# Three-Dimensional Magnetic Inversion Based on an Adaptive Quadtree Data Compression
## 3 Application in Mineral Exploration  
The adaptive quadtree compression algorithm was applied to the magnetic data set collected for the Ma'anshan magnetite deposit. The magnetite deposit is located in the Ningwu mining area in the middle and lower reaches of the Yangtze River. The magmatic activity in this area was a strong, mainly volcanic eruption and magmatic intrusion in the Yanshanian period. The main subvolcanic rock body in the survey area is diorite porphyrite, which is the mineralization mother rock of iron and sulfur deposits in the mining area. Diorite porphyrite with its medium magnetism and magnetite with high magnetism have an obvious magnetic difference from the surrounding rocks, which are the basis of magnetic exploration. There are many sulfur and iron ore mining points in this area (see Figure 8). To find ore in the periphery and deep part of the old mine, the Unmanned Aerial Vehicle (UAV) aeromagnetic survey system was used to investigate this area. The total survey line length is 111.9 km, the average flight height is 84 m, the line distance is 100 m, and the average point distance is 0.86 m. A total of 145495 data points were collected. After data preprocessing and IGRF International Geomagnetic Reference Field (IGRF) correction, the minimum curvature gridding was carried out with a grid size of 25 m. Finally, the contour map of the total magnetic anomaly obtained is shown in Figure 8a, and the amplitude of anomaly is \(-\)1800 nT-3400 nT. The total magnetic field data is the superposition effect of different magnetic geological bodies. To separate the local field from the background field, the upward continuation method was used. Upward continuation was  
Figure 7: Inversion results for model 2: (**a–c**) are the inversion results of the compressed data in the slice of z = 300 m, x = 1000 m, and y = 1000 m, respectively. (**d–f**) are the inversion results for the original data in the slice of z = 300 m, x = 1000 m, and y = 1000 m, respectively. The white line represents the model. used to calculate the abnormal value of a certain height above the observation plane according to the measured anomaly [46; 47]. Since the potential field value is inversely proportional to the square of the distance from the field source to the observation point, the field value of the field source with different depths has different changes in speed when the same height is extended. When the upward continuation is performed, the field source with large depth is highlighted because of its slow attenuation speed, thus the deep anomaly can be highlighted. In the upward continuation of the data, when the continuation height is greater than 300 m, the field change is very small, which can be approximately regarded as the regional magnetic field. As shown in Figure 8b, the residual gravity anomaly can be separated by subtracting the upward continuation anomaly from the total magnetic anomaly. There are two main North-East (N-E) trending high magnetic anomaly belts, in which there are many elliptical and equiaxed local anomalies with large amplitude variations. Some of the local anomalies correspond to the known iron deposits in the area. To restore the distribution of magnetic field sources, the underground was divided into \(64\times 64\times 20\) grids, each with a length of 50 m. Firstly, the adaptive quadtree decomposition method was used to compress the magnetic data, and the variance threshold was set to 7800 (see Figure 9). The location map of the sampling points is shown in Figure 10. The black cross in the graph represents the position of the sampling data, with 1534 sampling points, accounting for 1.05% of the original data. The compressed data were used for 3D magnetic inversion, and the inversion results are shown in Figure 11.  
Figure 8: (a) Contour map of the original magnetic anomaly; (b) contour map of the local magnetic anomaly. The symbol with a cross in the circle indicates the location of the existing mining points. Figure 9: Reconstruction error and compression ratio change with a threshold.