## 1 Introduction  
Direct current resistivity imaging surveying is a geophysical exploration technique widely applied in electrical prospecting. It involves injecting a current into the subsurface medium through electrodes deployed on the surface, in boreholes, or in well-to-surface interfaces. The resulting potential differences at various locations are measured to inversely derive the resistivity distribution of the subsurface medium [1, 2]. Due to the varying electrical properties of different geological formations, electrical resistivity surveying can effectively identify the electrical characteristics of the subsurface, thereby allowing for inferences regarding geological structures, fluid distribution, and the spatial locations of geological bodies. In recent years, electrical resistivity surveying has been extensively utilized in fields such as disaster prevention [3; 4], environmental engineering [5; 6; 7; 8], hydrogeology [9; 10; 11; 12; 13], archaeology [14; 15; 16; 17]. It has become one of the most commonly employed techniques in near-surface engineering geophysical prospecting, yielding outstanding results in its applications [18]. With the rapid development of computer technology, the numerical computation and inversion algorithms for resistivity imaging surveying have also progressed significantly. Currently, 2D resistivity numerical simulation and inversion imaging techniques are relatively mature and dominate data processing [4; 8; 10; 11; 15]. However, in complex geological environments or engineering problems, these often have higher requirements for exploration accuracy. At this juncture, 2D resistivity inversion imaging technology cannot be effectively visualized in 3D [17]. Therefore, it is necessary to develop more advanced 3D forward and inverse imaging technologies to meet these elevated exploration demands. To some extent, pseudo-3D [19; 20] and quasi-3D [21; 22] resistivity surveying can compensate for the limitations of 2D resistivity surveying techniques, demonstrating greater effectiveness in certain fields. However, it is important to note that these approaches fundamentally rely on extrapolating spatial information from limited 2D measurements, without adequately accounting for the complex three-dimensional variations in subsurface structures. Consequently, they cannot accurately represent the true 3D nature of geological features. In recent years, significant breakthroughs have been made in true 3D resistivity inversion imaging techniques, which have shown more stable performance in inversion imaging [23; 24; 25; 26; 27; 28; 29]. The implementation process of resistivity field surveys usually includes three main steps: the layout of electrode arrays, data acquisition, and inversion imaging. Three-dimensional resistivity imaging surveying needs to cover the exploration area with measurements in all possible directions using an electrode array [30]. In practical applications, the electrode array of resistivity imaging surveying is typically placed above the target body in a rectangular grid, which is referred to as a traditional electrode array [31]. However, such traditional electrode arrays are not suitable for confined areas with many obstacles, where it is difficult to deploy the electrodes regularly. To enhance the adaptability of 3D resistivity imaging surveying in complex geological environments, and to overcome the challenges posed by surface obstacles or the irregular shapes of anomalous bodies, which may prevent the proper placement of electrodes, many scholars have begun to explore 3D electrode arrays that are better adapted to such challenging conditions. Currently, one approach involves developing new types of electrodes, such as using plate-shaped electrodes instead of rod-shaped electrodes or adding auxiliary materials to the rod-shaped electrodes. This method aims to address the challenges of electrode placement on special surfaces like concrete pavements or riverbeds [32; 33; 34; 35].