Dissipation factors of inhomogeneous seismic waves in porous media and their special forms

The dissipation factors (1/Q) of three Biot waves, S-waves, fast P-wave and slow P-wave are derived as the concise and explicit expressions which enable to investigate the dependence of the waves characteristics on the degree of wave inhomogeneity. It is found that if the inhomogeneity parameter is infinite for all three Biot waves, then the dissipation factors only depend on the ratio of the imaginary to the real part of the complex shear modulus. The physical mechanics behind this phenomenon is explained. The explicit expressions for the dissipation factors of poroviscoelastic materials are also reduced to get their counterparts for viscoelastic media as a special case. As another special case, the 1/Q of the inhomogeneous waves in a fluid are also discussed. It is shown in the example porous material that the dissipation factor of fast P-waves may decrease with increasing degree of inhomogeneity, which contradicts previously published results.