289
http://journals.tubitak.gov.tr/earth/
Turkish Journal of Earth Sciences Turkish J Earth Sci
(2015) 24: 289-301
© TÜBİTAK
doi:10.3906/yer-1410-13
Spatial-temporal analysis of seismicity before the 2012 Varzeghan, Iran, Mw 6.5
earthquake
Mohammad TALEBI, Mehdi ZARE*, Rohollah MADAHI-ZADEH, Aref BALI-LASHAK
Seismological Research Center, International Institute of Earthquake Engineering and Seismology, Tehran, Iran
* Correspondence: mehdi.zare.iran@gmail.com
1. Introduction
The northwest of the Iranian plateau displays a tectonic
regime influenced by the motion of Arabia towards
Eurasia. Tectonically, NW Iran is an intracontinental
collision zone, and one of the main features in this
region is the North Tabriz Fault accommodating several
millimeters per year of right lateral strike slip motion, on
the basis of GPS studies (e.g., Vernant et al., 2004; Djamour
et al., 2011). NW Iran has been affected by seismic activity
during historical and instrumental time periods. Some of
these earthquakes are illustrated in Figure 1. An average
recurrence period of at least 350 years for earthquakes
with M > 7 is expected for the North Tabriz Fault (Hessami
et al., 2003).
The 11 August 2012 Mw 6.5 Varzeghan earthquake
(http://www.globalcmt.org/) was the latest catastrophic
event in this region, which happened in the northeast
of the North Tabriz Fault. Because of the poor quality of
local construction, the Varzeghan quake led to invaluable
costs of approximately 300 casualties and 3000 injuries
along with extensive property damages. However, before
the occurrence of this earthquake, no mapped faults
were documented in its epicentral area. Joint inversion of
teleseismic P and S wave data showed that the faulting in
this event was strike-slip, right-lateral motion on an E–W
plane. The centroid depth was assessed as 7 km (Copley
et al., 2013), which is in the crustal seismogenic zone
(Moradi et al., 2011).
This paper presents the results of an evaluation of
earthquake potential before this quake in NW Iran and
includes a study of 2 types of seismic precursors, i.e. seismic
quiescence and temporal variations of fractal properties.
The evaluation is based on some statistical characteristics
of seismicity, namely the z-value (Wiemer and Wyss, 1994)
and fractal dimension (Smalley et al., 1987). The findings
are related to the evolution of seismic activities in this
region. As mentioned by Polat et al. (2008), the results
of such kinds of studies help to detect seismic anomalies
before large earthquakes. Thus, they can provide useful
information to assess the seismic hazard, not only in the
study zone, but also in other active tectonic regions.
2. The area and data
The studied area is inside of a polygon bounded by (37°N,
44°E), (40°N, 44°E), (40°N, 49°E), and (37°N, 49°E) corner
points in NW Iran (Figure 1).
Abstract: In this work, the spatial and temporal variations of seismicity in northwestern Iran have been evaluated with a special focus
on seismic precursors of the 11 August 2012 Mw 6.5 Varzeghan earthquake. The precursors are defined by the z-value test and the
generalized fractal dimensions of earthquake epicenters. The investigation applies earthquakes that have occurred since 2006 in a region
that includes the main shock and collected by the Iranian Seismological Center. In order to eliminate the effect of explosions in the
processing, we removed the explosion from the used catalog by using the normalized ratio analysis of daytime to nighttime events.
Having done the preprocessing procedures, we removed the events with magnitudes of less than 2.5. As a result of our analysis, a period
of seismic quiescence has been identified, which started about 3 years before the Varzeghan main shock. In a nice coincidence with these
results, significant changes have been observed in the generalized fractal dimensions and the related spectra prior to the occurrence of
the Varzeghan earthquake. The changes indicate that the seismic activities of the studied area have had increasingly dense clustering in
space since about mid-2009, which suggests the regional preparedness for the occurrence of the main quake. Furthermore, the analysis
did not exhibit any significant seismic quiescence anomaly at the beginning of 2013.
Key words: Varzeghan earthquake, z-value, seismic quiescence, generalized fractal dimensions
Received: 20.10.2014 Accepted/Published Online: 18.03.2015 Printed: 29.05.2015
Research Article
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TALEBI et al. / Turkish J Earth Sci
The applied data were extracted from the catalog
of the Iranian Seismological Center (IRSC), which is
available at http://irsc.ut.ac.ir/bulletin.php/. The studied
area is approximately covered by the Tabriz local network.
This network began in 1995. However, Rezapour (2005)
discussed that the magnitude values for some years in the
data set were not on the basis of a specific method. The
present catalog lists events since 1 January 2006. In this
period, the catalog was published in a consistent form based
on the local magnitude scale (Mn) proposed by Rezapour
(2005). This is an important advantage for a catalog over
other composite catalogs to be almost homogenized and
not to introduce magnitude shifts. Furthermore, this
catalog is generally more accurate because it is based on a
local seismic array.
We applied the catalog for the selected region in the
period of 2006 to 2015. Up to the Varzeghan earthquake,
the used data set contains about 3150 events shallower than
36 km with M ≥ 2. As the distribution of the magnitude
of the data is mostly less than 4.5, the local magnitude,
reported in the data set, was simply considered as the
moment magnitude (Zare, 1999).
Figure 2 depicts the distribution of events in different
hours of a day. Since there is a maximum range between
0700 and 1400 hours, the histogram suggests a significant
contamination by explosions.
