Seismic Risk in Alborz: Insights from Geological Moment Rate Estimation and Fault Activity Analysis

Abstract

The Alborz mountain range in northern Iran is part of the active and seismic Alpide belt, where assessing seismic hazards is crucial due to the region’s history of large instrumental earthquakes and destructive seismic background. Moment rate estimation, which quantifies tectonic activity, offers a novel approach to understanding the energy potential of active tectonic regions. In this study, a regional perspective is employed to investigate the maximum horizontal acceleration for Tehran, the major city in Alborz, resulting from the Sorkh-e Hesar and Ghasr-e-Firuzeh faults located approximately 7.5 km southeast of Tehran. These faults have a seismic potential of Mw 6.5 and a gravity of ~0.5723. While previous studies have identified faults in northern Tehran as the greatest seismic risk, our findings suggest otherwise. The calculated geological moment was 5.18218 × 10¹⁷ Nm/y, with a seismic moment rate of 1.83375 × 10¹⁴ Nm/y, providing valuable insights into fault activity and seismic potential in the study area.

1. Introduction

The stress resulting from the continuous movements of the Earth’s crust plates, specifically the Arabian and Eurasian plates, is a primary driver of seismic activity in Iran, leading to the formation of distinctive geological structures in various sub-zones, including the Alborz mountain range (Figure 1). The Alborz region encompasses major cities such as Tehran, Rasht, Karaj, Zanjan, Qazvin, Sari, and Gorgan, which have experienced devastating historical earthquakes. The mechanism and density of faults in the Alborz mountain range significantly affect its seismicity parameters. Therefore, a thorough examination of these seismic parameters can provide valuable insights into the seismicity of these cities, particularly Tehran, the capital of Iran, in terms of the magnitude and timing of potential future earthquakes.

It is important to note that deformations resulting from stress can propagate and impact surrounding areas. Movements in one area can create deformations in adjacent regions, highlighting the interconnectedness of seismic activity in the Alborz region. As such, a holistic approach that considers all active faults and their hazards in relation to a specific point, such as Tehran city, can facilitate a more comprehensive analysis of seismic risks in different parts of the Alborz zone.

Understanding the seismic hazards and risks in the Alborz region, including its major cities, is of paramount importance for earthquake risk mitigation and disaster preparedness efforts. By examining the seismic parameters and taking into account the complex interplay of various factors, such as fault mechanisms, fault density, and regional deformation patterns, we can improve our understanding of the seismicity of the region and make informed decisions for disaster planning, infrastructure development, and public safety measures. This study aims to contribute to this understanding by employing a regional perspective to investigate the maximum horizontal acceleration for Tehran, the capital of Iran, resulting from specific faults in the Alborz region, and provide valuable insights into fault activity and seismic potential in the study area. The geological moment rate is considered an aggregate of the crustal deformation, including the plastic and elastic components. Comparing seismic and geologic data helps to illustrate areas where all deformation rates are related to the crustal seismicity with some physical uncertainties [1,2,3,4].

Furthermore, it is possible to consider regions with high seismic deformation rates and interseismic slip across the faults [5,6,7,8,9]. Therefore, a joint effort to assess the number of large missing earthquakes is required to balance the moment released by seismicity [1,2,7]. In this study, we describe the calculation of geological moment rates from all active faults by presenting the relevant relations and the assumed values. We justify our preliminary selection of moment-rate models, describe the steps taken to constrain the seismicity rates to be consistent with observations, and provide the reasoning for not including seismicity rates from fault strain rates for the PGA map.

2. Tectonic Setting and Seismicity

The Alborz mountain range is an intercontinental fold–thrust belt of about 1000 km in length and a width of about 500 km with an approximate east–west trend within the Alpine-Himalayan orogenic belt (Figure 1). The Alborz, located on the boundary between the Turan–Ural Platform and the Central Iranian Subcontinent, is the northernmost deformation zone resulting from the convergence of the Arabian and Eurasian Plates. The study area is located in the north of Iran and between the latitude of ~35°01′ N–38°48′ N and the longitude of 56°59′ E–48°01′ E (Figure 1). In seismically active regions is always a relationship between the identified active faults and the earthquakes in terms of location and depth. Thus, the study of characteristics of the active faults can be the basis for seismic surveys of a region. In the Alborz region, the active faults, which usually cut the Quaternary units, have been marked on the geological maps (scales; 1:250,000, 1:100,000) and satellite imagery in various international articles [10,11,12] (Figure 2).

The main active faults of the Alborz with a dominant component of thrust surround the area from the north (e.g., North Alborz, Khazar SSW-dipping faults) to the south (e.g., Garmsar, North Tehran, Jajarm, Pishva N-dipping faults), while the strike-slip movement is concentrated inside the range (e.g., Rudbar, Firuzkuh, Mosha) [14,15,16,17].

