## 3 MT Method  
### MT Data Acquisition and Processing  
MT is an electromagnetic (EM) method that measures the time-varying natural electric field \(\mathbf{E}\) and the magnetic field \(\mathbf{H}\) at the surface to provide information regarding the distribution of resistivity in the subsurface. The ratio of the electric field to the magnetic field is expressed as an impedance tensor \(\mathbf{Z}\) that correlates to the electrical resistivity \(\rho\)[36,37]:  
\[\mathbf{E}=\mathbf{Z}\mathbf{H}, \tag{1}\]  
\[\mathbf{Z}=\begin{bmatrix}Z_{xx}&Z_{xy}\\ Z_{yx}&Z_{yy}\end{bmatrix}. \tag{2}\]  
The apparent resistivity and phase that represent the measured data can be expressed as follows:  
\[\rho_{a}=\frac{1}{\omega\mu}|Z|^{2}, \tag{3}\]  
\[\varphi=\tan^{-1}\biggl{(}\frac{\mathbf{Im}(Z)}{\mathbf{Re}(Z)}\biggr{)}. \tag{4}\]  
Five EM field components were acquired during the measurements. There were two mutually orthogonal electric field components (\(E_{x}\) and \(E_{y}\)) and three mutually orthogonal magnetic field components (\(H_{x}\), \(H_{y}\), and \(H_{z}\)). Thirty-two MT stations were distributed throughout the study area, covering 73 km\({}^{2}\) near Limboto Lake, including the Gorontalo Fault and the surface manifestation area (Figure 3). The spacing between the stations was 1-2 km. The MT data were collected in 2013 using MTU-5A units manufactured by Phoenix Geophysics Ltd., Toronto, ON, Canada [38]. The EM time-series data were recorded for 8-22 h to obtain optimal MT transfer functions that fulfilled the need for adequate  
Figure 2: Rose diagrams showing the frequency (**a**) and length (**b**) of the stretch. The red line shows the main stress direction.  
penetration and good data quality. The measurement period ranged from \(3.125\times 10^{-3}\) to \(104\) s. The noise measured in the field was caused by the settlements and activities of residents around Limboto Lake, Pentadio.  
The time-series data were converted into frequency domain data by the Fourier-transform process, yielding other types of data that were expressed as apparent resistivities and impedance phases. In general, the data quality was good (up to 1 s). The curves of the apparent resistivity and impedance phase for all measuring stations are shown in Supplementary Material 1. Over longer periods, the data quality decreased because of the lack of data stacking in these range periods. Quality improvement of the measured data was achieved by performing a cross-power selection process. This cross-power selection process was guided by the dispersion relation [39]:  
\[\phi(\omega)=\frac{\pi}{4}-\frac{\omega}{4}\int_{0}^{\infty}log\frac{\rho_{a}( x)}{\rho_{0}}\frac{dx}{x^{2}-\omega^{2}}. \tag{5}\]  
Based on the principle of causality, this relationship indicates that neighboring frequencies provide similar transfer functions. This implies that the apparent resistivity at a certain frequency \(\rho_{a}\)(x) can be estimated from the impedance phase at the next neighboring frequency \(\phi(\omega)\). The data were then smoothed by cubic spline interpolation. Figure 4 depicts a comparison among the three types of apparent resistivity and phase curves for  
Figure 3: Location of MT and gravity stations in the Limboto Lake—Pentadio Area. The black dots depict the distribution of MT stations, and the green dots depict the distribution of gravity stations. The red dot represents the location of the hot spring, and the blue dot represents the cold spring.  
MT-01 and MT-03. The first is the raw data (denoted by blue circles), the cross-power selected data (denoted by red solid circles), and the final data, which were generated by interpolating the cross-power selected data (denoted by black solid lines). Smaller error bars were observed in the last type of data for longer periods.