Stochastic Finite Fault Modeling and Simulation of Strong Ground Motion of Mosha Fault in Iran

: This study aims at predicting large earthquakes caused by Mosha fault in Tehran, the capital of Iran with population of more than 13 million people which located alongside active faults. This study uses the EXSIM program to do the finite fault modeling of simulation. Using Geopsy software and programming in MATLAB we evaluated the site effect of 13 station. Using other required parameters of Mosha fault in EXSIM, we gained the artificial strong motions of the stations. Finally, using SeismoSignal and MATLAB software, we depicted the Acceleration -time graph and the semi-logarithm frequency spectrum with “Fourier transform” of each station. we compared the results of the finite fault simulation with Ambraseys attenuation relationship, semi-logarithm frequency spectrum with Fourier transform and spectrum-response graphs of 2009 earthquake in Shahr-e Rey measuring Mw = 4.2. In both cases of comparing meaningful results were found. Finally, in order to generalize the results to the city of Tehran, we evaluated the seismicity using Arc GIS software. The results show that if Mosha fault is activated, east of Tehran is influenced the most.


INTRODUCTION
Tehran city is the center of Tehran province. In the last population and housing census, more than 13.260.000 people inhabited Tehran, which makes it the largest city in Iran (Statistical Center 2018). Tehran is increasingly growing and needs safe constructions and infrastructures. Due to the inability of the spectrum-response method, analysis and design of the structures are not capable of providing time data about behavior and response of the structure. As a result, most of Building Cod Methods have required dynamic analysis in special cases such as Irregular structures. The ultimate design of important structures such as nuclear power plants, dams, tall buildings, cable bridges, etc., are made based on the time history analysis. It is important for this type of analysis to have the ground motion of the location of the structure. The recorded ground motions are to a great extent reliant on the mechanism, structure, local conditions etc. The suitable ground motion for analyzing each structure are records which have got similar characteristics for each location. Accordingly, considering the low number of recorded and analyzed ground motion, it is difficult, sometimes impossible, to select suitable ground motion based on reality. Due to the differences in geological properties, the records of the occurred earthquakes in other places do not meet the requirements. Regarding the short history of the establishment of Iran Strong Motion Network (most of the data belongs to the last fifty years), the lack of recorded strong motions and their limitations, and the increasing use of dynamic analysis, we need a method that uses the existing ground motion and artificially generated ground motion in which spectrum response of the artificial ground motion matches the design spectrum of the location. There are many ways to produce artificial strong ground motions including random sampling method. This method is widely used in predicting strong ground motions. It is based on the fact that considering the randomness of the movements, we can combine the suggested models for the earth movements with high frequencies. In the random sampling methods, there are two kinds of stochastic point effect: in the first kind the simulation is based on stochastic point source method and in the second one the simulation is based on the finite fault method. Stochastic point source method is based on the spectrum called ω2 and corner frequency. The spectrum range from the stochastic point source method has been predicted for 0.1 to 2HZ frequencies and a magnitude of more than 4. The stochastic point method can't take into account the key parameters of a big earthquake such as the long time and directional effect. Due to these limitations, the finite fault method was introduced by Hartzell in 1978 (Hartzell 1978). It has been widely accepted in recent years. This method of simulation is suitable and it is widely used in evaluating strong ground motion. As a result, this article uses the finite fault method to simulate the strong ground motion for Mosha fault.

University of University of Mohaghegh Ardabili
ABSTRACT: This study aims at predicting large earthquakes caused by Mosha fault in Tehran, the capital of Iran with population of more than 13 million people which located alongside active faults. This study uses the EXSIM program to do the finite fault modeling of simulation. Using Geopsy software and programming in MATLAB we evaluated the site effect of 13 station. Using other required parameters of Mosha fault in EXSIM, we gained the artificial strong motions of the stations. Finally, using SeismoSignal and MATLAB software, we depicted the Acceleration -time graph and the semi-logarithm frequency spectrum with "Fourier transform" of each station. we compared the results of the finite fault simulation with Ambraseys attenuation relationship, semi-logarithm frequency spectrum with Fourier transform and spectrum-response graphs of 2009 earthquake in Shahr-e Rey measuring Mw = 4.2. In both cases of comparing meaningful results were found. Finally, in order to generalize the results to the city of Tehran, we evaluated the seismicity using Arc GIS software. The results show that if Mosha fault is activated, east of Tehran is influenced the most. Consequently, it is of high importance to study different ways to reduce the risk of the possible earthquake caused by Mosha fault.

