During coal and rock loading, a significantly large number of electromagnetic signals are generated as a result of fracture appearance and crack expansion. The generation of electromagnetic signal is the comprehensive embodiment of the coal rock failure behavior. Therefore, the generated signals contain complex and rich messages that can reflect the damage process and degree of coal and rock. In this work, the multifractal theory is applied to analyze the nonlinear characteristics of the electromagnetic wave and its spectrum induced during coal rock, which present good correlation with failure process. The failure process of coal rock is non-uniform, non-continuous and nonlinear, during which, there is a good synchronization and correlation between the electromagnetic pulses and the stress drop, rather than the stress. Both waveform and its spectrum of electromagnetic signal have multifractal characteristics, the larger the fracture scale is, the more significant the multifractal characteristic of electromagnetic signal is, and the multifractal characteristic of electromagnetic signal from coal is higher than that from sandstone. The difference of fracture energy and size can be represented by the maximum of the multifractal dimension [Formula: see text] of the electromagnetic wave and its spectrum during coal rock failure. In the electromagnetic spectrum, small signals are always dominant, and the dominant frequency is only a few isolated points. What is more, with the increase of fracture size, the difference between the dominant frequency and the non-dominant frequency is gradually enhanced.

中文翻译：

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单轴压缩煤岩样品的电磁波形和频谱的多重分形

在煤和岩石加载过程中，由于裂缝的出现和裂缝的扩展，会产生大量的电磁信号。电磁信号的产生是煤岩破坏行为的综合体现。因此，生成的信号包含复杂而丰富的信息，可以反映煤岩的破坏过程和程度。本文运用多重分形理论分析了煤岩过程中感应出的电磁波及其频谱的非线性特征，与破坏过程具有良好的相关性。煤岩的破坏过程是非均匀、非连续和非线性的，在此过程中，电磁脉冲与应力降而非应力之间存在良好的同步性和相关性。电磁信号的波形及其频谱都具有多重分形特征，裂缝尺度越大，电磁信号的多重分形特征越显着，煤层电磁信号的多重分形特征高于砂岩。裂缝能量和大小的差异可以用煤岩破坏过程中电磁波及其频谱的多重分形维数[公式：见正文]的最大值来表示。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。裂缝尺度越大，电磁信号的多重分形特征越显着，煤层电磁信号的多重分形特征高于砂岩。裂缝能量和大小的差异可以用煤岩破坏过程中电磁波及其频谱的多重分形维数[公式：见正文]的最大值来表示。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。裂缝尺度越大，电磁信号的多重分形特征越显着，煤层电磁信号的多重分形特征高于砂岩。裂缝能量和大小的差异可以用煤岩破坏过程中电磁波及其频谱的多重分形维数[公式：见正文]的最大值来表示。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。煤的电磁信号的多重分形特征高于砂岩。裂缝能量和大小的差异可以用煤岩破坏过程中电磁波及其频谱的多重分形维数[公式：见正文]的最大值来表示。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。煤的电磁信号的多重分形特征高于砂岩。裂缝能量和大小的差异可以用煤岩破坏过程中电磁波及其频谱的多重分形维数[公式：见正文]的最大值来表示。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。在电磁频谱中，小信号总是占主导地位，而占主导地位的频率只是几个孤立的点。更重要的是，随着裂缝尺寸的增加，主频与非主频之间的差异逐渐增大。