Simulation of the first earthquake August 11, 2012 Ahar-Varzaghan using stochastic finite fault method

On 11th of August 2012 the region was surprisingly struck by a shallow Mw 6.4 (USGS) earthquake with pure right-lateral strike-slip character only about 50 km north of the North-Tabriz Fault. An east-west striking surface rupture of about 20 km length was observed in the field by Geological Survey of Iran. Only 11 minutes later and about 6 km further NW a second shallow event with Mw 6.2 occurred. It showed an NE-SW oriented oblique thrust mechanism (HRVD). This earthquake sequence provides an opportunity to better understand the processes of active deformation and their causes in NW-Iran.
In recent years, seismologists have attempted to develop quantitative models of the earthquake rupture process with the ultimate goal of predicting strong ground motion. The choice of ground-motion model has a significant impact on hazard estimates for an active seismic zone such as the NW-Iran. Simulation procedures provide a means of including specific information about the earthquake source, the wave propagation path between the source and the site and local site response in an estimation of ground motion. Simulation procedures also provide a means of estimating the dependence of strong ground motions on variations in specific fault parameters. Several different methods for simulating strong ground motions are available in the literature. A number of possible methods that could be used to generate synthetic records include (i) deterministic methods, (ii) stochastic methods, (iii) empirical Green’s function, (iv) semi-empirical methods, (v) composite source models, and (vi) hybrid methods.
The stochastic method begins with the specification of the Fourier spectrum of ground motion as a function of magnitude and distance. The acceleration spectrum is modeled by a spectrum with a ω² shape, where ω = angular frequency (Aki, 1967; Brune, 1970; Boore 1983). Finite fault modeling has been an important tool for the prediction of ground motion near the epicenters of large earthquakes (Hartzel, 1978; Irikura, 1983; Joyner and Boore, 1986; Heaton and Hartzel, 1986; Somerville et al., 1991; Tumarkin and Archuleta, 1994; Zeng et al. 1994; Beresnev and Atkinson, 1998). One of the most useful methods to simulate ground motion for a large earthquake is based on the simulation of a number of small earthquakes as subfaults that comprise a big fault. A large fault is divided into N subfaults and each subfault is considered as a small point source (introduced by Hartzel, 1978). The ground motions contributed by each subfault can be calculated by the stochastic point-source method and then summed at the observation point, with a proper time delay, to obtain the ground motion from the entire fault. We used the dynamic corner frequency approach. In this model, the corner frequency is a function of time, and the rupture history controls the frequency content of the simulated time series of each subfault.
 In this study, we identify the source parameters of the first earthquake August 11, 2012 Ahar-Varzaghan earthquake using stochastic finite fault method (Motazedian and Atkinson, 2005). We estimated the causative rupture length and the downdip causative rupture width using the empirical relations of Wells and Coppersmith (1994), from the best defined aftershocks zone and depth distribution of these aftershocks as 15km and 10km, respectively. The simulated results compared with recorded ones on both frequency and time domain. The good agreement between the simulations and records, at both low and high frequencies, gives us confidence in our simulation model parameters for NW-Iran. The estimated strike and dip of the causative fault are 85º and 83º. The fault plane was divided into 5×5 elements. Rupture was propagated at (i,j)= (4×3) element from east  to west. The focal depth is approximately 12 km. We then obtained a spectral decay parameter (κ) from the slope of smoothed amplitude of the Fourier spectra of acceleration at higher frequencies. The best fit coefficient for the horizontal component is κ=0.0002R+0.047.
The kappa factor for the vertical component is estimated based on the same procedure and estimated κ=0.0002R+0.034. These equations represent the κ_o for horizontal component is larger than that of the vertical component. This confirms that the attenuation of higher frequencies is much less on the vertical than the horizontal component, as the vertical component is less sensitive to the variation of shear-wave velocity of near-surface deposits. The clear difference between vertical and horizontal values suggests that κ_o contains dependence on near surface site specific attenuation effects. In the absence of three-component stations, values obtained from vertical components may be helpful for a first estimate of this parameter. We also calculated residuals for each record at each frequency, where the residual is defined as log (observed PSA) - log (predicted PSA), where PSA is the horizontal component of 5% damped pseudoacceleration. We sorted simulated records according to agreement between Fourier spectrum and response spectra into two groups, A and B. The simulation using A quality agrees betther with observed records than that using B quality. The lowest residuals averaged over all frequencies are from 0.4 to 18.3 Hz for A quality and from 1.2 to 18 Hz for B quality simulated.