Quantitative Analysis of Seismicity in Iran

Abstract

We use historical and recent major earthquakes and GPS geodetic data to compute seismic strain rate, geodetic slip deficit, static stress drop, the parameters of the magnitude–frequency distribution and geodetic strain rate in the Iranian Plateau to identify seismically mature fault segments and regions. Our analysis suggests that 11 fault segments are in the mature stage of the earthquake cycle, with the possibility of generating major earthquakes. These faults primarily are located in the north and the east of Iran. Four seismically mature regions in southern Iran with the potential for damaging strong earthquakes are also identified. We also delineate four additional fault segments in Iran that can generate major earthquakes without robust clues to their maturity.The most important fault segment in this study is the strike-slip system near the capital city of Tehran, with the potential to cause more than one million fatalities.

1 Introduction

The present tectonics of Iran result from the convergence of the Arabian and the Eurasian plates in the form of continental collision (Falcon 1974; Berberian and King 1981), with the exception of the Makran subduction zone to the southeast, where a remnant part of the Tethys oceanic lithosphere subducts northward beneath southeast Iran (Nilforoushan et al. 2003; Zarifi et al. 2014). Within Iran, most of the deformation is accommodated in major fold and thrust belts such as Zagros, Alborz and Kopeh Dagh and along large strike-slip fault systems, which tectonically define different blocks such as the Central Iran and Lut (Masson et al. 2005) (Fig. 1). A signature of this complex tectonic setting is the high rate of seismicity in the Iranian plate. Although incomplete, the USGS database records more than 30 documented earthquakes of $M>7.0$ in Iran during recent history.

Fig. 1

The known damaging earthquakes in the Iranian Plateau. The bars are colored based on date of the earthquake and the height of the bars show square root of the number of deaths (Ambraseys and Melville 1982; National Geophysical Data Center, NOAA 2016). The known surface ruptures and macroseismic areas are colored based on the date of the causative earthquake. KD in northeast of Iran stands for Kopeh Dagh ranges

A number of researchers have assessed the seismic hazard in Iran and assigned different seismic zonations (e.g., Nowroozi and Ahmadi 1986; Ahmadi et al. 1989; Mirzaei et al. 1997, 1999; Tavakoli and Ghafory Ashtiany 1999). Tavakoli and Ghafory Ashtiany (1999) divided the Iranian Plate into 20 seismotectonic provinces with the largest earthquakes ($7.9\pm 0.4$) in the Kopeh Dagh, Alborz, and Van area in Turkey. Mirzaei et al. (1997) considered five seismotectonic provinces for Iran where those zones with the largest estimated earthquakes include the areas presented in Tavakoli and Ghafory Ashtiany (1999). The association of destructive earthquakes in modern and historical times with populated areas presents a grim view on the number of future fatalities due to earthquakes in Iran. Bilham (2009) classified Iran among the six most hazardous countries worldwide, which have hosted both the most fatal earthquakes and the greatest number of events in the last 500 years.

Quantitative analysis of seismicity in Iran can advance our understanding of seismic hazard potential in this country. In this study, we use the available earthquake data from 1900 to 2016 to evaluate the seismic strain rate. Using geodetic data (1999–2013), we also evaluate the geodetic shear strain rate. Using regional seismicity from the IRanian Seismological Center (IRSC) since 1996, we compute variations in the Gutenberg–Richter (G–R) parameters (Gutenberg and Richter 1944), a- and b-value, around major fault systems in Iran and relate the variations to the maturity of the seismic cycle for a number of fault systems. We use the integrated results and the approximate location of the historical devastating earthquakes (before 1900) to delineate some areas which have a high potential of seismic hazard.

Two sets of numbering are used in this work. The first set refers to numbering of the macroseismic areas and earthquakes that are listed in Table 1 and are shown in Figs. 2 and 3. For simplicity, we cite earthquakes as 1997/05/10 (7.3, 170). The numbers in parenthesis refer to the magnitude and the numbering of earthquakes, respectively. The second set of numbers refers to numbering of zones used in computation of the G–R parameters as given in Table 2 and Figs. 10, 11 and 12.

Fig. 2

Earthquakes in the Iranian Plateau with known macroseismic area (blue) (Ambraseys and Melville 1982), surface rupture (red), or with a death toll of more than 100 (Ambraseys and Melville 1982; National Geophysical Data Center, NOAA 2016). See Table 1 for more information about the numbered earthquakes. The thin gray lines show the known faults in Iran

Fig. 3

The colored background shows the magnitude of seismic strain rate in the Iranian Plateau due to a large earthquakes since 1909. The color is based on the fourth root of seismic strain rate to better show the distribution. The ruptured fault segments (red lines) and macroseismic zones (blue ellipses) are the same as in Fig. 2. The crossing arrows, plotted at grid nodes every 100 km, show the surface projection of principal axes of the seismic strain rate tensor. The missing crosses are due to their small magnitudes. Circles show earthquakes with stress drop larger than 30 bar. The numbering refers to the codes in Table 1

2 Major Seismicity in the Iranian Plateau

The oldest documented major earthquake in the Iranian Plateau and its surroundings dates back to the second millennium BC. Based on macroseismic data from historical sources, field studies and instrumental data, more than 50 earthquakes with $M\geqslant 7$ are assigned to the Iranian Plateau (Ambraseys and Melville 1982; National Geophysical Data Center, NOAA 2016). These major earthquakes, along with additional large and moderate earthquakes, have caused more than 1,936,000 fatalities (Fig. 1). Major earthquakes in Iran primarily are associated with the Iranian Crescent, a zone that extends from northwest Iran, through north (Alborz), to the northeast (Kopeh Dagh) and then with a southward turn it covers the limits of the Lut Block (Ambraseys 1977).

Major historical earthquakes of 1042 (7.6, 28), 1721 (7.7, 63), 1780 (7.7, 68), and 1840 (7.4, 74) are associated with the NW-Iran zone. The North Tabriz fault ruptured in 1042. Approximately six centuries later, two overlapping earthquakes of 1721 (7.7, 63) and 1780 (7.7, 68) ruptured the North Tabriz Fault again and the rupture extended to the southeast of Tabriz. This fault system has not experienced any major earthquakes since 1780. Post-1900, major activity in the northwest Iran includes the 1905/10/21 (7.5, 106) Caucasus in Georgia, 1930/05/06 (7.2, 119) Salmas, 1976/11/24 (7.3, 152) Chalderan in Turkey, and 2011/10/23 (7.1, 176) Ercis in Turkey earthquakes. The 1976 Chalderan earthquake rupture experienced approximately 63 km of right-lateral surface rupture with an azimuth of 110° that stopped at the Turkey–Iran border, 45 km away from joining another fault system with azimuth of 145°, the 1840/07/02 (7.4, 74) Maku–Ararat earthquake. The 2011 Ercis event was a reverse earthquake, typical for the Zagros collision zone (Dogan and Karakas 2013).

Further to the east, Alborz hosts a substantial portion of the reported historical earthquakes. However, this might be due to greater reporting by the higher population of central Alborz. Earthquakes from sparsely populated areas could have remained undetected. The oldest documented event in Alborz dates back to the fourth century BC in the Ray region with an assigned magnitude of 7.6. Earthquakes of 0743 AD (7.1, 6) and 0958 (7.7, 23) are associated with the central and western Alborz. The sequence continued in the second millennium with the earthquakes of 1177 (7.2, 33), 1485 (7.2, 46) and 1608 (7.6, 49). Provided that the catalog of major historical earthquakes in Alborz is complete, which is very unlikely, the shortest quiescent period for the western Alborz is approximately 100 years. The eastern Alborz has experienced the largest historical intraplate earthquake of the Iranian Plateau in 0856 AD (7.9, 17). The post-1900 earthquakes in Alborz are limited to the 1962/09/01 (7.2, 142) along its south-western boundary and the 1990/06/20 (7.4, 166) earthquake in the western Alborz (Table 1; Fig. 2).

