados regionales obtenidos para las diferentes partes
de Turquía y el resto del mundo.
Palabras claves: Terremoto de Turquía, dimensión fractal,
valor-b, correlación.
Keywords: Turkish earthquake, fractal dimension, b-value,
correlation.
Record
manuscript received: 13/02/2012
Accepted for publications: 06/05/2012
Serkan Öztürk104
(2009), including duration magnitude (M
D
) for 73,530 earthquakes oc-
curring in Turkey between 1970 and 2006; Öztürk used empirical rela-
tionships to compile a homogenous and complete earthquake catalogue
(1970 to 2006). The Bogazici University’s Kandilli Observatory and
Research Institute (KOERI) catalogue was also used for 2006 to 2011;
KOERI usually gives local magnitudes (M
L
) for local earthquakes having
missing M
D
. If an M
D
was unknown in the KOERI catalogue for 2006 to
2011, then M
D
were calculated using the relationships given in Öztürk
(2009). 26,207 earthquakes in and around Turkey were thus selected for
the aforementioned period. This earthquake catalogue was homogeneous
for M
D and contained 99,737 earthquakes occurring between 1970 and
2011.
many authors have suggested tectonic zoning as a widely-used meth-
odology for evaluating the hazard of an earthquake occurring (e.g. Erdik
m. et al., 1999; Jiménez m. et al., 2001; Bayrak y. et al., 2009). The pres-
ent study’s new seismic source zones for Turkey and its adjacent areas were
based on tectonic zoning studies by Erdik (1999) and Bayrak (2009), the
existing tectonic structure and earthquake epicentre distribution (Figure
1). Turkey was divided into 55 different zones, as shown in Figure 1. New
smaller zones were selected to compare such tectonic zoning in detail, in
the same regions. Figure 1 shows Turkey’s active tectonics and many de-
tails regarding Turkey’s tectonic structure can be found in Şaroğlu (1992),
mcClusky (2000) and Bozkurt (2001). The numbers of earthquakes oc-
curring in each zone were sufficient for analysis; Table 1 shows the seismic
zones in this study (numbered 1 to 55) with their tectonic environments.
Earthquakes’ frequency-magnitude distribution
(seismic b-value)
Earthquakes’ magnitude distribution (Md) is usually parameterised
using gutenberg-Richter’s (g-R) power law relationship (gutenberg B.,
Richter C.F., 1944); such frequency-magnitude relationship has been
found to be applicable (in simplified form) as follows:
log
10 N(M) = a – bM (1)
where N(M) is the cumulative number of events having a magni-
tude greater than M, b describes the slope of the size distribution of
events and a is proportional to the productivity of a volume, or the seis-
micity rate.
The b-value is one of the most important statistical parameters
for describing the size scaling properties of seismicity; b-values change
Figure 1. Tectonic areas and active fault systems in Turkey. Tectonic structures
have been modified from Şaroğlu F. et al., (1992) and Bozkurt E. (2001).
roughly in the range of 0.3 to 2.0, depending on the different regions.
However, average regional scale estimates of b-value are usually equal to
1 (Frohlich C., Davis S., 1993). many factors can cause perturbation
of average b-value (b~1.0); regions having lower b-values are probably
regions subjected to higher applied shear stress after the main shock,
whereas regions having higher b-values are areas which have experienced
slip. High b-values are reported from areas having increased geological
complexity, indicating the importance of multi-fracture areas; a low b-
value is thus related to a low degree of heterogeneity of cracked medium,
large stress and strain, high deformation speed and large faults (Bayrak
y., Öztürk S., 2004).
