Regression relationships for conversion of body wave and surface wave magnitudes toward Das magnitude scale, Mwg

A reliable and standardized estimation of earthquake size is a fundamental requirement for all tectonophysical and engineering applications. Several investigations raised questions about the determinations of smaller and intermediate earthquakes using Mw scale. Recent investigations (Das et al. in Bull Seismol Soc Am 108(4):1995–2007, 2018b) show that the moment magnitude scale Mw is not applicable for lower and intermediate ranges throughout the world and does not efficiently represent the seismic source potential due to its dependence on surface wave magnitudes; therefore, an observed seismic moment (M0)-based magnitude scale, Mwg, which smoothly connects seismic source processes and highly correlates with seismic-radiated energy (Es) compared to the Mw scale is suggested. With the goal of constructing a homogeneous data set of Mwg to be used for earthquake-related studies, relationships for body wave (mb) and surface wave magnitudes (Ms) toward Mwg have been developed using regression methodologies such as generalized orthogonal regression (GOR) (GOR1: GOR relation is expressed in terms of the observed independent variable; and GOR2: GOR relation is used inappropriately in terms of theoretical true point of GOR line) and standard least-square regression (SLR). In order to establish regression relationships, global data have been considered during 1976–2014 for mb magnitudes of 524,790 events from the International Seismological Centre (ISC) and 326,201 events from the National Earthquake Information Center (NEIC), Ms magnitudes of 111,443 events from ISC along with 41,810 Mwg events data from the Global Centroid Moment Tensor (GCMT). Scaling relationships have been obtained between mb and Mwg for magnitude range 4.5 ≤ mb ≤ 6.2 for ISC and NEIC events using GOR1, GOR2 and SLR methodologies. Furthermore, scaling relationships between Ms and Mwg have been obtained for magnitude ranges 3.0 ≤ Ms ≤ 6.1 and 6.2 ≤ Ms ≤ 8.4 using GOR1, GOR2 and SLR procedures. Our analysis found that GOR1 provides improved estimates of dependent variable compared to GOR2 and SLR on the basis of statistical parameters (mainly uncertainty on slope and intercept, RMSE and Rxy) as reported in Das et al. (2018b). The derived global scaling relationships would be helpful for various seismological applications such as seismicity, seismic hazard and Risk assessment studies.