## 2 Methods  
### Design of Electrode Arrays for Constrained Sites  
#### 2.1.1 \"\(\square\)\"-Shaped Electrode Array  
The \"\(\square\)\"-shaped electrode array consists of a rectangular electrode array, with multiple electrodes deployed around a central area. It is well-suited for constrained scenarios where surface obstacles are present or when investigating the area beneath a structure, making it difficult to deploy a conventional rectangular electrode array. When the conditions around the obstacle allow for the deployment of electrodes, the \"\(\square\)\"-shaped electrode array can be considered for electrode array deployment. Since the \"\(\square\)\"-shaped electrode array involves placing electrodes around the periphery of the anomalous area, it is necessary to first determine the approximate extent of the target to be investigated. The electrode array is then deployed based on the size and boundaries of the target area. To achieve better detection results, multiple layers of electrode arrays need to be deployed around the target area to collect as much electrical information as possible from the target region.  
Assume that 64 electrodes are deployed on the surface around the target body and formed into two rectangular loops (the number of electrodes is determined by the instrument's capacity, with larger array coverage yielding more comprehensive subsurface information), as shown in Figure 1a. The resistivity data were acquired using a pole-pole electrode array (AM), with electrode A acting as the current electrode and electrode M as the potential electrode. The survey employs a single-transmitter, muti-receiver configuration with 64 electrodes numbered sequentially. Each electrode is activated as the current source in turn, while the remaining electrodes simultaneously record the resulting potentials. This systematic acquisition strategy ensures high-resolution and comprehensive resistivity coverage of the survey area, effectively capturing both fine-scale and large-scale subsurface variations. For easier qualitative analysis of the resolution capability of the electrode array in different directions, the apparent recording point coordinates of the data points can be calculated based on the planar coordinates of the current electrode \(A(x_{A},y_{A})\) and the potential electrode \(M(x_{M},y_{M})\). The spatial coordinates of the apparent recording points are given by the mean of the positions: \(x=(x_{A}+x_{M})/2\), \(y=(y_{A}+y_{M})/2\), \(z=\sqrt{\left(x_{A}-x_{M}\right)^{2}-\left(y_{A}-y_{M}\right)^{2}}/2\). This approach allows all data points to be plotted beneath the surface. The 3D spatial distribution and projection of the measurement points for the \"\(\square\)\"-shaped electrode array are shown in Figure 1b. The distribution of these measurement points represents the spatial sampling density of resistivity data, which directly influences the resolution and sensitivity of subsurface imaging. As can be seen from the figure, the measurement points cover a relatively large and evenly distributed area in the X and Y directions, ensuring robust lateral characterization of shallow subsurface features. In the Z direction, the number of measurement points initially increases with depth, reflecting enhanced sampling in the shallow to middle-depth regions. This approach ensures sufficient data coverage for both shallow and deep subsurface investigations. For a given electrode spacing, the number of measurement points increases as the number of square loops increases, resulting in a more pronounced response to underground anomalous bodies and improved detection performance.