## 3 Results
#### 3.1.1 Case Study in the Years 1991, 2012, and 2015  
On 24 March 1991, a powerful geomagnetic storm started at 04:30 UT and reached its negative extremum in the primary phase on 25 March 1991 at 00:30 UT, with Dst = \(-\)298 nT. At that time, the CRRES satellite was near L\(\sim\)2.6, and its instruments recorded powerful fluxes of electrons with E\(\sim\)15 MeV and protons with E\(\sim\)20-110 MeV [41]. The MIR orbital station also observed the newly created radiation belt for about 2 years [42]. On 1 September 2012, a moderate geomagnetic storm started at 22:30 UT and reached its negative extremum in the primary phase on 3 September 2012 at 10:30 UT, with Dst = \(-\)69 nT. At that time, the Relativistic Electron Proton Telescope (REPT) on NASA's Van Allen probes board recorded a flux of energetic electrons (3.6 MeV, 4.5 MeV, and 5.6 MeV) at geomagnetic lines 3.0 \(\leq\) L \(\leq\) 3.5. A newly formed belt of relativistic electrons was observed for about a month [43] and was then destroyed by the next strong geomagnetic storm on 1 October 2012 [38]. On 21 June 2015, a powerful geomagnetic storm started at 18:30 UT and reached its negative extremum in the primary phase on 23 June 2015 at 04:30 UT, with Dst = \(-\)204 nT. At that time, the Magnetic Electron Ion Spectrometer (_MagEIS_) on NASA's Van Allen probes board recorded a new belt of relativistic electrons with energy E\(\sim\)1.06 MeV at geomagnetic lines L\(\sim\)1.5-1.8, which persisted for \(\sim\)11 months [44]. Figure 2 presents monthly earthquakes of magnitude M \(\geq\) 4.5 that occurred in 1991, 2012, and 2015 near the footprints of the newly created belts of relativistic electrons. Figure 2a shows the histogram of the number of earthquakes of M \(\geq\) 4.5 near the footprint of the geomagnetic lines L = 2.5-2.7 in different months of 1991. It is seen that the most significant number of earthquakes occurred in May 1991. The strongest was the M7.0 earthquake in Alaska on 30 May 1991, with epicenter coordinates of 54.57\({}^{\circ}\)N, 161.61\({}^{\circ}\)E, near the footprint of the geomagnetic line L\(\sim\)2.69 and closely adjacent to the new radiation  
Figure 2: Histograms of the monthly number of earthquakes of M \(\geq\) 4.5 occurring near the footprints of geomagnetic lines belonging to the newly created belts of relativistic electrons: (**a**) 1991, L = 2.5-2.7; (**b**) 2012, L = 3.0–3.5; and (**c**) 2015, L = 1.5–1.8. belt created around L\(\sim\)2.6 after a magnetic storm on 24 March 1991 [41; 42]. We see that an increase in seismic activity at the base L = 2.5-2.7 in May 1991 occurred \(\sim\)2 months after the geomagnetic storm onset. Figure 2b shows the distribution by month across 2012 for the number of earthquakes with a magnitude of M \(\geq\) 4.5 that occurred near the footprint of the geomagnetic lines L = 3.0-3.5, around which a belt of high-energy electrons was formed due to a geomagnetic storm on 1 September 2012 [43]. For the base of L = 3.0-3.5, the number of earthquakes strongly increased in October 2012; the largest here was an earthquake of M = 7.8, which occurred off the coast of Canada on 28 October 2012, with coordinates 52.79\({}^{\circ}\)N, 132.1\({}^{\circ}\)W, near the footprint of L = -3.3. This earthquake also occurred \(\sim\)2 months after the geomagnetic storm onset on 1 September 2012, which created a storage ring of relativistic electrons. Figure 2c presents the monthly number of earthquakes with M \(\geq\) 4.5 in 2015 near the footprint of geomagnetic lines L = 1.5-1.8. A belt of high-energy electrons was formed due to a geomagnetic storm on 21 June 2015 [44]. The increase of seismic activity here started in June 2015, just after a strong geomagnetic storm, but it peaked in September 2015. The largest earthquake (M = 6.3) occurred on 7 September 2015, near New Zealand, with epicenter coordinates of 32.82 \({}^{\circ}\)S, 177.86 \({}^{\circ}\)W in the footprint of L\(\sim\)1.58. The M6.3 events again persisted over 2 months following the magnetic storm onset.