Estimation quality factor of Coda wave in the northeast of Iran



 Seismic waves when crossing the Earth in heterogeneous and anisotropic environments, having interaction. Recognizing the impact of these factors on the seismograms help us to find out more information about interior of the Earth. Coda waves are the main reason for the random heterogeneities in earth. Local earthquakes in the northeast region of Iran with epicentral distance less than 200 km is used with magnitude range of 2 - 6 recorded in period 2006 to 2013. Finally, data for five stations which have  (15441 earthquakes) were chosen. In this study, the attenuation parameters, Q, were estimated using the single scattering models. Aki and Chouet (1975) proposed a single backscattering model to explain the coda waves as a superposition of secondary waves from randomly distributed heterogeneities. The decrease of coda wave amplitude with lapse time at a particular frequency is due to energy attenuation and geometrical spreading, and is independent of earthquake source, path effect and site amplification (Aki, 1969). Generally, the Q factor increases with frequency (Mitchell, 1981) following the relation  where Q0 is the quality factor at the reference frequency f0 (generally 1 Hz) and n is the frequency parameter, which is close to 1 and varies from region to region depending on the heterogeneity of the medium (Aki, 1980). This relation indicates that the attenuation of seismic waves with the passage of time (distance from source) is different for different frequencies. Hence, the seismic data are first bandpass-filtered to calculate the attenuation. In the present study, the attenuation of the S-coda wave (Figure 5) is calculated at seven central frequencies after getting bandpass-filtered using a Butterworth four pole filter as given in Table 1.
The amplitude of the coda wave at lapse time t seconds from the origin time for a bandpass-filtered seismogram at central frequency f is related to the attenuation parameter Q by the following equation:
Where C(f) is the coda source factor at frequency f, which is independent of time and radiation pattern, α is the geometrical spreading parameter and is equal to 1.0, 0.5 or 0.75 for body waves, surface waves or diffusive waves, respectively (Sato and Fehler, 1998), Qc(f) is the quality factor of coda waves. As coda waves are backscattered body waves, α= 1. Equation (1) can then be rewritten as:
 is determined from the slope (b) of a least-squares straight-line fit between versus t, using the relation
Shows different steps involved in the computation of Qc (f) from the RMS values of amplitude with time. According to Rautian and Khalturin (1978), the above relation is valid for lapse times greater than twice the S-wave travel time for avoiding the data of the direct S-wave. Sato (1977) introduced the source receiver offset in a single scattering model so that the coda analysis begins after the arrival of the shear wave. In the present study, the time envelope for the coda decay observation is taken at twice the time of S-wave (2ts) from the origin time of the event.
Q0 and n values indicate the average values for each station in the surroundings of the station .As an outcome, average of quality factors and frequency-dependents, is given by: 
In addition, to evaluate the variation in depth direction, we used the quality factor of 18 Coda windows from five to 90 seconds by 5 seconds step. Low values of Q0 in the initial Q-coda windows, indicating strong heterogeneity in the shallow layers of the Earth. The results in studying region have been compared with another zone in Iran (SSZ) (Figure 8).