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

Ernes Mamyrov

Institute of Seismology of the National Academy of Sciences of the Kyrgyz Republic, Bishkek, Kyrgyz Republic.

DOI: 10.4236/ojer.2013.23007                

Abstract

In connection with conversion from energy class K_R (K_R = log₁₀E _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 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 (m_b , M_L , Ms) = K_i + z_i log₁₀M₀ , the coefficients k_i  and z_i  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 M_m (m_bm = m_b , M_Lm = M_L , M_Sm = M_S ) from log₁₀M_0,  log₁₀t₀  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 = 1.59m_bm – 3.06. According to the instrumental data the correlation M_s = 1.57m_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.

 

Keywords

Magnitude; Seismic Moment; Energy Class; Earthquakes; Frequency

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	B. Gutenberg, “Amplitudes of P, PP, an S waves and Magnitude of Shallow Earthquakes,” Bulletin of the Seismological Society of America, Vol. 35, No. 2, 1945, pp. 57-69.
[2]	B. Gutenberg and C. F. Richter, “Earthquake Magnitude, Intensity, Energy and Acceleration,” Bulletin of the Seismological Society of America, Vol. 46, No. 2, 1956, pp. 105-145.
[3]	В. Gutenberg and C. F. Richter, “Magnitude and Energy of Earthquakes,” Annali di Geofisica, Vol. 9, No. 1, 1956, pp. 1-15.
[4]	N. V. Kondorskaya, A. I. Zakharova and L. S. Chepkunas, “The Quantitative Characteristics of Earthquake Sources as Determined in the Seismological Practice of the U.S.S. R.,” Tectonophysics, Vol. 166, No. 1-3, 1989, pp. 45-52. doi:10.1016/0040-1951(89)90204-7
[5]	T. G. Rautian, “Energy of Earthquakes,” In: Y. V. Riznichenko, Ed., Methods for the Detailed Study of Seismicity, Akademii Nauk SSSR, Moscow, 1960, pp. 75-114.
[6]	T. G. Rautian, V. J. Khalturin, K. Fujita, K. G. Mackey, et al., “Origins and Methodology of the Russian Energy K-Class System and Its Relationship to Magnitude Scales,” Seismological Research Letters, Vol. 78, No. 6, 2007, pp. 579-590. doi:10.1785/gssrl.78.6.579
[7]	P. Chen and H. Chen, “Scaling Law and Its Applications to Earthquake Statistical Relations,” Tectonophysics, Vol. 166, No. 1-3, 1989, pp. 53-72. doi:10.1016/0040-1951(89)90205-9
[8]	L. B. Grant, “Paleoseismology, International Handbook of Earthquake and Engineering Seismology, Part A,” Academic Press, Waltham, 2002.
[9]	A. A. Gusev and V. N. Melnikova, “Relations between Magnitudes: Global and Kamchatka Data,” Volkanology and Seismology, Vol. 6, 1990, pp. 55-63.
[10]	K. Kasahara, “Earthquake Mechanics,” 1985.
[11]	P. Mai and G. C. Beroza, “Source Scaling Potpies from Finite-Fault-Rupture Models,” Bulletin of the Seismological Society of America, Vol. 90, No. 3, 2000, pp. 604- 615. doi:10.1785/0119990126
[12]	O. W. Nuttli, “Average Seismic Source-Parameters Relation for Mid-Plate Earthquakes,” Bulletin of the Seismological Society of America, Vol. 73, No. 2, 1983, pp. 519- 535.
[13]	K. Аki, “Generation and Propagation of G-Waves from the Niigata Earthquake of June 16, 1964. Part 2. Estimation of Earthquake Moment, Released Energy, and Stress-Strain Drop from the G-Wave Spectrum,” Bulletin of the Earthquake Research Institute, Tokyo, 1966.
[14]	K. Aki and P. A. Richards, “Quantitative Seismology. Theory and Methods, v. t., Moskau: Mir,” 1983.
[15]	J. N. Brune, “Tectonic Stress and the Spectra of Seismic Shear Waves from Earthquakes,” Journal of Geophysical Research, Vol. 75, No. 26, 1970, pp. 4997-5009. doi:10.1029/JB075i026p04997
[16]	V. Keilis-Borok, “On Estimation of the Displacement in an Earthquake Source and Dimension,” Annales Geo- physicae, Vol. 12, No. 1-4, 1959, pp. 205-214.
[17]	P. Debye, “Zur Theorie der Spezifischen W?rmen,” Annalen der Physik, Vol. 344, No. 14, 1912, pp. 789-839. doi:10.1002/andp.19123441404
[18]	E. Mamyrov, “Relations among Earthquake Source Parameters Derived from Debye Solid-Body Model,” Journal of Geodynamics, Vol. 22, No. 1, 1996, pp. 137-143. doi:10.1016/0264-3707(96)00005-1
[19]	H. Kanamori, “The Energy Released in Great Earthquakes,” Journal of Geophysical Research, Vol. 82, No. 20, 1977, pp. 2981-2987. doi:10.1029/JB082i020p02981
[20]	G. A. Bollinger, M. C. Chapman and M. S. Sibol, “A Compassion of Earthquake Damage Areas a Function of Magnitude across the United States,” Bulletin of the Seismological Society of America, Vol. 83, 1993, pp. 1064- 1080.