REGION OF STUDY
Faults are the stochastic point sources of earthquakes which can be the place of the possible earthquakes in the future. Displacement of faults can influence the structures located on them. Iran is located on the Alps-Himalayas seismic belt. Many parts of the north, center, and south of Iran are influenced by big and small earthquakes. Tehran is located in the southern part of the Alborz range and has many active faults including Mosha fault, the fault of the north of Tehran, The southern-northern Rey fault. Besieged by all these faults, Tehran has the potential to experience many earthquakes. Figure 1 shows Tehran and the faults surrounding it. Mosha fault is the most dangerous source of earthquakes in Tehran. It is located in Alborz range with a length of 220km, far away from Tehran. The closest bordering distance of Mosha fault is 25km from the northern ridges of Tehran. It has many parts and will influence Tehran more than other places. According to the seismic data, this area has experienced powerful earthquakes in the past including the earthquakes in 1665 AD and 1830 AD, measuring Mw= 6.5 and Mw= 7.1 respectively, which hit at the distance of 77 and 120km away from the north of Tehran respectively. These earthquakes happened in a time period of 165 years. The 1830 earthquake caused a lot of damage to Tehran (Berberian 1994). According to the data, the possibility of a similar earthquake in near future is so high. It is clear that the possible earthquake will cause lots of damages and will stirs up high casualty to Tehran due to the large population and distressed urban areas. For this reason, we have chosen Mosha fault to be studied in this research. Mosha fault was first called Mosha-Fasham by Dellenbach (Dellenbach 1964) and Tchalenko (Tchalenko and Braud 1974) used the same name. This fault was called Meiygon-Mosha expulsion by Assereto (Assereto 1966). Since Mosha-Fasham fault lies between the two villages, we call it Mosha fault. It is an important long fault which lies between the northern and southern parts of Alborz range. It stretches from east-southeast and west-northwest directions. Mosha fault has got a sinusoidal form on the map. Its slope is always northward between 35 to 70 degrees. It is almost 220km long and stretches from the east of Mosha village to Abyek village in the west. According to the researches, its expulsion occurred before the Jurassic period (Allenbach 1966). The rupture of the middle part of Mosha fault which is the most active part of it (Tatar, Hatzfeld et al. 2012) has been considered as a rupture scenario.

FINITE FAULT MODELLING WITH DYNAMIC CORNER FREQUENCY
One of the different ways of evaluating earthquakes by the use of acceleration time series is to simulate the strong ground motion movement. Simulation of this movement plays an important role in estimating different parameters particularly for those parts for which we don't have enough data. The properties of the strong ground motion are of high importance for designing, strengthening, and improving the structures. In the finite fault method, simulation of the movements caused by small earthquakes Caused by subfaults has been suggested as a way for predicting the Near-Fault Ground Motions (Mavroeidis and Papageorgiou 2003). In this method, the recorded strong motion is the result of the combination of the earthquake source (E), path (P), the site effect (G), and instrument or type of motion (I) (Boore 2003) which is presented in the frequency realm, as: Motazedian and Atkinson have presented a suitable method to simulate earthquake strong motions in the form of the EXSIM program (Motazedian and Atkinson 2005). This method uses the random sampling method of finite fault based on the dynamic corner frequency. In order to consider the pulse-like ground motions, the mathematical model of a pulse model, Papageorgiou and Mavroeidis (Mavroeidis and Papageorgiou 2003) were used. In this method, the fault is divided into elements and a subevent is simulated for each element. Finally, in the strong motions-recording station, the general strong motions are made by adding the effects of subevents. In this method, a large fault is divided into N subfaults. Each of these subfaults is considered as a small stochastic point. Strong ground motions in each subfault is calculated using the random sampling method of the stochastic point. Then, in the desired point with a suitable time delay, they are added to calculate the Strong ground motions in the whole area.
(2) Where nw and nl are the number of subfaults along the main part of the fault. As a result, nl×nw and ( ) are the time delay of radiated wave from ijth subfault which reaches the desired point. aij (t) is the calculated amount based on the random sampling method. The Acceleration spectrum of the ith subfault is defined as: In this relation, M 0ij ,F ij , R ij are seismic moment, corner frequency and the distance of ijth subfault from the main fault respectively. C=R θ∅ F×V/4πρβ 3 in which R_(θ∅) is radiation pattern which is approximately 0.55 for shear waves. F is the amplification factor of the surface layer which is 2; V is the participation of two shear waves of SV and SH which is 0.71; ρ is density and β is the speed of the shear wave. exp(− )is a high-cut filter to model near surface kappa effects: this is the commonly observed rapid spectral decay at high frequencies (Anderson and Hough 1982). Q(f), is inversely related to anelastic attenuation. The implied 1/R geometric attenuation term is applicable for body-wave spreading in a whole space (Motazedian and Atkinson 2005).

