## 2 Materials and Methods  
### TEC Values  
Anomalies in the TEC of the ionosphere can be obtained from the processing of continuously operating reference station GNSS networks or provided in the form of GIM files by the IGS and its various Analysis Centers (ACs) [30; 31]. As explained previously, these GIMs are used for the current study due to their reliability, global coverage, and availability for many years. From the different GIM files computed by the different ACs--namely the Chinese Academy of Science (CAS), the Center for Orbit Determination in Europe (CODE), the European Space Agency (ESA), the Jet Propulsion Laboratory (JPL), the Universitat Politecnica de Catalunya (UPC), and Wuhan University (WHU)--or the IGS average product, the rapid solution computed by UPC (files with the extension \"urprg\" downloadable from [31]) is used. For the 13.7 years under study, that is, from 1 January 2011 to 1 October 2024, these files provide TEC values in latitudinal and longitudinal grids of 2.5-degree spacing in the latitude (from 87.5\({}^{\circ}\) S to 87.5\({}^{\circ}\) N) and 5-degree spacing in the longitude (from \(-180^{\circ}\) W to 180\({}^{\circ}\) E, being the extremes coincident). These were consistently computed every two hours (it is worth mentioning that GIM files from other ACs changed at some point from 2 h to 1 h) for the entire period of the study, with the exception of day 283 of 2018 to day 205 of 2019, where there is a data gap also present for the other IGS ACs. The latency for the user to access these files is about 2 days (the same for the other IGS ACs), which should be enough for most of the predictions, taking into account the above-mentioned forecast period of up to one week. Beyond the tectonic stresses leading to an earthquake, there are other sources of anomalies in the TEC of the ionosphere coming from solar and geomagnetic activity, for example [14; 26]. Some indicators of them are the F10.7 index (representative of solar activity), the Disturbance Storm Time (Dst) index, which measures the severity of magnetic storms, the Kp index of global geomagnetic activity, and the Interplanetary Magnetic Field (IMF), which refers to the magnetic field carried by the solar wind as it passes through interplanetary space. While these variables could also be considered for the prediction, I can make use of the usually different signatures of TEC anomalies of seismic origin and those of other geomagnetic or solar origin that have been documented: while seismo-ionospheric disturbances usually last a few hours [14; 33; 34], ionospheric disturbances of solar and other geomagnetic origin usually last from several hours to a few days [35; 36]. It is therefore assumed that a detailed analysis of GIM files can be sufficient for earthquake prediction, at least for the largest events. Let us imagine that we would like to predict possible future earthquakes close to a location of latitude \(\varphi\) = 28\({}^{\circ}\) N and longitude \(\lambda\) = 84\({}^{\circ}\) N (indeed an earthquake of magnitude \(M_{w}\) = 7.8 happened on 25 April 2015, for example, with a quite close epicenter of \(\varphi\) = 28.231\({}^{\circ}\) N and longitude \(\lambda\) = 84.731\({}^{\circ}\) N). Considering a spherical Earth of radius \(R\) = 6371 km, some increments in latitude \(\Delta\varphi\) and longitude \(\Delta\lambda\) correspond to distances along the meridian \(d_{m}\) and the parallel \(d_{p}\) given, respectively, by the following:  
\[d_{m}=R\Delta\varphi \tag{3}\]  
\[d_{p}=R\cos\varphi\Delta\lambda \tag{4}\]  
The substitution of these \(d_{m}\) and \(d_{p}\) by the \(r\) in Equation (1) for a particular magnitude of a subsequent earthquake (say \(M_{w}\) = 8) gives the possible area of disturbance in the ionosphere to be looked for in the prior GIM files, Figure 2. That is, for \(M_{w}\) = 8 in Equation (1) the radius \(r\) results in 2981 km.