Three-dimensional magnetic inversion allows the distribution of magnetic parameters to be obtained, and it is an important tool for geological exploration and interpretation. However, because of the redundancy of the data obtained from large-scale investigations or high-density sampling, it is very computationally intensive to use these data for iterative inversion calculations. In this paper, we propose a method for compressing magnetic data by using an adaptive quadtree decomposition method, which divides the two-dimensional data region into four quadrants and progressively subdivides them by recursion until the data in each quadrant meets the regional consistency criterion. The method allows for dense sampling at the abnormal boundaries with large amplitude changes and sparse sampling at regions with small amplitude changes, and achieves the best approximation to the original data with the least amount of data, thus retaining more anomalous information while achieving the purpose of data compression. In addition, assigning values to the data in the quadrants using the averaging method is essentially equivalent to average filtering, which reduces the noise of the magnetic data. Testing the synthetic model and applying the method to mineral exploration a prove that it can effectively compress the magnetic data and greatly improve the computational efficiency.

Geothermal resources represent one of the most vital renewable energy sources, offering substantial development potential within the energy sector. Wudalianchi, renowned as one of China’s prominent volcanic clusters, has undergone extensive underground volcanic activities, suggesting a promising capacity for geothermal resource accumulation. This paper is the first to apply the cross-gradient gravity-magnetic joint inversion method to study the shallow structures in the Laoheishan Volcano and surrounding areas of Wudalianchi, based on high-precision measured gravity and magnetic data. The inversion results indicate the presence of a rock body at a depth of approximately 2 km beneath the Laoheishan and Bijiashan regions, which simultaneously exhibits characteristics of low density, high magnetization, and low seismic velocity. Integrating previous research findings, the rock body is interpreted as basalt formed during magmatic activity, retaining remanent magnetism. Furthermore, the rock body contains fractures filled with fluids, thereby excluding the possibility of a shallow magma chamber or dry hot rocks beneath the Laoheishan area. These rock bodies are interconnected at depth and align with the NE and SE fault directions in the Wudalianchi area, confirming that these faults govern the region’s volcanic activities. The inversion results, from the perspectives of density and magnetic susceptibility, elucidate the material distribution in the shallow subsurface of the Laoheishan and surrounding areas, providing new evidence for further exploration of geothermal resources in the region.