# Monitoring of Ionospheric Anomalies Using GNSS Observations to Detect Earthquake Precursors
## 2 Materials and Methods
### Model Products and Testing  
The model described in Section 2.1 was tested to detect anomalies produced by earthquakes. In order to identify cases to be studied, besides the magnitude, we must consider the density of the CORSs surrounding the epicenter and within a radius of thousands of kilometers.  
Finally, two cases were identified:  
1. The Nepal earthquake of 2015: * magnitude: 7.8 Mww (Mww means Moment W-phase. The generic notation is Mw [58].); * Location: 28.231\({}^{\circ}\)N, 84.731\({}^{\circ}\)E; * Depth: 8.2 km; * Origin time: 25 April 2015 06:11:26 UTC (DOY 115).
2. The Turkey earthquake of 2023: * magnitude: 7.8 Mww (Mww means Moment W-phase. The generic notation is Mw [58].); * Location: 37.226\({}^{\circ}\)N, 37.014\({}^{\circ}\)E; * Depth: 10.0 km; * Origin time: 06 February 2023 01:17:34 UTC (DOY 37).  
In both situations, we have a reasonable availability of permanent GNSS stations in certain areas, like Asia or Europe, in which they are homogeneously distributed, and conversely poor density on the sea and ocean surface as well as in the central part of Africa (where there are no active stations). This point is crucial since GNSS VTEC estimation is sensitive to the coverage of the IPPs over the area of interest. Inhomogeneous coverage can lead to negative VTEC value estimations during nighttime, and this is the case when a non-negligible part of the area of interest is covered by the ocean or is a territory without permanent GNSS stations [59].  
Starting from the model outputs, it is possible to generate plots of both time series at a point of the ionospheric layer and/or maps (latitude-longitude) at a given time. In this work, we generated the following for the seismic events mentioned above:  
* The time series of the VTEC in the epicenter;
* the time series of VTEC rate SNR in the epicenter (The SNR of the i-th element of an estimated parameter \(\hat{p}\) with covariance matrix \(Q_{\beta}\) can be estimated as \(\frac{\hat{p}_{i}}{\sigma_{p_{i}}}.\));
* The map of 24 h VTEC, that is, the time series of the VTEC in which the values are mapped with DOY on the \(x\) axis and the hour of the day on the \(y\) axis;
* The map of the 24 h VTEC rate SNR, that is, the time series of the VTEC rate SNR in which the values are mapped with DOY on the \(x\) axis and the hour of the day on the \(y\) axis;
* The maps of the differential VTEC, namely, the differential VTEC computed on every day with respect to the mean of the values of the previous 15 days, with a time step of 1h (\(x\) axis: longitude; \(y\) axis: latitude). DTEC (or DVTEC), as well as the other differential quantities, is computed according to the formula  
\[DTEC=100\cdot\frac{VTEC-\langle VTEC\rangle}{\langle VTEC\rangle}\]  
where \(\langle VTEC\rangle\) is the average value computed from 15 previous numerical values. VTEC is a function of latitude, longitude, and time, so in generating maps we compute DTEC starting from the VTEC of a specific day at a given hour and from the average values of VTEC for the same point of the previous 15 days at the same hour [60; 61; 62]. With reference to TEC, this approach is used to monitor the pattern of ionosphere parameter variations during the days before earthquakes. The corresponding maps allow to investigate the possible space-time correlation of the variation with the earthquake area and hour. In the past, it has been used for Nepal earthquake and also for earthquakes in Greece and Italy [61; 63; 64].;
* The maps of the VTEC rate SNR, with a time step of 1 h (\(x\) axis: longitude; \(y\) axis: latitude);
* The maps of the differential SNR (DSNR) of the VTEC rate, with a time step of 1 h (\(x\) axis: longitude; \(y\) axis: latitude).  
In addition, we compared time series of the VTEC and maps of the DTEC with those from GIMs. The overall methodology adopted in this work is reported in Figure 1.