Earthquakes and friction laws

The traditional view of tectonics is that the lithosphere comprises a strong brittle layer overlying a weak ductile layer, which gives rise to two forms of deformation: brittle fracture, accompanied by earth- quakes, in the upper layer, and aseismic ductile flow in the layer beneath. Although this view is not incorrect, it is imprecise, and in ways that can lead to serious misunderstandings. The term ductility, for example, can apply equally to two common rock deformation mechanisms: crystal plasticity, which occurs in rock above a critical temperature, and cataclastic flow, a type of granular deformation which can occur in poorly consolidated sediments. Although both exhibit ductility, these two deformation mechanisms have very different rheologies. Earthquakes, in turn, are associated with strength and brittleness—associations that are likewise sufficiently imprecise that, if taken much beyond the generality implied in the opening sentence, they can lead to serious misinterpretations about earthquake mechanics. Lately, a newer, much more precise and predictive model for the earthquake mechanism has emerged, which has its roots in the observation that tectonic earthquakes seldom if ever occur by the sudden appearance and propagation of a new shear crack (or 'fault'). Instead, they occur by sudden slippage along a pre-existing fault or plate interface. They are therefore a frictional, rather than fracture, phenomenon, with brittle fracture playing a secondary role in the lengthening of faults 1 and frictional wear 2 . This distinction was noted by several early workers 3 , but it was not until 1966 that Brace and Byerlee 4 pointed out that earthquakes must be the result of a stick-slip frictional instability. Thus, the earthquake is the 'slip', and the 'stick' is the interseismic period of elastic strain accumula- tion. Subsequently, a complete constitutive law for rock friction has been developed based on laboratory studies. A surprising result is that a great many other aspects of earthquake phenomena also now seem to result from the nature of the friction on faults. The properties traditionally thought to control these processes— strength, brittleness and ductility—are subsumed within the over- arching concept of frictional stability regimes. Constitutive law of rock friction In the standard model of stick-slip friction it is assumed that sliding begins when the ratio of shear to normal stress on the surface reaches a value ms, the static friction coefficient. Once sliding initiates, frictional resistance falls to a lower dynamic friction coefficient, md, and this weakening of sliding resistance may,