Frequency-dependent Q-estimation of Love-type channel waves and the application of Q-correction to seismograms

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 (Qs1) and country rock (Qs2) 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 Qs2-1, Qs2-1, and Qα-1 (Qα‐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, Qα 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 ...