# Recent Advances and Challenges in the Seismo-Electromagnetic Study: A Brief Review
## 6 Applications of Seismo-Electromagnetic Signals in Earthquake Forecasting  
There are some methods to evaluate whether the seismo-electromagnetic phenomena contain precursory information, among which the receiver operating characteristic (ROC) curve and Molchan's error diagram are the two most widely used [160; 210]. Statistical tests have shown that the electromagnetic anomalies may contain predictive information for major earthquakes, with probability gains of approximately 2-6 [74; 160; 210]. In addition to seismo-electromagnetic phenomena, other precursors were also be observed. A representative event of which various geophysical precursors were documented is the 2011 Tohoku earthquake (Mw 9.0) [38; 140; 211; 212; 213; 214; 215; 216; 217; 218; 219; 220]. Locations of seismo-geomagnetic anomalies in spatial distribution showed a good correlation with the epicenter of the earthquake [38; 220]. These spatiotemporal results were consistent with those obtained from other independent observations such as the groundwater level and GPS displacements [219]. The related precursory characteristics of the earthquake are listed in the Table 1 below. The coupling of multiple pre-earthquake phenomena provides new insights on earthquake preparation process, suggesting that incorporating multi-geophysical information might be a possible means of improving earthquake forecast. \begin{table}
\begin{tabular}{l l l l} \hline
**Observation** & **Leading Time** & **Characteristic** & **Reference** \\ \hline \multirow{3}{*}{Seismic activity} & 23 years & Seismic quiescence in rupture region & ([PERSON], 2011 [211]) \\  & 6 years & Decade-scale decrease in b value & ([PERSON] et al., 2012 [212]) \\  & A few months & Seismicity exhibited distinct minima & ([PERSON] et al., 2013 [213]) \\  & 1 month & Foreshock sequence and slow slip & ([PERSON] et al., 2012 [214]) \\ \hline \multirow{3}{*}{Deformation} & 2 months & Crustal movement changes & ([PERSON] et al., 2014 [215]) \\  & 1 month & Slow slip event & ([PERSON] et al., 2013 [216]) \\  & 1 month & GPS surface motion & ([PERSON] et al., 2014 [217]) \\ \hline Fluid & 3 months & Groundwater level decrease & ([PERSON] et al.,2016 [218]) \\ \hline Geomagnetism & 2 months & Geomagnetic diurnal variation changes & ([PERSON] et al., 2016 [219]) \\ \hline Ionosphere & 40 min & TEC enhancement & ([PERSON], 2011 [140]) \\ \hline \end{tabular}
\end{table} 
Table 1: Representative precursory characteristics before the 2011 Tohoku earthquake. As the earthquake process is rather complex, the earthquake preparation phase cannot be easily monitored using a single approach. To improve the reliability of earthquake forecasting, the two following models that could integrate precursory information from different approaches were proposed. One is the earthquake model that combines self-exciting and mutually exciting elements from the Hawkes process [62; 221; 222]. The core idea of this combined model is that the status of the earthquake event at present is controlled by the event itself (self-exciting) and all the external factors (mutually exciting) in the past. The conditional intensity function is a time-varying point process with rate \(\lambda(t)\) written as  
\[\lambda(t)=\mu+\lambda_{s}(t)+\lambda_{E}(t) \tag{1}\]  
where \(\mu\) represents the constant background rate, \(\lambda_{s}(t)\) is the self-exciting term that models the information from past seismic events, and \(\lambda_{E}(t)\) is the external excitation term that models the information from non-seismic observations such as the seismo-electromagnetic anomalies. The other is a network model based on machine learning, where multi-geophysical precursor information is taken as the input layer, and the factors of earthquakes such as time, location, and magnitude are taken as the output layers, as shown in Figure 1. Some important features in discriminating pre-earthquake perturbations may be established by the machine learning network.