Calculation method and characteristic analysis of dispersion curves of Rayleigh channel waves in transversely isotropic media

Abstract

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 ([Formula: see text]) 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.