Proposed modification on velocity attenuation relationships in West of Iran with special respect to Dorood fault

As a routine procedure, the estimation of source parameters such as focal mechanism and magnitude is known for moderate to great earthquakes, however some of them such as directivity effect and filing step are rarely taking into account. According to the radiation pattern, directivity effect is a source parameter, which causes significant spatial variations in near field strong ground motion. Its significant variations could be obtained on strike normal component of velocity in forward and backward directions. This study has an attempt on estimation of a modification factor, which can define the effect of directivity in empirical attenuation relationships in Dorood fault. In order to model unilateral and bilateral rupturing Finite Elements Method (FEM) is applied to achieve reliable functions.The authors used Somervill et al. (1997) directivity model parameter with some changes as variable parameter. To obtain modified ground motion parameters, these models were applied for earthquakes which Dorood fault caused them. These parameters consist of fault normal component to fault parallel component of velocity ratio ( Vn/Vp ) and fault normal component to average horizontal velocity ratio (Vn/V ). It shows Vn/V is controlled by directivity angle, distance between the site, epicenter and rupture length. This ratio has the same trend in studied region earthquakes velocity data.


Introduction
Earthquake caused by fault rupturing, starts from epicenter and propagates with the velocity, close to local shear wave velocity as indicated in figure1. This propagation motivates most of rupture energy arrives at the station as a peak pulse in the beginning of the records which represents the accumulated rupture energy effect. Shear wave radiation pattern produced this great pulse, aligned in the strikenormal direction, which is called forward directivity (Douglas et al., 1988). Forward directivity occurs when: 1. Rupture front propagates toward the site. 2. Slipping direction on the fault is aligned with the site. Backward directivity occurs when the rupture front propagates away from the site. It causes long duration motions with low amplitudes at long periods (Somervill et al., 1997). Some of the previous studies about this phenomenon are indicated in table (1).

Figure 1. Earthquake and effective parameters
In this study, the finite element method was performed to propose a model for Silakhor earthquake (Iran, 2006, M w 6.1) by using ANSYS software and the directivity effect on strong ground motion was evaluated. By taking into account of this fact that directivity effects are often on strike normal component, the authors were focused on the ratios of strike normal to strike parallel strong ground velocity and strike normal to average horizontal strong ground velocity, by consideration of dista pnce, rupture length and directivity angle. Therefore, a function as a directivity coefficient is defined to account in horizontal component of peak ground velocity attenuations relationships. Explained the increase of strong motion amplitude in forward and its decrease in backward direction. Haskell (1969) 1966 Park field earthquake accelerographs Obtained differences between strike normal ground motion amplitude in forward and backward directions.

Silakhor Earthquake (Iran, 2006)
This event was reported by national seismographic network and international agencies as indicate in table (2) and recorded by 15 digital accelerograms as their features illustrates in table (3).
Harvard Centroid Moment Tensor solution (CMT) determined the strike slip focal mechanism with normal component for this event. Pakzad and Mirzaei (2007)   and NW-SE trend has more than 100 km length, but just 44 km of it ruptured unilaterally from southeast to northwest during this earthquake (Pakzad and Mirzaei, 2007). Figure2 shows the regional faults, epicenter and focal mechanism of the event. By consideration of accelerograms distance to epicenter, northwest of the epicenter have larger amplitudes than those located on southwest. For instance, maximum acceleration amplitude, recorded by Dorood station (southeast of epicenter) with 31 km distance, is 0.379g, while Kushk-e-Ab-e-Sard station (northwest of epicenter) with 42 km distances, recorded 0.394g as maximum acceleration amplitude, which is present in figure3. Regarding to 2006 Silakhor focal mechanism (right strike slip), the rupture directivity is toward northwest, and therefore directivity effect causes larger acceleration amplitudes in northwest of epicenter station.

Accelerograph Correction
In this study the by use of Seismosignal the base line correction and filtering of the recorded acceleroghraphs were executed. As mentioned before, because of directivity affects on fault normal components, the recorded accelerographs should be rotated into normal and parallel direction of Dorood fault strike. By refer to figure4; equation (1) is used for rotation into normal and parallel fault strike directions (Kenneth and South, 2002):

Earthquake data and analysis
The variation of maximum V n /V p ratio on base of directivity angle (θ), which represents radiation pattern, is presented in figure5. This ratio increases in both forward and backward directions; however, it is larger in forward direction and equation (2) has obtained from trend line of this figure. It shows the relation between 2006 Silakhor event V n /V p ratio by directivity angle.
Variation of V n /V ratio on base of θ is shown in figure 6. It indicates that the ratio increases in both forward and backward directions. Equation (3) pointed the variation of V n /V ratio by directivity angle from Silakhor.

