## 4 The Inversion of Real Data  
The synthetic data constructed in Section 3 refers to the actual geological data and previous results, which are in line with the actual situation. From the synthetic data tests, the inversion results of synthetic models show that this method can obtain smooth solutions and describe the distribution of anomalous bodies well. The previous sections have discussed the influence of \(p\) and smoothness on the inversion results. It is concluded that \(q=2\) and \(p=1.2\) are suitable for the \(l_{p}\) norm smooth inversion of real data. However, the influence of the upper and lower bound constraints on the inversion results lacks discussion. Because some scholars have discussed in detail the influence of the parameters range on the results [43]. The inversion based on DE also has similar effects. The smaller the upper bound of the magnetic parameters, the larger the boundary of the recovered model, and on the contrary, the more concentrated they are. When dealing with real data, the upper and lower bound constraints need to be concerned. The Zaohuoxi study area is located at the junction of the Oimantag suture zone and the North Kunlun magma arc zone. Most of the area is covered by Quaternary sediments with an average thickness of more than 60 m. The mineral resources in the area were mainly contact skarn-type iron polymetallic deposits. According to the work in [64], the highest magnetic susceptibility of the mineral in this region was magnetite with an average of 0.37 SI. At the same time, there was strong remanence with a maximum of 33.4 A/m in the study area. The magnetic parameters of minerals and rocks in the study area are shown in Table 1. The geomagnetic inclination \(I_{0}\) and the geomagnetic field amplitude \(|\mathbf{B}_{0}|\) were 53.73\({}^{\circ}\) and 53,739 nT, respectively. Figure 13: The comparison of observed data and predicted results. (a) \(1\%\) noise, (b) 5% noise, (c) \(10\%\) noise. The drilling results show that there was magnetite with a small distribution range in line L, which is shown in Figure 14. The magnetic anomaly of line L is shown in Figure 15. The magnetic anomaly in the central and southern part of the study area was regular in shape and distributed in a north-west-west (NWW) band. The anomaly was positive in the south and negative in the north. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rock** & **Lithology** & **Number of Specimens** & **Average Susceptibility\(\chi\) (10\({}^{-5}\) SI)** & **Remament Magnetism \(J_{r}\)** \\ \hline Medium strong magnetism & magnetite ore & 9 & \(3.73\times 10^{4}\) & \(3.34\times 10^{4}\) \\  & chalcopyrite magnetite ore & 4 & \(8.97\times 10^{3}\) & \(2.89\times 10^{3}\) \\  & magnetized skarn & 5 & \(2.07\times 10^{3}\) & \(8.32\times 10^{2}\) \\ \hline Medium magnetism & graniodiorite & 4 & \(5.41\times 10^{2}\) & \(1.70\times 10^{2}\) \\  & biotite graniodiorite & 9 & \(4.02\times 10^{2}\) & \(3.52\times 10^{2}\) \\  & alteration graniodiorite & 9 & \(2.63\times 10^{2}\) & \(1.14\times 10^{2}\) \\ \hline  & marble & 14 & \(1.85\times 10^{2}\) & \(1.22\times 10^{2}\) \\  & alteration monzogranite & 31 & \(1.44\times 10^{2}\) & \(1.27\times 10^{2}\) \\  & biotite plagioclase gneiss & 11 & \(2.39\times 10^{2}\) & \(1.16\times 10^{2}\) \\  & quartz-diorite & 16 & \(1.98\times 10^{2}\) & \(1.29\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Magnetic parameters of minerals and rocks in the Zaohuoxi research area [64]. Figure 14: The magnetic contour map of \(\Delta\)T in the Zaohuoxi area. (ZK is the borehole position and L is the survey line). Figure 15: The magnetic anomaly of line L.  
The magnetic anomaly of line L has a sharp shape (in Figure 15), high intensity (the peak value up to 1980 nT), and a steep gradient. It is the strongest magnetic anomaly zone in the region. [PERSON] et al.