Calculation of magnitude M1 for earthquakes in the Tehran region

Reliable determination of earthquake moment magnitude is a fundamental problem of seismic hazard assessment. Short period data does not generally extend to sufficientlylow frequencies to allow for the reliable calculation of moment tensor. In the Tehran region, the available seismic data are mostly short-period records. To resolve this difficulty, following Motazedian and Atkinson (2005), the current study uses M1 magnitude, which closely follows moment magnitude for smallto moderate events. In addition, using this special magnitude scale aids in overcoming the difficulty with the different magnitude scales in the catalogue of the Tehran region. The M1 magnitude scale is obtainedfrom the spectral amplitude at 1 Hz. The Eigene-frequency of short period seismometers is always close to 1 Hz, thus M1 can be determined using data from short-period seismometers. Assuming a Brune point-source model, M1 magnitude is equal to the moment magnitude. To calculate M1 magnitude for a given event, the Fourier power spectrum of the S-window of each observed transverse component waveform is calculated. It is then corrected for geometrical and intrinsic attenuation using the attenuation relationship of Mottaghi (2007), developed for the Tehran region, and the applied to a Butterworth filter centered on 1 Hz to calculate spectrum amplitude at 1 Hz,. Next, using a trial and error method, M1 is calculated by fitting the to the corresponding synthetic Brune spectrum amplitudes. The fit is done over a frequency band of 0.4 to 3 Hz while the band is divided to equal logarithmic bins. A shear velocity of 3.73 km/s has been assumed to calculate the synthetic Brune spectrum, along with an average density of g/cm3 and a stress drop of 10 MPa. The fit is strongly sensitive to 0.1 magnitude unit fluctuations. Magnitude of an event is defined by the average of the calculated values of M1 over all stations that recorded the event. Since 1995, the seismicity of the Tehran region has been monitored by Iran Telemetered Seismograph Network (ITSN), a series of small regional subnetworks operated by the Institute of Geophysics, University of Tehran. A review of the operation of the Tehran subnetwork of the ITSN has been provided by Ghods and Sobouti (2005). The data used in this study are1804 records of 179 earthquakes having magnitudes larger than 3 and occurring in the period of 1996-2004. To ensure reasonable location accuracy and lower sensitivity on radiation pattern, the selected events have an azimuthal gap lower than 250 degree. The events were selected to provide relatively homogenous ray coverage inside the study area [Figure 1]. The selected records have hypocentral distribution in the range of 10 to 440 km with rather dense coverage of hypocentral distance of 350 km (Figure 2) The result of this study is a catalogue of 179 events with magnitude M1 greater than 3 which occurred in the Tehran region. Variations of M1 residues versus epicentral distance show insignificant dependency with distance [Figure 5], implying that the attenuation relationship used in this study (Motaghi, 2007) is appropriate for the Tehran region. A comparison of calculated M1 catalog with the corresponding ML catalog (Figure 4) shows a systematic difference between these two scales following a relationshipof. The fit is computed using Least Absolute Residual algorithm and has a RMS of 0.111.