Theory of time‐dependent rupture in the Earth

Abstract

Using the concepts of fracture mechanics, we develop a theory of the = earthquake mechanism which includes the phenomenon of suberitical crack growth.^.The theory specifically predicts the following phenomena: slow earthquakes, f i multiple events, delayed multiple events (doublets), postseismic rupture growth and afterslip, foreshocks, and aftershocks. The theory also predicts that there must be a nucleation stage prior to an earthquake, and suggests a physical mechanism by o _ which one earthquake may 'trigger' another, We investigate in detail two phenomena of special interest and which are not predicted by ordinary fracture mechanics: nucleation and delayed multiple events.In the first case we find that all earthquakes must be preceded by quesistatic slip over a portion of their rupture surfaces, but it may be difficult to deteet in practice. In the second case we studied two pairs of delayed multiple events that were separated by the same 'barrier' in order to calculate n. We find that the stress corrosion index, n -24. EMost oxides and silicates, however, exhibit more complicated behavior due to environmental effects. For these materials, the crack will propagate when k > Ko, where Ko < Kc, at a velocity X which is a well defined function of k.This propagation is stable and quasistatic and is referred to as suberitical crack growth. (We shall use the terms "stable", "quasi-static" and "subaritieal" to mein propagation at velocities much less than the sonic velocities of the medium). This behavior results from stress induced corrosion at the crack tip, the principal corrodent for the present application being H2O. This behavior has been firmly established in the laboratory for Mode I (tensile) cracks in a wide variety of materials including silicates and silicate glasses (see, e.g., Scholz, 1968aScholz, , 1972aMartin, 1972; Wiederhorn and Bolz, 1970;Atkinson, 1979;Lawn and Wilshaw, 1975; Knott, 19731.The form of the relationship between k and X does not vary significantly with the material; only the parameters in the law vary. As an example we show in Since n, the stress corrosion index, is large (12.5 in Fig. 1 Later we shall determine n for an earthquake and show that it is in remarkable agreement with Atkinson's results. Although we cannot prove this assumption, it seems entirely reasonable since when one considers the physical mechanism of stress corrosion there seems to be no physico-chemical reason why the process should depend on mode. The indirect evidence in support of this is that rock exhibits dilatant creep and static fatigue, both processes that result from stress corrosion, in compression and under high confining pressure (Scholz, 1968a; Kranz and Scholz, 1977; Kranz, 19801. We shall also assume that there is a lower limit, Ko, such that when k < K o no crack growth occurs. There is only limited data to K*c is a material property that for these materials can be measured only in a corrodent-free environment, e.g., a high vacuum. K c, on the other hand, is not an independent mater...

A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data

“…Many other mechanisms have been proposed for this temporal decay e.g. subcritical crack growth [35], visco-elastic relaxation [36], post-seismic creep due to stress corrosion in the regions of stress concentration after the mainshock [37], static fatigue [38], pore fluid flow [39], post-seismic slip [40] and earthquake nucleation under rate-and state-variable friction [41]. In general, it is assumed that the parameters c and τ are constants and are specific to a given aftershock sequence.…”

“…It may have more physical connotations as well; e.g. due to finite duration of earthquake nucleation time [35,41] or, for post-mainshock seismicity driven by afterslip, due to the response of aseismically creeping zones to the co-seismic stress change [43]. It recently has been suggested that τ and c may be considered functions of the lower magnitude cutoff M c , and thus may be written as τ (M c ) and c(M c ) [44].…”

Evolving towards a critical point: A possible electromagnetic way in which the critical regime is reached as the rupture approaches

“…Using equations from crack propagation (Das and Scholz, 1981) and damage mechanics (Leckie and Hayhurst, 1977;Bufe and Varnes, 1993) a formula for the cumulative elastic energy release ε(t) is derived:…”

Downscaling of fracture energy during brittle creep experiments

“…We do not investigate dynamic rupture (e.g., earthquakes) but slow, creeping fractures. This slow regime is relevant to many geophysical phenomena such as earthquake nucleation [Bouchon et al, 2011], slow slip events and postseismic slip [e.g., Das and Scholz, 1981].…”