Mechanical Properties of the Earth's Crust with Self-Similar Distribution of Faults

The mechanical behaviour of Earth’s curst with a self-similar structure of faults is modelled using a continuous sequence of continua each with its own size of the averaging volume element. The overall tensorial properties scale isotropically, i.e. according to a power law with common exponent. In fault systems modelled by sets of 2-D cracks, the scaling is isotropic for both isotropically oriented and mutually perpendicular cracks. In the extreme anisotropic case of one set of parallel cracks, all effective compliances but one become zero, the non-vanishing component being scale independent. For isotropically oriented or mutually orthogonal cracks the wave propagation is characterised by extreme scattering, since any wave path is almost certainly intersected by a crack. The waves are not intersected only in the case of one set of parallel cracks. However, in this case due to its extreme anisotropy only extremely long waves (longer than all faults) can propagate.