In certain regions of the Earth, significant seismic activity has been observed, including past occurrences of large earthquakes, as documented by [18,19,20,21]. Understanding historical seismic events and their locations is crucial for conducting seismic hazard analysis, as emphasized by [22]. This study has compiled and examined historical earthquake data from various sources, such as books and articles [23,24].

The seismicity of each structural zone has been studied over two periods: the pre—20th century (pre-instrumental) period and the instrumental period that followed the development of seismic instruments in the late 19th century. Figure 3 and

Table 1. Active faults [13,14] of the study area with the active fault type (T), fault length (L), and nearest fault distance to Tehran (R).

Fault Name	T	L (Km)	R (m)	Fault Name	T	L (Km)	R (m)
Sangavar	Earthquake Fault	81	360	F2 = Hokm Abad-Baba Cheshmeh	Quaternary Fault	152	366
Masuleh	Active, Thrust and Reverse	105	253	Jajarm	Active, Thrust and Reverse	78	435
F33 = Rudbar fault branch	Earthquake Fault	10	252	F36 = Siah Kuh	Quaternary Fault	100	392
Talesh	Active and Relative Fault	250	250	Rabat Garbil	Quaternary Fault	119	382
F33 = Rudbar fault branch	Earthquake, Thrust and Reverse	30	219	Sfarayen	Active Fault	40	512
Rudbar	Strike-Slip	37	178	Sabzevar	Active, Thrust and Reverse	7	498
F32 = Kabatteh fault branch	Active Fault	42	190	Doruneh1	Active Fault	31	481
Lahijan	Active Fault	42	217	Doruneh2	Active, Strike-Slip	35	477
F31 = North Alborz fault branche	Active Fault	45	196	Torud	Active Fault	80	241
North Rudbar	Quaternary Fault	100	162	F8 = Qods	Active Fault	23	280
Bonan	Active Fault	76	112	F9 = Alikhan	Active Fault	64	277
Alamutrud	Active, Thrust and Reverse	133	78	F10 = Mehrkardu	Active, Strike-Slip	33	348
F21 = Daryasar-Dikin	Active Fault	19	118	F11 = Mozaffar Abad	Active, Thrust and Reverse	69	336
F22 = Veneda-Veres	Active Fault	37	85	Ghachab	Quaternary, Thrust and Reverse	40	158
F23 = North of Ghazvin	Active Fault	10	105	Pishva	Quaternary Fault	35	50
F24 = Gharib Mazraeh-Veres	Active Fault	21	111	Garmsar	Active, Thrust and Reverse	70	65
North Ghazvin	Active, Thrust and Reverse	64	129	Eyvanaki	Thrust and Reverse	94	9
Zanjan	Quaternary Fault	104	196	Kahrizak	Active, Thrust and Reverse	4	21
F35 = Gomrokan	Quaternary Fault	15	193	South Tehran	Active, Thrust and Reverse	21	14
F34–F33 = Baghestan-Qeshlagh-Aldaghlu-Shinin	Quaternary Fault	25	170	Siah Kuh	Quaternary, Thrust and Reverse	38	62
Soltanieh	Quaternary, Thrust and Reverse	116	216	F27 = Abdareh-Khar Rud	Quaternary Fault	41	147
F25 = Hasan Abad	Active, Thrust and Reverse	6	111	Parandak	Quaternary Fault	42	111
Kandovan	Quaternary, Thrust and Reverse	80	51	F28 = Avaj-Ahmad Abad-Karvansara	Quaternary Fault	47	190
F19 = Kajur-Khachak	Quaternary, Thrust and Reverse	75	74	F29 = Indes Ardmin	Quaternary Fault	7	185
F14 = Ghasre Firozeh	Quaternary Fault	12	7	Kushk-e Nosrat	Quaternary Fault	116	105
F15 = Sorkhe Hesar	Quaternary Fault	12	12	F29 = Indes-Aremin	Quaternary Fault	31	151
F16 = Niavaran-North of Tehran	Quaternary Fault	16	15	F30 = Dokhan-Nobaran	Quaternary Fault	50	176
F17 = Telo-Pajen	Active Fault	12	9	Indes	Active, Thrust and Reverse	28	150
North Tehran	Active Fault	176	11	South Parandak	Quaternary Fault	107	78
Taleghan	Active, Thrust and Reverse	59	52	North Parandak	Earthquake fault, Strike-Slip	74	96
North Alborz	Active, Thrust and Reverse	463	87	Eshtehard	Active, Thrust and Reverse	67	50
Gorgan	Active Fault	85	268	Ipak	Active, Thrust and Reverse	52	76
Khazar	Active, Thrust and Reverse	314	99	F12 = Darin	Quaternary Fault	43	44
F13 = Allahabad	Active Fault	85	95	F26 = Vanedar	Active Fault	10	131
F7 = Anjilu	Quaternary Fault	102	237	Bozgush	Quaternary Fault	73	398
F5 = Chashm-Astaneh	Quaternary Fault	176	139	Mosha	Active, Strike-Slip	235	22
Damghan	Active and Relative	83	224	F18 = Ememzadeh Davood	Active, Strike-Slip	11	14
Astaneh	Active Fault	66	244	Meyamey	Quaternary Fault	137	316
F4 = Amiran	Quaternary Fault	53	314	F1 = Abr	Active, Relative Fault	38	324
Semnan	Quaternary, Thrust and Reverse	26	221	Shavar	Active, Thrust and Reverse	42	285
F6 = Attari	Quaternary Fault	60	224	Kushke Nosrat	Quaternary Fault	127	91
F3 = Ramishan-Sabzevar	Quaternary Fault	57	418	Atary	Quaternary Fault	165	134
Jagatai	Quaternary Fault	64	446	F20 = Taleghan-Kahar	Active, Thrust and Reverse Fault	78	29

