## 4 Results
### 3-D Magnetotelluric Data Inversion and Results  
A 3-D model of the electrical resistivity distribution beneath the study area was calculated using the nonlinear inversion algorithm within the academic version of the Modular Electromagnetic (ModEM) Inversion code [41; 42]. The recorded data for the diagonal components of the MT impedance tensors and phase elements exhibit substantial errors at specific periods. Multiple inversions were conducted using different data subsets, including full impedance tensor data, off-diagonal components exclusively, and phase information alone. The damping factor, \(\lambda\), was set to a value of 1 for all the inversions. A comparison of the four models obtained from the components, as stated above, reveals that the inversion of full impedance tensor data, diagonal components only, and phase components only produce the inverse model, with little change from the initial model. This generally degraded the performance of the inversion, and it was difficult to make sense of the models. This is because the amount of error is relatively high, and a large scatter hides the information which is needed for the inversion. The inversion  
Figure 6: The phase tensor response along a profile crosses the survey area from southeast to northwest, profile A-A\({}^{\prime}\) (Cf. : Figure 2). The red cross indicates the location of the hot spring. Phase tensor depiction, as introduced by [PERSON] et al. [40]. results of off-diagonal elements only yielded good RMS misfits. Considering the reasons above and the smooth curves of off-diagonal elements, the inversion results of off-diagonal components only are discussed in this article because, with proper Root Mean Square Error (RMSE), they can accurately reveal the structures in the study area. A total of 32 MT sites were acquired, but only 28 sites were used for the 3-D inversion, while 5 sites were discarded from the 3-D inversion because there were strongly affected by cultural noise. The geophysical inversion process was outsourced to a high-performance cloud computing environment, and most of them successfully completed after 50 iterations. The following settings were used for the inversion: 23 periods and four impedance tensor elements (real and imaginary parts of the two off-diagonal elements) regularly distributed in the range of 316 to 0.001 Hz, with a resistivity model consisting of 42 \(\times\) 59 horizontal and 66 vertical cells. The inner grid had lateral dimensions of 400 \(\times\) 400 m, and it was expanded with 10 padding cells in each direction, each increasing by a factor of 1.5. The vertical grid began at 50 m and increased by a factor of 1.2. In the context of 3-D modeling, a critical factor in creating an accurate model involves selecting an optimal prior resistivity model that closely matches the average resistivity observed in the study data, as emphasized by Reference [42]. Using two separate homogeneous half-space models with resistivity values of 100 \(\Omega\)m and 500 \(\Omega\)m in the process of forward modeling resulted in initial misfit values of 10 and 36, respectively. This observation suggests that the homogeneous half-space model with a resistivity of 100 \(\Omega\)m is in closer agreement with the average resistivity of the dataset, leading to the preference for a homogeneous, uniform half-space with a resistivity of 100 \(\Omega\)m. Regrettably, there is a lack of local borehole data to refine our observations. In Figure 7, we present a comparison of the observed and estimated data for the off-diagonal elements (XY and XX) of the apparent resistivities. This serves to evaluate the level of deviation in data acquired after 50 iterations for the favored model, which typically demonstrates a favorable match between the measured and predicted data. Figure 8 shows a model obtained by the 3-D inversion of data, with a final overall RMSE of 1.26. The model obtained by inverting the data in this study area reflects the upper crustal structure of the Kasane region.