## 4 Discussion
### Typical Models  
#### 4.2.1 Deep-Depth Model  
The resistivity in the x-direction of the Anis1 model, the Anis2 model, and the Iso1 model is consistently 50 \(\Omega\cdot\mathrm{m}\), while the resistivity in the y-direction of the Anis1 model, the Anis2 model, and the Iso2 model is consistently 200 \(\Omega\cdot\mathrm{m}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Grids in x-, y-, and z- Direction** & **Degrees of Freedom** & **Number of Non-Zero Elements** \\ \hline \multirow{4}{*}{Nodal method} & 20 \(\times\) 20 \(\times\) 20 & 37,044 & 1,914,046 \\  & 35 \(\times\) 35 \(\times\) 35 & 186,624 & 9,506,418 \\  & 50 \(\times\) 50 \(\times\) 50 & 530,604 & 27,283,608 \\ \hline \multirow{2}{*}{Mixed nodal and edge-based element method} & 20 \(\times\) 20 \(\times\) 20 & 35,721 & 1,290,361 \\  & 35 \(\times\) 35 \(\times\) 35 & 182,736 & 6,817,756 \\ \cline{1-1}  & 50 \(\times\) 50 \(\times\) 50 & 522,801 & 19,763,401 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the stiffness matrix of the two methods.  
Figure 12: The distribution of A and \(\phi\) on a nodal element.  
As depicted in Figure 6, RExB and REyB for the Iso1 model exhibit remarkable similarities to those of the Anis1 model; similarly, RExA and REyA for the Iso2 model closely resemble those of the Anis1 model. Notably, the fourth row mirrors the characteristics observed in the first row. As depicted in Figure 7, IExB and IEyB for the Iso1 model closely resemble those for the Anis1 model; IExA and IEyA for the Iso2 model demonstrate a similar pattern to those for the Anis1 model. Again, the fourth row closely resembles the first row.  
Comparing the electric fields of the Anis1 model with those of the Iso1 model, it can be inferred that if a principal resistivity is oriented in the x-direction, then the horizontal electric fields induced by \(Ex\) are primarily influenced by this principal resistivity. Similarly, comparing the Anis1 model with the Iso2 model leads to the conclusion that when a principal resistivity is oriented in the y-direction, the horizontal electric fields induced by \(Ey\) are predominantly affected by this principal resistivity. Lastly, comparing the Anis1 model with the Anis2 model reveals that if a principal resistivity is oriented in the z-direction, it has minimal impact on the horizontal electric fields. This third finding is consistent with the previous two.  
Considering the relationship between magnetic fields and electric fields, we can also infer that: (1) if a principal resistivity is oriented in the x-direction, then the horizontal magnetic fields induced by \(Ex\) are primarily influenced by this principal resistivity; (2) if a principal resistivity is oriented in the y-direction, then the horizontal magnetic fields induced by \(Ey\) are predominantly affected by this principal resistivity; (3) if a principal resistivity is oriented in the z-direction, it has minimal impact on the horizontal magnetic fields.  
Considering the relationship between electromagnetic fields and apparent resistivities or phases, we can further infer that: (1) if a principal resistivity is oriented in the x-direction, then the xy-mode apparent resistivity and the xy-mode phase are mainly influenced by this principal resistivity; (2) if a principal resistivity is oriented in the y-direction, then the yx-mode apparent resistivity and the yx-mode phase are mainly influenced by this principal resistivity; (3) if a principal resistivity is oriented in the z-direction, then this principal resistivity exhibits almost no influence on the MT responses. These phenomena are also consistent with the conclusions put forth in Reference [20].