Wave field forward modeling and theoretical analysis of weakness in discrete media

The elasticity, viscosity, and weakness properties are taken into account in the relationships derived from rheology mechanics. Comparing with the corresponding relationships derived from damage mechanics, we find the weakness factor has the same significance as the damage factor. We simulate the wave field using a staggered-grid pseudo-spectral method to show the influence of the weakness factor qualitatively. Applying the analytical solution of plane waves, we give the velocity and attenuation coefficient of three body waves, which are affected by the wave frequency and the weakness factor of saturated discrete media. Our results show that velocity decreases with increasing weakness factor, the attenuation coefficient increases with an increase in the weakness factor, and that the influence of weakness depends on the mode of the body waves.