Fractal approach in modelling of earthquakes

Abstract

A model for an earthquake simulation is proposed with the use of a fractal approach. Multiple generation and coalescence of shear faults in stochastic brittle media (modelled as a 2d lattice) are considered to be a source of seismicity. Dynamics of local failure events are governed by accumulation of shear defects, described in terms of continuum damage mechanics. Fractal tree structure is used as an analogue for a stress redistribution process. Energy release, caused by the non-uniform failure, is studied for a non-conservative case. Effect of various types of rocks' properties stochasticity on energy release dynamics is analysed with a utilization of multifractal formalism. The latter is shown to be an additional method for seismicity characterization.

On Self-Similar Traffic Modeling of Water Resources in Arid Regions

“…Modeling [10] is usually the ultimate goal of studying physical phenomena and mathematical concepts such as those of fractals and multi-fractals. Multi-fractal formalism is applied in many modeling applications, such as modeling the velocity fluctuations in turbulent flows [11] , rainfall modeling, modeling the Ethernet and Internet traffic [1,6,12,13] , modeling of swarming in innovative behavior and of innovations time series [14] , modeling of economic and financial entities such as exchange rates, stock and commodity prices [14,15] , and modeling of earthquakes [16] , river basins [17] , and environmental pollution [18] .…”

Dynamics and Scaling Characteristics of Shear Crack Propagation

“…The decisive role of slip in seismicity serves as a reason for restraint of the description to a case of shear damage (SILBERSCHMIDT, 1993(SILBERSCHMIDT, , 1996, considering for simplification the effect of other deformational modes on the process under study to be negligibly small. The respective kinetic equation for shear damage accumulation has the following form (SILBERSCHMIDT, 1994(SILBERSCHMIDT, , 1998.…”

“…Each element characterised by a pair of indices (i, j ) derives its shear modulus g ij from the interval [g m , 2g m ], where g m is the minimum value of modulus; details of the analogous distribution procedure are discussed elsewhere (SILBERSCHMIDT, 1996). One of the most intensively used ones is the distribution of stress threshold values; this concept is based on the simplest variant of strength theories.…”

“…In the author's recent paper (SILBERSCHMIDT, 1996) a shear damage accumulation was used for the description of the fracture process evolution at lower scale levels. Introduction of the critical damage value as a local failure criterion for elements of 2d-discretisation allows a simulation of a spatio-temporal evolution of fracture process and consequent energy release.…”