A multifractal model of crack coalescence in rocks

Geometric characteristics of fractal sets of cracks are investigated from the standpoint of their coalescence. A 1D computer model, in which a realistic character of forms of crack sets is achieved through the inducing of sets with the use of the multiplicative cascade procedure, is considered. The investigation is aimed at the determination of conditions of coalescence of cracks organized as a superposition of fractal subsets of a unified set of cracks. The process of crack coalescence is investigated for three different values of the coalescence criterion. The geometric characteristics of the sets of cracks that are necessary for the transition of the crack coalescence process into an avalanche-like stage are estimated.     

Phenomenology of seismic macrofracture formation

A phenomenological scheme is proposed for the formation of a seismic macrofracture in the crust through multiscale avalanche-like crack coalescence of the inverse cascade type. Relations connecting fractal dimensions of crack sets and the concentration criterion of coalescence of cracks that are required for the onset of multiscale fracture are obtained. It is shown that the enlargement of cracks from micro-to macroscales includes a relatively small number of hierarchical coalescence stages.     

Self-similar seismogenic structure of the crust: A review of the problem and a mathematical model

The paper presents a brief review of studies of the structural organization of a seismogenic medium showing that the crust of seismically active regions possesses a fractal structure. A new mathematical model of the self-similar seismogenic structure (SSS) of the crust generalizing the reviewed publications is proposed on the basis of the scaling correspondence between the fault, seismic, and seismic energy multifractal fields of the crust. Multifractal fields of other physical origin can also be incorporated in the SSS model.     

Nonlinear changes in seismic scaling before the Iceland earthquake of June 17, 2000

The multifractal fields modeling the spatial distribution of the epicenters and temporal behavior of weak seismicity before the earthquake that occurred on June 17, 2000 in Iceland (M = 6.6) are analyzed. It is shown that the main shock of this event was preceded by the broadening of the f(a) spectra of the proxy fields of both the spatial distribution of the epicenters and the temporal behavior of weak seismicity. The physical interpretation of this effect is presented.     

Nonlinear changes in seismic scaling before the Iceland earthquake of June 17, 2000

The multifractal fields modeling the spatial distribution of the epicenters and temporal behavior of weak seismicity before the earthquake that occurred on June 17, 2000 in Iceland (M = 6.6) are analyzed. It is shown that the main shock of this event was preceded by the broadening of the f(a) spectra of the proxy fields of both the spatial distribution of the epicenters and the temporal behavior of weak seismicity. The physical interpretation of this effect is presented.

     

Attractor reconstruction from the time series of information entropy of seismic kinetics process

The attractor is reconstructed from the time series of the information entropy of the seismic kinetics process. It is shown that the seismic kinetics process is governed by three order parameters and is characterized by a strange attractor in the three-dimensional phase space. The D_q-spectrum of the multifractal measure induced by the attractor, which describes the topological structure of the latter, is obtained. The monofractal dimension of the attractor is D_q(0) = 2.31…, and the correlation dimension is D_q(2) = 2.16…. The estimate of the largest Lyapunov exponent of the attractor λ1 = 0.331…. The positive signature of the largest Lyapunov exponent suggests that the attractor is chaotic and the behavior of the phase trajectory is unpredictable.