1. 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 strike- normal direction, which is called forward directivity (Douglas et al., 1988). Forward directivity occurs when:

1Rupture front propagates toward the site.

2Slipping 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 (, 2006, M_w6.1) 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.

Table 1. Previous study about the directivity effect

2. Silakhor Earthquake (, 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) obtained the same result by linear inversion of moment tensor in time domain.

Dorood fault is known as the most important seismic segment of Main Zagros Recent Fault, which is defined as 2006 Silakhor earthquake seismic source. However the fault with strike of 313and 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.

Table 2. Silahkor earthquake reported by agencies

Table 3. Feature of recording stations (Mirzaei Alavijeh et al, 2006)

Figure 2. Dorood region faults, epicenter and focal mechanism (NEIC) 2006 Silakhor earthquake (Mirzaei Alavijeh et al, 2006)

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.

Figure 3. Recorded accelerograph at Dorood and Kushk-e-Ab-e-Sard stations (Behzadafshar, 2008)

Figure 4. Rotation in to fault normal (SN) and fault parallel (SP) component (Kenneth and South, 2002)

3. 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):

(1)

Where; SP = fault strike parallel component, SN = fault strike normal component,= fault strike and is azimuthally angle of accelerograph installment.

4. 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.

(2)

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.

(3)

Figure 5. Maximum ratio of Vn/Vp for Dorood fault, by directivity angle (2006 Silakhor earthquake)

5. 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

Figure 6. Maximum ratio of Vn/V for Dorood fault, by directivity angle (2006 Silakhor earthquake)

6. 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:

(4)

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.

Figure 7. Directivity parameters for strike slip faulting (Somervill et al, 1997)

7. 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.

(5)

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.

Figure 8. Maximum of Vn/Vp ratio, by directivity angle for Silakhor earthquake and it’s modeling.

Figure 9. Maximum of Vn/V ratio, by directivity angle for Silakhor earthquake and it’s modeling.

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.

(6)

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. 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 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.

(7)

Figure 10. Radiation pattern for strike slip faulting Right: For point source (Lay and Wallace, 1995) Left: For unilateral rupturing (from south to north) (Somervill et al, 1997).

Figure 11. Maximum modeled Vn/V ratio, by.

9. 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 90directivity angle. It happens due to directivity effect, and both 2006 Silakhor earthquake and its modeling confirm these results. We apply to account distance, rupture length and directivity angle in our study. The results represents at distance less than or equal to rupture length 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.