many methods can be used for calculating any region’s b-value but
the maximum likelihood method is the most robust and widely-accepted
method for estimating b-values (Aki K., 1965):
b = 2.303 /(M
—
– M
min + 0.005) (2)
where M
—
is average magnitude value and M
min
is minimum mag-
nitude value. 0.05 in equation (2) is a correction constant. If b=1 and
M
min=1 is used, Maverage=3.25 will be obtained. However, this is an ex-
treme Mmin value. Mmin=1 did not occur in previous Turkish earthquake
catalogues; Mmin in Turkish earthquake catalogues was around 3.0 until
the beginning of the 2000s. many stations have been built in Turkey,
especially after two destructive earthquakes in 1999, minimum earth-
quake magnitude now being seen to be around 1.5 (average value may
sometimes be higher than 3.25 which is not high value for Turkish earth-
quakes). The standard deviation of seismic b-value (95% confidence
limit) may be determined using the equation suggested by Aki (1965) as
1.96b / √n, where n is the number of earthquakes used to make the
estimate. This would yield ±0.1–0.2 confidence limits regarding b-value
for a typical sample consisting of n=100 earthquakes. Such sample con-
sisting of n=100 events represents a specific calculation. The number of
earthquakes in this study was 97,737; Table 1 shows that sometimes 110
earthquakes were used (in region 13) or 10,328 earthquakes on other oc-
casions (in region 34). This value for n=100 earthquakes is thus a typical
sample for the aforementioned calculation.
Fractal dimension (correlation dimension, Dc)
of epicentres’ spatial distribution
Earthquake distribution spatial patterns and temporal patterns of oc-
currence were demonstrated to be fractal using a two-point correlation
dimension (Dc). Analysing correlation dimension is a powerful tool for
quantifying a geometrical object’s self-similarity. grassberger and Procac-
cia (1983) defined Dc and correlation sum C(r) as follows:
Dc = lim[logC(r)/logr] (3)
r
0
C(r) = 2NR<r / N(N – 1) (4)
where C(r) is the correlation function, r is the distance between two
epicentres and N is the number of pairs of events separated by distance
R<r. If the epicentre distribution has a fractal structure, the following rela-
tionship would be obtained:
C(r) rDc (5)
where Dc is the fractal dimension (more strictly, the correlation di-
mension). Distance r between two earthquakes would be calculated (in
degrees) from:
r = cos–1(cosi cosj + sini sinj cos (fi – fj)) (6)
Statistical correlation between b-value and fractal dimension regarding Turkish epicentre distribution 105
Table 1. Seismotectonic parameters b-value and Dc-value, as well as the number of earthquakes occurring in entire seismic areas of Turkey.
Region Tectonics
Earthquake
Number
b-value Dc-value
1 North East Anatolian Fault Zone (NEAFZ)
(Horosan Fault, Dumlu and Çobandede Fault Zones)
338 0.62±0.03 2.26±0.09
2 1234 1.05±0.03 2.08±0.07
3 Ağrı, Tutak, Balıklıgöl and Kağızman Faults (ATBKF) 219 0.86±0.06 2.30±0.04
4 Iğdır, Doğubeyazıt and Çaldıran Faults (IDÇF) 268 0.63±0.03 2.23±0.02
5 Başkale, Erciş, Muradiye and Süphan Faults (BEMSF)
and Hasan Timur Fault Zone (HTFZ)
159 0.98±0.09 2.09±0.03
6 350 0.95±0.05 2.12±0.03
7 Malazgirt and Bulanık Faults (MBF) 320 1.13±0.07 2.08±0.04
8
Bitlis-Zagros Thrust Zone (BZTZ)
(Kavakbaşı Fault, Muş Thrust Zone and
Yüksekova-Şemdinli Fault Zone)
442 1.05±0.06 2.08±0.04
9 238 0.77±0.05 2.28±0.01
10 116 1.21±0.10 2.03±0.01
