Bulletin of the Seismological Society of America, 89, 2, pp. 442-455, April 1999 Moment-Magnitude Relations Based on Strong-Motion Records in Greece by B. N. Margaris and C. B. Papazachos Abstract In this work, the variation of the local magnitude, MLSM, derived from strong-motion records at short distances is examined, in terms of moment magnitude, M w. Strong-motion data from Greek earthquakes are used to determine the strong- motion local magnitude, MLSM, by performing an integration of the equation of mo- tion of the Wood-Anderson (WA) seismograph subjected to an input acceleration. The most reliable strong-motion data are utilized for earthquakes with seismic mo- ments log M 0 -----22.0 dyne • cm and calculated local magnitudes, MLs M >-- 3.7. The correlation between the seismic moments, log M0, and the calculated local magni- tudes, MLSM, using strong-motion records is given by log M 0 = 1.5*Mcsu + 16.07, which is very similar to that proposed by Hanks and Kanamori (1979). Moreover, it is shown that MLs M is equal to moment magnitude, Mw, for a large MLs M range (3.9 to 6.6). Comparison of the strong-motion local magnitude and the ME magnitude estimated in Greece (ML~n) and surrounding area shows a systematic bias of 0.4 to 0.5, similar to the difference that has been found between M w and MLGR for the same area. The contribution of the local site effects in the calculation of the local magni- tude, MLSM, is also considered by taking into account two indices of soil classification, namely, rock and alluvium or the shear-wave velocity, vs30, of the first 30 m, based on NEHRP (1994) and UBC (1997). An increase of MLs M by 0.16 is observed for alluvium sites. Alternative relations showing the MLSM variation with, v3° are also presented. Finally, examination of the WA amplitude attenuation, -log A0, with distance shows that the Jennings and Kanamori (1983) relation for A < 100 km is appropriate for Greece. The same results confirm earlier suggestions that the 0.4 to 0.5 bias between MLGR and Mw (also MLsa4) should be attributed to a low static magnification (-800) of the Athens WA instrument on which all other M L relations in Greece have been calibrated. In~oduction Seismic ground motion depends on the size of the cor- responding earthquake, the most common relative measure being magnitude. Ordinary measures of magnitude are de- fined in terms of peak motions recorded on seismograms from particular instruments after correction for the attenua- tion to a reference distance. The seismic waves radiated from a seismic source are made up of a wide spectrum of fre- quencies, and the seismic instruments provide views into different frequency ranges of the released energy. Due to this fact, the size of any earthquake can be measured by various magnitude scales. The magnitudes for any earth- quake do not necessarily agree with one another, while it must be emphasized that each scale provides information concerning the spectral content of the seismic source at dif- ferent frequencies. The most commonly used magnitudes in engineering design are the Richter (1935) local magnitude, ML, the surface-wave magnitude, Ms (Gutenberg, 1945), and the moment magnitude, M w (Hanks and Kanamori, 1979). The local magnitude, ML, is based on the trace ampli- tude recorded by the Wood-Anderson (WA) torsion seis- mograph located within a few hundred kilometers of the earthquake source, with a natural period of 0.8 sec, a critical damping factor ~ = 0.80, and a static magnification V = 2800. In addition, My is determined closer to the seismic source than are other magnitude scales, thus the ground mo- tion at the instrument site resembles more closely to the strong ground motion recorded by accelerographs, both in frequency content and duration. For short epicentral dis- tances (A N 25 kin), the standard WA seismograph goes off scale for events with My >-- 4.5, so no reliable measurements can be made on this instrument for strong motion in these distances that have significant engineering importance. For this reason, Trifunac and Brune (1970) have proposed a method for the determination of local magnitude, MLSM, us- ing strong-motion accelerograms, for moderate to large earthquakes at distances for which the standard WA instru- ment would be driven off scale. This method, which en- hances the data base from which ML can be found, relies on 442