Micromorphic continuum, rotational wave and fractal properties of earthquakes and faults

It seems that internal structures and discontinuities in the lithosphere have an essential influence on the lithospheric deformation like faulting or earthquakes. The micromorphic continuum provides a good framework to study the continuum with microstructure, such as earthquake structures. Here we briefly introduce micromorphic continuum to consider the earthquake structures (e.g., rotational wave). Then the equilibrium equation in terms of the displacements (the Navier equation) is derived from this micromorphic continuum. This equation is the generalization of Laplace equation in terms of displacements and can lead to some Laplace equation such as the local diffusion-like conservation equations. Moreover, these conservation fields bear the fractal properties of fracturing in the lithosphere in the form of faults or earthquakes. Finally some scalling laws of faults or earthquakes are discussed.