Similar to Alborz, the Kopeh Dagh hosts substantial major historical earthquakes and the associated causative faults are aligned in the NW–SE direction. The events within Kopeh Dagh are primarily strike-slip. Nevertheless, those located along its north-eastern bound have dominant thrust components. The major earthquakes of 2000 BC (7.1, 1), 0010 AD (7.1, 3), 0943 (7.6, 21), 1209 (7.6, 35), 1270 (7.1, 36), 1389 (7.6, 41), 1405 (7.6, 42), 1871 (7.2, 84), 1893 (7.1, 92), 1929/05/01 (7.3, 115), 1946/11/04 (7.5, 131), 1948/10/05 (7.3. 134), 1963/03/31 (7.0, 144) and 2000/12/06 (7.0, 171) indicate more frequent major earthquakes and consequently shorter quiescent periods compared to Alborz.

The Lut Block in the east of Iran is surrounded mainly by strike-slip fault systems. Earthquakes of 0763 (7.6, 7), 1336 (7.6, 40) and 1618 (7.6, 50) are probably associated with rims of the Lut Block. Substantial parts of the strike-slip systems surrounding the Lut Block ruptured during the last century in the form of major earthquakes. The earthquakes of 1968/08/31 (7.3, 145), 1978/09/16 (7.3, 156), 1979/11/27 (7.0, 159), 1981/07/28 (7.2, 161), and 1997/05/10 (7.3, 170) indicate a high rate of seismicity in the last 70 years around the Lut Block (Table 1; Fig. 2).

The known historical major earthquakes in Zagros are limited to the 1008 (7.0, 26) and 1440 (7.1, 43) events. The post-1900 major earthquakes along the northeastern boundary of Zagros include the 1909/01/23 (7.4, 107) and 1957/12/13 (7.0, 138) events (Table 1; Fig. 2).

Table 1 Earthquakes in the Iranian Plateau with known macroseismic area (Ambraseys and Melville 1982), surface rupture, or more than 100 deaths (Ambraseys and Melville 1982; National Geophysical Data Center, NOAA 2016)

3 Analysis

We compute seismic strain rate, geodetic strain rate, stress drop and the Gutenberg–Richter parameters for the study area. In this section, the procedures employed in these analyses are explained briefly.

3.1 Seismic Strain Rate

Earthquakes are not only the result of tectonic deformation, but also contribute to it through quasi-plastic deformation. Kostrov and Das (1988) related seismic slip to seismic moment by considering an elementary area of the fault surface over which the sources of many earthquakes during a particular time interval are distributed. Earthquakes are related to many irregularly distributed faults and the location precision generally is not accurate enough to be associated with a particular fault.Therefore, it seems reasonable to describe the involved tectonic process as deformation in a volume. Kostrov and Das (1988) used the description presented by Riznichenko (1965), assuming that fractures at the earthquake source are randomly distributed in space, to define the average of the strain rate due to earthquakes as

$$\begin{aligned} \dot{\varepsilon _{s}}=\frac{1}{2\mu \triangle V\triangle t}{\displaystyle \sum _{k=1}^{n}}M_{0}^k, \end{aligned}$$

(1)

where $\mu$ is bulk shear modulus, $M_{0}^k$ is the seismic moment of the kth earthquake of the n earthquakes, $\triangle V$ is the volume of interest and $\triangle t$ is the time interval. Equation 1 gives the magnitude of the seismic strain rate and we can rewrite it for each component of the strain rate tensor as in Masson et al. (2005)

$$\begin{aligned} \dot{\varepsilon _{ij}}=\frac{1}{2\mu \triangle V\triangle t}{\displaystyle \sum _{k=1}^{n}}M_{ij}^k, \end{aligned}$$

(2)

where $M_{ij}^k$ shows the ij component of the moment tensor for the kth earthquake. We used the focal solutions of larger earthquakes for the period 1909 to 1975 from Jackson et al. (1995) and the Global CMT solutions for the period 1976 to 2016 to calculate the seismic strain rate. We divided the study area into $1^\circ \times 1^\circ$ cells, 20 km thick. We chose this thickness according to the depth distribution of earthquakes in Iran (e.g., Engdahl et al. 2006) and the fact that the dip extent of major earthquakes, primarily strike-slip, derived through waveform inversion requires approximately a 20 km crustal thickness. All the earthquakes located in every cell were used in calculating the seismic strain rate in that cell. Crustal earthquakes whose depths might have reached 30 km also were included in the analysis. We justified this by considering the larger uncertainty of the earthquake depth and the likelihood of rupture extension into shallower depths for those earthquakes.

Figure 3 shows the surface projection of the principal axes and also the magnitude of seismic strain rate associated with the aforementioned earthquakes since 1909.

3.2 Geodetic Shear Strain Rate

We densified the most recently available combined GPS velocity field (1999–2011) reported by Zarifi et al. (2014) with new published velocities (1997–2008) for eastern Iran (Walpersdorf et al. 2014) to compute geodetic strain rates (Table 3). Similar to Zarifi et al. (2014), the VELROT program (Herring et al. 2010) was used to generate a homogeneous velocity field for this combination in a unique Eurasia-fixed frame based on ITRF2008 (Altamimi et al. 2012). The RMS fit for the 82 components from the 41 common stations, used in both studies, was 0.43 $mm\ year^{-1}$. The total number of GPS stations increased from 239 in Zarifi et al. (2014) to 281 stations, which better densified the eastern part of the country (Fig. 4).

Fig. 4

GPS stations and GPS velocity field (in stable-Eurasia fixed frame) in Iran, integrated from Zarifi et al. (2014) and Walpersdorf et al. (2014), (see also Table 3)

We used SSPX program (Cardozo and Allemindigner 2009) to compute infinitesimal horizontal strain rates from GPS horizontal velocities. The SSPX program and its predecessor Strain SimPro have been successfully used in previous studies for deformation analysis of GPS networks (Allmendinger et al. 2007; Unglert et al. 2011; Mullick et al. 2009; Zarifi et al. 2014). Following Allmendinger et al. (2007) and Zarifi et al. (2014), the grid-distance neighbor method was applied to estimate the heterogeneous tectonic deformation in our study area. The grid-distance neighbor method uses weighted least squared adjustment, where each station is weighted by its distance to the center of the cell: $W=\mathrm{exp}(\frac{-d^{2}}{2\alpha ^{2}})$ where W is the weighting factor, d is the distance and $\alpha$ is a constant that specifies how the closeness of the stations to the center of the cell influences the strain solution. Stations within 1$\alpha$ distance contribute more than 67% to the solution, whereas those at a distance greater than 3$\alpha$ contribute less than 1% (Cardozo and Allemindigner 2009).

Using the SSPX program, we estimated the strain rate at the center of each cell of a $100 \times 100$ km$^2$ rectangular grid by inclusion of 281 Eurasia-fixed GPS velocities, Grid-distance neighbor method and $\alpha =75$ km (Fig. 5). We also estimated the maximum shear strain rates, the difference of the two principal infinitesimal strain rates (Fig. 6). The orientations of the maximum shear strain rates are always at 45° to the principal axes (Allmendinger et al. 2007). We summarized our geodetic computations in Tables 3 and 4.

Fig. 5

Geodetic strain rates (crossing arrows) deduced from our combined velocity field in Iran. The grid cells for calculations of strain rates are rectangles with 100 km dimension (see also Table 4). The colored background shows the magnitude of seismic strain rate. The ruptured fault segments (red lines) and macroseismic zones (blue ellipses) are the same as in Fig. 2

Fig. 6

Strike of geodetic maximum shear strain rate in Iran. Geodetic shear strain rates were computed as the difference of the two principal infinitesimal strain rates (see also Table 4)

The distribution of GPS stations across a number of strike-slip faults in Iran allows for the construction of transects across faults and projecting velocities of the stations inside into fault-parallel and fault-perpendicular components. The velocity profiles extracted from the stations inside these transects allow us to drive the geodetic slip rates for some strike-slip faults in Iran and compare the rates with geological estimates. However, the accuracy of such geodetic estimations depends on the distribution of GPS velocities in these transects (McGill et al. 2015).