11 254 0.63±0.04 2.28±0.05
12 251 0.83±0.06 2.25±0.05
13
Karacadağ Extension Zone (KEZ)
110 1.17±0.04 2.00±0.03
14 510 1.49±0.08 1.94±0.04
15 East Anatolian Fault Zone (EAFZ) 2272 0.96±0.02 2.11±0.06
16 Junction of A part of Dead Sea
Fault and EAFZ
298 0.84±0.05 2.31±0.06
17 1118 0.93±0.04 2.12±0.03
18 Northern part of Cyprus 179 1.61±0.05 2.00±0.03
19 Southern part of Cyprus, including
Eastern part of Cyprus Arc
369 1.20±0.07 2.07±0.02
20 340 1.28±0.05 1.99±0.04
21
Western part of Cyprus Arc
350 1.05±0.07 2.10±0.03
22 1161 1.15±0.05 2.10±0.02
23 Acıgöl, Dinar and Çivril Faults (ADÇF) 2154 1.36±0.09 2.06±0.04
24
Muğla and Rhodes Region
1534 1.64±0.09 1.94±0.04
25 5392 1.38±0.09 1.97±0.03
26 Aegean Arc 1914 1.38±0.09 2.21±0.03
27 Burdur Fault Zone (BFZ) 1787 1.01±0.02 2.15±0.05
28 Büyük and Küçük Menderes
Grabens (BKMG)
3428 1.24±0.08 2.02±0.04
29 1408 1.34±0.07 2.08±0.04
30 Aliağa and Dumlupınar Faults (ADF) and
Zeytindağ-Bergama Faults (ZBF)
926 1.30±0.07 2.08±0.04
31 3770 1.13±0.02 2.10±0.07
32 Alaşehir and Gediz Grabens (AGG) 1782 1.24±0.06 2.03±0.02
33 Sultandağı, Beyşehir and Tatarlı Faults (SBTF) 3252 1.35±0.05 2.05±0.04
34
Kütahya and Simav Grabens (KSG)
10328 1.15±0.01 2.08±0.05
35 8036 1.62±0.04 2.03±0.05
36
Soma and Bakırçay Grabens (SBG)
6422 1.93±0.05 1.95±0.07
37 1710 1.65±0.08 2.04±0.05
38 1168 1.18±0.04 2.06±0.05
39 Eskişehir, İnönü-Dodurga and Kaymaz Faults (EİDKF) 2527 1.41±0.03 1.98±0.05
40 Manyas and Ulubat Faults (MUF) 1432 1.44±0.03 2.04±0.04
41 Yenice-Gönen and Sarıköy Faults (YGSF) 4220 1.41±0.04 2.03±0.04
42 Etili Fault (EF) 1398 1.65±0.07 1.92±0.04
Serkan Öztürk106
where (i,fi) and (j,fj) are the latitudes and longitudes of the i
th and
jth events, respectively (Hirata T., 1989). By plotting C(r) against r on a
double logarithmic coordinate, fractal dimension Dc would be obtained
from the slope of the graph.
Fractal analysis is often used to quantify size scaling attributes and
seismotectonic variables’ clustering properties. Fractal dimension Dc can
be calculated to determine possible unbroken sites and such unbroken
sites have been suggested as being potential seismic gaps to be broken in
the future. Variations in fractal correlation dimension mainly depend on
the complexity or quantitative measurement of the degree of heterogeneity
of seismic activity in a fault system. In areas of increased complexity in an
active fault system (higher Dc) associated with lower b-value, stress release
occurs on fault planes having smaller surface area (Öncel A.O., Wilson
T.H., 2002).
Results and Discussion
An investigation of seismotectonic parameters in and around Tur-
key involved using the b-value of the g-R relationship (Equation 1) and
fractal correlation dimension Dc-value of Turkish earthquake distribution
from 1970 to 2011; Turkey was divided into 55 seismic source zones in an
attempt to find an empirical relationship between b-value and Dc-value.
ZMAP software was used for calculating b and Dc-values for each region
(Wiemer S., 2001). The b-values were calculated by using the maximum
likelihood method (95% confidence limit) because it yields a more robust
estimate than the least-square regression method (Aki K., 1965). The Dc-
values for all Turkish areas were obtained with 95% confidence limits by
linear regression. Table 1 shows the results for two seismotectonic param-
eters with their standard deviations as well as the number of earthquakes
for entire tectonic areas.