and

Table 2. Historical earthquakes in the study area. M = Magnitude, q = The quality of determining the location of the center of the earthquake, i0 = The intensity of the earthquake in the center, r = Radius of perceptibility, r′ = Epicenter distance, Ref. = Reference, A = Ambraseys and Melville, 1982, B = Berberian and Yeats, 1999.

No.	Date	Lat.	Long.	M	q	i0	r	r′	Ref.
1	c.1.8 Ma	36.11	50.78	>7	c	>IX	-	-	B
2	c. 38,500–10,000 Bp	35.82	52.11	>6.5	c	>VIII	-	-	B
3	c. 4500 Bp	36.7	49.98	>6.5	c	>VIII	-	-	B
4	c. 4000–3000 Bp	35.6	49.9	-	-	-	-	-	A
5	c. 4000–3350 Bp	34.45	47.92	-	b	-	-	-	B
6	c. 2400–2300 Bp	35.5	51.8	7.6	-	1	-	-	A
7	c. 4th cent.	35.5	51.8	7.6	-	1	-	-	A
8	743	35.3	52.2	7.2	c	2	30	-	A
9	855	35.6	51.5	7.1	b	2	-	540	A
10	January 864	35.7	51	5.3	c	3	-	-	A
12	23 February 958	36	51.1	7.7	b	1	50	700	A
13	27 April 1008	34.6	47.4	7	c	1+	-	-	A
14	1052	36.6	50.3	6.8	b	>VII+	-	400	B
15	10 December 1119	35.7	49.9	6.5	c	2	-	-	A
16	May 1177	35.92	50.83	7.2	c	-	-	650	B
17	15 October 1485	36.7	50.5	7.2	a	2	28	650	A
18	3 July 1486	36.43	50.45	-	c	-	-	-	B
19	20 April 1608	36.4	50.5	7.6	b	1	26	600	A
20	1665	35.75	52.08	6.5	c	2	-	-	B
21	1687	36.3	52.6	6.5	e	2	-	-	A
22	July 1721	35.68	50.2	-	d	-	-	-	B
23	1805	36.2	52.4	-	c	2	-	100	A
24	26 June 1808	35.3	54.5	6.6	b	2	-	320	A
25	9 October 1808	36.2	52.4	-	d	5	-	-	A
26	16 December 1808	36.4	50.3	5.9	b	-	-	200	A
27	1809	36.3	52.5	6.5	b	2	15	290	A
28	June 1815	35.9	52.2	-	d	4	30	-	A
29	1825	36.1	52.6	6.7	b	2	24	360	A
30	27 March 1830	35.7	52.5	7.1	b	2	37	570	A
31	6 April 1830	35.73	52.6	5.3	b	3	-	-	B
32	1 November 1854	-	-	-	-	VI	-	-	B
33	18 April 1857	-	-	-	-	VI	-	-	B
34	1868	34.9	52.5	6.4	c	-	-	300	A
35	20 October 1876	35.8	49.8	5.7	b	2	19	150	A

provide information on instrumental and historical earthquakes in the study area. The region has experienced several significant instrumental earthquakes, such as the 1935 Mw 6.8 Kusut, 1953 Mw 6.5 Troud, 1957 Mw 7 Sangchal, 1962 Mw 7.2 Buin-Zahra, 1980 Mw 6.6 Shirabad, 1990 Mw 7.3 Rudbar, 2002 Mw 6.5 Avaj, and 2004 Mw 6.4 Baladeh earthquakes, resulting in considerable economic and human losses, as reported by [23,25,26,27].

The historical sites in the immediate southern foothills of the Central Alborz, particularly around Tehran, have been devastated multiple times by historical earthquakes, as noted by [23,26]. The Eivanaki, North Tehran, and Rey faults have been identified as sources of historical earthquakes, occurring in 1384 AD, 1177 (Ms 7.2), 855 (Ms 7.1), 743 (Ms 7.2), and 312–280 BC (Ms 7.6), as reported by [23,26]. Thus, considering the current population of approximately 13 million, Tehran may face significant seismic hazards.