3.3 Static Stress Drop

The static stress drop reflects tectonic unloading (Brown et al. 2015), which can remain almost constant over several orders of magnitude (Lengliné et al. 2014). This is due to the consistent level of differential stress, $\sigma _1-\sigma _3$, in the vicinity of the rupture area as the main controlling factor in shear faulting. Here, $\sigma _1$ and $\sigma _3$ represent the maximum and minimum principal stresses. Therefore, stress drop can be used as an indicator of stress level and its variation shows snapshots of the unloading state at different fault segments. Some generalizations on the variation of stress drop are proposed. Kanamori and Allen (2013) concluded that the stress drop is greater for earthquakes with larger repeat time. Allmann and Shearer (2009) found that strike-slip earthquakes show a three to five times larger stress drop than others. Kanamori and Anderson (1975) demonstrated that stress drop for intraplate earthquakes is larger than those for interplate earthquakes and Allmann and Shearer (2009) claimed a two times larger stress drop for intraplate earthquakes. Zielke and Arrowsmith (2008) numerically showed the temperature dependence of friction and consequently variation of stress drop with depth. Frohlich (2006) suggested that intermediate and deep earthquakes show an approximately one order of magnitude larger stress drop when compared to shallow events.

Static stress drop $\Delta \sigma$ is proportional to the spatial derivative of slip $\frac{D}{l}$ (Vallée 2013)

$$\begin{aligned} \Delta \sigma \propto \frac{M_0}{l^3}\propto \mu \frac{D}{l}, \end{aligned}$$

(3)

where $\mu$ is bulk shear modulus, D is average slip and l is a characteristic rupture dimension. The explicit relations for stress drop in terms of seismic moment $M_0$, Lamé parameters $\lambda$ and $\mu$, rupture length L and rupture width w are expressed as Eqs. 4 and 5, respectively, for strike-slip and dip-slip faulting (Lay and Wallace 1995)

$$\begin{aligned} \Delta \sigma =\frac{2M_0}{\pi w^2L}, \end{aligned}$$

(4)

$$\begin{aligned} \Delta \sigma =\frac{4(\lambda +\mu )M_0}{\pi (\lambda +2\mu )w^2L}. \end{aligned}$$

(5)

We find Lamé parameters at different depths by interpolating the corresponding parameters from the Preliminary Reference Earth Model (RREM) (Dziewonski and Anderson 1981). The most accurate stress drop values are found for earthquakes with available surface rupture and slip distribution. These include all the post-1900 earthquakes with $M>7$ and some other smaller events. For such earthquakes, the variables $M_0$, w and L are derived from the slip inversion. For those events without slip distribution or surface rupture, the dimensions L and w can be approximated from the half-duration time $t_\mathrm{hd}$. $t_\mathrm{hd}$ is given in the Global CMT catalog and represents half the duration of the moment rate function (Ekströem et al. 2012). Although $t_\mathrm{hd}$ is assumed for the CMT inversion and is not derived from the analysis, we think that it affects the robust results of CMT inversion and therefore is valid for use here. By assuming average rupture velocity $v_\mathrm{r}$ of 2.1 km/s, the length L and width w of the rupture can be computed as

$$\begin{aligned} \begin{array}{ll} L = 2 c t_\mathrm{hd} v_r, \\ w = \text {min}(2 c t_\mathrm{hd} v_\mathrm{r}, \frac{20.0}{sin(\delta )}), \end{array} \end{aligned}$$

(6)

where $\delta$ represents the dip angle and c is a constant that is related to rupture directivity. For a bilateral rupture, assuming all other parameters unchanged, the computed dimension is twice that computed for a unilateral rupture with the same rupture duration. We consider c as 0.75, somewhere between 1.0 for bilateral and 0.5 for unilateral ruptures. We limit the width of the rupture such that it remains in the brittle upper 20 km of the crust.

A number of earthquakes in Iran show stress drop of larger than 30 bar including all the events larger than 7 (Fig. 3). The majority of events show $3 \le \Delta \sigma \le 30$ bar (Fig. 8). The computation of stress drop is challenging and different methods may find values that vary by one or two orders of magnitude. This is due to uncertainties in the estimation of rupture dimension. The most accurate values for stress drop can be found if the rupture dimensions are obtained through direct measurements in the field or through well-resolved slip distributions. In such cases, Eqs. 4 and 5 can be implemented directly. We consider stress drop values for 30 earthquakes in Iran, with known rupture dimensions, as a benchmark. Figure 7 shows four differently estimated sets of stress drop. The values found through half-duration method are comparable with the benchmark values. The half-duration method overestimates the values for larger than seven earthquakes. However, for all such earthquakes the rupture dimensions are available by field measurements and/or slip inversions and we use those dimensions in the computations. Therefore, we consider the computed stress drop values in this article as valid. The P-wave spectra method (Allmann and Shearer 2009) overestimates for all obtained values substantially. The values found through S-wave spectra method (Hassani et al. 2011; Zafarani et al. 2012; Zafarani and Hassani 2013) cover a wide range and it seems that the values for a number of the events are overestimated. In both P- and S-wave spectra methods, the rupture area is found by using Brune’s method (Brune 1970).

Fig. 7

Static stress drop for a number of earthquakes in Iran that are found by using four different methods. The circles show the values that are found by using the half-duration data in the Global CMT catalog (Ekströem et al. 2012) and by employing the method of Sect. 3.3. The colored point inside each circle indicates its correspondence to another value that is found by another method which has the same symbol color and magnitude. The diamonds represent the stress drop for those earthquakes that their rupture dimensions were known through field measurements, slip inversion and aftershock distribution. In such cases, Eqs. 4 and 5 can be used directly. The inverted triangles show the values that are obtained by using S-wave source spectra of local strong-motion data (Hassani et al. 2011; Zafarani et al. 2012; Zafarani and Hassani 2013). The squares show the values which are found through isolation of P-wave source spectra of broadband data at teleseismic distances (Allmann and Shearer 2009). Any of the earthquakes used in the latter three methods is also used in the first method. However, only some of the earthquakes used in the latter three methods are common

Fig. 8

The circles show earthquakes and are colored based on their stress drop level. The white circles represent earthquakes with $\Delta \sigma \ge$ 30 bar and are shown separately in Figure 3. The colored background shows the fourth root of the magnitude of seismic strain rate. The ruptured fault segments (red lines) and macroseismic zones (blue ellipses) are the same as in Figure 2

3.4 Gutenberg–Richter Parameters

3.4.1 Basics on Gutenberg–Richter Parameters

Bak and Tang (1989) interpreted the Gutenberg–Richter (G–R) power law distribution as a consequence of the self-organized critical state of the Earth’s crust. Such systems evolve toward criticality and display scale invariance near that critical point. Scale invariance shows that the well-constrained regions of the G–R distribution, here the lower-magnitude portion, can be used for estimating the associated parameters. Heimpel (1997) suggested that self-similarity and criticality displayed by a fault during the earthquake cycle can be used to reveal how advanced a fault is within its cycle. Numerically, Heimpel (1997) showed that self-similarity is violated during the early stages of an earthquake cycle and emerges in the later stages. More specifically, the b value of G–R distribution decreases linearly with increasing differential stress, $\sigma _1-\sigma _3$ (Scholz 2015). The low differential stress at early stages of an earthquake cycle causes failure of small and weak patches. However, larger patches fail at later stages with increased stress. Numerically, this process results in reduction of the b value. Therefore, G–R scaling is more closely approximated during the later stages of the cycle (Heimpel 1997).

The G–R relation may have a predictive dimension provided that the computed a and b parameters represent those for the later stages of the earthquake cycle. Occurrence of a characteristic earthquake on a fault segment marks the end of the cycle for that segment. Assuming $N=1$, the unique characteristic earthquake in G–R relation, log(N) $=a-bM$, would have a magnitude of $M_\mathrm{p}=a/b$. Here, N is the cumulative number of events, M is magnitude and a and b are the G–R parameters. $M_\mathrm{p}$ is the predicted largest earthquake based on G–R relation. This value is small at the beginning of the cycle and increases as the cycle matures.

