SEISMOLOGICAL CRITICALITY CONCEPT AND PERCOLATION MODEL OF FRACTURE

Abstract

In 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. © 2005 The Authors Journal compilation © 2005 RAS.