In connection with conversion from energy class KR (KR = log10E R, where ER — seismic energy, J) to the universal magnitude estimation of the Tien Shan crustal earthquakes the development of the self-coordinated correlation of the magnitudes (mb , ML, Ms ) and KR with the seismic moment M0 as the base scale became necessary. To this purpose, the first attempt to develop functional correlations in the magnitude—seismic moment system subject to the previous studies has been done. It is assumed that in the expression M (mb , ML , Ms) = Ki + zi log10M0 , the coefficients ki and zi are controlled by the parameters of ratio (where ; f0 —corner frequency, Brune, 1970, 1971; M0, N×m). According to the new theoretical predictions common functional correlation of the advanced magnitudes Mm (mbm = mb , MLm = ML , MSm = MS ) from log10M0, log10t0 and the elastic properties (Ci) can be presented as , where , and , for the averaged elastic properties of the Earth’s crust for thembmthe coefficients Ci= –11.30 and di = 1.0, for MLm: Ci = –14.12, di = 7/6; for MSm : Ci = –16.95 and di = 4/3. For theTien Shan earthquakes (1960-2012 years) it was obtained that , and on the basis of the above expressions we received that MSm = 1.59mbm – 3.06. According to the instrumental data the correlation Ms = 1.57mb – 3.05 was determined. Some other examples of comparison of the calculated and observed magnitude - seismic moment ratios for earthquakes of California, the Kuril Islands, Japan, Sumatra and South America are presented.
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