The representation of spatial discrete data is crucial for the data analysis of meteorology, agriculture, geological exploration and other fields. Among various methods for scattered data interpolation, the multiquadric (MQ) method is the most favorable in the field of surface construction. However, the classical MQ method has accuracy concern on the boundary and is time consuming for large data set. This study proposes an algorithm by integrating the MQ method with trend surface analysis. In which, the low-order polynomial trend surface equation is firstly used to model the overall trend. Then, the MQ equation is applied to fit the residual surface after removal the trend from the data. Our implementation can eliminate the distortion in data missing areas by the classical MQ method, and the modeling efficiency can be improved significantly since the local MQ method divide the residual surface into a group of subsurfaces. The accuracy and efficiency of the proposed algorithm are validated on a synthetic model. The performance of the developed algorithm is further examined on the elevation data collected in Tibet and the seabed of a strait in Norway. The results show that with an equivalent resolution, the developed algorithm can be much more efficient than the classical MQ method and well-developed Kriging method.

Topographic undulations often have non-negligible influence on frequency-domain airborne electromagnetic method (FAEM) exploration. To study this effect caused by complex topography, this paper proposed a numerical simulation method based on the boundary element method (BEM) to calculate the 3D topography EM field of frequency-domain magnetic dipole source with arbitrary inclination angle. First, according to the vector integral equations and boundary conditions of the EM field, the boundary integral equations are derived, which describes the coupled electric and magnetic fields that are integrated only for the 3D surface. Then, the 3D surface identified by the area of influence of the magnetic dipole source is used as the integration region (Footprint) with unstructured triangular dissection, and the boundary integral equations are solved in this region using BEM. The EM field at the geometric center of gravity of each element on the surface is obtained by solving the dense linear equations using the conjugate gradients squared (CGS) method, and the influence of the 3D topography on the magnetic field (secondary field) at the receiving coil can be calculated according to the magnetic field boundary integral equation in the upper half space. The algorithm is then tested with synthetical models to validate its feasibility and evaluate its performance, where the response characteristics of the magnetic field with different model conditions are analyzed.

The 3D resistivity imaging surveying is adept at identifying structural details at various subsurface depths, and it can acquire valuable underground information even in complex geological environments. This technique has been widely applied in fields such as geological exploration, hydrogeology, and environmental monitoring. Currently, the 3D electrical resistivity surveys in the field are primarily deployed using regular grid and equidistant electrode layouts. However, when the survey area is influenced by obstacles or when the target being investigated is particularly complex, this may hinder the deployment of the electrode array in accordance with a rectangular grid. In some instances, it may even be impossible to position the electrodes directly above the target of investigation. The only viable option is thus to place electrodes around obstacles or special targets. In view of this, this paper studied unconventional electrode arrays and inversion imaging techniques of 3D electrical resistivity surveying in confined areas. It presents the design of three electrode arrays: “□”-shaped, “U”-shaped, and “L”-shaped. Furthermore, the study explores 3D resistivity finite element numerical simulation and inversion imaging techniques based on continuous electrical media. Finally, model experiments were conducted to verify the feasibility of these three special electrode arrays. We have applied the “□”-shaped electrode array to investigate the foundation structure of an ancient pagoda in Zhejiang Province, achieving promising results. This study provides valuable reference for the research and application of special observation in 3D electrical resistivity exploration.

Soil heavy metal contamination poses a serious threat to soil ecosystems and human health. Geochemistry is often used in soil heavy metal contamination research to identify pollution sources, identify elemental cycling mechanisms, and assess the spatial distribution and risk of contamination. However, it is difficult to directly reflect the spatial continuity and deep distribution patterns of contamination. Three-dimensional electrical resistivity tomography (3D ERT) technology often indirectly predicts the distribution of soil contamination by leveraging the electrical structure of the subsurface medium. However, many factors influence this electrical structure, leading to biased predictions. This paper combines geochemistry with 3D ERT technology. A nonlinear statistical model is established based on the geochemical analysis results and resistivity of soil samples. A 3D ERT model is then constructed. This model is used to further investigate the spatial distribution patterns of soil heavy metal contamination and assess the extent of contamination. This study investigated soil sample collection and chemical analysis of heavy metal content at a heavy metal contaminated site in Hunan Province. Antimony contamination was particularly severe in the soil. The 3D ERT data collection and inversion imaging were performed in the soil sample collection area. A 3D ERT model was established to analyze and evaluate the distribution range and extent of antimony contamination in the area. Comparing the antimony content predicted by the model with the actual test data, the results show that the error range is 0.6–16.6%, and the average error is 5.8%. The model has high accuracy, achieving good overall prediction and evaluation results.

As strategic critical metals, tungsten (W) and tin (Sn) require efficient exploration methods for effective resource development. This study implemented an advanced spread-spectrum induced polarization (SSIP) method in the Xitian mining district of southern China. Through optimized survey system configuration (maximum current electrode spacing of 5200 m, 12-channel acquisition, and five discrete frequency points), we achieved significant advancements: (1) a penetration depth of 1200 m, and (2) three- to five-times higher data acquisition efficiency compared to conventional symmetrical quadrupole arrays. Inversion results of resistivity and chargeability profiles from two parallel survey lines (total length 2.4 km) demonstrated an 85% spatial correlation between resistivity and chargeability anomalies, successfully identifying three mineralized veins. Drill-hole verification confirmed the presence of greisen veins (characterized by low resistivity 3%) and skarn veins (moderate resistivity 150–200 $\mathrm{\Omega }\cdot \mathrm{m}$ and chargeability 1.5–2%). The method exhibits a detection sensitivity of 0.5% chargeability contrast for deep-seated W-Sn polymetallic deposits, providing quantitative technical references for similar deposit exploration.