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Homogenizing earthquake catalogs is an effort critical to fundamentally improving seismic studies for next-generation seismology. The preparation of a homogenous earthquake catalog for a seismic region requires scaling relations to convert different magnitude types, like the mb and Ms, to a homogenous magnitude, such as the seismic moment scale, Mwg, and energy magnitude scale, Me. Several recent studies addressed the preparation of homogenized earthquake catalogs, usually involving the estimation of proxies of moment magnitude Mw from local, ML, and teleseismic (Ms and mb) magnitude estimates. Instead of the standard least squares (SLR), most of such studies used the general orthogonal regression (GOR), while some used the Chi-square regression method. Here we critically discuss GOR and Chi-square regression theory and find that both are the same for the linear case — as expected since both stem from the same mathematical concept. Thus to foster an improved understanding of seismicity and seismic hazard, we used GOR methodology and derived global scaling relations individually between body, surface, energy, and seismic moment magnitude scales. For that purpose, we have compiled 13,576 and 13,282 events for Ms from ISC and NEIC, respectively, mb magnitude data for 1,266 events from ISC, 614 events from NEIC, and Mwg magnitude values for 6,690 events from NEIC and GCMT. We have also derived MS,ISC-to-Me and MS,NEIC-to-Me conversion relations in magnitude ranges of 4.7≤MS,ISC≤8.0 and 4.5≤MS,NEIC≤8.0, respectively. Likewise, we obtained mb,ISC-to-Me and mb,NEIC-to-Me conversion relations for ranges of 5.2≤mb,ISC≤6.2 and 5.3≤mb,NEIC≤6.5. Since the number of data points was insufficient to derive the relations, we considered mb,NEIC up to M6.5. Finally, we derived an MWg-to-Me conversion relation for the 5.2≤Mw≤8.2 range of magnitudes with focal depths <70 km. Our scaling relations can be used for homogenizing earthquake catalogs and conducting seismicity and seismic hazard assessment studies with enhanced realism.
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