The distribution of the hypocenters of great seismic events with M >= 7.0 and, consequently, the seismic energy released in their sources is asymmetric along the Earth radius. According to our estimates, 90% of the energy is released relatively close to the Earth's surface, at the average depth of 50 km. The bulk of the remaining 10% is associated with seismic events that take place at large depths, on average 630-640 km above the boundary between the transition zone and lower mantle. These very deep earthquakes (depth >= 350 km) significantly differ from the shallow events. Their sources, in contrast to the shallow focus events, are located inside the plate. The examination of seven seismic zones described in the present study, except for the Honsu-Kamchatka zone which accommodates both the shallow and deep M >= 7.0 earthquakes, shows that the linear distribution of the hypocenters of deep earthquakes is considerably shorter than that of the shallow earthquakes, which, in turn, determines the length of the seismic zones at depth. In the zones of the Solomon Islands and the Izu-Bonin-Mariana arc, there are no seismic events with M >= 7.0 deeper than 450 km. In the zones of Indonesia, Philippines, Tonga-Kermadec, and Chile-Peru, the mentioned length's shortening at the top of the lower mantle (660-km discontinuity) relative to the length of the zone observed close to the surface is unequivocal. The relationship between the lithospheric plates is supported by the spatial distribution of the hypocenters. The position of the foci of very deep (>= 500 km) earthquakes indicates where the descending lithospheric plates conflict with the upper boundary of the lower mantle, and where in some cases they cross it. This passage generates the compression and elongation inside the slab. A comparison of the time distribution of the shallow and deep seismic events suggests the absence of direct relationship between these two different earthquake activities. For studying the fairly uncommon deep earthquakes, important additional information was provided by the largest of the deep earthquakes, the May 24, 2013 M 8.3 event beneath the Sea of Okhotsk, in an area where significant deep earthquakes have already occurred. Based on our studies of the records provided by the Russian and Hungarian national seismological networks, we concluded that this seismic event was preceded by an earthquake swarm, which consisted of 58 M >= 5 events between May 15 and 24, 2013 in the higher part of the sinking slab east of Kamchatka within the segment of increased historical seismicity. Most probably, the interaction of two distinct active source zones took place. The aftershock activity beneath the Sea of Okhotsk was moderate: thirteen events with magnitudes above De >= 4.0 were observed by June 27, 2013. Nevertheless, the unusually small number of aftershocks determined a fault area (2.64 x 10(4) km(2)), generally similar to that in the case of the assumed shallow M 8.3 event.