Stability and seismicity of fractal fault systems in a fractional image

摘要

Fractal fault systems are analyzed mechanically by means of the fractional calculus. Small elastic deviations from equilibrium are captured by vectorial wave equations which imply elastic energy and conservation of momentum with spatiotemporal isofractality. Laplace and Fourier transformations lead to an eigenvalue problem which enables a diagonalization for the stable range with convex elastic energy. A degenerate fractional wave equation is proposed for a collapse at the verge of stability. The divergence at collapse is limited to small ranges and times. Substituting such a jerk by a stress jump, its propagation into a stable near-field is analyzed with a commuted isofractional wave equation. Novel solutions are presented which capture some features of earthquakes. These findings can be extended with less symmetry than first assumed for the ease of presentation. The outlook comprehends anelastic effects, coupling with pore water and multi-fractality. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim