## 5 Coupling Analysis of the ME Signal and EMR Signal
### Analysis of the Signal Coupling Effect  
The generation of EMR signals during rock fractures relies on the clear synchronization of fracture events, vibrations, and ME signals in a time sequence. Consequently, the ME acceleration sensor is affixed to the surface of the rock specimen, while the EMR antenna receiver is strategically positioned near the specimen, enabling comprehensive and synchronized monitoring of the EMR and ME signals under full load conditions. As the dolomite progresses through different stages, distinctive fracture development characteristics become apparent. Therefore, the specimen's loading process is inherently accompanied by the emission characteristics of ME, AE, and EMR signals (Figure 8). It can be seen in Figure 8 that the low-frequency EMR and ME signals of the final main fracture of the dolomite specimen are synchronized in the time domain. The AE signal monitored by the AE sensor lags behind the synchronous EMR and ME signal, indicating that the synchronous EMR and ME signal wave velocity is higher than the AE wave velocity; this is because AE signals propagate through molecular vibrations in the air, which usually travel at a slower speed. EMR signals propagate at speeds equal to the speed of light, and ME signals propagate through elastic waves in a solid medium. In addition, ME and AE still occur in the pre-stage and post-stage of the final AE signal and ME signal, indicating that the ME signal and AE signal are generated and expanded by cracks before the main fracture of the rock. At the same time, the EMR signal intensity of dolomite will increase to a certain extent in the compaction stage, which is caused by the piezoelectric effect, and then the EMR signal intensity of the material is maintained at the same level in the elastic deformation stage and the plastic deformation stage. Due to the strong brittleness of dolomite specimens, there is no obvious signal fluctuation before the micro-cracks penetrate and produce macroscopic cracks visible to the naked eye. There is almost no charge induction signal in the compaction and elastic stage of natural dolomite specimens, and there is less charge and ME signal in the fracture development stage. The reason is that the development degree of micro-fractures in dolomite is weak, and the storage energy in the compaction and elastic stage is not enough to lead to large-scale micro-fracture expansion. There is almost no charge sensing and low-frequency geophysical signal generation because when the micro-fracture is weakly developed, the frequency of the ME signal is a high-frequency signal, and the weak fracture network  
Figure 8: Comparison of the monitoring results of the EMR, ME, and AE of the J-4 specimen. cannot provide sufficient stress release and energy transfer paths, nor does it have a richer high-frequency signal composition [31]. However, entering the plastic deformation stage, the energy accumulation inside the rock specimen increases, and the stress is concentrated in local areas. Due to the deformation and stress release inside the specimen, micro-cracks are generated and expanded, resulting in charge redistribution and generating charge induction signals, at the same time, they are accompanied by the generation of ME signals. The different cracks begin to penetrate during the complete failure of the specimen, and the number of EMR and ME signal events increases. Therefore, during the instability failure, the crack expands rapidly, the energy is released instantaneously, the damage changes sharply, the bearing structure surface is rapidly destabilized, and the amplitude of the charge induction signal reaches the maximum. In Figure 9, the frequency comparison of the EMR and ME signals of the J-4 dolomite specimen at each stage is presented. Figure 9a corresponds to the four stages of the uniaxial compression failure of dolomite: the compaction stage and the early stage of elastic deformation (OA\({}^{\prime}\)). No noticeable EMR and ME signals were collected during this phase.