3. Results and Discussion

The Gutenberg–Richter [28] method is a widely used mathematical approach for describing the seismicity of a region. This method involves investigating the seismic state of the region and defining the magnitude–frequency relationship of earthquake events. The constant coefficients in this equation provide insights into the different levels of seismicity in the area. The equation for the Gutenberg–Richter method is represented as:

Log Nc = a − bMs

(1)

where Nc represents the cumulative frequency of earthquakes, a and b are constant coefficients (with a denoting the number of earthquakes and b denoting the relative frequency of earthquakes with different magnitudes), and Ms indicates the magnitude of the earthquakes. For this study, earthquakes with a magnitude of Ms ≥ 3 that occurred over 120 years (from 1900 to 2020) in the Alborz mountain range were selected. By plotting the graph of Log N − Ms, the seismic parameters of the region (a and b) were obtained (Figure 4). According to the seismic formula obtained for the region (Figure 4), the values of the seismic parameters were determined as a = 1.832508913 and b = 0.6918.

The earthquake return period formula can be used to calculate the time of occurrence of two similar events. The average time interval between a given event and a more significant event or equivalent is called the return period (T), which is calculated from the following relation [29]:

T = 1/N

(2)

where N is the number of earthquakes of equal or greater magnitude than the one of interest that occurred during the time period of interest. According to Equation (1), the average return period for earthquakes in the Alborz region can be calculated using the following Equation (3):

T = 10^(−a + bM)

(3)

where M is the magnitude of the earthquake. The return period of earthquakes in the Alborz region is calculated and presented in

Table 3. Estimates of the earthquake return period (T) with different magnitudes (Ms) in the region (based on [30]). N represents the cumulative frequency of earthquakes, while a and b are constant coefficients.

a	b	Ms	log N	N	T (Year)
1.832508913	0.6918	3	−0.255856	0.55481	1.8
		3.2	−0.394216	0.403445	2.4
		3.4	−0.532576	0.293376	3.4
		3.6	−0.670936	0.213336	4.6
		3.8	−0.809296	0.155133	6.4
		4	−0.947656	0.112809	8.8
		4.4	−1.224376	0.059652	16.7
		4.6	−1.362736	0.043377	23.0
		4.8	−1.501096	0.031543	31.7
		5	−1.639456	0.022937	43.5
		5.2	−1.777816	0.01668	59.9
		5.4	−1.916176	0.012129	82.4
		5.6	−2.054536	0.00882	113.3
		5.8	−2.192896	0.006414	155.9
		6	−2.331256	0.004664	214.4
		6.2	−2.469616	0.003391	294.8
		6.4	−2.607976	0.002466	405.4
		6.6	−2.746336	0.001793	557.6
		6.8	−2.884696	0.001304	766.8
		7.2	−3.161416	0.00069	1450.1
		7.4	−3.299776	0.000501	1994.2
		7.6	−3.438136	0.000365	2742.4
		7.7	−3.507316	0.000311	3216.0

.

Horizontal ground acceleration rates are typically chosen based on two possible boundaries: 10% and 64% [31]. The limit of 10% represents the maximum credible earthquake (MCE), which is the highest magnitude earthquake that can be expected to occur within the next 50 years, with a probability of 10% or less. The limit of 64% represents the design basis earthquake (DBE), which is the earthquake that can be expected to occur within the next 50 years with a probability of 64%. These parameters can be calculated using the relations proposed by Trifunac and Brady [32]. The equation used to calculate the probability of exceedance for a given return period (Rp) is:

Rp = 1 − exp(−T × 10^(a − bMs))

(4)

where T is the return period in years, Ms is the earthquake magnitude, and a and b are the coefficients obtained from the Gutenberg–Richter relation.

Therefore, the equation used to calculate the DBE is:

0.64 = 1 − exp(−T × 10^(a − bMs))

(5)

and the equation used to calculate the MCE is:

0.1 = 1 − exp(−T × 10^(a − bMs))

(6)

For the region, the DBE and MCE were calculated to have a useful life of 10 to 100 years (

Table 4. Estimates of DBE and MCE for a useful life of 10 to 230 years.

a	b	MS	Earthquake Return Period	Useful Life (T)	DBE (R = 64%)	MCE (R = 90%)
1.832509	0/6918	3	1.8	10	4.08	5.51
		3.2	2.4	20	4.52	5.94
		3.4	3.4	30	4.77	6.2
		3.6	4.6	40	4.95	6.38
		3.8	6.4	50	5.09	6.52
		4	8.8	60	5.21	6.63
		4.4	16.7	70	5.3	6.73
		4.6	23.0	80	5.39	6.81
		4.8	31.7	90	5.46	6.89
		5	43.5	100	5.53	6.95
		5.2	59.9	110	5.59	7.01
		5.4	82.4	120	5.64	7.07
		5.6	113.3	130	5.69	7.12
		5.8	155.9	140	5.74	7.16
		6	214.4	150	5.78	7.21
		6.2	294.8	160	5.82	7.25
		6.4	405.4	170	5.86	7.29
		6.6	557.6	180	5.9	7.32
		6.8	766.8	190	5.93	7.36
		7.2	1450.1	200	5.96	7.39
		7.4	1994.2	210	5.99	7.42
		7.6	2742.4	220	6.02	7.45
		7.7	3216.0	230	6.05	7.48

).

