## 3 Results
#### 3.1.1 Case Study in the Years 1991, 2012, and 2015
Figure 3 visualizes the correlation between geomagnetic storm onset and the strongest earthquake in the footprints of magnetic lines belonging to newly created radiation belts. Figure 3: Variations of hourly mean Dst index for 3 92-day periods: (**a**) 1991, from 19 March, 04:30 UT; (**b**) 2012, from 27 August, 22:30 UT; and (**c**) 2015, from 16 June, 18:30 UT. Upper red star marks dates of geomagnetic storm onsets in March 1991, September 2012, and June 2015, and red vertical lines indicate the dates of the strongest earthquakes that occurred in the footprint of magnetic lines belonging to the radiation belts newly created in the inner magnetosphere due to indicated magnetic storms: M7.0 in Alaska on 30 May 1991, near the footprint of L\(\sim\)2.69; M7.8 near Canada on 28 October 2012, near the footprint of L\(\sim\)3.3; and M6.3 in New Zealand on 7 September 2015, near the footprint of L\(\sim\)1.58. It is seen from Figure 3 that the time delay between storm onset and earthquake occurrence was about 67 days in 1991, 57 days in 2012, and 78 days in 2015; its mean value equals ~67 days. Figure 3b shows that the geomagnetic storm on 1 September 2012 was only moderate, but the strong one occurred on 1 October 2012, with Dst = \(-\)122 nT. One may suggest that this stronger storm induced the M7.8 earthquake. As we see it, finding a correlation between a particular magnetic storm and an induced earthquake is only possible under some initial idea. Our idea was to investigate seismicity in the footprint of magnetic lines belonging to the new radiation belts created by magnetic storms in the inner magnetosphere, and this allowed us to obtain similar results for all three considered cases. It was mentioned in [46] that long-living radiation belts are rarely created due to magnetic storms; more often, the newly created belts survive for a few days. The moderate geomagnetic storm on 1 September 2012 (Dst = \(-\)69 nT) produced a relatively long-lasting radiation belt [43], but the next strong magnetic storm (Dst = \(-\)122) destroyed it [38]. To test whether the relationship of seismic activity with the magnetic storm was significant in the spatial domain (near the footprints of magnetic lines belonging to a new radiation belt created due to the storm), we present Figure 4. It shows the distribution by month in 2012 for the number of earthquakes of M \(\geq\) 4.5 that occurred near the footprint of L = 3.0-3.5 (red bars), as well as in neighboring geomagnetic lines L = 2.5-2.99 (green) and L = 3.51-5.0 (blue). It is seen from Figure 4 that the distribution of earthquakes by month was uniform at the base of the lower (L = 2.5-2.99) and higher (L = 3.51-5.0) lines. For the base of L = 3.0-3.5 (around which the belt of high-energy particles was formed due to a magnetic storm in September 2012), the number of earthquakes strongly increased \(\sim\)2 months after the onset of the magnetic storm. On the other hand, we present Figure 4 only as an example to demonstrate the situation for the year 2012. One cannot expect the picture to be the same for all possible cases because there are many reasons for earthquake occurrence. Sometimes, earthquakes may occur at the base of the nearest magnetic lines; these do not relate to the lines of the newly formed radiation belt. This could possibly be the next step in a more detailed investigation. Figure 4: Distribution by month in 2012 for the number of earthquakes of magnitude M \(\geq\) 4.5 that occurred at the base of geomagnetic lines L = 2.5–2.99 (green, 115 events), L = 3.0–3.5 (red, around which a belt of high-energy electrons was formed after the geomagnetic storm on 1 September 2012, 119 events), and L = 3.51–5.0 (blue, 29 events).