## 2 Materials and Methods
### Methods of Analysis
In case the anomaly is compatible with more than one seismic event, one of the following four methods is used to select which earthquake is associated with the anomaly:  
1. **Method 1 \"All anomalies-EQs\"**. This method selects all earthquakes compatible with the investigated anomaly. The advantage is that we do not apply any assumption for the analysis, and we can suppose that, in case the statistics are sufficient, the \"wrong\" anomaly-earthquake couples increase just the background without creating additional artificial concentrations of anomalies. On the other side, one disturbance can be produced only by one earthquake, and so, unless the signal is superposed (or under the satellite resolution), the anomaly could not be associated with more than one event. For this reason, we also introduce the following methods. 2. **Method 2 \"Min [log(AT R)]\"**. This method selects the closest earthquake in space (\"R\") and time (anticipation time \(\Delta\text{T}=time_{EQ}-time_{anomaly}\)). The selection is made by searching for the minimum of the following equation: \(\log_{10}(\mid\Delta\text{T}\cdot\text{R}\mid)\). The criterion is based on the assumption that an anomaly is more likely to be produced by the closest earthquake in space and time. 3. **Method 3 \"Max (magnitude)\"**. This method selects the earthquake with the highest magnitude in the space and time domains of interest. The assumption is that a larger earthquake produces more anomalies before its occurrence that can be detectable in the ionosphere. 4. **Method 4 \"Closer (Rikitake)\"**. This method takes into account that a larger earthquake with a magnitude \(M\) is expected to have a longer anticipation time \(\Delta T\) of its possible precursors, according to the Rikitake law [37], expressed as: \[\Delta T=a+b\cdot M\] (1)  
With this method, the anticipation time \(\Delta T\) is calculated using the \(a\) and \(b\) coefficients found for the _Swarm_ satellite data (magnetic field or \(Ne\)) by [PERSON] et al. [29] and inserted in the Rikitake law expression. On the other side, the decimal logarithm of the real anticipation time is calculated, and the earthquake that presents the minimum difference with respect to the Rikitake law is selected. Please note that the first three methods are the same as those used by [PERSON] et al. [29], while here, a new fourth method is also proposed. Hereafter, if no indication is given about the method, the analysis will follow Method 1, i.e., all anomalies are associated with all the compatible earthquakes. Finally, it is worth noticing that any method presents advantages and disadvantages, as we do not know the exact mechanism behind the generation of ionospheric disturbances (even if several theories have been proposed). We can rely on the concentrations of anomalies confirmed by several of these methods and expect that a future better understanding of the LAIC mechanism can improve the selection of the best of the above methods or help formulate a new one. Of course, all methods take advantage of the fact that all analyses are retrospective. It would be more difficult to adapt the methods for a real time analysis rather than establish a significant correlation between ionospheric anomalies and earthquakes, but this is not within the present scope of the work. The results are illustrated in a \"standard\" representation graph (see, for example, Figure 1), where the horizontal axis represents the time of the anomaly with respect to the earthquake occurrence (i.e., negative days before the earthquake occurrence and positive days after), and the vertical axis is the distance of the detected anomaly in terms of degrees from the epicenter. Therefore, each anomaly is placed on this graph in terms of distance in time and space from its associated earthquake (according to one of the four previously listed methods). All the anomalies and earthquakes are superposed on the same graph, and, in the end, the results are binned in 50 horizontal and 10 vertical cells (or bins).