[21]	D. M. Boore, “The Richter Scale: Its Development and Use for Determining Earthquake Source Parameters,” Tectonophysics, Vol. 166, 1989, pp. 1-14. doi:10.1016/0040-1951(89)90200-X
[22]	T. S. Hanks and D. M. Boore, “Moment-Magnitude Relations in Theory and Practice,” Journal of Geophysical Research, Vol. 89, No. B7, 1984, pp. 6229-6235. doi:10.1029/JB089iB07p06229
[23]	E. M. Scordilis, “Empirical Global Relations Converting MS and mв to Moment Magnitude,” Journal of Seismology, Vol. 10, 2006, pp. 225-236. doi:10.1007/s10950-006-9012-4
[24]	T. Utsu, “Relationships between Magnitude Scales, International Handbook of Earthquake and Engineering Seismology, Part A,” Academic Press, Waltham, 2002.
[25]	C. F. Richter, “An Instrumental Earthquake Magnitude Scale,” Bulletin of the Seismological Society of America, Vol. 25, No. 1, 1935, pp. 1-32.
[26]	N. I. Christensen, “Poisson’s Ratio and Crustal Seismology,” Journal of Geophysical Research, Vol. 101, No. B2, 1996, pp. 3139-3156. doi:10.1029/95JB03446
[27]	N. I. Christensen and W. D. Mooney, “Seismic Velocity Structure and Composition of the Continental Crust: A Global View,” Journal of Geophysical Research, Vol. 100, No. B6, 1995, pp. 9761-9788. doi:10.1029/95JB00259
[28]	E. Mamyrov, “New System of Quantitative Correlations between Seismic Energy, Magnitude and Energy of Seismic Radiation of the Crust Earthquakes in Tien Shan,” The 33rd General Assembly of the European Seismological Commission, Moscow, 19-24 August 2012, pp. 29-30.
[29]	H. Houston and H. Kanamori, “Source Spectra of Great Earthquakes: Teleseismic Constraints on Rupture Process and Strong Motion,” Bulletin of the Seismological Society of America, Vol. 76, No. 1, 1986, pp. 19-42.
[30]	W. Thatcher and C. Hahks, “Source Parameters of Southern California Earthquakes,” Journal of Geophysical Research, Vol. 78, No. 35, 1973, pp. 8547-8575. doi:10.1029/JB078i035p08547
[31]	K. K. Zapolskii, J. L. Nersesov, T. G. Rautian and V. I. Halturin, “Physical Basis of Magnitude Classification of Earthquakes,” 1974.
[32]	F. Scherbaum and D. Stoll, “Source Parameters and Scaling Laws of the 1978 Schwabian Jura (Southwest Germany) Aftershocks,” Bulletin of the Seismological Society of America, Vol. 73, No. 5, 1983, pp. 1321-1343.
[33]	A. Jin, C. A. Moya and M. Ando, “Simultaneous Determination of Site Responses and Source Parameters of Small Earthquakes along the Atotsugawa Fault Zone, Central Japan,” Bulletin of the Seismological Society of America, Vol. 90, No. 6, 2000, pp. 1430-1445. doi:10.1785/0119990140
[34]	H. S. Hasegawa, “Lg-Spectra of Local Earthquake Recorder by the Eastern Canada Telemeters Network and Spectral Scaling,” Bulletin of the Seismological Society of America, Vol. 73, 1983, pp. 1041-1061.
[35]	G. Grunthal and R. Wahlstrom, “An MW Based Earthquake Catalogue for Central, Northern and North-Western Europe Using a Hierarchy of Magnitude Conversions,” Journal of Seismology, Vol. 7, No. 4, 2003, pp. 507-531. doi:10.1023/B:JOSE.0000005715.87363.13
[36]	J. G. Ristau, G. C. Rogers and F. Cassidy, “Moment Magnitude-Local Magnitude Calibration for Earthquake in Western Canada,” Bulletin of the Seismological Society of America, Vol. 95, No. 5, 2005, pp. 1994-2000. doi:10.1785/0120050028
[37]	J. Ristau, “Comparison of Magnitude Estimates for New Zealand Earthquakes: Moment Magnitude, Local Magnitude, and Teleseismic Body-Wave Magnitude,” Bulletin of the Seismological Society of America, Vol. 99, No. 3, 2009, pp. 1841-1852. doi:10.1785/0120080237
[38]	Y. M. Wu, R. M. Allen and C. W. Wu, “Revised ML Determination for Crustal Earthquake in Taiwan,” Bulletin of the Seismological Society of America, Vol. 95, No. 6, 2005, pp. 2517-2524. doi:10.1785/0120050043
[39]	G. L. Choy and J. Boatwright, “Global Patterns of Radiated Seismic Energy and Apparent Stress,” Journal of Geophysical Research, Vol. 100, No. B9, 1995, 18205- 18228. doi:10.1029/95JB01969
[40]	Y. Zhuo and H. Kanamori, “Regional Variation of the Short-Period (1 to 10 Second) Source Spectrum,” Bulletin of the Seismological Society of America, Vol. 77, No. 2, 1987, pp. 514-529.
[41]	O. J. Perez, “Revised World Seismicity Catalog (1950- 1997) for Strong (MS≥6) Shallow (h?70 km) Earthquakes,” Bulletin of the Seismological Society of America, Vol. 89, No. 2, 1999, 335-341.