## 3 MT Method
### MT Data Acquisition and Processing  
MT data were recorded in the northern domain of Aceh using MTU-5A units manufactured by Phoenix Geophysics Ltd., Toronto, ON, Canada, with 33 total stations spread out as shown in Figure 3. All the data recorded include five components of the time-varying electromagnetic field, which comprises two components of electric field \(\left(E_{x},E_{y}\right)\), two components of horizontal magnetic field \(\left(H_{x},H_{y}\right)\), and one component of vertical magnetic field \(\left(H_{z}\right)\). In data acquisition, MT stations can be grouped into 4 lines based on the similarity of data acquisition, namely Line A, Line B, Line C, and Line D (Table 1). The frequency measurement ranged from 320 to 0.05 Hz.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Line** & **Acquisition Time** & **Recording Time** & **Spacing (km)** & **Direction** & **Site Name** \\ \hline \multirow{2}{*}{A} & October and & & & & **ACH01**, **ACH02**, **ACH04**, **ACH05**, \\  & November 2008 & 12 h & 6–10 & SW-NE & **ACH06**, **ACH07**, **ACH08**, **ACH09**, \\ \end{tabular}
\end{table}
Table 1: Description of line, acquisition time, line direction, and site name.  
Figure 3: The distribution of MT stations (black triangle) at the northern Aceh research site, which is divided into 4 lines (yellow line) based on data acquisition time into Line A (October and November 2008), Line B (August 2009), Line C (July–August 2012), and Line D (July–August 2012).  
The first step involves preprocessing the time series data (TS3, TS4, TS5), where the data are grouped based on the duration of data collection. Next, noise peaks are removed from the recorded electric field data, and corrections are made to the recorded electric field data. Then, the MT time series data were transformed into the frequency domain using Fast Fourier Transform (FFT) and filtered using robust processing [40,41], producing results in MTH and MTL files using SSMT 2000 software. To choose good and bad data, we used MT-corrector software v.5.6.0.0 (Nord-West Ltd., Moscow, Russia), which used cross-power (smoothing) XPR analysis and the dispersion relation (DR) concept, which provides a more intuitive insight into how data should be corrected [42]. The dispersion relation constrained the cross-power selection is written in Equation (6) [43]  
\[\phi(\omega)=\frac{\pi}{4}-\frac{\omega}{4}\int_{0}^{\infty}log\frac{\rho_{a}( x)}{\rho_{0}}\frac{dx}{x^{2}-\omega^{2}} \tag{6}\]  
where \(\phi\) is the impedance phase, \(\omega\) is the frequency, \(\rho_{a}\) is the apparent resistivity, and \(\rho_{0}\) is \(1/\sigma_{0}(\omega)\).  
The smoothness property of the MT curve data was validated using smoothing splines for robust estimation [39]. The data were then smoothed by cubic spline interpolation. The unknown constants for correcting data were solved by automatically fitting the calculated curves to the corresponding real part (log amplitude) spline using dispersion relation constraint [42]. Dispersion relation (DR) in post-processing MT detects and eliminates noisy/biased MT data [18]. It is an efficient quality assessment tool for MT data at broad-band frequencies [42]. The result of post-processing data using cross-power XPR analysis and smoothing using DR was reported to produce smoother resistivity response curves with smaller error bars compared to processing without using DR, especially at low frequencies, as shown in Figure 4. Figure 4a,c,e shows the cross-power XPR analysis and smoothing without the concept of DR. In contrast, Figure 4b,d,f shows the cross-power XPR analysis and smoothing with the DR concept. The result of the post-processing is found in the form of an EDI file, which provides information about impedance, apparent resistivity, phase, and the tipper parameter.