Perhaps, the a / b parameter is as important as the b parameter for the seismic maturity of a seismogenic zone. Comparison of the a / b value with the maximum expected earthquake based on historical and geological information may reveal the earthquake cycle stage of a fault system. The main controlling factors on the seismicity are the dimension and strength of asperities. A large, strong asperity behaves differently under stress compared to a number of smaller and weaker asperities. The absence of larger earthquakes results numerically in smaller maximum predicted earthquake, $M_p$. To clarify this issue, assume a typical G–R distribution with two main deviations. These deviations occur at a lower limit for smaller than threshold magnitudes and at a higher limits for different reasons; e.g., a short catalog span or sparsity of larger events due to the strength and extensiveness of asperities. Practically, we discard the lower limit deviation. However, the higher limit deviations contribute by steepening the G–R fit in the interpolation process. This results in higher b values and also in a smaller magnitude crossing along the magnitude axis.

Smaller values of the maximum predicted earthquake, $M_\mathrm{p}$, are expected at the beginning of an earthquake cycle or during the mature stages of a cycle for strongly coupled and extensive asperities along a fault system. Therefore, a large a / b indicates that the fault system is in its mature stages. However, a small a / b does not necessarily indicate that the fault system is in the early stages of a cycle.

The correlation between low b value areas along a fault system with the location of asperities has been reported for several case studies (e.g. Wyss et al. 2000; Schorlemmer and Wiemer 2005; Wiemer and Schorlemmer 2007; Sorbi et al. 2012; Sugan et al. 2014). Schorlemmer and Wiemer (2005) suggests that b values may act as stress meters for the Earth’s crust. Wiemer and Schorlemmer (2007) suggested that low b value ($b<0.7$) areas in their model for California were more likely to produce large ruptures than high b value ($b>1$) regions.

The b value increases systematically beyond a critical moment of $M_0\approx$(1.5–2) $\times 10^{27}$ dyn-cm, magnitudes of 7.4–7.5, which is attributed to a genuine physical change in the nature and scaling of the earthquake source that is the result of the saturation of the transverse dimension of the fault which cannot be more than the brittle crustal thickness (Okal and Romanowicz 1994). For smaller moments, the associated faulting is considered scale invariant and the observed deviations relative to the G–R curve (bimodality) may be due in part to the short span of the catalog. Zielke and Arrowsmith (2008) suggested that abrupt increase in rupture width explains the bimodal character of G–R distribution. Abrupt changes in rheology within the seismogenic zone control the depth extent of earthquakes and therefore the deviations in the G–R relation. A characteristic earthquake of the fault system is expected when the rupture width covers the width of the seismogenic zone. Amitrano (2003) experimentally showed that by increasing the confining pressure, the behavior of the rock mass becomes more ductile and the b value decreases. They concluded that the b value is controlled by variations of the internal friction angle induced by changes in the confining pressure. The Mohr–Coulomb failure criterion, $\tau =C+\sigma _n \tan (\phi )$, relates the internal friction angle $\phi$, normal stress $\sigma _n$, and cohesion C to shear stress $\tau$. Reducing the internal frictional angle decreases the b value and increases the ductile behavior. Another important outcome of reduction of internal friction angle is the development of the bimodal character of the G–R relation [Fig. 9 in Amitrano (2003)].

3.4.2 Gutenberg–Richter Parameters in Iran

High-resolution spatial mapping of the G–R parameters can be achieved using methods such as Wiemer and Wyss (2002), which finds anomalies at the nodes of a grid covering the target area or section. However, we apply the traditional method of estimating the parameters in separate zones which are manually chosen based on the location and extent of known faults or clustering of events along unknown trends. In spatial mapping methods, an earthquake may contribute to the parameter determination of several grid nodes. This may not be the optimal case for a closely spaced fault systems, such as those in this study. A thorough discussion of this and similar issues is given by Kamer and Hiemer (2015). Associating earthquakes with each fault restricts us to use only the recent high-quality data. While the span of time associated with that improved earthquake catalog is much shorter than the return period of the large magnitude events. In this case, we apply it based on the scale invariance of the G–R distributions (Bak and Tang 1989; Heimpel 1997), provided that the catalog is: 1—complete, 2—contains high-quality small magnitude data only and 3—its duration covers the return period of substantial number of the earthquakes that are used in the parameter estimation.

We used the earthquake catalog of the IRanian Seismological Center (IRSC) for the period 1996–2016 to determine the a and b parameters in the vicinity of different fault systems or earthquake clusters in Iran. The ever-expanding catalog includes more than 96,000 events with magnitude larger than 0.2 as of March 2016. The availability of a fault map in addition to the distribution of the seismic events enables us to determine the proper zonation. However, the catalog includes a substantial number of unreported mine or construction explosions.

We used the “exfilter” tool in the SEISAN computer code (Ottemöller et al. 2013) to remove probable explosions. The tool identifies likely explosions based on normalizing the time of day distribution of seismic events as a function of area. The hourly distribution of the entire catalog indicates that blast activities take place primarily between 06:00 and 16:00 GMT (08:30–18:30 local time). Careful analysis of events in each zone showed that 54 of the 129 zones included explosion activities. The “exfilter” tool marked approximately 16,500 events, 17% of the catalog, as probable explosions. The majority of the removed events fall in the group of events smaller than the completeness magnitudes, about 2–2.5. Therefore, any explosions remaining in the catalog do not effectively contribute to the determination of G–R parameters. The events in the blast-free catalog are almost uniformly distributed over different times of day.

The next preparation step is declustering of the catalog to remove the dependent events, foreshock and aftershock sequences. For this process, we used the Java implementation of the Gardner and Knopoff declustering method (Knopoff and Gardner 1972; Gardner and Knopoff 1974). The declustering process eliminated about 29,700 additional events or about 30% of the entire catalog. In total, 47% of the events were eliminated in the preparation process.

Next, we computed a and b parameters for each zone using a code particularly designed for such a task, “GRTo” (Amorése 2007). GRTo finds the completeness magnitudes automatically. However, in several cases we assigned larger completeness magnitudes to obtain reliable parameters.

In this study we found seven types of G–R distributions (Fig. 9). The deviations are mainly to the left of the G–R curve and indicate fewer events than the G–R relation predicts. Type I is the most expected but one of the rarer forms, with almost no deviation from the G–R relation. Type II is the most common form and shows minor deviations from the curve. In type III, fewer earthquakes occur at smaller magnitudes than predicted by the G–R relation. However, at larger magnitudes it again follows the G–R relation. Therefore, the deviation is not due to the short span of catalog. Rather, it indicates that some of the cracks preferentially join into larger ones. Types IV and V show significant deviation from the G–R curve which indicates a potential for substantial seismic energy release in the form of type VI. Type VI exclusively represents a fault system that has recently experienced its characteristic earthquake. Although type V shows partial compensation of the deviation with one or more larger events, the fault system has not yet experienced its characteristic earthquake. Except for fault systems with very strong to complete locking, the magnitude of the characteristic earthquake in type VI is approximately one unit larger than that predicted by a / b. Type VII mainly indicates an area where seismicity of more than one fault system contributes to the G–R curve.

Fig. 9

Different types of G–R distribution found by analyzing earthquakes recorded by the IRSC during the period 1996 to 2016. The Roman numbering to the top right of each panel shows the type

Figure 10 shows an a value map for those zones with reliable parameters. We ignored the zones with fewer than 100 events greater than their completeness magnitude. a values greater than 6.5 are found for small zones that are known mining sites. For most of the other zones, the a values range from 2.5 to 5. Figure 11 presents a b value map for the same zones as Fig. 10. While b values larger than 1.2 are found for zones with known mining sites, the majority of the zones show b values in the range 0.5–1.1. Figure 12 shows the a / b map with values generally ranging between 4.0 and 6.7.