There are some studies in the literature for earthquakeexplosion discrimination (e.g., Wiemer and Baer, 2000;
Horasan et al., 2009; Yılmaz et al., 2013). In order to
remove explosions, the normalized ratio (Rq) of daytime
to nighttime events (Wiemer and Baer, 2000) is mapped
based on seismic tool ZMAP 6.0. The 99th percentile
was used as our significance threshold and N = 50 as the
sample size for iterative removal of events from the data.
After some iteration steps, 1114 daytime events, belonging
to nodes with high Rq values, were excluded from the data
44˚
44˚
46˚
46˚
48˚
48˚
38˚ 38˚
40˚ 40˚

45˚
45˚

47˚
47˚

˚
49˚
37˚ 37˚

39˚ 39˚

Mw = 6.5
45˚ 60˚
30˚
40˚
800 1000 1200 1400 1600 1800
Time frames for historical events
Magnitude Scale
Historical
5 6 7 8
Not Defined
Instrumental
2.5
3.5
4.5
5.5
6.5
Varzeghan earthquake
NTF
49
Figure 1. Historical and modern instrumental seismicity of 2006 to 2015 (M ≥ 2.5) in the Varzeghan-Azarbayjan zone: historical earthquakes (Ambraseys and Melville, 1982; Berberian, 1995), modern instrumental seismicity (IRSC), epicenter of the 2012
Varzeghan earthquake, and major faults are shown by stars, circles, black square, and solid lines respectively. NTF shows the North
Tabriz Fault.
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TALEBI et al. / Turkish J Earth Sci
set (consisting of 5932 events). Approximately 90% of the
total number of removed events had magnitudes of less
than 2.3.
Figure 3a illustrates the Rq map based on the cleaned
catalog. It is obvious that there are still some volumes with
unacceptable values of Rq. After that, a magnitude bin
of M = 2–2.3 was eliminated from the modified catalog
and the ratio Rq was computed again. As can be seen in
Figure 3b, approximately all the nodes have Rq ≤ 2.2 (or
probability of occurrence Rq of less than 99%).
The magnitude of completeness (Mc) over time
was then checked by the maximum curvature function
(Wiemer and Wyss, 2000) using a sample size of 100 events.
Figure 4a shows that Mc mostly varies between 2.4 and 2.5.
However, there is a large fluctuation of Mc between 2012
and 2013 that is related to the 2012 Varzeghan earthquake
sequence. This may be due to an aftershock sequence in
which the small events may not be located (Öztürk, 2013).
After the aforementioned treatments, in the cleaned
catalog, we selected a total number of 2164 events having
magnitudes of greater than 2.5. Figure 4b shows hourly
distribution of the number of events for the final catalog.
The histogram suggests a uniform distribution of events
in different hours of a day, which is expected in reporting
earthquakes.
To remove dependent events for detecting the
precursory seismic quiescence, the catalog was declustered
by the Reasenberg’s algorithm (1985), as modified by
Helmstetter et al. (2007). The error values of depth
and epicenter location were changed to 10 and 7 km,
respectively, and the rest of the parameters were considered
as presented by Helmstetter et al. (2007). The declustering
approach found 85 earthquake clusters (954 events out of
2164), and the obtained declustered catalog includes 1295
earthquakes.
In addition, Figure 5 indicates the distribution of
earthquakes in time in the final catalog before and after
declustering. The cumulative number curve of events for
the declustered catalog is smoother than that of the raw
catalog, showing that most of dependent events have
been eliminated from the raw catalog by the declustering
0 5 10 15 20
0
100
200
300
400
500
600
700
Hr
Number
Figure 2. Histogram of events at different hours of a day for all
events in the data set. Since there is a maximum range between
0700 and 1400 hours, the histogram suggests a significant contamination by explosions.
Figure 3. Quarry blast mapping: a) for the cleaned catalog, b) after removing events with M ≥ 2.3 within the cleaned catalog. In part
b, approximately all the nodes have Rq ≤ 2.2 (or probability of occurrence Rq of less than 99%).
44 45 46 47 48 49
37
37.5
38
38.5
39
39.5
40
Longitude [deg]
Latitude [deg]
44 45 46 47 48 49
Longitude [deg]
a b
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
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TALEBI et al. / Turkish J Earth Sci
process. However, there is a great seismicity change
between 2012 and 2013, showing a relatively large number
of aftershocks for the 2012 Varzeghan earthquake.
3. Methods
3.1. Seismic quiescence
Among premonitory phenomena preceding a main
shock, seismic quiescence is one of the most considerable
precursors. Many authors proposed this phenomenon
for main shocks in a wide magnitude-range (e.g., M =
4.7 to 8 in Wyss and Habermann, 1988) as well as a wide
duration range (e.g., 9 months for the Chi-chi quake (Wu
and Chiao, 2006) and ~23 years for the Tohoku quake
(Katsumata, 2011)).
Seismic quiescence is a significant reduction of the
mean seismicity rate as compared to that corresponding to
the background seismicity (Wyss and Habermann, 1988).
The hypothesis of seismic quiescence can be considered as
static (or elastic) stress change before large earthquakes.
In order to study seismicity rates, statistical methods
must be applied (Matthews and Reasenberg, 1988).
Accordingly, to detect quantitatively the time of maximum
change, the z-value method has been applied using the
LTA function, implemented in software package ZMAP
6.0 (Wiemer, 2001). This method has been extended to
detect significant variations of seismicity rate within a
catalog. The z-value is defined as follows (Wiemer and
Wyss, 1994):
(1)
where R is defined as the average of seismicity rate, σ is the
standard deviation of seismicity rate, and n is the number
of samples in the first and second periods, which are
compared with each other. The LTA-function compares
the seismicity rate in a time window (TW) with the overall
average rate for a given area. The TW also moves at every
possible point in time. For a more detailed definition of
this function, we refer the reader to Öztürk and Bayrak
(2012).
