Energy attenuation patterns of microseismic signals in the "three zones" of goaf based on variational mode decomposition

In order to investigate the energy attenuation of microseismic signal in the "three-zone" structure of goaf, a similar model test of the overburden of goaf is proposed to collect the artificially excited microseismic signals propagated through the structure of goaf. The relationship between the central frequency and energy of the mode components of the microseismic signal via variational mode decomposition (VMD) is analysed. The optimal number of mode components of the microseismic signal is determined according to the central frequency method, and the energy of each component is calculated for the under-decomposition, optimal decomposition and over-decomposition states of the microseismic signal. The relationship between the energy of each mode component and the central frequency distribution is fitted for the optimal decomposition state of the signal under each source, and the energy of each mode component is analysed for different propagation states of the microseismic signal in the "three-zone" structure. The effect of each structural layer on the energy of the microseismic signal under different propagation states of the "three-zone" structure is analyzed. The results of the study show that: (1) The number of effective modes of the artificially excited vibration signal in the VMD process ranges from 6 to 11, and the energy of the microseismic signal varies significantly with the number of modes. (2) The power function can be used to fit the mode energy versus frequency of the microseismic signal, and the fitting state is good (the coefficient of determination is greater than 0.9), in which the low-frequency mode component contains nearly 50% of the total energy of the signal. The Gaussian function can be used to fit the distribution performance of the energy of each component of the source in the frequency domain, and the fitting state is good and shows the Gaussian single-peak characteristic. (3) The microseismic signal traverses through the "three-zone" structure of goaf, and the energy of the microseismic signal decreases as the distance between the source location and the sensor increases. The collapse zone has a significant attenuating effect on the signal compared to the fracture zone and the bending zone. The energy of the microseismic signal does not change as it passes through the "three-zone" structure of goaf.