Fig. 10

a values of Gutenberg–Richter relation at different zones in Iran computed from the IRSC catalog. The zones with more than 100 earthquakes larger than their corresponding completeness magnitude are shown. The numbers in each zone correspond to the numbering in Table 2. The thin gray line segments show the known faults

Fig. 11

b values of the G–R relation at corresponding zones shown in Fig. 10

Fig. 12

a / b values at different zones corresponding to those in Figs. 10 and 11

4 Discussion

Joint interpretation of variations in the G–R parameters, stress drop, seismic and geodetic strain rate fields, in conjunction with major historical earthquakes, can provide important information on the stage of maturity for different fault systems in the Iranian Plateau. In particular, negligible seismic strain rate in conjunction with high geodetic strain rate for a region that has not experienced a large earthquake for a long period of time may indicate a seismically mature area. As explained in Sect. 3.4.1, we pay particular attention to areas with larger a / b values.

As expected, we found that high seismic strain rates are associated with the areas which experienced major 7+ earthquakes during the past 100 years. These events show stress drops in the range of 30–80 bar, and most often in the range of 30–40 bar. These values may seem low for intraplate earthquakes, but the strongly shattered brittle crust of the Iranian Plateau, particularly along the existing large fault systems, justifies that level of stress drop. Interestingly, even the major intraplate earthquakes in the subducting Makran slab, e.g., 2013/04/16 (7.7, 178), show stress drop of about 36 bar. This might indicate that earthquakes in the subducting Makran slab also take place along pre-existing weak structures. The largest stress drop, 80 bar, is computed for the 1968/08/31 (7.3, 145) Dasht Bayaz earthquake along the northern bound of the Lut Block. The highest seismic strain rate is in the area of the 1945/11/27 (8.2, 132) Makran interplate earthquake. The coastal area to the west of this earthquake, between 57°E and 64°E, shows very small seismic strain rate that is not comparable to those values in the area of 1945 earthquake (Fig. 3). However, Fig. 5 shows the largest geodetic strain rate of about 1.3E−07 $year^{-1}$ for the aforementioned coastal area. This slip deficit for the coastal interplate zone eventually will be compensated in the form of a major or great interplate earthquakes. The seismicity in the Makran zone is sparse; however, major extensional earthquakes [e.g., the 2013/04/16 (7.7, 178) earthquake] occur in the subducting slab. The difference between GPS-derived velocities to the west of 61°E along the coasts of the Oman Sea (where overriding and subducting plates meet) indicate partial coupling of the plate interface (Fig. 4). No GPS measurement was available east of 61°E along the Makran coast and the easternmost coast of Oman is at 59.8°E. However, the major intermediate depth and extensional earthquakes of 2011/01/18 (7.2, 175) and 2013/04/16 (7.7, 178) to the east of 61°E most likely indicate strong coupling in the slab interface.

Further to the north, several major earthquakes, primarily strike slip, ruptured the boundaries of the Lut Block. Earthquakes of 1968/08/31 (7.3, 145), 1978/09/16 (7.3, 156), 1979/11/27 (7.0, 159), and 1997/05/10 (7.3, 170) occurred in the northern part of the Lut block. These earthquakes are located in zones 21, 82 and 90 of b value zones (Figs. 3, 10; Table 2).

Zone 76, with an a / b of 5.3, covers a major strike-slip fault system with conspicuous dislocations along the western boundary of the Lut Block (Fig. 12). The lack of any reported major earthquake associated with this zone is most likely due to the sparsity of the population, the result of its proximity to the Lut desert. The seismic strain rate of this zone is 0.0 $year^{-1}$ (Fig. 3). The geodetic strain rate seems comparatively small, $\sim$1.88E−08 $year^{-1}$, at the western bound of the Lut Block (Fig. 5). However, the distribution of GPS stations (Fig. 4) shows that there is no station in this zone and most likely the low values for geodetic strain rate emerge as a result of unconstrained interpolation. The distribution of moderate earthquakes in the last four decades (Fig. 8) shows no earthquakes in this zone. This may indicate strong and extended asperities of the fault system. This is in line with the conspicuous structure of the system. If so, then a moderate a / b value of 5.3 is large enough to conclude that the system is toward the end of its seismic cycle. Type II of the G–R distribution is inconclusive regarding the maturity stage of the zone (Fig. 9; Table 2).

The eastern side of the Lut Block is bounded by a major strike-slip system covered by zones 81 and 102 with a / b of 5.9 and 5.1 respectively (Fig. 12). The respective b values of the zones are 0.68 and 0.79 (Fig. 11). Although the seismic strain rate for these two zones are very small ($\sim$1.0E−10 $year^{-1}$, Fig. 3), the geodetic strain rate (2.0E−08 $year^{-1}$, Fig. 5) shows substantial aseismic deformation.

The stress drop values for moderate earthquakes along these zones are in the range of 25–30 bar (Fig. 8), which suggests the potential for larger earthquakes with large stress drop. These values are comparable with the stress drop of the 1997/05/10 (7.3, 170) earthquake, 31 bar, which occurred along the northern part of the same fault system. Ambraseys and Melville (1982) reported approximately 2 years of aftershocks for the 1838 (7.?, 73) earthquake. The northern limit of the surface rupture of the 1838 earthquake extended to approximately 30°N. The distance between the northern limit of the surface rupture of the 1838 earthquake and the southern limit of the surface rupture of the 1997/05/10 (7.3, 170) earthquake is approximately 360 km. Based on the rupture lengths of the other major earthquakes around the Lut Block, this seismic gap may rupture in four to five major earthquakes along the eastern boundary of the Lut Block. The high a / b value of Zone 81 and its G–R curve of type V (Fig. 9; Table 2) suggests that the zone is in the mature stage of cycle. Although major strike slip faults cut through alluvium in Zone 102, there is no report of recent or historical earthquakes in this zone. Despite its moderate a / b value of 5.1, it may be in the final stages of its earthquake cycle. The successive rupture of the 1968/08/31 (7.3, 145), 1979/11/27 (7.0, 159) in Zone 21 and the 1979/11/14 (6.6, 158) and 1997/05/10 (7.3, 170) earthquakes in Zone 90 suggests that rupture of the major strike-slip fault system in Zone 102 is very likely.

Zone 28, with b and a / b values of 0.65 and 5.69, respectively, is mature enough to generate earthquakes of about 6.5 to 7 (Figs. 11, 12).

The southwestern boundary of the Lut Block ruptured in 1981/06/11 (6.7, 160) and 1981/07/28 (7.2, 161) earthquakes located in the northwestern part of Zone 9 with high a / b value of 6.3 and b of 0.66. About 2000 of the 3000 fatalities of the 1981/06/11 earthquake were in the town of Sirch, with a total population of 3500 (Adeli 1982). The southern part of this zone ruptured during the 2003/12/26 (6.6) Bam earthquake, with 26,271 fatalities. The unbroken segment between these two earthquakes may rupture in a single earthquake in a sparsely populated region. It is unlikely that the moderate 2003 Bam earthquake released the entire stored energy of the main fault system. This hypothesis is supported by the fact that the causative fault of the 2003 Bam earthquake, with minor surface expression, was located approximately 5 km to the west of the main fault system in the region. That main fault system did not rupture during the 2003 earthquake. However, very large surface deformations from past historic events are readily observable in the local alluvium on low-resolution satellite images (Talebian et al. 2004; Nakamura et al. 2005) provide strong evidence for its seismic potential. The relatively low stress drop of the Bam earthquake (18 bar) and the low seismic strain rate ($\sim$1.8E−08 to 4.8E−11 $year^{-1}$, Fig. 3), in contrast to the substantial geodetic strain rate for Zone 9 ($\sim$3.5E−08 $year^{-1}$, Fig. 5), also support this conclusion.

