Rock as a critical-point system and the inherent implausibility of reliable earthquake prediction

Abstract

SUMMARY The statistical mechanics of critical-point thermodynamic systems provide a powerful conceptual tool with which to examine the plausibility of reliable earthquake prediction. The issue turns on how rock is heterogeneous. If the correlation range of a spatially fluctuating rock property is bounded by a characteristic length ξ, then the spatial average of that property over dimensions greater than ξ may be regarded as defining an ‘effective’ continuum value for that property. Ideas about earthquake preparation in rock with an effective continuum mechanical strength can plausibly focus on failure that is initiated at small anomalous zones and grows to instability with access to a continuous volume of strain energy; the dimensions and temporal evolution of the growing anomaly can then be expected to relate to the size, location and timing of the impending seismic event. Borehole log evidence indicates, however, that rock-heterogeneity correlation lengths ξ are unbounded (ξ∞) and hence that the ‘effective’ continuum approximation for rock must be applied with discretion. An infinite correlation length indicates a statistical mechanical critical-point system in which the correlation length ξ is related to a singularity in a physical property. In thermodynamic critical systems, the singularity occurs at the critical system temperature Tc, ξ∝ 1/√|T - Tc|; in rock the singularity occurs at the critical percolation probability Pc, ξ∝ 1/√|P - Pc|. Statistical physics descriptions of critical-point spatial correlations are based on nearest-neighbour inter-actions at every scale length. Nearest-neighbour interactions at one scale, say that of large failure structures (the loci of large earthquakes), involve minimal coupling to structures at other scales, in particular small-scale failure structures (the loci of small earthquakes). The mechanics of nearest-neighbour interactions plausibly form a fundamental constraint on the role of small-scale failure or related nucleating activity as a prelude to large-scale failure. In light of (1) the evidence against rock being an effective medium notionally supporting localized precursory activity that reliably grows to large-scale mechanical failure, and (2) the history of failure to identify reliable precursors to major earthquakes, the onus should now be on advocates of earthquake prediction schemes to evaluate their claims for precursory activity in terms of rock as a critical-point system.