A homogenous earthquake catalog is a basic input for seismic hazard estimation, and other seismicity studies. The preparation of a homogenous earthquake catalog for a seismic region needs regressed relations for conversion of different magnitudes types, e.g. m b , M s , to the unified moment magnitude M w. In case of small data sets for any seismic region, it is not possible to have reliable region specific conversion relations and alternatively appropriate global regression relations for the required magnitude ranges and focal depths can be utilized. In this study, we collected global events magnitude data from ISC, NEIC and GCMT databases for the period 1976 to May, 2007. Data for m b magnitudes for 3,48,423 events for ISC and 2,38,525 events for NEIC, M s magnitudes for 81,974 events from ISC and 16,019 events for NEIC along with 27,229 M w events data from GCMT has been considered. An epicentral plot for M w events considered in this study is also shown. M s determinations by ISC and NEIC, have been verified to be equivalent. Orthogonal Standard Regression (OSR) relations have been obtained between M s and M w for focal depths (h \ 70 km) in the magnitude ranges 3.0 B M s B 6.1 and 6.2 B M s B 8.4, and for focal depths 70 km B h B 643 km in the magnitude range 3.3 B M s B 7.2. Standard and Inverted Standard Regression plots are also shown along with OSR to ascertain the validation of orthogonal regression for M s magnitudes. The OSR relations have smaller uncertainty compared to SR and ISR relations for M s conversions. ISR relations between m b and M w have been obtained for magnitude ranges 2.9 B m b B 6.5, for ISC events and 3.8 B m b B 6.5 for NEIC events. The regression relations derived in this study based on global data are useful empirical relations to develop homogenous earthquake catalogs in

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In their article, Yadav et al. (2009) made two major approximations that have a significant impact on the estimates of M w,HRVD proxies for the catalog that they considered. The first approximation is to consider the unspecified magnitudes equivalent to M S,ISC for all magnitude ranges, and the second relates to estimating M w,HRVD proxies as the average of the two M w,HRVD conversions wherever available both from m b,ISC and M S,ISC . They also used a small number of data pairs of M w,HRVD & M S,NEIC and M S,ISC & M S,NEIC for estimating representative regional relationships to be used for corresponding M w,HRVD conversions. In this comment we examine the inaccuracy involved in these approximations and in correlations based on small sample sizes, and we propose improved regression relations and an alternative scheme for calculating the averages of M w,HRVD proxies. TREATMENT OF UNSPECIFIED MAGNITUDES OF GUPTA et al. (1986) CATALOGFor the period 1897 to 1962, magnitudes are not specified for about 186 events in the catalog of Gupta et al. (1986). Yadav et al. (2009) adopted this catalog and considered these unspecified magnitudes equivalent to M S values of the International Seismological Centre (ISC) for calculating proxy M w,HRVD values using the regression relation (Equation 3 of Yadav et al. 2009): M w, HRVD = 0.62(±0.03)M S ,ISC + 2.28(±0.13).(1)Such a treatment of unspecified magnitudes is subject to error resulting in lower estimatesof M w,HRVD proxies for magnitude range 5.5 ≤ magnitude ≤ 6.8, if the unspecified magnitude primarily was a body-wave magnitude estimate rather than M S . This is demonstrated by performing conversions of different unspecified magnitudes to corresponding proxy M w,HRVD values using the same conversion relationships by considering them both m b,ISC as well as M S,ISC as shown in Table 1.It is, therefore, more appropriate to introduce conservatism when converting M w estimates by treating the unspecified magnitudes in the catalog of Gupta et al. (1986) as m b,ISC proxies for magnitude range 5.5 ≤ magnitude ≤ 6.8, and M S,ISC proxies for other magnitudes. SURFACE WAVE MAGNITUDE CONVERSION RELATIONSHIPSYadav et al. (2009) have estimated an empirical relation between M S,ISC and M S,NEIC based on only 28 events. We have obtained 87 events having both M S,ISC and M S,NEIC values with depths ≤ 50 km from the ISC bulletin database through 2005. An improved regression relation based on these 87 data pairs is given by M S ,ISC = 0.99(±0.02)M S ,NEIC + 0.13(±0.10),with R 2 = 0.97 and σ = 0.11 ( Figure 1A). Yadav et al. (2009) have observed that their regional relationships between M w , HRVD and M S,NEIC (Equation 2 of their article) and between M w , HRVD and M S,ISC (Equation 3 of their article) are found to differ significantly even though M S,ISC and M S,NEIC are more or less equivalent as these are estimated by a similar technique (Utsu 2002;Scordilis 2006). This difference in the two regional relationships is mainly due to the small sample size (16 data pairs) used by them for deriv...

SUMMARY In this study, a procedure for the application of general orthogonal regression (GOR) towards conversion of different magnitude types is described. Through minimization of the squares of orthogonal residuals, GOR relation is obtained in terms of the abscissas (Mx*) of the projected points corresponding to the observed data pairs (Mx, obs, My, obs). In many studies, Mx* is replaced by Mx, obs in the GOR relation for convenience of obtaining the estimates of a preferred magnitude type for given magnitude values. Such forms of GOR, however, lead to biased estimates of the dependent variable. To represent the GOR relation correctly in terms of Mx, obs, a linear relation has been obtained between Mx* and Mx, obs using given points and the corresponding projected points on the GOR line. Based on events data for the whole globe during the period 1976–2007, GOR relations have been derived for conversion of mb to Mw,mb to Ms,mb to Me and Ms to Mw following the proposed procedure and using specific error variance ratio (η) values. The superiority of the GOR relations obtained following the proposed procedure over the commonly used forms has been shown by computing the absolute average difference and standard deviation between the observed and the estimated values using events data not used in the derivation. It is observed that the proposed GOR relations yield better estimates compared to the commonly used GOR forms. This procedure has been further tested for a wide range of η values between 0.1 and 7.0. The procedure proposed in this study can be used for the purpose of catalogue homogenization where GOR relations are applicable for conversion of different magnitude types.

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For regression of variables having measurement errors, general orthogonal regression (GOR) is the most appropriate statistical procedure that yields a linear relation between the true values of the dependent (y t ) and independent (x t ) variables. However, the GOR procedure to obtain unbiased estimate of the dependent variable for a given error-affected value of the predictor variable is not well addressed in the literature.In the conventional GOR approach, the error-affected value of the predictor variable is substituted as such in the GOR relation, yielding biased estimates of y t . In another approach, the orthogonal projections of the given points on the GOR line are used to first estimate x t and then y t . In this study, a procedure making use of true points on the GOR line is proposed to obtain improved estimates of y t .The proposed GOR procedure is applied to the magnitude conversion problem between m b to M w and M s to M w , using real data set. The absolute average differences of the estimates obtained and their standard deviations are compared, indicating that the proposed GOR procedure provides improved estimates of the dependent variable (y t ) compared with the conventional GOR approach.The improved unified magnitudes obtained using the proposed GOR procedure will result in more realistic seismic hazard for a given catalog and seismotectonic environment.