Seismological criticality concept and percolation model of fracture

Abstract

S U M M A R YIn the present paper we consider an anisotropically correlated percolation model of fracture (PMF), namely, the geometry of fracture structures, the energy emission model and the evolution of scatter of emitted (effective) amplitudes at attaining the critical point (CP; percolation threshold). The sequences of effective amplitudes calculated from PMF are considered as proxies of seismic catalogues and are analysed by various linear and non-linear methods, developed in modern time-series analysis. It is shown that the drastic increase in the scatter of amplitudes is a good precursor of the impending CP even in the case of an individual percolation run. The Lempel-Ziv (LZ) complexity test reveals clear non-linear structure in the sequence of effective amplitudes; the value LZ = 0.750 is significantly less than LZ for random process (LZ = 1) and the Hurst exponent is in the range 0.8-0.85. Both these results point to the appearance of some order in the generation of effective emission events, due, probably, to the memory property of percolation processes. Various tests (curvature parameter, Shannon entropy) show that the acceleration of model seismicity close to the CP increases with the growth of anisotropic correlation (AC). The role of AC in the acceleration of energy emission, and Shannon entropy behaviour close to the CP, are analysed.

Seismicity dynamics and earthquake predictability

“…The final rupture can be predicted by monitoring the process of clustering of small faults (Chelidze, 1982). The same conclusion was reached in the case of anisotropical geometry of fracture structures (Chelidze et al, 2006). Some hybrid models appeared that integrated CP and SOC theories.…”

“…Let us take a look at the changes in the seismic situation near the epicenters of the Kronotskoe and Simushirskoe earthquakes over several years preceding these events. The power law acceleration of acoustic emission before fracture and foreshocks acceleration before earthquakes as the signs of criticality was given in (Chelidze, 1982;Chelidze et al, 2006). A practical useful approach to describe possible acceleration of the seismic process prior to an earthquake was offered in (Varnes, 1989).…”

On the puzzling feature of the silence of precursory electromagnetic emissions

“…It has been shown that the problem of fracture of heterogeneous media corresponds mathematically to problems of the percolation theory, which describe quantitatively the connectivity of components in a non-homogeneous system (Chelidze, 1979(Chelidze, , 1980a(Chelidze, , b, 1982(Chelidze, , 1986(Chelidze, , 1987(Chelidze, , 1993Chelidze at al., 2006;Arbadi and Sahimi 1990). It appears that the elastic modulus, M, decreases from the initial value for an intact lattice over nearly five orders of magnitude according to the expression M ∝ M 0 (x − x cr ) −3.6 , where x is the current concentration of breakages and x cr is the percolation threshold for a given finite system; it has been found that x cr = 0.494.…”

Time-scale invariant changes in atmospheric radon concentration and crustal strain prior to a large earthquake

“…(8) has been also investigated based on the percolation model (e.g. Chelidze, 1993;Xie, 1993;Main, 1999;Chelidze et al, 2006).…”