## 4 Data Acquisition and Analysis
### Dimensionality and Strike Analysis  
Dimensionality analysis provides valuable insights into the dimensionality and strike direction of the underlying subsurface structure. Understanding whether the subsurface is 1D, 2D, or 3D is crucial for selecting the appropriate modeling approach. Dimensionality analysis can be performed in several ways, one of which involves using the phase tensor (PT), which is less sensitive to galvanic distortion [45]. The phase tensor can be represented graphically by PT ellipses, which contain three key pieces of information: the minimum phase (\(\phi_{\text{min}}\)), the maximum phase (\(\phi_{\text{max}}\)), and the skew angle (\(\beta\)). The values of \(\phi_{\text{min}}\) and \(\phi_{\text{max}}\) define the shape of the ellipses, indicating the likely direction of the geoelectrical strike. The shape of the PT ellipses also provides insights into the dimensionality of the structure: they are perfectly circular for 1D structures and elongated for 2D or 3D structures. The PT skew angle (\(\beta\)) is another measure of dimensionality, quantifying the asymmetry of the phase tensor. A perfectly 1D condition typically has a \(\beta\) value of zero, while larger \(\beta\) values indicate higher-dimensional structures. For 2D conditions, \(\beta=0\) is necessary, but not sufficient. The commonly suggested threshold for a 2D condition is \(\beta\pm\)3, though \(\beta\pm\)5 is often used due to field conditions [46; 47; 48]. For our analysis, we set the maximum threshold for \(\beta\) at \(\pm\)5 to define a 2D condition. Figure 4 displays the PT ellipses for several periods across the study area, with the color bar representing \(\beta\) values. The computed PT values suggest a 1D/2D response at short periods, transitioning to 3D at longer periods. Stations F2 and N2 exhibit consistent 3D features across all periods, which may be attributed to noise effects shown in Figure 3. This suggests that the shallow subsurface below the study area is predominantly 1D, becoming more complex at greater depths. Therefore, in addition to 1D inversion, it is advisable to perform 2D and 3D modeling. For the strike analysis, we excluded the noisy data, as such data can cause unstable estimations [27]. Figure 5 presents a rose diagram illustrating the geoelectrical strike orientation derived from both the impedance invariant and the phase tensor across all MT sites. The plots are divided into several period ranges, showing how the strike estimation is distributed locally. Both the \(Z\)-strike and PT rose plots reveal that the strike estimation is primarily oriented between N-S and NNE-SSW, with a noticeable shift to a nearly W-E orientation at the intermediate period range of 1-10 s. This shift is likely due to local effects within that period. Overall, the dominant strike direction from both the \(Z\)-strike and PT-derived strike is N10\({}^{\circ}\)E.  
Figure 3: Apparent resistivity and phase curves of all 10 observation stations in this study. Red and blue circle represents the xy and yx component respectively. Since both strike estimations have a \(\pm\)90\({}^{\circ}\) ambiguity [45,49], further verification is needed to confirm the precise orientation. Commonly, tipper data, the transfer function of the vertical \(H\), is used to resolve this ambiguity. However, since no tipper data were available in our observations, we relied on existing geological records. Most geological features in the Pingtung Plain are oriented between N-S and NNE-SSW, as depicted in Figure 1. Therefore, our estimated strike direction aligns closely with the geological data, and we determined that the strike derived from our survey is N10\({}^{\circ}\)E. This direction was used to rotate the data, aligning them parallel to the strike (TE) and orthogonal to the strike (TM) prior to the inversion. Figure 4: Phase tensor ellipse distribution along the survey lines, mapped at six different periods, shows characteristics change from 1D/2D nature to 3D.