## 2 Materials and Methods
### Estimation of the Ionospheric TEC  
We evaluated the period of days around both eclipses (\(\pm\)5 days compared to the eclipse day). We imposed several conditions for the selection of reference days. First, the geomagnetic conditions for an entire day had to have quiet levels (Kp \(\leq\) 2\({}^{+}\), Dst \(>\) \(-\)30 nT), as well as the Bz component of the interplanetary magnetic field (1 IMF-Bz \(\mid\) \(\leq\) 10 nT) and the solar wind speed (Vsw \(<\) 450 km/s) conditions (see Section 2.4). Second, the days chosen had to have the closest trajectories of the two satellites (SwA and F18) with respect to each eclipse day, both longitudinally and temporally. Third, we wanted to preserve the symmetry of days with regard to the eclipse's day, even though this is less important than the two previous points. Therefore, we worked with the eclipse day, and we took the fifth day before and the fifth day after the eclipse as reference days. Using the GPS-TEC analysis program version 2.9.5, we estimated the vertical TEC (VTEC) at 350 km altitude from RINEX observation files of the dual-frequency signals (\(f_{1}\) and \(f_{2}\)) ([[https://seemala.blogspot.com](https://seemala.blogspot.com)]([https://seemala.blogspot.com](https://seemala.blogspot.com)), last accessed on 25 July 2023) (PSE2018) wherein two types of delay are continuously recorded by the dual-frequency GPS receiver: the carrier phases and the pseudoranges of the \(f_{1}\) and \(f_{2}\). The acquired data were then utilized to determine the slant TEC (STEC) and VTEC. To limit potential errors, we calculated the VTEC values at a 350 km ionospheric height with a 30\({}^{\circ}\) satellite elevation angle as the cut-off (ionospheric pierce point, IPP). TEC values are delivered by software every 30 s and are corrected for receiver and satellite bias using the data obtained from the Center for Orbit Determination in Europe (CODE) ([[ftp://ftp.aiub.unibe.ch/CODE](ftp://ftp.aiub.unibe.ch/CODE)]([ftp://ftp.aiub.unibe.ch/CODE](ftp://ftp.aiub.unibe.ch/CODE)), last accessed on 25 July 2023). We evaluated the quality of the files on the chosen days for each GNSS station before making the final selection of its RINEX files. In order to ensure high-quality data, we preprocessed the RINEX observation files using TEQC software (version of 25 February 2019, [[https://www.unavco.org](https://www.unavco.org)]([https://www.unavco.org](https://www.unavco.org)), last accessed on 20 August 2023) (PSE2018). We made sure that the 24 h RINEX observation files with 30 s intervals were complete and of good quality. For example, we discarded GNSS stations wherein files had general RINEX formatting issues, truncated files, and the like. Also, we verified that there were no errors or data gaps after TEC estimation. This quality checking is critical to making a good comparison of the ionospheric TEC changes between the chosen days. The Chilean network set up by the National Seismological Center (CSN in Spanish); the Argentine network (RAMSAC) (RBMC); the Brazilian network (RBMC); and UNAVCO provided RINEX files of more than 390 GPS stations that fulfilled our specifications (see Figure 1). This study mainly focused on the South American and Antarctic regions. Then, we used 507 and 398 GPS stations used in PSE2018 (see Figure 1 left panel) and PSE2022 (see Figure 1 right panel), respectively. Additionally, we use differential VTEC (DVTEC in TECu and %) to analyze ionospheric irregularities, as shown in Equations (1) and (2) [34; 57; 61]. \[DVTEC_{t}=VTEC_{t}-\overline{VTEC_{t}} \tag{1}\]  
\[DVTEC[\%]_{t}=\frac{DVTEC_{t}}{\overline{VTEC_{t}}}\cdot 100 \tag{2}\]  
where the mean value of VTEC (\(\overline{VTEC_{t}}\)) at the same time of the day, and \(t\) represents the epoch. Also, \(\overline{VTEC_{t}}\) is calculated using the reference days, Days of Year (DoYs) 41 and 51, which correspond to the fifth day before and fifth day after the day of the eclipse (DoY 45) the day of the eclipse in 2018.