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Control Parameters of Magnitude—Seismic Moment Correlation for the Crustal Earthquakes

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In connection with conversion from energy class *K*_{R} (*K*_{R }= log_{10}*E*_{ R}, where *E*_{R }— seismic energy, J) to the universal magnitude estimation of the Tien Shan crustal earthquakes the development of the self-coordinated correlation of the magnitudes (*m*_{b }, *M*_{L}, *Ms *) and *K*_{R} with the seismic moment *M*_{0} 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 *(*m*_{b }*, M*_{L }*, Ms )* =

*K*

_{i }+

*z*

_{i }log

_{10}

*M*

_{0 }, the coefficients

*k*

_{i}and

*z*

_{i}are controlled by the parameters of ratio (where ;

*f*

_{0 }—corner frequency, Brune, 1970, 1971;

*M*

_{0}, N×m). According to the new theoretical predictions common functional correlation of the advanced magnitudes

*M*

_{m }

*(m*

_{bm }

*= m*

_{b }

*, M*

_{Lm }

*= M*

_{L }

*, M*

_{Sm }

*= M*

_{S }) from

*log*

_{10}

*M*

_{0, }

*log*

_{10}

*t*

_{0 }and the elastic properties (

*C*

_{i}) can be presented as , where , and , for the averaged elastic properties of the Earth’s crust for thembmthe coefficients

*C*

_{i}= –11.30 and

*d*

_{i }= 1.0, for

*M*

_{Lm}:

*C*

_{i }= –14.12,

*di*= 7/6; for

*M*

_{Sm }

*: C*

_{i}= –16.95 and

*d*

_{i }= 4/3. For theTien Shan earthquakes (1960-2012 years) it was obtained that , and on the basis of the above expressions we received that

*M*

_{Sm }= 1.59

*m*

_{bm }– 3.06. According to the instrumental data the correlation

*M*

_{s }= 1.57

*m*

_{b }– 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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*Open Journal of Earthquake Research*, Vol. 2 No. 3, 2013, pp. 60-74. doi: 10.4236/ojer.2013.23007.

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