Global-Magnitude Scaling Relations for Intermediate-Depth and Deep-Focus Earthquakes by A. D. Tsampas, E. M. Scordilis, C. B. Papazachos, and G. F. Karakaisis Abstract Robust relations correlating 10 different magnitudes of intermediate- depth and deep-focus earthquakes to moment magnitude are proposed, in order to be efficiently incorporated into the compilation process of homogeneous (with respect to magnitude) earthquake catalogs. By using global data available from International Seismological Centre (ISC), National Earthquake Information Center (NEIC), Com- prehensive Nuclear-Test-Ban Treaty Organization’ s International Data Centre (IDC), Institute of Physics of the Earth in Moscow, Russia, and China Earthquake Networks Center in Beijing, the performance of several widely used magnitude scales, such as body wave (m b , m B ) and surface wave (M s ), is examined with respect to the moment magnitude scale (M w ). Similarly, appropriate M w -calibrated relations are also pro- vided for regional magnitude scales such as the M JMA magnitude calculated by the Japan Meteorological Agency. The analysis also involves the integration of focal depth as an additional variable to some of the above magnitude-conversion relations. This depth effect proved to be important for ISC/NEIC’ s body-wave (m b IN) and surface-wave (M s IN) magnitudes, leading to significant corrections for the estimated magnitudes. More specifically, a major change in the magnitude residual variation around the depth of 230 km was identified for the case of m b IN. Furthermore, the obtained results provide important observations on the behavior of certain magnitude scales. A typical case is the m b scale reported by IDC, which shows a systematic and large bias, with respect to the published M w data values. Introduction The first observations of intermediate-depth and deep- focus earthquakes are historically attributed to Turner (1922), but a turning point for modern research was Wadati’ s work on the existence of a deep earthquake zone beneath Honshu (Wadati, 1928, 1929), widely acknowledged as the first to denote the distinct nature of this particular type of seismic activity. The concept that intermediate-depth and deep-focus earthquakes occur only in certain geographical areas (Wadati–Benioff zones) and follow different time and mag- nitude distributions was established several decades later (Dziewonski and Gilbert, 1974; Abe and Kanamori, 1979; Astiz et al., 1988; Giardini, 1988; Okal and Kirby, 1995). The evaluation of earthquake size still remains a contro- versial issue for events with focal depths h ≥ 60 km. This is mainly due to the numerous estimates published from differ- ent magnitude sources, even though the seismic moment is, perhaps, the most appropriate parameter for representing their physical size. In practice, body-wave magnitude scale m b is the predominant conventional magnitude parameter, widely used for the quantification of intermediate-depth and deep-focus seismicity. However, other methods of magnitude determination for such events, e.g., by using regional velocity– amplitude data (Katsumata, 2001) among others, have been proposed as well. In 1979, Abe and Kanamori used the broadband body- wave magnitude m B (estimated using body waves of 5–20 s average period) to quantify a number of intermediate and deep-focus earthquakes that occurred globally between 1904 and 1974. According to their results, a similar pattern in the temporal variation of the number of events is observed be- tween the intermediate and deep-focus earthquakes with m B ≥ 7:0 and the shallow events with M s ≥ 7:0. In the present work, reliable magnitude-converting rela- tions are proposed exclusively for intermediate and deep- focus events, following similar studies of global shallow seismicity (Utsu, 2002; Scordilis, 2006; Das et al., 2011, etc.). Such relations can be efficiently employed for the com- pilation of homogeneous (with respect to magnitude) global earthquake catalogs, which are essential inputs for seismicity and seismic-hazard studies. So, a considerable improvement in the aggregated magnitude information could be achieved, through utilizing various regional data and on the condition 418 Bulletin of the Seismological Society of America, Vol. 106, No. 2, pp. 418–434, April 2016, doi: 10.1785/0120150201