The first seismic parameter b-value ranged from 0.62 to 1.93 for 55
Turkish areas. b-values smaller than 0.8 were found in regions 1, 4, 9 and
11, including the north-eastern Anatolian fault zone (NEAFZ) including
the Dumlu and Çobandede fault zones, Iğdır, Doğubeyazıt and Çaldıran
faults (IDÇF) and two parts of the Bitlis-Zagros thrust zone (BZTZ). Such
low values may have depended on the position of these regions neighbour-
ing the easternmost part of the north Anatolian fault and the BZTZ. The
conjugate strike-slip fault system related to these areas dominates eastern
Anatolia’s active tectonics and thrust faults can produce destructive earth-
quakes in the Bitlis thrust which forms a complex continent-continent
and continent-ocean collision boundary (Bozkurt E, 2001). These systems
generate major earthquakes, such as Patnos in 1903 (M
S=6.3), Pasinler
in 1924 (MS=6.8), Lice-Diyarbakır in 1975 (MS=6.6), Çaldıran in 1976
(MS=7.5) and Horasan in 1983 (MS=6.8). global positioning system
(gPS) data gives 10±2 mm/yr for total shortening between the strike slip
faults in eastern Turkey and thrusting along the Caucasus. The BZTZ’s
north-western motion is 18±2 mm/yr and such motion is related to that
of Eurasia (mcClusky S. et al., 2000); small b-values in these regions are
thus related to a low degree of heterogeneity and large faults resulting in
strong earthquakes.
The other small b-values changing between 0.8 and 1.0 were observed
in regions 3, 5, 6, 12, 15, 16, 17 and 50 covering the Ağrı, Tutak, Balıklıgöl
and Kağızman faults (ATBKF), the Başkale, Erciş, muradiye and Süphan
faults (BEmSF) and the Hasan Timur fault zone (HTFZ), the western
part of BZTZ, the east Anatolian fault zone (EAFZ), the junction of a
part of the Dead Sea fault and EAFZ, the eastern part of the north Ana-
tolian fault zone (ENAFZ) including the Bingöl-Karakoçan and Sancak-
Uzunpınar fault zones. Table 1 shows that regions 15, 16 and 17 are con-
nected with the east EAFZ which is not as seismically active as the NAFZ.
Unlike NAFZ, the EAFZ in region 15 has been relatively quiescent in the
instrumental period compared to the historical period (mcClusky S. et al.,
2000). The data used in this study only included the instrumental period
for earthquakes occurring from 1970 to 2011. According to the fault slip
rate and observed seismicity during recent years, relatively larger b-values
were observed in these regions than in regions 1, 4, 9 and 11. According
to Scholz (1968), low b-values indicate that the state of stress is high.
Special interest should thus be given to whole regions where low b-values
have been observed, especially after the occurrence of the M
W=6.0 Elazığ
earthquake (in region 15) on 8th march 2010 and the MW=7.2 Van Lake
earthquake (in region 6) on 23rd September 2011.
Regions such as 2, 8, 21, 27, 46, 48, 49 and 52 have almost the similar
b-values (very close to 1.0); these regions are related to the NEAFZ, the east-
ern part of BZTZ, the western part of the Cyprus Arc, the Burdur fault zone
(BFZ), the Düzce fault (DF), the yağmurlu-Ezinepazarı fault zone (yEFZ)
the another part of the ENAFZ and Sürgü fault. The maximum b-value was
estimated as being 1.93 in region 36, such region lying around the Soma and
Bakırçay grabens. Other largest b-values greater than 1.5 were calculated in
regions 18, 24, 35, 37 and 42; these zones were covered by the northern part
of Cyprus, the muğla and Rhodes region, the Kütahya and Simav grabens
(KSg) and the Etili fault (EF). The b-values obtained for the rest of the
zones were between 1.1 and 1.5. The NAFZ is a very active structure and,
according to geodesy, accommodates 24±2 mm/yr of dextral motion (mc-
Clusky S. et al., 2000). Two large earthquakes occurred in regions 44 and 46
during August and November 1999 and, of course, the stress level in these
Region Tectonics
Earthquake
Number
b-value Dc-value
43
Marmara part of North
Anatolian Fault Zone (MNAFZ)
1378 1.10±0.07 2.10±0.06
44 7859 1.26±0.02 2.05±0.03
45 1430 1.35±0.07 2.05±0.03
46 Düzce Fault (DF) 2011 1.02±0.03 2.14±0.05
47 Ismetpaşa Segment (IS) 1684 1.38±0.09 2.04±0.05
48 Yağmurlu-Ezinepazarı Fault Zone (YEFZ) 1369 1.04±0.03 2.10±0.04
49 Eastern part of North Anatolian Fault Zone (ENAFZ)
(Bingöl-Karakoçan, Sancak-Uzunpınar Fault Zones)
794 1.03±0.05 2.13±0.03
50 2236 0.87±0.07 2.28±0.06
51 Ovacık and Malatya Fault Zone (OMFZ) 1340 1.20±0.04 2.05±0.03
52 Sürgü Fault (SF) 577 1.06±0.05 2.06±0.03
53 Central Anatolian Fault Zone (CAFZ)
(Yakapınar-Göksun and Yıldızeli Fault Zones )
659 1.27±0.05 1.99±0.03
54 738 1.25±0.04 2.02±0.03
55 Tuzgölü Fault Zone (TFZ) 2178 1.19±0.03 2.03±0.06
Statistical correlation between b-value and fractal dimension regarding Turkish epicentre distribution 107
regions would thus not have been so high in recent years. The regions char-
acterised by large b-values had a greater proportion of low magnitude earth-
quakes whereas regions having low b-values represented areas in which large
magnitude earthquakes occurred. b-values estimated using the maximum
likelihood approach for the g-R method seemed to have a good relationship
to the tectonics and level of seismicity.