2007 2008 2009 2010 2011 2012 2013 2014
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Mc
Time [year]
Mc
δMc
0 5 10 15 20
0
50
100
150
a b
Hr
Number
Figure 4. a) Magnitude completeness (Mc) as a function of time for the final catalog. This figure shows that Mc mostly
varies between 2.4 and 2.5. b) Histogram of events in different hours of a day for the final catalog; the histogram suggests
a uniform distribution of events in the different hours of a day.
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
0
500
1000
1500
2000
Year
Cumulative number
raw catalog
declustered catalog
Figure 5. Temporal distribution of earthquakes in the final catalog before and after declustering. The curves indicate that most of
the dependent events have been eliminated from the raw catalog
by the declustering process.
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TALEBI et al. / Turkish J Earth Sci
3.2. Multifractal analysis
Regional distributions of seismicity have often been
considered as clustered. In other words, seismic patterns
are not Poisson, even in declustered catalogs (e.g., De
Natale and Zollo, 1986). Earthquakes are expected to
happen within a range of magnitudes. The magnitude
dependence of frequency usually satisfies the fractal
scales. It can also be expected that the temporal behavior
of seismicity influences the fractal clustering (Smalley et
al., 1987). King (1983) suggested a fractal methodology for
tectonics and Turcotte (1986a, 1986b) developed it.
Based on geological and seismological investigations,
fault surfaces display mechanically heterogeneous
properties at all scales (Candela et al., 2009). This kind
of heterogeneity is related to differences of the material
strength and the geometry in fault planes. In this way,
seismic sequences, including foreshocks and aftershocks,
are due to the faults’ heterogeneities (Pechmann and
Kanamori, 1982). Considering these heterogeneities, one
is able to explain the fractal distributions and clustering
of seismicity, which are quantified by means of fractal
dimensions (Oncel and Wilson, 2006).
It is believed that a single fractal dimension is not
enough to describe the heterogeneities. In other words,
seismicity patterns and their variations through time
and space are imprinted in the multifractals defined by
generalized fractal dimensions D
q
of the seismicity. Using
a multifractal approach (Hentschel and Procraccia, 1983)
in some different seismic zones, several studies have
considered the sequential changes of the heterogeneity
in seismicity (e.g., Hirata and Imoto, 1991; Li et al., 1994;
Teotia et al., 1997; Dimitriu et al., 2000; Sunmonu et al.,
2001; Telesca et al., 2005; Teotia and Kumar, 2007, 2011).
In addition, variations in the parameter q are useful to
describe spatial-temporal patterns of clustering. Hence,
changes in the seismicity behavior prior to the occurrence
of strong seismic events can be inspected using the
temporal behavior of D
q
(Li et al., 1994; Teotia and Kumar,
2007, 2011). Even for small data sets, multifractal analysis
has been used for assessing generalized fractal dimension
in several seismic zones, defined spatially as follows
(Grassberger and Procaccia, 1983):
(2)
(3)
where r is the scaling parameter of distance, N includes
all the events occurring inside a region that is studied in
a given time period, H(.) is the Heaviside step operator,
X
i and Xj are respectively the epicentral locations of the
ith and jth events, and C
q
(r) is the qth correlation integral.
Similar to the spatial association, the temporal relation is
defined by replacing r, Xi, and Xj with the scaling parameter
of time (t), ith occurrence time (T
i), and jth occurrence
time (T
j), respectively, in Eqs. (2) and (3).
In this study, q varies between 2 and 15 in the generalized
dimensions of seismicity distribution (D
q
). The related
measures of small q (e.g., q = 2) are associated with the
regional scale clustering, whereas those of bigger q (e.g.,
q = 15) are related to local scale patterns of seismicity. As
will be discussed later, the difference between D
2 and D15
is a tool to measure the heterogeneity of fractal properties.
In order to estimate temporal changes of spatial D
q
,
similar to the study of Teotia and Kumar (2011), the data of
subseries (subsets) obtained from all earthquake epicenters
were used. There is no restriction on the number of data
points within each subset and data points applied for a
shift from one subset to another. Nevertheless, there is a
trade-off between reliability and time resolution of fractal
dimensions, in such a way that the larger the number of
events is, the more reliable results are, but with less time
resolution.
However, some authors have proposed several criteria
to estimate the minimum number of samples (Nmin) for
evaluation of D
q
(e.g., Smith, 1988; Sornette et al., 1991).
Smith (1988) suggested Nmin with a quality value Q (0 ≤ Q
≤ 1) as follows:
(4)
where R
min and Rmax are minimum and maximum distances
of the points and M is the integer part of D
q
. If the distance
of epicenters is used in this formula, D
q
is estimated to be
less than 2, and therefore M equals 1.
4. Results
4.1. Changes in the seismicity rate
In order to calculate the seismic quiescence period, a set
of TWs, i.e. 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5 years, has been
used in the analysis. Additionally, for continuous time
coverage, a 28-day interval is considered for moving the
TW. The z-value for the area is drawn as a map in Figure
6, in which the values have been computed for nodes with
spacing of 0.1°. The neighbor earthquakes are taken as N
= 200, by which the calculations are performed in each
node. For a better comparison, the same color scale is used
for all figures. In general, it can be said that TW and N
are usually selected in a way that makes the quiescence
signal more obvious (Öztürk and Bayrak, 2012). Due to
the importance of the 2012 Varzeghan earthquake in this
study, in all the maps in Figure 6, the z-values are depicted
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TALEBI et al. / Turkish J Earth Sci
for different TW values at the beginning of mid-2012
(before the occurrence of the Varzeghan earthquake).