The ground motion parameters, such as velocity, acceleration, and displacement in the vertical and horizontal directions at the earthquake epicenter, were estimated using the formulas proposed by [31]. Additionally, various formulas, including some from [30,32,33,34], were used to calculate the relationship between fault length (L) and earthquake magnitude (Ms) in the study area. These formulas were employed to estimate the seismic potential of the faults, and the calculations are presented in

Table 5. Surface rupture length (SRL) in meters, rupture width (WR) in meters, and rupture area (AR) in square meters of each earthquake by the fault activities. Ms (Av) is the mean magnitude.

Fault Name	Ms (Av)	SRL lr	WR	AR	Fault Name	Ms (Av)	SRL lr	WR	AR
Sangavar	7.24	0.204	0.564	0.267	Jagatai	7.02	0.194	0.554	0.257
Masuleh	7.33	0.208	0.568	0.272	F2	7.56	0.218	0.578	0.282
F33	5.91	0.143	0.496	0.199	Jajarm	7.14	0.2	0.56	0.262
Talesh	7.86	0.231	0.59	0.296	F36	7.31	0.207	0.567	0.27
F33	6.58	0.174	0.533	0.234	Rabat Garbil	7.41	0.212	0.572	0.276
Rudbar	6.7	0.179	0.538	0.24	Sfarayen	6.75	0.182	0.541	0.243
F32	6.77	0.183	0.542	0.244	Sabzevar	5.69	0.132	0.482	0.186
Lahijan	6.77	0.182	0.542	0.244	Doruneh1	6.6	0.175	0.534	0.235
F31	6.86	0.187	0.546	0.248	Doruneh2	6.74	0.181	0.541	0.242
North Rudbar	7.36	0.209	0.57	0.273	Torud	7.23	0.203	0.564	0.267
Bonan	7.2	0.202	0.562	0.265	F8	6.5	0.17	0.529	0.23
Alamutrud	7.47	0.214	0.574	0.278	F9	7.02	0.194	0.554	0.257
F21	6.34	0.163	0.52	0.222	F10	6.7	0.179	0.539	0.24
F22	6.78	0.183	0.543	0.244	F11	7.14	0.199	0.56	0.262
F23	5.95	0.144	0.498	0.201	Ghachab	6.75	0.182	0.541	0.243
F24	6.36	0.163	0.521	0.222	Pishva	6.74	0.181	0.541	0.242
North Ghazvin	7.03	0.194	0.554	0.257	Garmsar	7.14	0.2	0.56	0.262
Zanjan	7.32	0.208	0.568	0.271	Eyvanaki	7.32	0.208	0.568	0.271
F35	6.17	0.155	0.511	0.212	Kahrizak	6.84	0.186	0.546	0.247
F34	6.47	0.169	0.527	0.228	South Tehran	6.44	0.167	0.525	0.227
Soltanieh	7.4	0.211	0.571	0.275	Siah Kuh	6.8	0.184	0.544	0.245
F25	5.71	0.133	0.484	0.188	F27	6.76	0.182	0.542	0.243
Kandovan	7.18	0.201	0.561	0.264	Parandak	6.77	0.183	0.542	0.244
F19	7.2	0.202	0.562	0.265	F28	6.85	0.186	0.546	0.248
F14	6.03	0.148	0.503	0.205	F29	5.83	0.139	0.491	0.194
F15	6.01	0.147	0.502	0.204	Kushk-e Nosrat	7.4	0.211	0.571	0.275
F16	6.19	0.156	0.512	0.214	F29	6.59	0.174	0.533	0.235
F17	6.01	0.147	0.502	0.204	F30	6.89	0.188	0.548	0.25
North Tehran	7.69	0.224	0.583	0.288	Indes	6.55	0.173	0.531	0.233
Taleghan	6.99	0.192	0.552	0.255	South Parandak	7.34	0.208	0.569	0.272
North Alborz	8.23	0.247	0.604	0.313	North Parandak	7.19	0.201	0.562	0.265
Gorgan	7.2	0.202	0.562	0.265	Eshtehard	7.12	0.199	0.559	0.262
Khazar	7.99	0.237	0.595	0.303	Ipak	6.98	0.192	0.552	0.254
F13	7.2	0.202	0.562	0.265	F12	6.85	0.186	0.546	0.248
F7	7.32	0.207	0.567	0.271	F26	6.04	0.149	0.503	0.205
F5	7.64	0.222	0.581	0.286	Bozgush	7.11	0.198	0.558	0.261
Damghan	7.19	0.202	0.562	0.265	Mosha	7.82	0.229	0.588	0.294
Astaneh	7.05	0.196	0.556	0.258	F18	5.96	0.145	0.499	0.201
F4	6.98	0.192	0.552	0.254	Meyamey	7.48	0.214	0.575	0.279
Semnan	6.58	0.174	0.533	0.234	F1	6.73	0.181	0.54	0.242
F6	7	0.193	0.553	0.255	Shavar	6.77	0.182	0.542	0.244
F3	6.97	0.192	0.552	0.254	Kushk-e Nosrat North	7.44	0.213	0.573	0.277
Atary	7.61	0.22	0.58	0.285	F20	7.21	0.203	0.563	0.266

.