Zone 49 covers the 300 km-long Kuhbanan fault system which hosted the 1933/11/28 (6.2, 123) Bahabad, 1977/12/19 (5.8, 155) and 2005/02/22 (6.4, 174) Zarand earthquakes. The type V G–R curve for this region, together with the high a / b value of 6.2 and b value of 0.71, suggest that this zone is in the mature stage of the earthquake cycle and may experience earthquakes of $M>6.2$ (Table 2; Fig. 9). An unusual feature of the pure right-lateral 1977 earthquake is its coseismic surface rupture, approximately 19.5 km long, with minor dislocation of less than 20 cm (Berberian et al. 1979). Assuming an average slip of about 15 cm suggests a maximum width of about 10 km. This indicates that the upper half of the brittle crust has ruptured. However, this needs to be verified by slip modeling. If true, then the rupture of the 1977 earthquake should be considered part of the process of the next major earthquake. Due to the remoteness of the region, there is a lack of documentation on historical earthquakes. However, there is a legend about a destructive earthquake that ruined Kuhbanan sometime in th twelfth century (Ambraseys and Melville 1982). Several moderate right-lateral earthquakes have ruptured the southern half of the Kuhbanan fault system over the last 26 years. The pattern of moderate earthquakes in this region align along the Kuhbanan fault system; however, they show less than 20 bar of stress drop (Fig. 8). The seismic strain rate along the zone is minor ($\sim$5.0E−09 $year^{-1}$, Fig. 3), while the geodetic strain rate is moderate ($\sim$2.0E−08 $year^{-1}$, Fig. 5). The distribution of GPS stations suggests that the estimated geodetic strain rate is properly constrained (Fig. 4).

The SE–NW trending zones of 50 and 52 (Fig. 10) and those in Central Iran (zones 8, 18, 27, 32, 39, 41, 66 and 70) show small a / b values (Fig. 12). Zones 50 and 52 correspond to part of the forearc of an ancient subduction zone. The other aforementioned zones are located within the backarc of the same subduction zone. All these zones have a low level of seismicity, negligible seismic strain rate for those events used in our calculation ($\sim$0.0E+00 $yearr^{-1}$, Fig. 3) and a small geodetic strain rate ($\sim$ 1.0E−08 $year^{-1}$, Fig. 5).

As a collision zone that emerged from closure of the Neotethys, the Zagros Mountains have a high level of seismic activity. However, due to the presence of incompetent and mobile layers in most parts of the sedimentary cover of Zagros, the deformation is mainly in the form of ductile folding and the brittle part is characterized by frequent small and considerable moderate earthquakes (Berberian 1995; Bahroudi and Koyi 2003; Nissen et al. 2014). The seismic strain rate for Zagros is very low (Fig. 3), while a substantial geodetic strain rate is measured, particularly to the east of 49°. Major earthquakes are missing in the folded region away from the collision front, the Folded Zagros (e.g., zones 4, 10, 11, 22, 24, 29, 35, 43, 45, 59, 74 and 79). However, the High Zagros (e.g., zones 96 and 97) next to the collision front has experienced 7+ earthquakes.

Zone 96, with a b value of 0.69 and an a / b value of 6.34, covers the macroseismic area of the 1909/01/23 (7.4, 107) Silakhur earthquake, with 6000 to 8000 fatalities (Figs. 11, 12). The 1957/12/13 (6.5–7.0, 138), 1958/08/16 (6.7, 139) and 2006/03/31 (6.1) earthquakes occurred to the northwest of the 1909 earthquake. Approximately 180 km to the southeast of the 1909 earthquake, the 1977/04/06 (6.0, 154) Naghan earthquake, with a dominant strike-slip mechanism, occurred in Zone 97 with a b of 0.61 and an a / b of 6.26. In addition to their G–R distributions of type V and IV, the high a / b values for zones 96 and 97 indicate the seismically mature stage of these zones. The strike-slip earthquakes in this region are associated with the right-lateral system of the Main Recent Fault (MRF) with a NW–SE trend. The 1977 Naghan earthquake indicates that the MRF extends to at least 51°E, where it joins the almost N–S right-lateral fault system of Kazerun. The Kazerun fault is located primarily in zones 14 and 43, with respective a / b values of 5.9 and 6.1. The respective b values of the zones are 0.69 and 0.72 (Fig. 11). We found the fault-parallel geodetic surface velocity of $3.13\pm 1.16$ $mm\ year^{-1}$ for the Kazerun fault and $3.48\pm 0.69$ $mm\ year^{-1}$ for the MRF system. It is likely that the Kazerun fault system delimits the SE end of the MRF. The similar characteristics of the Kazerun and MRF fault systems suggest that they can be considered as part of one system. Tavakoli et al. (2008) and Authemayou et al. (2009) suggested that the strike-slip motion is distributed from the MRF to the Kazerun system.

The 1909 Silakhur earthquake was along the strike-slip system of MRF. However, the associated surface rupture had an average of 1–2 m of vertical displacement with the northeastern side down-thrown and no indication of strike-slip displacement (Ambraseys and Melville 1982). Since normal faulting is unlikely, we interpret the relative vertical displacement as reverse faulting, which is consistent with the compressional system. The seismic strain rate for the region of the 1909/01/23 (7.4, 107) earthquake, as shown in Fig. 3, is representative of a strike-slip system. This can be reliable if the mechanism of the 1909 event, the main contributor to the seismic strain rate, is strike-slip as interpreted by Jackson et al. (1995).

The known strike-slip events along the MRF are typically less than magnitude 7 and the larger events may not be purely strike-slip. Zones 96 and 97 are the location of the highest peaks in the Zagros Mountains (Fig. 13). This is consistent with the uplift of the southwestern side during the 1909 earthquake. The strike-slip system cannot explain these high peaks. Therefore, we suggest that earthquakes as greater than or equal to the magnitude of the Silakhur event should be expected, particularly to the southeast of that earthquake. The process behind the uplift of this section of Zagros causes extensive tight folding in the neighboring zones of 54 and 79 that also have high a / b values of 6.4 and 6.5, respectively. The respective b values of the zones are 0.70 and 0.67 (Fig. 11). However, the events in these two zones show the lowest stress drop in the Iranian Plateau, approximately 5 bar, while Zone 79 hosts the most active earthquake swarm activity in Iran (Fig. 8). The low level of stress drop for these two zones may show that earthquakes within the zones fall short of magnitudes larger than 7. Zones 22 and 35, located to the west of Zone 79, have significantly different values for stress drop. Earthquakes in Zone 22 have a stress drop of 5–15 bar, while all earthquakes in Zone 35 have a stress drop in the range of 25–30 bar. Their a / b values are 6.28 and 5.98, respectively.

Fig. 13

Elevation contours of 3200 m, irregular small black patches, shown on the a / b map. The contours in zones 14, 96 and 97 represent the highest peaks in the High Zagros. The other set of these contours locate in the West Alborz along zones 57 and 95

Zone 45, which covers the northwestern portion of the MRF, has b and a / b values of 0.67 and 5.92, respectively. This indicates maturity of the zone for generating earthquakes of magnitude 6.5–7 (Fig. 11, 12).

Zone 11, with a b value of 0.71 and an a / b value of 6.4 (Fig. 11), hosts a large number of salt domes. However, the largest salt domes of Zagros are located to the east, parallel to and outside of Zone 11. No historically damaging earthquake of 7+ has been reported in this zone, but the 1960/04/24 (5.9, 140) Lar earthquake took more than 1300 lives. The 1961/06/11 (6.4) event occurred less than 10 km to the north of the 1960 event.

The largest known earthquake in Zone 103, with an a / b value of 6.3, is the 1977/03/21 (6.9, 153) Khurgo event with 167 fatalities. The zone is located in the southeastern part of Zagros and has experienced a number of 6+ earthquakes and is likely to experience more earthquakes of magnitude 6 to 7. The geodetic strain rate along this zone is as large as $\sim$4.5E−08 $year^{-1}$.

Zones 6 and 94, with a / b values of 6.4 and 6.7, respectively, delimit the Eurasian plate to the north from the Iranian plate (Fig. 12). The respective b values of these zones are 0.65 and 0.67 (Fig. 11). Zone 6 covers the macroseismic area of the 1948/10/05 (7.3, 134) Ashkhabad earthquakes that resulted in at least 110,000 fatalities. The 1946/11/04 (7.5, 131) earthquake occurred in the eastern part of Zone 94, while the 1895/07/08 (7.4, 94) Uzun-Ada (Turkmenistan) earthquake also caused a tsunami in the Caspian Sea (Kondorskaya and Shebalin 2010; Ambraseys 1997). The most recent major event in the eastern part of Zone 94 is the 2000/12/06 (7.0, 171) earthquake. Therefore, it is reasonable to expect events of this size for the unruptured segments along the system.