METHODOLOGY
The required parameters for the simulation of the finite fault modeling include the geometry of the fault, the describing parameters of zonal damping, and the data related site effect.

Geometry of the fault
Using the relations provided by Wells and Coopersmith (Wells and Coppersmith 1994), the geometry of the fault is determined by the following formulas: (5) In these relations, RLD, is the subsurface rupture length and Rw, is the downdip rupture width (Wells and Coppersmith 1994). a and b are stable parameters gained empirically. Based on this, Mosha fault dimensions are 78km in length, along the rupture and its width is 23km.

Site effect
In order to evaluate the Site effect, the Nakamura method is used to eliminate the source effects (Nakamura 1989). This method is based on the modification of the transfer function of the location. In this method, the transfer function is gained by dividing the microtremor spectrum of the horizontal to the vertical parameters. Most often the ratio of the horizontal parameter spectrum to the vertical parameter in resonance frequency results in the shear wave frequency. Based on this, dividing the horizontal parameter to the vertical parameter allows the removal of stochastic-like effects of the Rayleigh wave. Nakamura method is a practical method to determine the features of the earth movements (Nakamura 1989). Based on this, we selected 13 stations as shown in figures 2.   Table 1 shows the results of the evaluation of the site effect.

ANALYSIS
We used simulation of the strong motions of possible earthquakes in Tehran using the finite fault modeling; In this study, the EXSIM program was used to Prediction of strong ground motion for the possible scenario of Tehran earthquake caused by Mosha fault. Regarding the fact that the amount of the slip distribution and asperity model on the fault were not available, we used this program to evaluate the slip distribution randomly. Other parameters of this program are shown in table 2. Considering this model's parameters, the simulation of Tehran earthquake strong ground motion was done by the finite fault method. In this study, the dimensions of the fault for the Tehran earthquake were determined to be are 78km in length, along the rupture and its width is 23km. The fault plate which causes the earthquake is supposed to be strike 281 degrees with a dip of 70 degrees. Its stress drop is 130 bars (Motazedian 2006).  (Motazedian 2006) The outputs of the EXSIM program have been depicted in the form of acceleration time series and Fourier semi logarithmic for each station     Table 3 shows the results of EXSIM outputs. In order to validate and confirm the strong ground motion of finite fault method by EXSIM program, we used two methods to compare the produced strong ground motion.

statistical comparison with Ambraseys attenuation relationship
Comparing the range of the greatest ground motion of attenuation relationship (Ambraseys, Simpson et al. 1996), table 4 shows that the simulated parameters of this research have a meaningful overlap in almost all of the stations.
To generate the strong ground motions by Ambraseys attenuation relationship method, we use the following formula; We get the amounts of the parameters of this formula from the Ambraseys table (Ambraseys, Simpson et al. 1996) to calculate the PGA of each station with Eq. (6).
= 1 + 2 + ( 3 + 4 ) × √ 2 + 5 2 + 6 + 7 + 8 + 9 + 10 (6) =soft soil sites =stiff soil sites =normal faulting earthquakes =thrust faulting earthquakes =odd faulting earthquakes   Geographical coordinates of 008 station for artificial strong ground motion for Mosha fault is very similar to the Shar-e Ray earthquake "Tehran 13" station; we compared these two with each other. These stations (Tehran 13 and 008) have similar features and different coordinates, but we considered them as one station. The 001 and 010 stations, which were tested by an artificial strong motion simulation, have exactly the same features and overlaps with Shar-e Ray earthquake stations. Table 7 shows the results. The existing difference in Tehran 13 and 008 stations are due to the fact that they don't have the exact coordinates, but the results are perfectly aligned with each other in the 001 and 010 stations. Fig 34. Comparing the real and artificial response spectrum record (left) and semi logarithm record (right) of Tehran13 (real data) and the 008 stations (artificially generated data).

CONCLUSIONS
Considering the fact that in both Ambraseys attenuation relationship and the real strong motion in the stations we had meaningful results, we can state that the generated strong motion for Mosha fault in 13 stations in Tehran were almost precise and it can be inferred that the range of the biggest PGA belongs to the 109 station in the eastern part of the Tehran which is 664.07 2 ⁄ and the lowest PGA belongs to the 012 station which is 87.198 2 ⁄ . Generally, the volume of acceleration distribution in Tehran city for Mosha fault is 87.198 2 ⁄ to 664.07 2 ⁄ . Accordingly, fundamental studies for reducing the hazardous events and the risk of the earthquakes caused by Mosha fault in Tehran, east of Tehran in particular, gives the impression to be of high importance.