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Laboratory data (Fig. 3) show, however, that both ∆τb and Dc are an increasing function of σn, so that the assumption of ∆τb being constant is not justified for more rigorous discussion. From Eqs. 4, 5, and 20,

[21]

which shows that Xc is directly proportional to λc, and that Xc is independent of σn if M=1. If M≠1, Xc depends not only on λc, but also on σn. However, the dependence of {m(σn)}1−M on σn is modest, so that Xc is practically prescribed by λc alone. One can thus conclude from Eqs. 19 and 21 that Xc and Lc are virtually prescribed and scaled by λc alone. If it is tentatively assumed that the critical size of the nucleation zone is attained at a value in the V/Vs range 0.1–0.5, and that τi/∆τb=0.5−0.8, then Lc=(4.9−9.7)×103λc from Eqs. 19 and 21 by considering that μ=2×104 MPa for the granite sample used, and assuming that M=1 and ∆τb0=3 MPa (see Fig. 3). This theoretical estimate agrees with the experimental result (Fig. 4).

During the nucleation, the energy is exclusively consumed in and around the zone of nucleation, since the nucleation is the process (or zone) in which slip failure deformation is concentrated and accelerated. Accordingly, dynamic instabilities of small to microscopic scales (microseismicity or acoustic emission) are induced and activated during the nucleation process, when the rupture growth resistance on the fault varies on small to microscopic scales. This has been demonstrated by recent laboratory experiments (unpublished data). It has also been found that seismic b values decrease as the nucleation proceeds (unpublished data). These observations suggest that microcrack interactions in the fault zone play a crucial role in the nucleation process.

Earthquake Rupture Nucleation and Immediate Precursors

We have seen that geometrical and/or mechanical inhomogeneities play a crucial role in the shear rupture nucleation process. Such inhomogeneities prevail in the brittle seismogenic layer in the Earth’s crust. The seismogenic layer contains a large number of preexisting faults of microscopic to macroscopic scales, and therefore the seismogenic layer is inherently inhomogeneous. In addition, a preexisting fault itself in the Earth’s crust exhibits geometrical irregularities and mechanical inhomogeneities of various scales on the fault surfaces and in the fault zones. This strongly suggests that earthquake dynamic rupture is necessarily preceded by a quasistatic to quasidynamic nucleation process. However, whether or not a sizable zone of the nucleation appears prior to earthquake dynamic instability depends on how nonuniformly the constitutive law parameters prevail on the fault in the lithosphere (18).

The shear rupture nucleation model presented in this paper (see also ref. 18) can explain why and how short-term (or immediate) precursors are intrinsically related to the earthquake nucleation that proceeds quasistatically to quasidynamically prior to the mainshock dynamic rupture and how essential it is in carrying immediate foreshocks that the rupture growth resistance is distributed nonuniformly on a local to small scale in the fault zone in the brittle regime. The model shows that immediate foreshock activity is a part of the mainshock earthquake nucleation (18, 22). This provides a physical explanation for observations commonly made for decades that immediate foreshocks are concentrated in the vicinity of the epicenter of the pending mainshock. Whether or not immediate foreshocks occur during the mainshock nucleation depends on how the rupture growth resistance varies on a local to small scale in the nucleation zone (18, 22).

During the nucleation, local shear stresses decrease gradually in the breakdown zone, and at the same time the corresponding premonitory slip also proceeds in the zone, since the shear strength degrades with ongoing slip in the nucleation zone. Premonitory stress (or strain) changes are also observed outside (but adjacent to) the nucleation zone; that is, local shear stresses on the remaining unslipped parts adjacent to the nucleation zone increase with time because the unslipped segments must bear extra stress loads that have been sustained by the slipped parts. These gradual, accelerating changes in both local stress and slip are inevitable precursors that occur locally in or adjacent to the zone of the rupture nucleation. However, no such precursory slip and stress degradation necessarily occurs in a region distant from the nucleation zone, and the precursory deformation and stress changes can locally be confined in (or adjacent to) the zone of the nucleation. This suggests that the key to the short-term (or immediate) earthquake prediction is to identify where the nucleation occurs on the fault that has the potential to cause a major earthquake.

If the critical size of the nucleation zone for a real major earthquake is small enough, it may be meaningless to regard the nucleation process as an effective tool for the immediate prediction. In this sense, it is important to know how large is the critical size of the nucleation zone for a real major earthquake. The critical size of the nucleation zone has recently been estimated for a number of major earthquakes (B.Shibazaki and M.Matsu’ura, personal communication; see also refs. 22 and 23), showing that Lc for major earthquakes with M=7.0−7.7 is 5−10 km.

For a given Lc of 5–10 km, λc=0.5−2 m from Eqs. 19 and 21. This estimate suggests that for earthquakes of M=7.0−7.7, the breakdown process behind the tip of propagating rupture is virtually governed by a characteristic length of the order of 1 m, which is 104–105 times greater than λc for shear rupture in the laboratory.

I am deeply grateful to Professor L.Knopoff and the other organizers for inviting me to present this paper and for their courtesy during the Colloquium.

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