Two Slow Waves

We assume that the two permeabilities in the double-porosity model differ greatly in magnitude so that $\kappa_1 \gt\gt \kappa_2$ and that the corresponding porosities satisfy $0 < \phi_1 << \phi_2$. Thus, the first porosity type is transport-like and the second is storage-like. The analysis of the preceding section of the present paper would suggest that the smaller of the two permeabilities would result in a diffusive mode at all frequencies and the larger of the two would result in a propagating slow wave at high frequencies while then degenerating into another diffusive mode at low frequencies. This behavior is exactly what was found in the numerical examples presented by Berryman and Wang (2000).