Monte Carlo Markov Chain and General Orthogonal Regression to Investigate the Relationship of Earthquake Magnitudes

Abstract Due to the saturation of the body (mb) and surface (MS ) earthquake magnitudes, the moment magnitude (MW ) is a more convenient parameter for representing earthquake energies. We use the HRVD including 12015 earthquakes recorded from 1976 January 1 to 2001 December 31 for five regions on the Earth (Middle East-Oceania, Europe, Africa, North America, and South America), to investigate the relationship between the body-Wave (4.6 ≤ mb ≤ 7.4), surface-Wave (2.4 ≤ MS ≤ 8.3), and moment magnitudes (4.8 ≤ MW ≤ 8.4) via Monte Carlo Markov chain (MCMC). Applying the MCMC approach, we obtain a linear relationship between mb and MW magnitudes with slopes slightly varying in the range of 0.89 to 11.02 for five regions. Also, we find a linear dependency of MW and MS with a slope ranging from 0.63 to 0.69 for the areas. We also use parameters of the linear relations of the magnitudes and the general orthogonal regression(gor) method to estimate magnitudes’ upper and lower limits of error magnitudes. Keywords: magnitude, earthquake, body-Wave, surface-Wave, moment magnitude