Characteristics of dispersion curves for Love channel waves in transversely isotropic media

Dispersion computation of guided waves in a layered transversely isotropic elastic medium sandwiched between two half‐spaces

“…(2020) for Love waves and Ji, Zhang, Wu et al. (2020) for Rayleigh waves with the corresponding models obtained through the generalized reflection‐transmission method as mentioned in the Introduction.…”

“… The dispersion equation of guided Love waves in a vertical axis of symmetry (VTI) medium consisting of layers sandwiched between two half‐spaces can be obtained from a dispersion equation in a similar isotropic medium (Buchanan, 1987) just by replacing a few parameters. For guided Rayleigh waves, dispersion equation for a VTI‐layered half‐space has been obtained by Bhattacharya (2017), where through a recursive relation the transfer matrix of the first layer of finite thickness is linked to that of the last layer (half‐space). Here, the first layer of finite thickness is replaced here by a half‐space for which necessary (5 × 1) matrix (Equation ) has been obtained to be used in the derived dispersion Equation () for a VTI medium consisting of multilayers sandwiched between two half‐spaces. Unlike complex terms in dispersion equations in earlier studies in a VTI medium consisting of sandwiched layers (Ji, Zhang, Wu et al., 2020; Ji, Zhang, Guo et al., 2020), we present here the dispersion equations for the same medium containing only real terms making root finding easier as described in the Introduction section. As an application, we compute dispersion curves for a three‐layered model, where VTI coal seam is sandwiched by host rocks. Further, in a five‐layered model, there are two additional layers of mudstone on both sides of VTI coal seam layer along with host rocks.…”

“…Bhattacharya (2017) has shown that Rayleigh wave dispersion equation by usual transfer matrix formulation (Haskell, 1953; Watson, 1970) becomes complex depending on VTI parameters; however, the dispersion equation could be obtained in real terms through algebraic manipulations. Dispersion curves in sandwiched VTI multilayers were obtained for Love waves (Ji, Zhang, Guo et al., 2020) and Rayleigh waves (Ji, Zhang, Wu et al., 2020); the differences between a dispersion curve with a VTI coal seam and that with the corresponding isotropic coal seam are small but become relatively larger at higher modes. To obtain dispersion equations, Ji, Zhang, Wu et al.…”

“…To obtain dispersion equations, Ji, Zhang, Wu et al. (2020) and Ji, Zhang, Guo et al. (2020) used a generalized reflection–transmission method (Kennett, 1983; Luco & Apsel, 1983; Chen, 1993).…”

Propagation Features of Channel Wave Signal in Coal Seam with Scouring Zone

“…By vibration direction, channel waves can be divided into love-type channel wave (L wave) and Rayleigh-type channel wave (R wave) [14][15][16][17].…”