# The Conditional Probability of Correlating East Pacific Earthquakes with NOAA Electron Bursts
## 2 Materials and Methods  
Data from the NOAA-15 polar satellite were used in this study. Particle counting rates (CRs) were produced by detectors on board the satellite that monitors protons and electrons flying in polar orbits at altitudes between 808 and 824 km at perigee and apogee, respectively, with an inclination of 98.7\({}^{\circ}\) and a period of 101.2\({}^{\prime}\)[29]. The particle detectors, where the analysis was applied, were composed of eight solid-state telescopes called medium energy proton and electron detectors (MEPED). The latter was measuring proton and electron fluxes on 0\({}^{\circ}\), 90\({}^{\circ}\), and Omni-directions from 30 keV to 200 MeV [30]. MEPED data were provided every 2 s, whereas all the sets of orbital parameters were provided every 8 s; consequently, 8 s averages of the CRs were calculated, discarding unreliable negative values, and correcting for proton contamination [31]. Only the zenith telescope, 0\({}^{\circ}\), was used to count electrons in this, as both the 90\({}^{\circ}\) and omnidirectional telescopes were investigated in the past, reporting no positive correlations [26; 27; 28]. The detected electron energies were within three ranges of 30-2700 keV, 100-2700 keV, and 300-2700 keV, so three differences in CRs were calculated to create new sets of data from 30 keV to 100 keV, 100 keV to 300 keV, and 300 keV to 2700 keV. In fact, different behaviors in particle dynamics are determined by energy, and, thus, the new sets resulted in a simpler analysis. When the mirror point of such electrons goes under 100 km, particles are sure to be stopped in the residual atmosphere. This occurs when electrons enter the loss cone, which can be determined by minimizing electron mirror point altitudes through the UNILIB libraries [32]; so, the minimum mirror altitude was also added to the data. The International Geomagnetic Reference Field model (IGRF-13) was used to precisely determine the B-field and the L-shell at the satellite orbit. The dynamics of electrons were described using adiabatic invariants as they are more stable. Therefore, the analysis parameters were the geomagnetic field at mirror points \(\rm{Bm}=\rm{B}/\cos^{2}\alpha\), where \(\alpha\) is the pitch angle that is the difference between the electron velocity and geomagnetic field direction, and the L-shell. A 4-dimensional matrix (t; L; \(\alpha\); B) was filled with data relative to electron CRs where t is the time. Intervals were chosen to be of 8 s for t, 0.1 for L, 15\({}^{\circ}\) for \(\alpha\), and non-linear for B, with the shortest of these latter used where CRs were highest, to better describe the CR spatial variations and with the largest intervals used where the CRs were less frequent, so to obtain a greater number of samples [26; 27; 28]. The time period was from July 1998 to December 2014. The parameter L was restricted to a range between 1.0 and 2.2 to focus the analysis on the inner Van Allen Belts. Moreover, the \(\alpha\) range was 180\({}^{\circ}\), and the geomagnetic field range was between 16 uT and 47 uT. The solar activity is the primary cause of precipitating electrons, it is also able to influence the inner Van Allen Belts, thus, days of moderate to high solar activity were excluded from the analysis. This was performed by neglecting data when the daily Ap index overcame a threshold. The threshold was set according to the seasons and years due to the solar cycle using the relation \(\rm{Ap}=\rm{11.1}+\rm{0.8}\) sin [\(\rm{0.37(year-1996)}\)] + \(\rm{\{2.1-0.1\sin\) [\(\rm{0.37(year-1996)}\)]}}\) cos [\(\rm{0.0172(day-27)}\)]. The phase shift defined by the above relation corresponds to the minimum of the Sun's activity in 1996, whereas the 27-day modulation was dictated by the Sun's rotation. Furthermore, CRs were not included in the analysis whenever the Dst index resulted in being lower than \(-\rm{27\ nT}\). This was done so as not to be influenced by any substorm activity.