Donovan [34] studied 670 acceleration maps from various countries, including 100 from Japanese earthquakes and 210 from California. From this analysis, he proposed Equation (7) to calculate the maximum acceleration of gravity:

Y = 1.320 exp(0.58 Mb)/(R + 25)^1.52

(7)

Additionally, Campbell [35] provided Equation (8) for shallow earthquakes with magnitudes ranging from 5 to 7.7 and distances of less than 50 km between the earthquake source and the site, considering solid rock or alluvial sediments:

Y = 0.0159 exp(0.868 M) [R + 0.0606 exp(0.7 M)]^−1.09

(8)

Equations (7) and (8) were used to calculate the maximum horizontal ground acceleration due to gravity in the study area, and the results are presented in

Table 6. The maximum ground acceleration (PGA) of each fault in the area. DT = Distance to Tehran.

Fault Name	Fault Length (km)	DT (km)	Ms (Av)	PGA (Av)	Fault Name	Fault Length (km)	DT (km)	Ms (Av)	PGA (Av)
Sangavar	81	359/2	7/2	0/0132	F2	152	365/9	7/6	0/0133
Masuleh	105	252/7	7/3	0/0204	Jajarm	78	434/5	7/1	0/0104
F33	10	251/7	5/9	0/0246	Sfarayen	40	511/8	6/7	0/0086
Talesh	250	250/7	7/9	0/0222	Sabzevar	7	497/9	5/7	0/0110
F33	30	219/4	6/6	0/0253	Doruneh1	31	481/1	6/6	0/0094
Rudbar	37	178/3	6/7	0/0321	Doruneh2	35	476/5	6/7	0/0094
F32	42	190/4	6/8	0/0293	Torud	80	240/6	7/2	0/0215
Lahijan	42	217/3	6/8	0/0249	F8	23	279/6	6/5	0/0189
F31	45	195/7	6/9	0/0281	F9	64	276/8	7/0	0/0182
North Rudbar	100	161/8	7/4	0/0348	F10	33	348/1	6/7	0/0140
Bonan	76	111/8	7/2	0/0535	F11	69	336/3	7/1	0/0143
Alamutrud	133	77/9	7/5	0/0800	Ghachab	40	158/3	6/7	0/0368
F21	19	118/5	6/3	0/0556	Pishva	35	50/2	6/7	0/1326
F22	37	84/9	6/8	0/0756	Garmsar	70	64/9	7/1	0/0978
F23	10	105/0	5/9	0/0702	Eyvanaki	94	8/9	7/3	0/4400
F24	21	111/2	6/4	0/0597	Kahrizak	42	21/0	6/8	0/2789
North Ghazvin	64	128/7	7/0	0/0458	South Tehran	21	14/0	6/4	0/3863
Zanjan	104	195/7	7/3	0/0277	Siah Kuh	38	62/0	6/8	0/1059
F35	15	192/5	6/2	0/0322	F27	41	147/4	6/8	0/0400
F34	25	170/2	6/5	0/0352	Parandak	42	111/0	6/8	0/0557
Soltanieh	116	215/9	7/4	0/0247	F28	46	189/7	6/8	0/0292
F25	6	111/2	5/7	0/0701	F29	7	185/3	5/8	0/0368
Kandovan	81	50/6	7/2	0/1261	Kushk-e Nosrat	116	104/6	7/4	0/0577
F19	76	74/4	7/2	0/0843	F29	31	151/3	6/6	0/0397
F14	12	7/3	6/0	0/5723	F30	49	176/1	6/9	0/0318
F15	12	12/1	6/0	0/4561	Indes	27	150/2	6/6	0/0403
F16	16	14/7	6/2	0/3927	South Parandak	107	78/0	7/3	0/0798
F17	12	8/6	6/0	0/5364	North Parandak	74	95/6	7/2	0/0639
North Tehran	176	11/2	7/7	0/3878	Eshtehard	67	50/2	7/1	0/1274
Taleghan	59	51/9	7/0	0/1247	Ipak	52	75/9	7/0	0/0837
North Alborz	463	87/2	8/2	0/0785	F12	43	443/9	6/9	0/0102
Gorgan	85	268/1	7/2	0/0189	F26	10	131/1	6/0	0/0529
Khazar	314	99/2	8/0	0/0652	Bozgush	73	398/2	7/1	0/0116
F13	85	94/8	7/2	0/0645	Mosha	235	22/4	7/8	0/2535
F7	102	237/2	7/3	0/0220	F18	11	13/8	6/0	0/4275
F5	176	139/3	7/6	0/0423	Meyamey	136	316/0	7/5	0/0157
Damghan	83	224/4	7/2	0/0234	F1	38	324/1	6/7	0/0153
Astaneh	66	243/7	7/1	0/0212	Shavar	42	284/6	6/8	0/0179
F4	53	314/2	7/0	0/0156	Kushk-e Nosrat North	127	91/4	7/4	0/0672
Semnan	26	220/9	6/6	0/0251	Atary	165	134/1	7/6	0/0440
F6	60	223/6	7/0	0/0236	F20	78	29/2	7/2	0/2083
F3	57	418/3	7/0	0/0109	Jagatai	64	445/7	7/0	0/0101