In all the maps, an area with a significant quiescence
anomaly can be observed. Nevertheless, as is seen, the
anomaly with the 2-year TW is the strongest. This anomaly
is visible in a wide area around the epicenter of the 2012
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Latitude [deg]
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Latitude [deg]
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(lta); 2006.0016 to 2014.9948 - cut at 2009; iwl = 3.5 yr
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Latitude [deg]
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Longitude [deg]
Latitude [deg]
44 45 46 47 48 49
37
38
39
40
(lta); 2006.0016 to 2014.9948 - cut at 2011; iwl = 1.5 yr
Longitude [deg]
–5 0 5
Figure 6. Mapped z-values for the area at the beginning of mid-2012 with a set of TWs, i.e. 1.5, 2, 2.5, 3, 3.5, 4,
4.5, and 5 years. Stars show epicenter location of the 2012 Varzeghan main shock.
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Varzeghan earthquake. As Öztürk and Bayrak (2012)
stated, the z-value analysis applied in this study can help to
ensure the reliability of the results.
In addition, for estimating the start-time of seismic
quiescence, the values of the LTA function were calculated
and plotted for earthquakes located around the epicenter
of the 2012 Varzeghan earthquake (Figure 7). Since the
anomaly is best revealed in Figure 6 with TW = 2 years,
here this TW is located at every possible point in time,
moving by 28 days. As it is seen, this function has a peak
of z = 5.3 at 2010.2.
In order to illustrate the spatial distribution of z-values
over time, the z-value map is presented for different cut-off
times between 2007.5 and 2013 with a 2-year TW (Figure
8). As shown in this figure, no significant anomalies of
seismic quiescence between 2006 and 2009 can be seen for
anomalous area observed in Figure 6, but after 2009.5, a
clear anomaly emerged there. No significant quiescence
anomaly is observed between 2012.5 and 2013.
4.2. Multifractal values
In order to investigate multifractal values up to the 2012
Varzeghan earthquake, events that occurred in a circular
area centered on the epicenter of the main shock were
selected. Based on the average critical range of space related
to the precursors of earthquakes with magnitudes of ~6 to
7 (Bowman et al., 1998), a radius of 150 km was supposed
for the region affected by the seismicity associated with the
Varzeghan earthquake.
Multifractal relationships within the data set are
illustrated in Figure 9 until the Varzeghan quake. The
fractal dimensions are estimated spatially in the linear
region of the plot of versus (or of versus for the temporal
generalized dimensions).
Similar to previous studies (e.g., Smalley et al., 1987;
Tosi, 1998; Teotia and Kumar, 2011), the raw catalog is
employed to estimate the fractal dimensions. On the basis
of the data resolution in both time and space, with the
time period of the data set (01/01/2006–11/08/2012) and
the total number of data points (N = 351), the minimum
time and space interval have been selected to be 1 min and
7 km, respectively.
Since random errors superimpose the earthquake
locations, it is possible to define more than 1 straight
line in the log–log plot of the correlation integral versus
distance. It may suggest nonspecific results for the spatial
generalized fractal dimension. This creates complexity
in understanding which line is truly associated with
earthquake clustering. Eliminating the data points ranging
inside the estimated errors can solve the problem, without
sacrificing the statistics of the calculations.
As mentioned above, error of the epicenter location
of the selected data was estimated to be less than 7 km.
Furthermore, there is an applied upper limit (due to edge
effect) after which the correlation integral will cease to
increase. Accordingly, distribution of seismicity in the
data set obeys the spatial multifractal relation with D2(r) =
1.26 and D
15(r) = 0.82 (Figure 9a) as well as the temporal
relation with D
2(t) = 0.93 and D15(t) = 0.72 (Figure 9b)
before the occurrence of the Varzeghan quake.
4.3. Temporal variations of spatial fractal values
According to Smith (1988) and by assuming Q = 0.9, in the
current study a value of ~80 was estimated as the minimum
number of points (Nmin) in each subset for calculating the
fractal dimensions.
Here, the data set of the selected region, containing 530
earthquakes that occurred from 01/01/2006 to 13/08/2012,
was divided into 10 subsets (S1–S10). Each subset consists
of 80 events, and all of them have a coverage area of 30
events with each other (Table). All the subsets having the
same number of earthquakes can avoid some effects of
nonstationary signals in the data set (Teotia and Kumar,
2011).
The fractal dimensions D
2(r) and D15(r) for all 10
subsets of the catalog are listed in the Table. Figure 10 also
shows the temporal changes of these generalized fractal
dimensions in all the subsets. The subset S7 contains the
2012 Varzeghan earthquake.
2007 2008 2009 2010 2011 2012 2013 2014
0
50
100
150
200
Time in years
Cumulative Number
LTA(t) Function; iwl = 2
Zmax: 5.3 at 2010.2
Circle: 46.79; 38.4
−5
5 0
10
Figure 7. Cumulative number and the values of LTA function
versus time for data located around the epicenter of the 2012 Varzeghan earthquake. The function has a peak of z = 5.3 at 2010.2.
Star shows occurrence time of the 2012 Varzeghan earthquake.