The second seismotectonic parameter Dc-value ranged from 1.92-2.31
for the 55 tectonic source regions in Turkey and the surrounding areas. Dc-
values smaller than 2.0 were estimated in regions 14, 20, 24, 25, 36, 39, 42
and 53. These zones were related to the Karacadağ extension zone (KEZ),
the southern part of Cyprus including the eastern part of the Cyprus Arc,
the muğla and Rhodes region, the SBg, the Eskişehir, İnönü-Dodurga and
Kaymaz faults (EİDKF), the EF, the central Anatolian fault zone (CAFZ)
including the yıldızeli fault zone. Dc-values greater than 2.2 were observed
in regions 1, 3, 4, 9, 11, 12, 16, 26 and 50 which were related to the NEAFZ
including the Dumlu and Çobandede fault zones, the ATBKF, the IDÇF,
the BZTZ, the junction of part of the Dead Sea fault and the EAFZ, the
Aegean Arc and the ENAFZ. Dc-values ranged from 2.0 to 2.2 in the rest
of the seismic source areas. The results obtained from analysis of data along
the NAFZ (regions 43-49) suggested that epicentre distribution became less
clustered (higher Dc) as the probability of larger magnitude earthquakes be-
came smaller (larger b-value). This implied greater fracture toughness in the
central portions of the NAFZ. As stated in Öncel and Wilson (2002), stress
becomes released on fault planes having smaller surface area in regions of
increased complexity in an active fault system (higher Dc) associated with
lower b-values. This means that areas in a fault network characterised by
higher Dc-values would be associated with greater complexity in a fault pat-
tern and the persistence of such complexity on smaller scales. Higher order
fractal dimension (especially greater than 2.0) is increasingly sensitive to
heterogeneity in magnitude distribution, suggesting that seismicity is more
clustered at larger scales (or in smaller areas) in these fault zones. It may also
be related to the number of events to a certain extent. Since the uniform
distribution of earthquakes decreases with an increase in the clustering of
events, it is reasonable to assume that higher Dc values (≥2.2) and lower b-
values (0.8≤) are the dominant structural feature in the study area and may
have arisen due to clusters.
Correlation between b and Dc-value
This study was aimed at determining a statistical relationship between
seismic b-values and fractal dimension Dc-value for Turkish epicentres.
The orthogonal regression (OR) method (e.g, Carroll R.J., Ruppert D.,
1996) was used to find the most suitable correlation between both seis-
motectonic parameters selected here. As the standard least squares method
Figure 2. Dc-value compared to b-value for Turkish earthquakes occurring
between 1970 and 2011. The statistical relationship (with its coefficient of
correlation) is also given
is based on the assumption that horizontal axis values are estimated with-
out error (Carroll R.J., Ruppert D., 1996), OR was applied in fitting the
relationship. Figure 2 gives a graphical representations of OR fit between
b and Dc-values for Turkish earthquake epicentres. Figure 2 shows that the
correlation coefficient of regression fit was very strong (r=-0.82). Linear fit
was used for regression and the following equation was derived:
Dc = 2.44 – 0.30*b (7)
The correlation between fractal dimension and b-value has been
studied in several parts of the world (e.g. Aki K., 1981; Hirata T., 1989;
Henderson J. et al., 1992; Caneva A., Smirnov V., 2004; Roy S. et al.,
2011) and particularly the Turkish region (e.g. Öncel A.O. et al., 1995
and 1996; Öncel A.O., Wilson T.H., 2002 and 2007). Since Aki (1981)
proposed a simple relationship between b-value and fractal dimension hav-
ing D=2b positive co-relationship, both positive (e.g. Öncel A.O., Wilson
T.H., 2004; Roy S. et al., 2011) and negative co-relationships (e.g. Hirata
T., 1989; Henderson J. et al., 1992; Öncel A.O. et al., 1995 and 1996) be-
tween these two scaling exponents have been reported and debated in the
pertinent literature. Such co-relationships could even change from nega-
tive to positive (e.g. Öncel A.O., Wilson T.H., 2002 and 2007).
