- journal_title：Geophysics
- Contributor：Xiao-Ping Li ; Wolfgang Schott ; Horst Rueter
- Publisher：Society of Exploration Geophysicists
- Date：1995-
- Format：text/html
- Language：en
- Identifier：10.1190/1.1443911
- journal_abbrev：Geophysics
- issn：0016-8033
- volume：60
- issue：6
- firstpage：1773
- section：Articles
We present the absorption dispersion relation of Love-type channel waves for a simple, symmetric, homogenous, three-layered, linear elastic model assuming that the quality factors of coal (Q s1 ) and country rock (Q s2 ) are constant. We introduce complex propagation functions into the known dispersion relation describing most of the properties of the Love-type channel waves. The complex dispersion relation is expanded into power series of Q (sub s1 (super -1) ) , Q (sub s2 (super -1) ) , and Q (sub alpha (super -1) ) (Q (sub alpha ) -quality factor of the Love-type channel wave). The real part of the ensuing dispersion relation gives the usual dispersion relation. The imaginary part yields the frequency relation between the quality factor of Love-type channel waves and the constant quality factors of coal and rock. In this case, Q (sub alpha ) depends on the frequency because the phase velocity is a function of frequency. Therefore, the attenuation coefficient is a nonlinear function of frequency. The analysis of the analytical result shows that at high frequencies the Love-type channel wave energy is completely propagating inside the coal seam, and hence its propagation is determined by the physical properties of the coal alone. As the frequency approaches zero, the Love-type channel wave energy is completely propagating in the rock, since the thickness of the coal is small compared to the wavelength of the channel wave, and hence the channel wave does not 'see' the coal seam.The spectral ratio method is used to estimate the frequency-dependent quality factor Q (sub alpha ) of Love-type channel waves. This technique is demonstrated by applying it first to synthetic data and then to data of a well-designed transmission survey. Finally, we use the estimated Q (sub alpha ) to derive an inverse Q-operator and apply it for Q-correction to both data sets.