Dispersion and attenuation characteristics of Love channel waves in the three-layer model of viscoelastic TI coal seam media

The coal seam is a typical viscoelastic anisotropic medium. At present, there is little research on channel waves that combine viscoelasticity and anisotropy. By taking weakly anisotropic coal seams as the research object, applying the Thomsen equivalent medium theory, and adopting the Kelvin-Voigt viscoelastic model, the frequency dispersion and attenuation characteristics of the Love channel waves in the horizontal three-layer model of viscoelastic TI (Transverse Isotropy) medium is studied. The solution of dispersion equation of the Love channel waves for the horizontal three-layer model is derived, which can calculate the case that the quality factor parameter changes with frequency. The influence of the anisotropic parameters γ, the change of coal seam Qs (shear wave quality factor) and the change of Qs with frequency on the dispersion and attenuation characteristics of Love channel waves is analyzed. The propagation process of 3D (three dimensional) channel wave field with coal seam Qs of 10 and 20 is simulated. The following conclusions can be obtained. The difference between quality factor and attenuation coefficient curves of the fundamental-mode Love channel waves of TI and isotropic medium is small. The anisotropic parameter γ has little effect on the quality factor and attenuation coefficient of the Love channel waves. The Qs of the coal seam has little influence on the velocity dispersion curves of the Love channel waves, and it mainly affects the quality factor and attenuation coefficient curves of the Love channel waves. When the Qs of the coal seam is 10, the value of attenuation coefficient of the love channel waves is much larger than that the Qs is 20 and 30. Whether the Qs of the coal seam changes with frequency within the range of 0–1 000 Hz is not yet definitive at present. Assuming that the Qs of coal seam decreases linearly with frequency, the difference of the low-frequency part of the quality factor curves is small, the difference in the low-frequency part of the quality factor curves of different mode Love channel waves is small, and the difference in the high-frequency part becomes larger. When the Qs is reduced to 10, the attenuation coefficient of Love channel waves increases rapidly with the frequency. For the 3D channel wave field, when the Qs of the coal seam is 20, the energy of the transmission Love channel waves and the transmission fundamental-mode Rayleigh channel waves is strong, and when the Qs is 10, these waves attenuate quickly and cannot be received by the opposite roadway. It shows that the reason why these waves can not be received in practical engineering is probably that the Qs of coal seam is very small. When the Love channel waves and the fundamental-mode Rayleigh channel waves cannot be received in the field working surface detection, the high-mode Rayleigh channel waves with high speed and relatively small attenuation can be used.