Hirata’s results (1989) did not support Aki’s assumption that D=2b
but showed, on the contrary, a negative co-relationship Dc=2.3-0.73*b
(r=-0.77) between b and fractal dimension of epicentres in the Tohoku
region of Japan. Henderson (1992) obtained a similar result for the Riv-
erside catalogue in southern California. Similarly, a study of seismic-
ity in the NAFZ, Turkey, revealed a long-term negative co-relationship
between b and Dc (Öncel A.O. et al., 1995). The b-value was found to
be weakly negatively correlated with fractal dimension Dc=2.74-1.52*b
(r=-0.56) for the NAFZ (including the northern Aegean sea) by Öncel
(1995). Öncel (1996) has also observed a strong negative correlation (r=-
0.85) between Dc and b-values as Dc=2.32-1.09*b was associated with
the NAFZ. By contrast, Öncel and Wilson (2002) found weak posi-
tive correlation (r=0.48) between variations in b and Dc in the western
NAFZ. However, variability between b and Dc along the length of the
fault zone in this study revealed divergence between b and Dc in the
central NAFZ and spatial variation yielded a strong negative correlation
(r=-0.85) between b and Dc. Analysis presented in Öncel and Wilson
(2004) revealed a strong positive correlation (r=0.81) between Dc and
b-values along the NAFZ preceding the 1999 Izmit earthquake. Öncel
and Wilson (2007) observed a strong positive co-relationship between
Dc and b-value during 1992-1994 (r=0.84) and 1996-1998 (r=0.94) and
negative correlation (r=-0.71) extending from mid-1994 to mid-1996 in
north-western Turkey. Table 2 gives previous studies on the b-value and
Dc-value relationship.
Reference Relation
Aki K., (1981) D=2*b
Hirata T., (1989) Dc=2.3-0.73*b
Öncel A.O. et al., (1995) Dc=2.74-1.52*b
Öncel A.O. et al., (1996) Dc=2.32-1.09*b
Öncel A.O., Wilson T.H., (2002) positive correlation
Öncel A.O., Wilson T.H., (2004 positive correlation
Öncel A.O., Wilson T.H., (2007)
positive and negative
correlation
Table 2. Some examples of previous studies of the relationship between b-value
and Dc-value.
Serkan Öztürk108
Conclusions
This study tried to estimate a suitable and reliable correlation between
two seismotectonic parameters: b and Dc-values for Turkish earthquakes.
Statistical analysis of the available data included 99,737 earthquakes from
1970 to 2011. The maximum likelihood method was used for calculating
b-values and the linear regression technique for obtaining Dc-values (95%
confidence limit). It was observed that the largest events were associated
with low b and high Dc-values, respectively, implying relatively high stress
intensity and stronger epicentre clustering.
Orthogonal regression was used for correlating the chosen seismotec-
tonic parameters. The results showed strong negative correlation between
b-value and fractal dimension Dc-value for Turkish earthquakes Dc = 2.44
- 0.30*b (r=-0.82) given by OR. The results had good agreement with
previous studies for different parts of Turkey and the rest of the world.
Acknowledgements
The author would like to thank to Prof. Dr. Stefan Weimer for provid-
ing ZMAP software and anonymous reviewers for their useful and construc-
tive suggestions in improving this paper. I am grateful to Dr. Doğan Kalafat
(KOERI) for providing us with the earthquake catalogue. I would also like
to thank KOERI for providing an earthquake database via internet.
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