WAVE PROPAGATION IN ROCKS MODELED AS REDUCED COSSERAT CONTINUUM WITH WEAK ANISOTROPY

摘要

Wave propagation in rocks can exhibit frequency dependence and attenuation due to the complex microstructure. From this frequency dependence, important microscale properties of the rock can be obtained with the aid of an appropriate constitutive model. Well established effective medium methods do not address this frequency dependence. We develop the reduced Cosserat theory for modelling rocks with inclusions possessing proper rotational dynamics (cracks, heterogeneities), where the stress tensor is asymmetric. The dispersive behaviour and attenuation have been predicted for shear-wave propagation in a certain frequency range. These effects are similar to the ones observed in scattering problems. To obtain similar effects for the P-wave, we consider an infinitesimal anisotropic coupling between symmetric and antisymmetric parts of strain in the elastic energy of deformation. The weak anisotropy may be related to the preferred direction of cracks or to the layered structure of the medium.