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TALEBI et al. / Turkish J Earth Sci
5. Discussion
5.1. Seismicity rate
According to the investigation by Öztürk and Bayrak
(2012) and taking into account the results in Figures 7 and
8, possibly seismic quiescence began in 2009 to 2010. In
other words, the average length of the seismic quiescence
period before the 2012 Varzeghan earthquake had been
3 years. Similar variations in the seismic behavior of the
Iranian plateau were also documented ~3 years before the
26 December 2003 Bam, Iran, earthquake by means of
z-test (Ashtari Jafari, 2012).
In recent years, some other similar studies have been
done for different parts of Turkey, in the vicinity of our
study area (e.g., Yılmaz et al., 2004; Öztürk et al., 2008). For
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Latitude [deg]
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40
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Latitude [deg]
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Longitude [deg]
Latitude [deg]
–5 0 5
Figure 8. Spatial distribution of z-values for different cut-off times between mid-2007 and 2013. The length of the TW is
chosen as 2 years. Stars show epicenter location of the 2012 Varzeghan earthquake.
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TALEBI et al. / Turkish J Earth Sci
example, in a statistical study, Yılmaz et al. (2004) assessed
the seismic hazard in the North Anatolian Fault Zone,
based on which Öztürk (2011) claimed that the average
probability of earthquakes with magnitudes of greater than
5 in areas where significant quiescence anomalies emerged
is more than 70%. Results of the present study are largely
in accordance with their results and confirm the important
role of the evaluation of seismic quiescence anomaly for
the risk analysis of large earthquakes.
With regard to Figure 8, after the occurrence of the
2012 Varzeghan earthquake, no significant quiescence
anomaly is seen in the study area up to 2013. Assuming an
average length of ~3 years for the seismic quiet period in
the study region, probably no earthquake with magnitude
of greater than 6 (comparable to that of the 2012 Varzeghan
earthquake) will occur up to 2016. However, due to the
standard deviation of the average quiet period (Öztürk and
Bayrak, 2012), which is ±1.5 years, the period predicted
to be without occurrence of a major earthquake may be
extended up to mid-2017.
5.2. Multifractal dimensions
The value of fractal dimension of q = 15, which is lower
than that of q = 2 (Figure 9), indicates that the seismicity
before the occurrence of the Varzeghan earthquake was
dominated by clustering in local scales. The difference
between D
2(r) and D15(r) can help in assessing the behavior
of complexity of a fault system. Because of differences
between regional and local scales of fault complexity, and
according to Oncel and Wilson (2006), the difference of
0.44 between D
2(r) and D15(r), shown in Figure 9a, can
0 0.5 1 1.5 2 2.5
−2.5
−2
−1.5
−1
−0.5
0
a b
D15=0.82±0.03
Log C(r)
Log r (km)
D2=1.26±0.02
4 4.5 5 5.5 6 6.5
−2.5
−2
−1.5
−1
−0.5
0
D15=0.72±0.04
Log C(t)
Log t (minute)
D2=0.93±0.00
Figure 9. The plots illustrate the multifractal relationships observed in spatial and temporal analyses within data collected up
to the occurrence of the 2012 Varzeghan earthquake. a) The linear region for space exists between ~7 and 100 km (i.e. between
0.85 and 2). b) The linear region in the temporal response extends from days to ~1.5 years (i.e. between 4.3 and 5.9).
Table. The subset descriptions and fractal dimensions of the subsets.
Subset name Subset events Time period D2 D15
S1 1–80 2006/01/01–2007/07/18 1.36 1.16
S2 51–130 2007/03/31–2008/04/07 1.43 1.17
S3 101–180 2007/11/16–2008/01/12 1.38 1.14
S4 151–230 2008/06/26–2010/01/04 1.26 0.83
S5 201–280 2009/04/18–2011/01/29 1.13 0.94
S6 251–330 2010/06/02–2012/02/25 0.95 0.62
S7 301–380 2011/06/16–2012/08/11 0.73 0.43
S8 351–430 2012/07/15–2012/08/11 0.67 0.45
S9 401–480 2012/08/11–2012/08/12 0.46 0.29
S10 451–530 2012/08/12–2012/08/13 0.54 0.34
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TALEBI et al. / Turkish J Earth Sci
reflect the existence of significant fractal heterogeneities in
the pattern of the seismicity. Moreover, it is inferred that
the area had had high spatial complexity before the main
shock.
The differences between D
2(t) and D15(t) also assess the
variations of complexity of seismicity over time (Oncel and
Wilson, 2006). In the current case, a small value of ΔD(t)
(i.e. 0.21) can imply that high spatial complexity varied
little or maybe gradually over the time period leading up
to the 2012 Varzeghan earthquake.
Based on the work of Kagan and Jackson (1991) on
seismic clustering for interpreting the results of D2(t), the
following criteria can be used:
1) Temporal behavior of seismicity may be divided
into long-term (with D2(t) = 0.8–1) and short-term
clustering (with D2(t) ~0.5).
2) Highly clustered seismicity is mainly attributed
to a sequence of earthquakes (short-term foreshock, main
shock, and aftershock activity), whereas weakly clustered
seismicity is mainly associated with main shocks.
3) Seismicity distribution in time is periodic with
D
2(t) ~0.5, quasiperiodic with D2(t) ~0.75, and random
with D
2(t) ~1.
Accordingly, the results reflect that the seismic
distribution of the Varzeghan-Azarbayjan area was
random through time. In other words, it was close to
a Poisson process. In addition, the lack of strong events
in the area for the time duration of the analysis indicates
that earthquake clustering in this area is not effectively
influenced by aftershock and foreshock activities.
