Fractal dimension modeling of seismology and earthquakes dynamics

Abstract

In this study, we constructed the seismic wave equation in fractal dimensions based on the concept of product-like fractal measure introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic media. The solutions of the fractal seismic wave have proved the effect of fractal dimensions on the propagation of this type of wave in anisotropic media. The plane wave solutions were proved to be affected and deformed by fractal dimensions. It was observed that earthquakes in fractal dimension are characterized by a modified total energy which may be used to estimate the range of the fractal dimension. In particular, slow earthquakes with fractal dimension α= 1 / 2 are characterized by a particular total energy Eα which is Eα≈ 10 Ec, Ec being the conventional total energy. Several additional points were discussed and analyzed.