. A network of 1565 points in the study area was analyzed to generate the seismic hazard map. Fault lengths were calculated using the X-Tools lateral extension in the ArcGIS software 10.6, and the distances between each fault and the center of each point were determined using the ArcView software. The PGA values were then interpolated and mapped to the PGA points, as shown in Figure 5. The Qasr-e Firuzeh and Sorhk-e Hear fault systems (F14), located approximately 7.5 km southeast of Tehran, were found to have a seismic magnitude of 6.3 Richter and a gravity acceleration of 0.55723 g.

As per Zolfaghari’s research [36], higher seismic slip rates have been observed on the western side of the Central Alborz and the west side of the Eastern Alborz depicted. This suggests that the probability of a large earthquake occurring in these regions with high slip rates is higher than in other areas. This observation aligns with the seismic hazard map generated in the current study (Figure 5). Additionally, considering the seismic and geodetic strain, as well as the moment rates from the research [14], it is evident that the Central Alborz region, where major faults such as the North Alborz fault exist, poses a significant seismic hazard.

On the one hand, the comparison of the amount and the stress vectors of the dynamic fault structures of the Central Alborz shows a drop in the stress rate and a sudden loss of nearly 1 MM/y from the slip rate seen on eastern faults such as the Astana fault [37]. Firouzkoh fault [38], and Mosha fault [39] compared to the Taleghan fault [40] and North Tehran fault [41] on the western side. Considering that deformation and stress were previously estimated from geodetic measurements [42,43] in the Central Alborz area, unlike Zagros, it is considered to have more seismic nature, so it is possible that 1 mm of missing shear stress is accumulating in the central part of the Mosha fault or the eastern part of the fault zone north of Tehran; in other words, this part of the Mosha fault could be a single fault. It can be considered locked with a relatively high probability of seismic failure in the future evolution of its tectonic earthquake [44]. Also, according to the results of this research, which estimates the risks of the eastern faults of Tehran to be higher, it seems that the studies of [38,44,45,46] also confirm the same opinion. This study argues that the Sorkh-e Hesar and Ghasr-e Firuzeh fault systems include a system that has not been introduced and show that we need to focus on the Mosha–Parchin system in studies, so according to the results of this study, the shown stress accumulation in this fault system can be attributed to the fault locking of this system northeast, east, and southeast of Tehran and the high seismic potential in this fault that ought to be the focus of studies.

To calculate the geological moment rate, several parameters including fault length, fault dip, fault slip rate, and thickness of the seismic layer in the region are required. Assuming a constant seismic layer thickness throughout the seismotectonic zone, the seismic moment rate can be obtained using Equation (9) [47]:

M = µ ∑ (Li.Hs.Si)/|Cos δı|

(9)

where µ is the shear coefficient (with a value of 3 × 10^10 N/m²), Li is the fault length, Si is the fault slip rate, δı is the fault dip, and Hs is the seismic thickness. In this study, considering the depth of the Alborz earthquakes, a seismic layer thickness of 18 km was assumed, and the absolute value of the cosine function was used to ensure that the calculation is positive. Consequently, the geological moment for each main fault (

Table 7. Geological moments of major faults in the region categorized by fault type: T = Thrust, SS = Strike-slip, N = Normal, SS-T = Strike-slip with Thrust, T-SS = Thrust with Strike-slip, RS = Reverse-Slip, T-RS = Thrust with Reverse-Slip.