5.3. Temporal changes of spatial fractal properties
According to Figure 10, it is evident that the period
of the increase in clustering (lowering value of fractal
dimensions) was before the occurrence of the 2012
Varzeghan quake. A similar observation was also reported
by Teotia and Kumar (2011) for the occurrence of the
October 2005 Muzaffrabad-Kashmir, India, earthquake.
Additionally, for checking the robustness of the results,
a set of different numbers of points (N) for each subset
(i.e. 80, 90, 100, 110, 120, 130, 140, and 150) and for the
shifting intervals (i.e. 30, 50, and 70) was used (Figure 11).
The mean and standard deviation of the obtained values
are presented in Figure 11. According to Smith (1988),
in the present study N = 80 and 150 are estimated as
the minimum number of points (Nmin) in a subset at the
quality levels of 0.9 and 0.95, respectively. In Figures 11a
and 11b, the values of D
q
estimated for the subsets are
assigned to the center of the corresponding time intervals.
In concert with the results presented in Figure 10, a period
of low values of D
2 (Figure 11a) and D15 (Figure 11b) is
evident since about mid-2009 to the occurrence time of
the Varzeghan earthquake for all the sets of the parameters.
Therefore, the interpretations of the decrease in the fractal
dimensions prior to the main shock will be strengthened
more as the sensitivity test rejects the dependence of the
results on the inputs.
D
q
-q spectra (Figure 12) are also plotted to show the
clustering in the zone of preparation for the Varzeghan
earthquake. This confirms the decrease in fractal
dimensions before the main shock.
Subset S2 (Figure 12) is situated ~5 years prior to the
occurrence of the Varzeghan earthquake, and its relatively
large values of D
q
imply that the seismicity relevant to
background activities can be observed in this subset.
Subset S6 was laid ~1.5 years before the main quake,
and moderate values of its corresponding D
q
indicate
that seismicity of subset S6 is going to present clustering
and arrangement of the main shock. Low values of D
q
for subset S7, including the Varzeghan earthquake, show
that seismicity of this subset is highly localized in space.
Subsets S9 and S10 consist mostly of highly clustered
seismic activities causing very small values of fractal
dimensions. In fact, this stage introduces a new seismic
clustering caused by aftershocks.
The fractal dimensions D
2(r) and D15(r) not only can
indicate the amount of earthquake clustering for a zone,
but also characterize the stress state over it. Hence, it can
be suggested that the decline of these dimensions before
the Varzeghan earthquake is possibly because of effective
stress variations.
Overall, the regular reduction of the spatial fractal
dimensions since ~2009 is thought to be due to the
decrease in the fault complexity, an activation of seismic
Figure 10. Bar graphs of the generalized fractal dimensions D
q
(r)
(q = 2 and 15) in subsets S1–S10. The graphs display the temporal variations of the generalized fractal dimensions in the studied
period. Darkened regions at tops of bars show the upper ranges
of confidence intervals of the values. Subset S7 contains the Varzeghan 2012 earthquake. This figure illustrates the decrease in
the fractal dimensions before the main shock.
1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Subset number
Value
D2
D15
299
TALEBI et al. / Turkish J Earth Sci
clustering in the area, and regional preparedness before the
occurrence of the Varzeghan main shock. Approximately
99% of the total number of earthquakes that occurred in
this period had magnitudes of less than 3.5. Furthermore,
the anomaly of the seismic quiescence is in good agreement
with the reduction in the fault complexity.
As Oncel and Wilson (2002) illustrated, it can be
interpreted that during the period of seismic quiescence,
the reduced complexity in the active fault network
accommodates seismicity of smaller magnitudes along
the fault planes with relatively smaller surface areas. With
respect to our results, it can be inferred that during the quiet
period, only a small part of stress in this region had been
released through small-sized earthquakes. Additionally,
the major part of stress probably caused the occurrence of
the main shock and its interrelated earthquakes. This can
be evidenced by a relatively large number of aftershocks
related to the 2012 Varzeghan earthquake.
As mentioned in Sections 5.1 and 5.3, the observed
anomalies of seismic quiescence and fractal dimensions
are largely in accordance with those of some other similar
studies carried out for some active tectonic regions. They
can provide an opportunity to get an insight into the
temporal-spatial dynamics of seismicity. Thus, such kinds
of seismic precursors could contribute to the forecasting
of future strong earthquakes. From this point of view, our
results (Sections 4.1 and 5.1) suggest a period without any
major earthquakes up to mid-2017 for the studied area.
However, it is obvious that there may be precursory
anomalies unrelated to the main shocks, called false
alarms, and/or main shocks with missed alarms. This
means that precursors such as seismic quiescence are not
necessarily associated with a forthcoming main shock and
vice versa. Hence, for the utilization of such a precursor
for risk management, measurements of other short-term,
mid-term, and long-term precursors should be made
concurrently.
2007 2008 2009 2010 2011 2012
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Year
2007 2008 2009 2010 2011 2012
Year
a b
Value (D15)
mean
±1 δ
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Value (D2)
mean
±1 δ
Figure 11. Sensitivity of D
q
to different numbers of points (N) in each subset (i.e. 80, 90, 100, 110, 120, 130, 140, and 150) and to shifting intervals (i.e. 30, 50, and 70). a) D2, b) D15. According to Smith (1988), N = 80 and 150 are estimated to be the minimum number
of points (Nmin) in a subset for Q = 0.9 and 0.95, respectively. The results for the sets of the input parameters are shown by solid lines.
