Coal seams have beddings and fissures and are typically anisotropic media. Current channel wave theories are mainly based on isotropic media, and few studies exist on the dispersion characteristics of Rayleigh channel waves in anisotropic models, such as transversely isotropic (TI) media. We chose the generalized reflection-transmission coefficient method to solve the dispersion curves of Rayleigh channel waves in TI media. However, it is difficult to solve the associated dispersion equations of Rayleigh channel waves using this method directly. Therefore, we have extended the generalized reflection-transmission coefficient method and determined the improved accuracy through numerical simulation. We analyzed the dispersion characteristics of Rayleigh channel waves of several typical coal seam models in TI media. The results showed that in the three-layer model, the difference in fundamental-mode dispersion curves between vertically transversely isotropic (VTI) media and isotropic media was relatively small; however, the differences in the higher order dispersion curves were slightly larger. The difference in the Airy phase velocity between horizontal transversely isotropic (HTI) and isotropic media was relatively large. When the coefficient of variation in the qP waves (${\delta }^V$) was greater than 0, the fundamental-mode and first-order phase velocity curves of HTI media exhibited an evident intersection at the head end. In the dirt-band-containing coal seam model, within the 350 and 550 Hz band, the high-frequency velocity of fundamental-mode phase velocity curve of isotropy and HTI media was slightly higher than the low-frequency velocity, which is a notable phenomenon.

中文翻译：

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横观各向同性介质中瑞利通道波频散曲线的计算方法和特性分析。

煤层具有层理和裂隙，通常是各向异性介质。当前的通道波理论主要基于各向同性介质，在诸如横观各向同性（TI）介质等各向异性模型中，关于瑞利通道波的色散特性的研究很少。我们选择广义反射-透射系数方法来求解瑞利信道波在TI介质中的色散曲线。然而，使用这种方法很难求解瑞利信道波的相关色散方程。因此，我们扩展了广义反射-透射系数法，并通过数值模拟确定了提高的精度。我们分析了TI介质中几种典型煤层模型的瑞利通道波的频散特性。结果表明，在三层模型中，垂直横观各向同性（VTI）介质与各向同性介质之间的基本模色散曲线差异较小；但是，高阶色散曲线的差异稍大。水平横观各向同性（HTI）与各向同性介质之间的Airy相速度差异较大。当qP波的变化系数（${\delta }^V$）大于0，则HTI介质的基模和一阶相速度曲线在头端表现出明显的相交。在含尘带的煤层模型中，在350和550 Hz频带内，各向同性和HTI介质的基模相速度曲线的高频速度略高于低频速度，这是值得注意的现象。