# Co-Seismic Magnetic Field Perturbations Detected by Swarm Three-Satellite Constellation
## Appendix A Automatic Detection of Possible Co-Seismic Anomalies  
In this Appendix, a completely automatic procedure to detect possible co-seismic anomalies is presented. The advantage of this procedure, with respect to the one presented in the paper, is that it is completely objective and re-producible by the defined criteria. With this procedure, we want to support the results of our work. However, we recognize that an automatic procedure cannot fully evaluate the signal the way a human can, even if some constraints can replace our considerations to the selected anomalies presented in our paper. The automatic procedure starts from the filtered signal, i.e., the magnetic Y component of the Swarm satellite minus the IGRF-12 model and filtered with high pass filter with a 0.25 Hz frequency cut-off. The geomagnetic latitude is computed, taking into account the dipole calculated with the IGRF-12 model. Only the data inside \(-50^{\circ}\) and \(+50^{\circ}\) are taken into account to avoid the auroral and polar regions that are geomagnetically too active to identify any possible co-seismic signal. The Root Mean Square of the whole track is computed in analogy with the procedure used in [22; 27; 37]. A moving window of 20 s length is then used from 1 min after the earthquake occurrence until to search the first anomaly in time if any. One minute was chosen as the minimum time that the signal needs at least to be transmitted from the epicentre to the satellite altitude (\(\geq\)450 km). A pure electromagnetic wave requires less than one second, but this eventual phenomenon was not the goal of this paper, and a pure gravity wave would take around 3.5 min. The anomaly is defined with a threshold (kt) equal to 2.0 comparing its root mean square rms into the moving window with the one of the whole track, i.e., rms/RMS \(>\) kt. This threshold corresponds to about two standard deviations commonly used in similar approaches. Thresholds of 1.5, 1.75, 2.25 and 2.5 have been tested too, but they provide worst results (i.e., lower correlation coefficient of the results) with respect to kt = 2.0. The automatic procedure found anomalies in 31 tracks out of 37 investigated tracks, i.e., 83.8%. This number is much higher than the selected anomalies in the main text (12). Despite this, we need to note that several anomalies are not reliable; for example, they occur too early in relation to the distance from the earthquake epicenter or too late and close with respect to the earthquake epicenter. The latter case could be a continuation of the co-seismic effect in ionosphere after its arrival. The distance from the epicentre and satellite versus the time for the 31 tracks is represented in Figure 11. The time to reach the epicentre from the hypocenter has been estimated by a velocity of 4 km/s and subtracted from the data. The linear regression provides a slope of \((2.60\pm 0.41)\)\(10^{-3}\) min/km that corresponds to a mean propagation velocity of \((6.4\pm 1.0)\) km/s. The obtained velocity is quite similar to the one calculated in the main text, but the dispersion of the data is higher (in fact, the correlation coefficient is much lower). In analogy with the analyses of the main text, the model with two velocities has been tested with the same approach, using all the 31 anomalies and taking into account the air temperature and the height of hmF2 in addition to the simple model with one velocity. Figure 12 shows the results obtained by the models with one and two velocities for the automatically detected anomalies. Additionally, in this case, the model with two velocities presents lower residuals with respect to the first one. We note that the residuals are about 10 times more than the corresponding calculus in the main text (Figure 16). This is partly due to the higher number of cases (31 instead of 12), the longer analyzed time (until about 30 m instead of 20 m) and, finally, to the lower quality of the co-seismic anomaly detection of the automatic approach.