The corresponding means and error bars are both shown by dashed lines. All of the results illustrate the decrease in the fractal dimensions before the 2012 Varzeghan main shock.
2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
q
D (q)
S2
S6
S7
S9
S10
Figure 12. D
q
-q spectra of subsets S2, S6, S7, S9, and S10. Corresponding values of subset S7, which contains the Varzeghan
Mw = 6.5 earthquake, are highlighted by filled circles. This figure
illustrates the decrease in the fractal dimensions before the main
shock.
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TALEBI et al. / Turkish J Earth Sci
Acknowledgments
The authors would like to acknowledge International
Institute of Earthquake Engineering and Seismology
(IIEES) for its help in providing research documents and
methodological aspects of the job and Iranian Seismological
Center (IRSC) for providing earthquake database via
internet. We would like to thank numerous colleagues,
namely Dr H Zafarani, Dr A Ansari, E Noroozinejad, M
Mahmudabadi, M Farrokhi, and M Ahmadi-Borji, for
sharing their points of view on the manuscript. We are
grateful to Dr O Polat and two anonymous reviewers for
their valuable comments. We also thank S Wiemer for use
of his software, ZMAP 6.0.
Ambraseys NN, Melville CP (1982). A History of Persian
Earthquakes. 1st ed. Cambridge, UK: Cambridge University
Press.
Ashtari Jafari M (2012). Seismicity anomalies of the 2003 Bam, Iran
earthquake. J Asian Earth Sci 56: 212–217.
Berberian M (1995). Natural Hazards and the First Earthquake
Catalogue of Iran, Historical Hazards in Iran Prior to 1900. 1st
ed. Tehran, Iran: IIEES.
Bowman DD, Ouillon G, Sammis CG, Sornette A, Sornette D (1998).
An observational test of the critical earthquake concept. J
Geophys Res 103: 24359–24372.
Candela T, Renard F, Bouchon M, Brouste A, Marsan D, Schmittbuhl
J, Voisin C (2009). Characterization of fault roughness
at various scales: implications of three‐dimensional high
resolution topography measurements. Pure Appl Geophys 166:
1817–1851.
Copley A, Faridi M, Ghorashi M, Hollingsworth J, Jackson J, Nazari
H, Oveisi B, Talebian M (2013). The 2012 August 11 Ahar
earthquakes: consequences for tectonics and earthquake
hazard in the Turkish–Iranian Plateau. Geophys J Int 196:
15–21.
De Natale G, Zollo A (1986). Statistical analysis and clustering
features of the Phlegraean Fields earthquake sequence (May
1983-May 1984). B Seismol Soc Am 76: 801–814.
Dimitriu PP, Scordilis EM, Karacostas VG (2000). Multifractal
analysis of the Arnea, Greece seismicity with potential
implications for earthquake prediction. Nat Hazards 21: 277–
295.
Djamour Y, Vernant P, Nankali HR, Tavakoli F (2011). NW Iraneastern Turkey present-day kinematics: results from the Iranian
permanent GPS network. Earth Planet Sc Lett 307: 27–34.
Grassberger P, Procraccia I (1983). Measuring the strangeness of
strange attractors. Physica D 9: 189–208.
Helmstetter A, Kagan YY, Jackson DD (2007). High resolution, timeindependent grid-based forecast for M ≥ 5 earthquakes in
California. Seismol Res Lett 78: 78–86.
Hentschel HGE, Procraccia I (1983). The infinite number of
generalized dimensions of fractals and strange attractors.
Physica D 8: 435–444.
Hessami K, Pantosti D, Tabassi H, Shabanian E, Abbassi MR, Feghhi
K, Solaymani S (2003). Paleoearthquakes and slip rates of
the North Tabriz Fault, NW Iran: preliminary results. Ann
Geophys 46: 903–915.
Hirata T, Imoto M (1991). Multifractal analysis of spatial distribution
of micro earthquakes in the Kanto region. Geophys J Int 107:
155–162.
Horasan G, Boztepe-Güney A, Küsmezer A, Bekler F, Öğütçü Z,
Musaoğlu N (2009). Contamination of seismicity catalogs
by quarry blasts: an example from Istanbul and its vicinity,
northwestern Turkey. J Asian Earth Sci 34: 90–99.
Kagan YY, Jackson DD (1991). Long-term earthquake clustering.
Geophys J Int 104: 117–133.
Katsumata K (2011). A long-term seismic quiescence started 23 years
before the 2011 off the Pacific coast of Tohoku Earthquake (M
= 9.0). Earth Planets Space 63: 709–712.
King G (1983). The accommodation of large strains in the upper
lithosphere of the earth and other solids by self-similar fault
systems: the geometrical origin of b-value. Pure Appl Geophys
121: 761–815.
Li D, Zhaobi Z, Binghong W (1994). Research into the multifractal
of earthquake spatial distribution. Tectonophysics 223: 91–97.
Matthews MV, Reasenberg P (1988). Statistical methods for
investigating quiescence and other temporal seismicity
patterns. Pure Appl Geophys 126: 357–372.
Moradi A, Hatzfeld D, Tatar M (2011). Microseismicity and
seismotectonics of the North Tabriz fault (Iran). Tectonophysics
506: 22–30.
Oncel AO, Wilson T (2002). Space-time correlations of seismotectonic
parameters: examples from Japan and from Turkey preceding
the Izmit earthquake. B Seismol Soc Am 92: 339–349.
