Gravity data inversion is of critical importance in geophysics, encompassing a range of applications, such as the exploration of geological resources, the identification of geological structures, and the detection of groundwater resources. This study proposes a three-dimensional (3D) machine learning approach to enhance the efficiency of the aforementioned exploration tasks by leveraging gravity data. The mapping relationship between gravity data and subsurface density structures is modeled by the broad learning network, distinguished by its high training efficiency and robust modeling capability. Notably, the proposed inversion method obviates the constraints on the number of anomalies prior to the inversion process. This is achieved by setting one anomaly with varied locations for different training samples. Numerical and field data applications demonstrate the efficiency of the proposed 3D machine learning gravity data inversion method, especially in automatically determining the number of anomalies. In particular, the proposed method produced accurate density inversion results in the field application, aiding in the identification of potential oil and gas reservoirs in the target region and offering the potential for broader application in other resource exploration. The proposed inversion method can promote the construction of density structures of subsurfaces based on gravity data.

Three-dimensional (3-D) magnetic inversion is an essential technique for revealing the distribution of subsurface magnetization structures. Conventional methods are often time-consuming and suffer from ambiguity due to limited observations and non-uniqueness. To address these limitations, we propose a novel inversion method under the machine learning framework. First, we design a training sample generation space by extracting the horizontal positions of magnetic sources from the analytic signal amplitude and the reduced-to-the-pole anomalies of magnetic field data. We then employ coordinate transformation to achieve data augmentation within the designed space. Subsequently, we utilize a broad learning network to map the magnetic anomalies to 3-D magnetization structures, reducing the magnetic inversion time. The efficiency of the proposed method is validated through both synthetic and field data. Synthetic examples indicate that compared to the traditional inversion method, the proposed method approximates the true model more closely. It also outperforms traditional and deep learning methods in terms of computational efficiency. In the field example of the Danzhukeng Pb-Zn-Ag deposit in South China, the inversion result is consistent with drilling and controlled-source audio frequency magnetotelluric survey data, providing valuable insights for subsequent exploration. This study provides a new practical tool for processing and interpreting magnetic anomaly data.