Directivity Modeling by Finite Element Method (FEM)
Simulation of rupture directivity by FEM is applied to define the directivity coefficient, which should be accounted in velocity attenuation relationships. At the first step and by the suggested Aagaard et al (2004) algorithm, the earthquake was modeled by ANSYS. It is necessary to note the following: Modeling the rupture zone in ANSYS Exercise rupturing at modeled fault to provide strong ground motion and determination of them at same distance but different directivity angles Directivity function representation

Directivity Model Parameters
As shown in figure7, Somervill et al. (1997) identified directivity angle (θ) and X [the ratio of rupture length (s) to fault length (L)] as directivity model parameters and they chose X Cosθ as an independent parameter to evaluate directivity effect. Based on figure6, these parameters can be written as: Where, R is closest distance between site and epicenter. In the case of study on uncertain rupture length, X can be defined by L and R.

Comparison of Silakhor Earthquake and Modeled Data
Figure8 illustrates the variations of V n /V p ratio on base of θ° for silakhor and its modeled earthquake. According to shear wave radiation pattern and directivity effect, it can be seen that in forward direction, V n increases where as V p decreases, and the ratio of V n /V p is largest in forward direction (Vn/Vp=1.76). In perpendicular direction to the fault strike (θ=90°) increase of Vn and decrease of V p cause slump in V n /V p ratio (V n /V p =0.75). It can be seen the V n /V p ratio (V n /V p =1.58) from directivity angle 90° to 180°. Directivity effect provides asymmetry in S wave radiation pattern (Lay and Wallace, 1995), which is obvious in forward and backward directions. V n /V p ratio in forward is larger than backward and is shown in figure8. Equation (5) shows the variation of Vn/Vp ratio by θ which is obtained from the modeling.
These two diagrams have good correlations together. According to S wave radiation pattern, the authors expected equality of V n and V p at 45° directivity angle. It shows this equality at 50° directivity angle, which indicates accuracy in both Silakhor earthquake and modeling data analysis. By refer to figure8, V n /V p ratio soars both in forward and backward directions. Minimum value at 90° directivity angle (perpendicular to the fault strike) indicates increase of V p at 90° directivity angle, whereas V p >V n . So briefly, it can be said that the ratio of V n /V p is controlled by θ.   By refer to figure9, in forward direction; V n increase causes to reach the peak of V n /V ratio (around one). This increase is also clear in backward but it is less than forward. Minimum amount of V n /V is happened in θ=90  (V n /V=0.6), which has a good fitting condition with radiation pattern in strike slip faulting as indicated in figure10. In equation (6) the variation of V n /V by θ, is obtained for 2006 Silakhor earthquake modeling.
It can be seen, these two diagrams coincide well. In both diagrams increase of V n /V ratio in forward and backward directions and decrease of V n /V at θ= 90° signifies directivity effect on strike normal component of velocity.
Figure11 shows the variation of V n /V ratio against the 2 ( ) R L Cos θ . Equation (7) defines this variation, which is obtained from this figure. Maximum value happens for the stations in forward direction (θ=0°). At the end of the fault (R=L) the (R/L) Cos2θ will reach to one in forward direction. Equation (7) indicates that at distance R L ≤ directivity effect soars by increase of R up to the end of the fault, where R equals to L. Then at distance R>L, decrease of directivity effect due to R increasing can be seen. Therefore, equation (7) is not reliable for R>L.

Conclusions
Considering to more effect of directivity on strike normal component, variation of maximum strike normal to strike parallel velocity ratio by directivity angle is defined. It indicates increase of V n /V p in forward and backward directions as we expect from strike slip fault radiation pattern. Directivity effect on strike-normal component causes minimum of this ratio at 90° directivity angle.
It can be seen that the increase of V n /V in forward and backward directions and decrease of this value in 90  directivity angle. It happens due to directivity effect, and both 2006 Silakhor earthquake and its modeling confirm these results. We apply θ 2 ) ( Cos L R to account distance, rupture length and directivity angle in our study. The results represents at distance less than or equal to rupture length ) ( L R ≥ the ratio soars by distance increasing. It indicates directivity phenomena, effects more by R increasing in distance of R< L. Maximum directivity effect happens at the end of the fault, where R=L. Silakhor earthquake and earthquake modeling state that it is necessary to apply equation 7 to account directivity effect in velocity attenuation relationships in near field. It is useful to achieve more reliable results in near field studies.