Oncel AO, Wilson T (2006). Evaluation of earthquake potential along
the Northern Anatolian Fault Zone in the Marmara Sea using
comparisons of GPS strain and seismotectonic parameters.
Tectonophysics 418: 215–218.
Öztürk S (2011). Characteristics of seismic activity in the Western,
Central and Eastern parts of the North Anatolian Fault Zone,
Turkey: temporal and spatial analysis. Acta Geophys 59: 209–
238.
References
301
TALEBI et al. / Turkish J Earth Sci
Öztürk S (2013). A statistical assessment of current seismic
quiescence along the North Anatolian Fault Zone: earthquake
precursors. Austrian J Earth Sci 106: 4–17.
Öztürk S, Bayrak Y (2012). Spatial variations of precursory seismic
quiescence observed in recent years in the eastern part of
Turkey. Acta Geophys 60: 92–118.
Öztürk S, Bayrak Y, Çinar H, Koravos GC, Tsapanos TM (2008).
A quantitative appraisal of earthquake hazard parameters
computed from Gumbel I method for different regions in and
around Turkey. Nat Hazards 47: 471–495.
Pechmann JC, Kanamori H (1982). Waveforms and spectra of
preshocks and aftershocks of the 1979 Imperial Valley,
California, earthquake: evidence for fault heterogeneity? J
Geophys Res 87: 10579–10597.
Polat O, Gök E, Yılmaz D (2008). Earthquake hazard of the Aegean
extension region (West Turkey). Turk J Earth Sci 17: 593–614.
Reasenberg P (1985). Second order moment of central California
seismicity 1969–1982. J Geophys Res 90: 5479–5495.
Rezapour M (2005). Magnitude scale in the Tabriz seismic network.
J Earth Space Phys 31: 13–21.
Smalley RF Jr, Chatelian JL, Turcotte DL, Prevot A (1987). A fractal
approach to the clustering of earthquakes: applications to the
seismicity of New Hebrides. B Seismol Soc Am 77: 1368–1381.
Smith LA (1988). Intrinsic limits on dimension calculations. Phys
Lett A 133: 283–288.
Sornette A, Dubois J, Cheminde JL, Sornette D (1991). Are sequences
of volcanic eruptions deterministically chaotic? J Geophys Res
96: 11931–11945.
Sunmonu LA, Dimri VP, Prakash MR, Bansal AR (2001). Multifractal
approach to the time series of M ≥ 7.0 earthquake in Himalayan
region and its vicinity during 1895–1995. J Geol Soc India 58:
163–169.
Telesca L, Lapenna V, Macchiato M (2005). Multifractal fluctuations
in seismic inter spike series. Physica A 354: 629–640.
Teotia SS, Khattri KN, Roy PK (1997). Multifractal analysis of
seismicity of the Himalayan region. Curr Sci India 73: 359–366.
Teotia SS, Kumar D (2007). The great Sumatra-Andaman earthquake
of 26 December 2004 was predictable even from seismicity
data of mb ≥ 4.5: a lesson to learn from nature. Indian J Mar
Sci 36: 122–127.
Teotia SS, Kumar D (2011). Role of multifractal analysis in
understanding the preparation zone for large size earthquake
in the North-Western Himalaya region. Nonlinear Proc Geoph
18: 111–118.
Tosi P (1998). Seismogenic structure behavior revealed by spatial
clustering of seismicity in the Umbria-Marche region (Central
Italy). Ann Geophys 41: 215–224.
Turcotte DL (1986a). Fractals and fragmentation. J Geophys Res 91:
1921–1926.
Turcotte DL (1986b). A fractal model for crustal deformation.
Tectonophysics 132: 261–269.
Vernant P, Nilforoushan F, Hatzfeld D, Abbassi MR, Vigny C, Masson
F, Nankali H, Martinod J, Ashtiani A, Bayer R et al. (2004).
Present-day crustal deformation and plate kinematics in the
Middle East constrained by GPS measurements in Iran and
northern Oman. Geophys J Int 157: 381–398.
Wiemer S (2001). A software package to analyze seismicity: ZMAP.
Seismol Res Lett 72: 373–382.
Wiemer S, Baer M (2000). Mapping and removing quarry blast
events from seismicity catalogs, short notes. B Seismol Soc Am
90: 525–530.
Wiemer S, Wyss M (1994). Seismic quiescence before the Landers
(M=7.5) and Big Bear (6.5) 1992 earthquakes. B Seismol Soc
Am 84: 900–916.
Wiemer S, Wyss M (2000). Minimum magnitude of completeness
in earthquake catalogs: examples form Alaska, the western
United States, and Japan. B Seismol Soc Am 90: 859–969.
Wu YM, Chiao LY (2006). Seismic quiescence before the 1999
ChiChi, Taiwan Mw7.6 earthquake. B Seismol Soc Am 96:
321–327.
Wyss M, Habermann RE (1988). Precursory seismic quiescence.
Pure Appl Geophys 126: 319–332.
Yılmaz Ş, Bayrak Y, Çınar H (2013). Discrimination of earthquakes
and quarry blasts in the eastern Black Sea region of Turkey. J
Seismol 17: 721–734.
Yılmaz V, Erişoğlu M, Çelik HE (2004). Probabilistic prediction
of the next earthquake in the NAFZ (North Anatolian Fault
Zone), Turkey. Doğuş Üniversitesi Dergisi 5: 243–250.
Zare M (1999). Contribution a l’etdue des mouvements forts en Iran;
du catalogie aux lois d’attenuation. PhD, Universite Joseph
Fourier, Grenoble, France (in French).