Reply to «Comment on ‘Unbiased Estimation of Moment Magnitude from Body- and Surface-Wave Magnitudes’ by R. Das, H. R. Wason, and M. L. Sharma and ‘Comparative Analysis of Regression

Pujol has made certain observations on the papers by Das et al. (2014) and that of Gasperini et al. (2015). He discussed the theoretical background of the research work being undertaken for magnitude conversion problems. The efficiency of the statistical regression model generally is based on the closeness between the predicted and the observed values, and it is statistically proven that the new general orthogonal regression (GOR) approach suggested by Das and coauthors provides improved estimates, especially for magnitude data pairs mb; Mw. A dataset of 19,466 global moment magnitude (Mw) values estimated from body-wave magnitudes (mb) shows that 65% of the total data yields better results through the new GOR approach compared with the conventional GOR approach for error variance value 0.2.
This value further increases when η ≤ 0:2 and, therefore, statistically it is better to use the new GOR approach than the conventional approach, at least in the case of mb and Mw data pairs for η ≤ 2. Hence, unified moment magnitude catalogs prepared using the new GOR approach will be useful for realistic seismic hazard assessment.
We acknowledge the comments of Pujol on our paper (Das et al., 2014), and on the paper published by Gasperini et al. (2015). For the sake of continuity, we will refer to the comments of Pujol (2017) as Pujol. The equations of Fuller (1987), Das et al. (2014), Gasperini et al. (2015), and Pujol (2017) will be cited with F, D, G, and P prefixes, respectively.