Kopeh Dagh, with many historical earthquakes, is located to the south and next to the boundary between the Eurasian and the Iranian plates (Ambraseys and Melville 1982). Zones 12 and 33 have significant a / b values of 6.3 and 6.0, high geodetic strain rate, $\sim$3.0E−08 $year^{-1}$, and negligible seismic strain rate based on our calculation. The respective b values of the zones are 0.67 and 0.77 (Fig. 11). Geological maps show that north dipping thrust faulting is the main mechanism in these two zones (e.g., Berberian 1976). While these results indicate the maturity of the earthquake cycle in this zone, no major earthquakes have been reported for these two zones. Zone 59, with an a / b value of 5.2 (Table 2), is the location of four major earthquakes in 1209 (7.6, 35), 1270/10/07 (7.1, 36), 1389/02 (7.6, 41) and 1405/11/23 (7.6, 42). The relatively short time interval between these four major earthquakes is similar to the successive rupture of different segments of a strike-slip system. However, both strike-slip and thrust faults exist in the vicinity of Neyshabur valley. It seems that at least the major portion of the causative fault system ruptured during these four earthquakes over a time window of about 200 years. Shabanian et al. (2012), using geological and morphological evidence, found slip rates of $2.4\pm 0.5$ and $2.8\pm 0.6$ $mm\ year^{-1}$ for right-lateral and reverse components of active faulting in Neyshabur region. Our GPS-derived right-lateral slip rate along the Neyshabur fault is $2.5\pm 0.9$ $mm\ year^{-1}$, which is consistent with the geologically derived value. We expect an average slip of approximately 2–3 m for these major earthquakes. Assuming that part of the GPS-derived motion contributes to aseismic deformation (Table 3 in Khodaverdian et al. 2015), the slip deficit in this zone does not seem to be large enough for recurrence of the aforementioned four earthquakes.

The four neighboring zones of 71, 37, 23, and 42 have very low b values of 0.63, 0.6, 0.68, and 0.61 respectively, which are among the lowest values in the Iranian Plateau (Figs. 11, 12). However, moderate a / b values in the range of 5.56–5.87 are found for these zones. Zone 23 encompasses part of a major left-lateral fault system, Doruneh–Herat, which runs from Central Iran to Central Afghanistan. The seismicity along the system is low and the geodetic strain rate is smaller than that of Kopeh-Dagh in north and Lut to the south. Most likely, the poor GPS station distribution around the fault resulted in unconstrained interpolation (Figs. 4, 5). The damaging historical and recent earthquakes along the fault include 1618/12/19 (?, 50), 1903/05/25 (6.5, 105) and 1923/05/25 (5.7, 109) events. Because there is virtually no settlement in the western part of the system as it passes through the desert, the resulting sparse population may explain the absence of documented historical earthquakes for Zone 23. Based on the morphology of the fault system, major earthquakes are expected here. Zone 42 covers the right-lateral basement fault system of Kalmard. The seismicity in Zone 42 is low and no historical earthquakes are reported for this sparsely populated zone. Based on the low b values and moderate a / b values for these zones, we suggest that they are mature for generating earthquakes of about 6.5–7.

The overlapping zones of 20 and 34, with a / b values of 5.05 and 5.28, cover the macroseismic area of the devastating 0856/12/22 (7.9, 17) Qumis earthquake (Ambraseys and Melville 1982). The low to intermediate a / b values here are inconclusive with regard to the maturity of the zones, unless the fault systems are strongly coupled. Types II and III of the G–R distribution (Fig. 9) do not hint at the maturity of the zones. However, the slip deficit suggests differently. The magnitude of the 0856 Qumis earthquake, the extent of its devastation and the bending of the causative fault segments in the middle of the macroseismic area, all suggest that strike-slip fault segments with different geometries were involved. This can occur when fault segments with different return periods synchronize and suggests that the next major earthquake in these zones may occur sooner than expected, as a result of separate rupture of the segments, from the return period of a 7.9 earthquake but with smaller magnitudes. The left-lateral GPS-derived velocity for the macroseismic area of the 0856 Qumis earthquake, Zone 20, is $4.5\pm 0.8$ $mm\ year^{-1}$, based on our analysis. We also found a similar value of $4.5\pm 1.1$ $mm\ year^{-1}$ for the larger strip from 52.6°E to 57.0°E covering zones 20 and 34. Mousavi et al. (2013), using a GPS network in NE Iran, found a left-lateral slip rate of 4–6 $mm\ year^{-1}$ for the eastern Alborz, which includes the macroseismic area of the 0856 Qumis earthquake. In a paleoseismology study of a single trench along the bending fault system, Hollingsworth et al. (2010) proposed that a rupture occurred prior to 1300 A.D. and significantly later than 600 B.C., which is consistent with the 0856 earthquake. The GPS-derived velocity results in more than 5.2 m of slip deficit since the 0856 earthquake. However, part of the deficit is accommodated by aseismic deformation. Khodaverdian et al. (2015) found that seismic deformation constitutes 78–92% of deformation in Alborz, 62–94% in Kopeh Dagh and 28–39% in Zagros. Intuitively, the deformation along the strike-slip systems that are not involved with folding should include less aseismic deformation. We expect variable coupling along this fault system that, assuming an average coupling of 75%, results in about 4 m of net slip deficit. This is a large value and points to the maturity of the fault system, particularly if, as discussed above, the segments rupture separately.

Zones 1 and 95 in the West Alborz, with a / b values of 4.84 and 5.17, respectively, are the location of major, devastating earthquakes. The b values are 0.92 and 0.74, respectively (Fig. 11). Zone 1 experienced the 1990/06/20 (7.4, 166) Rudbar earthquake, with about 50,000 fatalities (Berberian et al. 1992; Gao and Wallace 1995; National Geophysical Data Center, NOAA 2016). The last known devastating earthquakes in Zone 95 are the 0958/02/23 (7.7, 23) and 1608/04/20 (7.6, 49) Taleghan earthquakes (Ambraseys and Melville 1982). The elongation of macroseismic areas of these two earthquakes and their correspondence with strike-slip fault segments suggest that these events were strike-slip, similar to the 1990 Rudbar earthquake (Fig. 2). The relatively low a / b value for Zone 95 is inconclusive with regard to the maturity of the zone. The area surrounding the surface rupture of the 1990 Rudbar earthquake, Zone 1, is poorly covered by GPS stations and the few GPS measurements show fault-parallel surface velocity of $1.62\pm 0.6$ $mm\ year^{-1}$. The macroseismic area of the 0958 earthquake, Zone 95, is covered by more GPS stations. However, the fault-parallel strike-slip component of surface velocity is inconclusive. Djamour et al. (2010) found 1 and 2 $mm\ year^{-1}$ of strike-slip surface velocity for the southern edge and the northern edge of the mountain range in West Alborz.

The negligible fault-parallel surface velocity may indicate full locking along the main strike-slip system that passes through zones 1 and 95. However, a dense near-fault network of GPS stations is necessary to determine the locking condition (Meade and Hager 2005; Walters et al. 2014; Yamasaki et al. 2014). Nevertheless, the small fault-parallel velocities show that the system is in the latter stages of the earthquake cycle. Savage and Prescott (1978) illustrated, based on the analytical work of Nur and Mavko (1974), that rapid postseismic deformation occurs in the early stages of an earthquake cycle, while strain accumulation is concentrated in later stages. A rare observation of the numerical results of Savage and Prescott (1978) is the GPS data before and after the 1999/08/17 (7.5) Izmit and 1999/11/12 (7.2) Düzce earthquakes in Turkey, which revealed a preseismic strain localization within about 25 km of the fault and a rapid postseismic transient (Yamasaki et al. 2014).

