Comparison of generalized inversion and Pujol’s methods in determination of local magnitude scale (ML) for Central Alborz


1 M.Sc. in Geophysics, Earth Physics Department, Institute of Geophysics, University of Tehran, Iran

2 Associate Professor, Earth Physics Department, Institute of Geophysics, University of Tehran, Iran


The idea of measuring the size of an earthquake by means of an instrumental estimation of the energy released at the focal point led Richter (1935) to the creation of the first scale of magnitude. The concept of magnitude is based on the fact that amplitudes of seismic waves depend on the energy released at the focal point after it has been corrected for their attenuation during their propagation. Distance-correction function with the assumption

*نگارنده رابط:      تلفن: 09141761984     دورنگار: 88630479-021              


that when a maximum amplitude of 1 mm is observed at a distance of 100 km, ML = 3.0; There are several different approaches to invert the empirical distance-correction functions to the local magnitude scales (e.g., Kanamori and Jennings, 1978; Hutton and Boore, 1987; Anderson, 1991). In this study we use the approach suggested by Hutton and Boore (1987). Following Hutton and Boore (1987), empirical attenuation curve can be expressed with an explicit distance-correction function. In distance-correction function n and k are parameters related to the geometrical spreading and anelastic attenuation. After rearranging distance-correction function we can be cast into a standard matrix formation that represents a typical linear inversion problem in geophysics that can be solved using least-squares, maximum likelihood, or generalized inversion methods (e.g., Aki and Richards, 1980; Menke, 1984; Lay and Wallace, 1995; Aster et al., 2005). In this study, used both generalized inversion and Pujol’s methods for inversion to determine the empirical attenuation curve in the Central Alborz region.
Amplitude variation against distance in recent inversion methods is the basic approach for determination of the magnitudes of a number of earthquakes, site-specific correction terms for each of the recording stations, and the two constants that can be obtained in one step and simultaneously, result there is a trade-off between magnitude and station corrections. It is possible to determine these parameters in two steps without trade-off. In this method, we will use the separation of parameters technique introduced by Pavlis and Booker (1983) as modified by Pujol (1988, 2000). Therefore we used two, Generalized Inversion and Pujol’s methods (Pujol, 2003) for calculating the empirical attenuation relation and local magnitude (ML) in the Central Alborz, northern of Iran.
We used a large dataset of 3886 events including 62523 waveforms which were recorded by Tehran, Semnan and Sari seismic networks during 02/03/1997 to 13/03/2011. These seismic networks comprise of 19 three component stations. We calculated synthetic W-A seismograms by removing the instrument response of each record and convolving the resulting signal with the response of the standard W-A torsion seismograph. We assumed a static magnification of 2080 for the W-A instrument (as shown by Uhrhammer and Collins 1990, the W-A instrument has a magnification of 2080 and not 2800 as often assumed). Based on Richter’s method we used amplitudes which are arithmetic means of those of horizontal components. Therefore maximum zero-to-peak amplitude was then measured on both horizontal synthetic seismograms. For a given event, the ML is independently calculated for each recording station. The values of ML from each station are averaged to give the magnitude of event, then magnitude residuals obtained from the attenuation curves of this study were plotted as a function of hypocentral distances, and the results obtained from the two methods are very similar.
Eventually, the corresponding values of geometrical spreading parameter (n) and inelastic attenuation parameter (k)are 0.9819 and 0.0028 and 0.9073 and 0.0035 respectively from Generalized Inversion and Pujol’s methods. The two methods yielded similar results. But due to the reasons mentioned the result obtained by Pujol’s method was chosen as the final result. Station corrections are related to the local ground conditions and instrument installation (Richter, 1958). A station with positive correction will yield a smaller ground-motion value than a station with a negative correction for any seismic event before the station corrections are applied. In other words, a station with a negative correction will amplify seismic waves compared to a station with a positive correction for the same event when the instrument installation conditions are the same. The station corrections resulted from this study vary between -0.378 to 0.725 suggesting that the local site effects may have a strong influence on the amplitudes.