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Moment Magnitude (M W ) Conversion Relationsfor Use in Hazard Assessment in EasternCanadaAllison L. BentAllison L. BentCanadian Hazards Information Service, Geological Survey of CanadaABSTRACTTo be unbiased and uniform across a wide geographical area,seismic hazard assessments based primarily on earthquakerecurrence rates require that the same magnitude scale be usedfor all earthquakes evaluated. Increasingly, moment magnitude,M W , is seen as the magnitude of preference. Momentmagnitude, however, was not routinely calculated in the pastfor earthquakes in Canada, necessitating the conversion fromother magnitude types in common use. This step is complicatedby the fact that several magnitude scales are routinely reportedfor Canadian earthquakes with the choice being influencedprimarily by geography and to a lesser extent by the size of theearthquake. This paper focuses on eastern Canada, where m Nis the most commonly used magnitude scale. Conversions toM W are established and evaluated. The simple conversion ofapplying a constant is sufficient. However, the conversion istime dependent with the constant changing from 0.41 to 0.53in the mid-1990s.INTRODUCTIONMagnitude recurrence rates are an important factor in seismichazard assessment in Canada and elsewhere. The (Canadian)National Earthquake Database (NEDB 2010), hereafterreferred to as the NEDB, routinely reports several earthquakemagnitude scales for Canadian earthquakes, with m N and M Lbeing the most commonly used for eastern Canada. 1 Whenevaluating magnitude recurrence curves for use in seismic hazardassessment there exists the possibility that a mixed dataset will lead to non-uniform or even erroneous results. Thus,it becomes imperative to use the same magnitude scale for all1. For hazard purposes a conversion equation only for offshore eventswith M L is required. For these, m N is not appropriate because theirS wavetrain lacks Lg energy or the Lg energy is clearly attenuated.There are at least two other types of M L used in eastern Canada: pre-1980 onshore earthquakes for which magnitudes were computedbefore m N was defined (m N s for most of these back to about 1940have subsequently been determined from amplitude data but someevents remain as M L s) and small earthquakes up to the present forwhich there is no amplitude data at a station beyond 50 km (these arenot important for seismic hazard).earthquakes in the data set. Moment magnitude, or M W , hasbecome the preferred magnitude scale as it can be related tothe physical properties of the earthquake rupture and does notsaturate at high magnitudes. However, this magnitude has notbeen routinely calculated in the past in Canada and using it forhazard assessment requires that reliable M W s be determinedfor all earthquakes used in the hazard calculations. This paperfocuses on eastern Canada but similar studies have been undertakento derive M W conversions for western Canada (Ristau etal. 2003, 2005).Moment magnitude has been determined for many ofthe largest earthquakes in eastern Canada and for some of themoderate ones. In a recent study Bent (2009) evaluated data forthe 150 largest earthquakes that met the completeness criteriafor use in hazard assessment in eastern and northern Canadaand determined M W s for each of them. While instrumentallydetermined M W s were given preference, conversions fromother magnitude types or felt information were sometimesnecessary given the long time period covered. Furthermore, itis now almost always possible to determine M W for eastern andnorthern Canadian earthquakes of magnitude 5.0 or greaterand also possible for many of the magnitude 4 to 5 earthquakes.Therefore, in developing a conversion scale, the emphasis is onthe smaller (less than magnitude 5.0) earthquakes.The approach used in this study is to assemble a databaseof eastern and northern Canadian earthquakes for which aninstrumentally determined m N and M W are available, establisha conversion relation, and evaluate it with respect to several previouslypublished relations based on smaller data sets. The M Wdata set for offshore regions where M L is the primary magnitudewas insufficient to establish a reliable conversion relation.It may be necessary to employ a two-step conversion from M Lto m b and then m b to M W . This conversion relation is underinvestigation by the author.A variety of conversions of varying complexity were testedbut the author verified that the more complex conversions didnot result in a statistically significant improvement over thesimple application of a constant, and in some cases did notprovide a better absolute fit in terms of mean residual. Thesenew simple conversions were, however, found to be statisticallysignificant improvements over previously published relations.984 Seismological Research Letters Volume 82, Number 6 November/December 2011 doi: 10.1785/gssrl.82.6.984