Fault Name	Fault Length (KM)	Mechanism	Dip	cos (Dip)	Vertical Movement (mm/y)	Horizontal Movement (mm/y)	Average Geological Moment
Khazar	550	T	35	−0.904	2.5	3.05	1.00239 × 1018
North Alborz	350	T	50	0.965	1	1.5	2.93793 × 1017
Kashachal	190	SS	80	−0.110	1	1	9.29455 × 1017
Kandovan	85	SS	50	0.965	1	1	4.75664 × 1016
Taleqan	90	N	55	0.022		1.3	2.85537 × 1018
Mosha-S	50	SS	70	0.633	2.3	2.3	9.80548 × 1016
Apic	95	T	45	0.525	1	1.4	1.36716 × 1017
North Tehran	125	T	45	0.525	0.7–1.0	1.4	1.7989 × 1017
Mosha	70	SS	70	0.633	2.3	2.3	1.37277 × 1017
Firuz Kuh	45	SS	70	0.633		2.3	8.82493 × 1016
Chashm	35	SS-T	70	0.633		2.3	6.86384 × 1016
Astaneh	60	SS	90	−0.448	2.3	2.3	1.66312 × 1017
Shahrud	100	SS-T	45	0.525	1.3–2.3	3.2	3.28941 × 1017
Bastam	110	SS-T	45	0.525	1.0–4.0	1.4	1.58303 × 1017
Maraveh Tappeh	250	T	45	0.525	1	1.4	3.59779 × 1017
Takal Kuh	125	T	45	0.525	1.5	2.1	2.69835 × 1017
Kurkhud	135	SS-T	70	0.633	0.75	1	1.15108 × 1017
Shoqa	150	SS-T	70	0.633	1	1.5	1.91846 × 1017
Jajarm	120	SS-T	80	−0.110	0.75	1	5.87024 × 1017
Eshqabad	230	SS	80	−0.110	5.0–8.0	5	5.62565 × 1018
C. Eshkabad	80	T-SS	70	0.633	2	5	3.4106 × 1017
N. Kopehdagh	315	T	45	0.525	1	1.4	4.53322 × 1017
Baghan-Garmab	155	RS	90	−0.448	4	4	7.47199 × 1017
Shirvan	90	RS	90	−0.448	2	2	2.16929 × 1017
Naveh	90	RS	90	−0.448	1	1	1.08464 × 1017
Gareh Dagh-Khademan	130	RS	90	−0.448	1.3	1.3	2.03672 × 1017
Kashafrud	165	RS-T	80	−0.110	1	1	8.07158 × 1017
Amrudak	150	RS	90	−0.448	1.4	1.4	2.53083 × 1017
Eshtehard	190	T	50	0.965	1	1.5	1.59487 × 1017
Kushk-e Nosrat	250	T	45	0.525	1	1.4	3.59779 × 1017
Indes	145	T	45	0.525	1	1.4	2.08672 × 1017
Qom	140	T-RS	45	0.525	1	1.4	2.01476 × 1017
Robatkarim-Siahkuh	180	T-RS	60	−0.952	1	1.5	1.53085 × 1017
Kahrizak-Garmasar	190	T	45	0.525	1	1.4	2.73432 × 1017
N. Semnan-Atari	90	SS-T	80	−0.110	1	1	4.40268 × 1017
Torud	50	SS	80	−0.110	0.5	0.5	1.22297 × 1017
Dochah	65	SS	90	−0.448	0.5	0.5	3.91677 × 1016
Mayamey	175	SS	80	−0.110	2.5	2.5	2.14019 × 1018
N-Sabzevar	130	T	45	0.525	2.5	3.5	4.67713 × 1017
Samghan	130	SS-T	90	−0.448	0.5	0.5	7.83353 × 1016
Rivand	150	T	45	0.525	0.5	0.7	1.07934 × 1017
Esfarayen	125	T	45	0.525	0.6	0.8	1.02794 × 1017
Doruneh	700	SS	85	−0.984	1.5–2.5	2.5	9.59998 × 1017

) and the average geological moment for the region (~5.18218 × 10¹⁷ Nm/y) were calculated. Based on the calculations, the Eshkabad, Taleqan, and Mayamey faults exhibit the highest geological moment rates (Table 7; Figure 6).

4. Conclusions

In conclusion, our study reveals that northern Iran, particularly the Central Alborz, is a highly active region in terms of seismicity. Our findings highlight the high risk of significant earthquakes in Tehran, Alborz, and Qazvin, given the long recurrence period of earthquakes with magnitudes greater than 6. Therefore, cities in high-risk areas, specifically the western side of the Central Alborz and the western side of the Eastern Alborz, are at the highest seismic risk due to their proximity to fault zones.

The seismic hazard map generated in this study provides valuable information to mitigate the potential damage caused by future earthquakes. The estimated maximum horizontal acceleration for Tehran due to the Qasr-e Firuzeh and Sorhk-e Hesar fault systems is 0.5757, with a seismic potential of 6.3 Richter. These findings have significant implications for the region’s urban planning, building design, and emergency response strategies.

Furthermore, the geological moment rates, encompassing both seismic and aseismic deformations, provide insight into the potential of faults to release the stored elastic energy in the crustal rocks of the region. Our study identified the Eshqabad, Taleqan, and Mayamey faults as exhibiting the region’s highest geological moment rates. These findings can aid in understanding the potential for future earthquakes and inform seismic hazard assessments in the area.

In summary, our study highlights the need for continued monitoring and evaluation of seismic hazards in northern Iran to improve earthquake preparedness and mitigate potential damage to infrastructure and communities in the region.