## 2 Materials and Methods
### Methods of Analysis
For each bin, the number of anomalies falling in the bin is divided by its geographic area (circle or annulus), obtaining the anomalies' density represented by a color bar scale. For the first row (which represents the 50 temporal bins closer to the epicenters), the maximum concentration of such density is searched, and its location (pxmax), the number of anomalies (Nmax), the number of EQs associated with these anomalies (NEQmax), and the total sum of the released energy (E\({}_{\text{EQ}}\)) is reported in the second line of the heading. Furthermore, for such a maximum density/concentration bin, other statistical quantities are evaluated and described in the following paragraph. To evaluate if the results obtained from the WSC of real earthquake and anomaly data are statistically significant, 30 random space-time homogeneous distributions of anomalies, with the same number of anomalies as each real data analysis, have been generated. Then, the WSC algorithm has been applied with the same parameters used for the real satellite anomalies. In particular, for the maximum concentration, we estimate the quantity, \(D_{MAX}\)/\(D_{0}\), that represents the density of anomalies in the maximum (\(D_{MAX}\)) with respect to a theoretical homogeneous distribution of anomalies (\(D_{0}\)):  
\[D_{MAX}/D_{0}=\frac{N_{anom}^{MAX}\cdot\Delta T^{Tol}\cdot Area^{Tol}}{N_{ anom}^{Tol}\cdot\Delta T^{pixel}\cdot Area^{pixel}\cdot n_{EQ}} \tag{2}\]  
where \(N_{anom}^{MAX}\) is the number of anomalies in the maximum pixel (which, in the title of the graphs, is indicated as \"\(N_{MAX}\)\") that has a duration \(\Delta T^{pixel}\) and covers an area \(Area^{pixel}\). The total number of identified anomalies (independently from the earthquakes) is \(N_{anom}^{Tol}\), and it is also indicated in the first line of the heading of the graph as the second number (63,178 in the case of Figure 1). The whole analyzed area (i.e., the spherical zone between \(50^{\circ}\)S and \(50^{\circ}\)N of geomagnetic latitude) is \(Area^{\text{Tot}}\), and the total analyzed time is \(\Delta T^{\text{Tot}}\) (in this work, it is 8 years). The quantity \(D_{MAX}/D_{0}\) has been calculated for real analysis, i.e., \([D_{MAX}/D_{0}]_{\text{real}}\), and its mean random value \([\overline{D_{MAX}/D_{0}}]_{random}\) and its standard deviation (\(\sigma\)) have been estimated over a set of 30 random simulations. By these quantities, we defined the two statistical parameters, \(d\) and \(n\):  
\[d=\frac{[D_{MAX}/D_{0}]_{real}}{[D_{MAX}/D_{0}]_{random}};n=\frac{[D_{MAX}/D_{0 }]_{real}-\overline{[D_{MAX}/D_{0}]}_{random}}{\sigma([D_{MAX}/D_{0}]_{random })} \tag{3}\]  
According to the above definitions, \(d\) represents how many times the real maximum concentration is higher than the one expected from random simulations, and \(n\) estimates how many standard deviations (of random simulations) the real concentration is higher than the random one. The number of random simulations was chosen as a function of the results in terms of the reached stability of the obtained values of \(d\) and \(n\). We found that, generally, even with one or two random simulations, the estimation of \(d\) is accurate up to one decimal digit (if the number of anomalies is greater than 30,000), while \(n\) requires more random runs, i.e., at least 15 or 30 simulations for about 30,000 anomalies. When the concentration of the real anomalies is compatible with a homogeneous random simulation of anomalies, we expect \(d\cong 1\) and \(n\cong 0\). At the same time, we define a statistically significant concentration, i.e., a real distribution of anomalies with the largest concentration significantly differing from a random distribution, if \(d\geq 1.5\) and \(n\geq 4.0\), as suggested by [PERSON] et al. [29].