# Design of Three-Dimensional Electrical Impedance Tomography System for Rock Samples
## 2 Principle and Methods  
In the practical measurement process, the initial step entails determining the suitable number of electrodes based on the characteristics of the targeted rock or ore specimen, including parameters such as the base diameter and height. Insufficient electrode quantity impedes the acquisition of ample data, hindering a comprehensive reflection of the electrical properties of the rock or ore. Conversely, an excessive number of electrodes results in extended measurement time without a commensurate improvement in measurement precision. Subsequently, a judicious arrangement of electrodes is required. The schematic diagram depicting the operation of the instrument is illustrated in Figure 1. The positive terminal of the signal source incorporated in our instrument is linked to the current electrodes, serving the purpose of delivering a consistent voltage or current signal to the rock or ore specimen. Following this, the negative terminal of the signal source is interconnected with the central region of the lower surface of the rock or ore specimen, having been serially connected with a high-precision sampling resistor. The ellipsis in the figure denotes the prospective arrangement of additional electrodes based on particular circumstances. During operation, each current electrode activates in sequence, with the corresponding set of potential electrodes (Every five are grouped together) conducting data collection and switching. Once the potential electrode switching is completed, the next current electrode initiates its operation, and the potential electrodes repeat their previous cycle. The measurement concludes upon the completion of the operation of all current electrodes. The electrode arrangement method employed in this study introduces a streamlined and convenient procedure for configuring electrodes, concomitantly diminishing measurement time and enhancing the efficiency of data collection. This approach confers distinct advantages, especially considering the significant quantity of electrodes within our system. Given the dual-purpose design of our system for laboratory and field measurements, this method amplifies its adaptability to intricate topographical conditions. For instance, in the subsequent experiments detailed in this paper, we opted for 48 current electrodes and 48 potential electrodes, distributed across four horizontal planes and 24 vertical lines spaced at \(15^{\circ}\) intervals. For rock samples with lower resistance values, a constant current source measurement method is utilized to avoid generating large currents within the circuit, which could increase power consumption and damage circuit components. Conversely, for rock samples with higher resistance values, a constant voltage source measurement method is employed to mitigate the influence of smaller currents on measurement accuracy. The system directly acquires voltage and current data. Subsequently, we applied fast Fourier transform (FFT) to convert the time-domain signal into the frequency-domain signal, enabling us to compute impedance and phase results from the obtained complex numbers. After the system measurement is completed, the raw data collected by the Android software are exported for inversion processing [20]. In the process of forward modeling, we utilized the finite element numerical simulation method to simulate cylindrical rock sample. The strength of this approach lies in its adaptability to handle diverse irregular geological models and boundary conditions, along with its ability to tackle intricate non-linear and heterogeneous media. Based on the Occam smooth inversion [21; 22], we performed inversion on the measured data. The inversion objective function is constructed as Equation (1).