Q values and wave inhomogeneity parameters of reflected inhomogeneous P and S waves at the free surface of an effective Biot solid

In this study, new methods are developed to estimate the dissipation factors, inhomogeneity parameters and phase velocities of the reflected waves at the free surface of a poro-viscoelastic solid in which the seismic wave propagation is described by effective Biot theory. The Christoffel equations of an effective Biot medium are solved for a general harmonic plane wave and the three complex velocities obtained corresponding to the shear wave (SV), fast-P wave and slow-P wave, together with their polarizations. Based on the complex form of the energy balance equation in an effective Biot material, expressions are derived for the energy ratios at the free surface. Moreover, the equations for the inhomogeneity parameters are derived as functions of the complex slowness or the unit polarization vectors. Based on the implicit and the explicit dissipation factor expressions, two methods are developed to obtain the dissipation factors, the inhomogeneity parameters and the phase velocities of mode-converted waves. These methods are illustrated by numerical examples which show that the dissipation factors, inhomogeneity parameters and phase velocities of reflected waves can strongly depend on the incidence angle (also reflected angle), the incident wave inhomogeneity parameter and the wave frequency. Ignoring these dependencies and using dissipation factors only valid for homogeneous waves can cause discrepancies in computed phase velocities and dissipation factors for interface generated (reflected/transmitted) inhomogeneous waves.