Journal of Seismology (2006) 10: 225–236 DOI: 10.1007/s10950-006-9012-4 C  Springer 2006 Empirical global relations converting M S and m b to moment magnitude E.M. Scordilis Department of Geophysics, School of Geology, Aristotle University, Thessaloniki 54124, Greece, e-mail: manolis@geo.auth.gr Received 28 December 2005; accepted in revised form 12 January 2006 Key words: magnitude scales, moment magnitude, global empirical relations, homogeneous catalogs Abstract The existence of several magnitude scales used by seismological centers all over the world and the compilation of earthquake catalogs by many authors have rendered globally valid relations connecting magnitude scales a necessity. This would allow the creation of a homogeneous global earthquake catalog, a useful tool for earthquake research. Of special interest is the definition of global relations converting different magnitude scales to the most reliable and useful scale of magnitude, the moment magnitude, M W . In order to accomplish this, a very large sample of data from international seismological sources (ISC, NEIC, HRVD, etc.) has been collected and processed. The magnitude scales tested against M W are the surface wave magnitude, M S , the body wave magnitude, m b , and the local magnitude, M L . The moment magnitudes adopted have been taken from the CMT solutions of HRVD and USGS. The data set used in this study contains 20,407 earthquakes, which occurred all over the world during the time period 1.1.1976–31.5.2003, for which moment magnitudes are available. It is shown that well-defined relations hold between M W and m b and M S and that these relations can be reliably used for compiling homogeneous, with respect to magnitude, earthquake catalogs. Introduction One of the most important parameters characterizing an earthquake is its “size”, which is a measure di- rectly related to the energy released. Since the first work of Richter (1935) when the local magnitude scale, M L , was initially defined using trace ampli- tudes of local earthquakes recorded on typical Wood Anderson seismographs (T 0 = 0.8 s, critical damping 0.8, V = 2, 800), the earthquake magnitude became the most common measure of the size of an earthquake. Its linear relation with the logarithm of physical quanti- ties characterizing the earthquake (seismic energy, seis- mic moment) turned it into a tool suitable for solving several important problems of practical and theoreti- cal interest. In the course of time, new seismographs were constructed and different wave types, recorded at various distances, were used for magnitude estima- tion, which resulted in the definition of new magnitude scales. Thus, Gutenberg (1945a) defined the surface wave magnitude scale, M S , using the ground amplitudes of surface waves with period 17–23 s measured at epi- central distances 15 ◦ –130 ◦ . This magnitude could be estimated using the formula: M S = log A + 1.656 log  + 1.818 (1) where A is the ground amplitude in μm and  the epicentral distance in degrees. Gutenberg (1945b,c) and Gutenberg and Richter (1956) introduced the body wave magnitude scale based on the recordings of P-waves with periods up to about 10 s by medium to long period instruments. It was denoted as m B and was originally determined from the ratio of amplitude to period for P or S waves according to the relation: m B = log  A T  + q (, h ) (2)