The very low seismicity along the macroseismic areas of the 0958 and 1608 earthquakes supports the strong locking conclusion. Another indicator of full locking of the system is the aftershock distribution of the 1990/06/20 Rudbar earthquake. Aftershocks of this event were mainly located to the north of the surface rupture and abnormally distributed for about 90 km to the north and perpendicular to the surface rupture. Intuitively, the interseismic strain is distributed primarily in the block under stress. Slip deficit, with its maximum on the fault plane, extends to larger distances away from the fault plane in the case of stronger locking. This mechanism causes the interseismic and postseismic processes, including aftershock activity, to extend far from the shear zone, which is the fault plane. This mechanism may explain other observations such as severe water level change in the Caspian Sea before or after each of the three aforementioned earthquakes (Ambraseys and Melville 1982). However, this should be scrutinized carefully in the future.

The strike-slip earthquakes in West Alborz are complicated because their principal stress axes are inconsistent with those derived from the conventional geodetic velocity field. Figure 6 shows the maximum geodetic shear strain directions which should be parallel to one of the nodal planes of the strike-slip systems (Wyss et al. 1992). For the region of 0958, 1608 and 1990 earthquakes, the geodetic shear strain rate directions are oblique to the fault traces.

The comparatively small geodetic strain rate of the region of the 1990 earthquake ($\sim$1.0E−08 $year^{-1}$, Fig. 5) is very different from the high seismic strain rate, $\sim$2.3E−07 $year^{-1}$. In contrast, the macroseismic areas of the 0958 and 1608 earthquakes have seismic strain rates of $\sim$0.0 $year^{-1}$. The sharp arrest of the rupture of the 1990 Rudbar earthquake at its southeastern end in addition to frequent micro-seismic activity in the same region (Tatar and Hatzfeld 2009), even a decade after the earthquake, suggest that the rupture of the 1990 event is incomplete. A number of small and moderate reverse aftershocks, e.g., 1990/06/21 09:02 (5.7), with their nodal planes perpendicular to the strike of the 1990 faulting at the southeastern end of the 1990 faulting, indicate continued northwestward motion of the unbroken block in Zone 95. The next strike-slip segment marks a 9 km distance to the southeastern end of the 1990 faulting in the form of a compressional step-over and is most likely the reason for the rupture halt (Hu et al. 2016). All these factors indicate the likely maturity of the fault segment to the northwest of Zone 95.

Since short-term slip rates using GPS measurements are inconclusive for the left-lateral system in West Alborz, we prefer to use the long-term estimates for the fault slip rate. Berberian and Walker (2010) considered the left-lateral shear of the overall Alborz belt at a rate of $4\pm 2$ $mm\ year^{-1}$. This value matches the left-lateral surface rate for East Alborz which is about 4.5 $mm\ year^{-1}$. Nazari et al. (2009), using morphological and paleoseismological methods, estimated minimum horizontal slip rate of 0.6–1.6 $mm\ year^{-1}$ for the Taleghan fault. Based on geological evidence, Guest et al. (2006) estimated a slip velocity of $2.7\pm 0.5$ $mm\ year^{-1}$ of long-term left-lateral slip for Taleghan and Mosha faults located in Zone 95. Assuming a slip rate of about 3.0 $mm\ year^{-1}$, the slip deficit for the causative faults of the 0958 and 1608 earthquakes amount to 3.1 and 1.2 m, respectively. A fault system with 3.1 m of slip deficit is mature enough to generate a 7.4 earthquake. There is no reason to consider the macroseismic area of the 0958 earthquake as less mature, compared to the macroseismic area of the 1608 earthquake. As mentioned earlier, this region shows signs of southeastward continuation of the rupture of the 1990 Rudbar earthquake.

The exact location of the left-lateral system in West Alborz is not well known. This also was the case for the causative fault of the 1990 Rudbar earthquake. In most studies the Mosha fault, which is located about 16 km north of Tehran, is considered to be the continuation of the left-lateral system in West Alborz (e.g., Guest et al. 2006). However, existence of a huge rock-slide, $\sim 1.2$ km $\times 0.25$ km, approximately 7 km to the W–NW of Tehran at 35.819250°N, 51.243044°E, suggests that there may be other possibilities for the location of the left-lateral fault system in the vicinity of Tehran.

With a b value of 0.64 and an a / b value of 5.61, Zone 83 is the location of several devastating strike-slip earthquakes along the North Tabriz fault. The most recent major earthquakes of 1721/04/26 (7.7, 63) and 1780/01/08 (7.7, 68) caused widespread devastation with approximately 40,000 and 50,000 deaths, respectively. The relatively high geodetic strain rate in Zone 83 ($\sim$3.2E−08 $year^{-1}$, Fig. 5) is anti-correlated with the relatively small seismic strain rate, $\sim$2.0E−10 $year^{-1}$. The fault-parallel geodetic surface velocity for the region surrounding the North Tabriz fault is $6.23\pm 1.12$ $mm\ year^{-1}$, based on our analysis. Therefore, the slip deficit values of less than 2 m since the occurrence of these two earthquakes is much smaller than expected for such major earthquakes. The likely unbroken segments along the North Tabriz fault may be the potential location of future damaging earthquakes. However, we have no clues as to the location of these segments. The low b value of the zone supports this viewpoint but the moderate a / b value suggests maturity of the zone for earthquakes of about 6.5–7. The main segments of the system ruptured during the 1721 and 1780 earthquakes. The unusual feature of these two earthquakes was their largely overlapping surface rupture and the major difference between them was the large normal slip component that reached 4–10 m for the 1780 earthquake in places (Ambraseys and Melville 1982).

5 Conclusion

Simultaneous analysis of geodetic slip rate and slip deficit, geodetic and seismic strain rates, stress drop, G–R distribution and historical and recent seismicity is employed here to identify zones and fault systems in the Iranian Plateau that are favorable candidates for likely future major earthquakes (Fig. 14). However, this does not rule out the occurrence of large earthquakes in other fault systems.

Fig. 14

The fault systems which may host future large earthquakes in the Iranian Plateau based on this study. The fault segments in red show stronger evidences of maturity compared to those in yellow. The four zones of 11, 54, 79 and 103 are in the mature stage of the earthquake cycle. For better rendering, the third root of population density is shown as background

Of the identified faults, F4 is the most important because it passes through a heavily populated area near or in Tehran megacity. Another important segment is F1, which passes next to Baku, the capital of Azerbaijan. F3 is the segment with indications of rupture initiating from its NW tip and propagating southeastward, a continuation of the 1990/06/20 (7.4) Rudbar faulting. Along the border between the Iranian and the Eurasian plates, F2 is among the most mature fault segments. F6 is part of the system that hosts the 0856 (7.9) earthquake and the associated fault type is likely strike-slip in nature. F7 is expected to be of reverse-type faulting. F9 is the continuation of the 1997/05/10 (7.3) faulting. The four zones of 11, 54, 79 and 103 are identified along the Zagros fold-thrust belt, where blind faulting prevents delineation of the causative faults.

Additional, detailed studies on the fault segments proposed here are necessary. However, the population density along F3 and F4 means that studies in those regions are most imperative. The coupling along F4 seems to be close to 100% and researchers may have been misled by the lack of geodetically-derived differential motion along the fault strike. Therefore denser seismic and geodetic networks and observations are required to better characterize the seismic hazard in the region.

Table 2 Gutenberg–Richter (G–R) parameters for different seismogenic zones (Fig. 10) in Iran are shown in columns 2–4. SD, N and $N_\mathrm{v}$, respectively, show standard deviation, number of events in each zone, and number of events used in computation of the G–R parameters

Appendix

See Tables 3 and 4.

Table 3 GPS stations in Iran and Oman, their locations, velocities ($mm\,year^{-1}$) and their $1\sigma$ uncertainties with respect to Eurasia-fixed frame (EURA$\_$I08)

Table 4 Geodetic (G) and seismic (S) strain rate axes or magnitude at grid nodes 100 km apart