This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

The Mechanics of Earthquakes and Faulting

To understand whether the 1992 M = 7.4 Landers earthquake changed the proximity to failure on the San Andreas fault system, we examine the general problem of how one earthquake might trigger another. The tendency of rocks to fail in a brittle manner is thought to be a function of both shear and confining stresses, commonly formulated as the Coulomb failure criterion. Here we explore how changes in Coulomb conditions associated with one or more earthquakes may trigger subsequent events. We first consider a Coulomb criterion appropriate for the production of aftershocks, where faults most likely to slip are those optimally orientated for failure as a result of the prevailing regional stress field and the stress change caused by the mainshock. We find that the distribution of aftershocks for the Landers earthquake, as well as for several other moderate events in its vicinity, can be explained by the Coulomb criterion as follows: aftershocks are abundant where the Coulomb stress on optimally orientated faults rose by more than one-half bar, and aftershocks are sparse where the Coulomb stress dropped by a similar amount. Further, we find that several moderate shocks raised the stress at the future Landers epicenter and along much of the Landers rupture zone by about a bar, advancing the Landers shock by 1 to 3 centuries. The Landers rupture, in turn, raised the stress at site of the future M = 6.5 Big Bear aftershock site by 3 bars. The Coulomb stress change on a specified fault is independent of regional stress but depends on the fault geometry, sense of slip, and the coefficient of friction. We use this method to resolve stress changes on the San Andreas and San Jacinto faults imposed by the Landers sequence. Together the Landers and Big Bear earthquakes raised the stress along the San Bernardino segment of the southern San Andreas fault by 2 to 6 bars, hastening the next great earthquake there by about a decade.

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Static stress changes and the triggering of earthquakes

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,

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Earthquakes and friction laws

The concept of self-organized criticality was introduced to explain the behaviour of the sandpile model. In this model, particles are randomly dropped onto a square grid of boxes. When a box accumulates four particles they are redistributed to the four adjacent boxes or lost off the edge of the grid. Redistributions can lead to further instabilities with the possibility of more particles being lost from the grid, contributing to the size of each ‘avalanche’. These model ‘avalanches’ satisfied a power-law frequency‐area distribution with a slope near unity. Other cellular-automata models, including the slider-block and forest-fire models, are also said to exhibit self-organized critical behaviour. It has been argued that earthquakes, landslides, forest fires, and species extinctions are examples of self-organized criticality in nature. In addition, wars and stock market crashes have been associated with this behaviour. The forest-fire model is particularly interesting in terms of its relation to the critical-point behaviour of the sitepercolation model. In the basic forest-fire model, trees are randomly planted on a grid of points. Periodically in time, sparks are randomly dropped on the grid. If a spark drops on a tree, that tree and adjacent trees burn in a model fire. The fires are the ‘avalanches’ and they are found to satisfy power-law frequency‐area distributions with slopes near unity. This forest-fire model is closely related to the site-percolation model, that exhibits critical behaviour. In the forest-fire model there is an inverse cascade of trees from small clusters to large clusters, trees are lost primarily from model fires that destroy the largest clusters. This quasi steady-state cascade gives a power-law frequency‐area distribution for both clusters of trees and smaller fires. The site-percolation model is equivalent to the forest-fire model without fires. In this case there is a transient cascade of trees from small to large clusters and a power-law distribution is found only at a critical density of trees.

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Self-organized criticality

Characterizing flow and transport in fractured geological media: A review

A conceptual model for the origin of fault damage zone structures in high-porosity sandstone

We investigate the effects of interaction between growing normal faults on the creation of accommodation in extensional half grabens. Fault evolution is simulated using a numerical model in which we calculate both the stress field around each fault and the changes in stress level on neighbouring faults caused by individual slip events (earthquakes). These stress changes govern the interaction and determine both the direction and rate of lateral fault
propagation and the accumulation of displacement. The spatial distribution of subsidence resulting from fault growth is examined parallel and transverse to strike to document the three-dimensional evolution of accommodation creation. The numerical experiment permits analysis of the geometry, inception and growth history of individual fault-controlled depocentres during development of a linked normal fault array. Model results indicate that the pattern of fault-controlled subsidence, and hence hangingwall accommodation creation, is
spatially and temporally variable as the timing and rates of fault movement vary considerably. In general, there is a progression from many relatively small and isolated subbasins initially, to the development of a larger laterally continuous half graben in the hangingwall to a major through-going linked fault system. Many smaller faults initially active in footwall and
hangingwall areas become inactive as the extension localizes onto the major structure. This switching-off of some faults, combined with focusing of the extensional deformation, leads to an increase in the rate of displacement accumulation on the remaining active fault. As dip-slip displacement is a proxy for hangingwall subsidence, we interpret this prominent rate change in terms of the ‘rift-initiation’ to ‘rift-climax’ transition, previously recognized in synrift stratigraphy. A general picture of depocentre development relative to timing of linkage emerges from the simulated fault evolution that provides some simple conceptual models to be tested. However, the important result of this paper is that it shows the degree to which fault activity can vary in space and time both along the same fault zone and also across strike. We briefly discuss the implications of model results for stratigraphic architecture in rift basins.
Our conclusion is that some of the stratigraphic complexity of rifts previously ascribed to other controls (e.g. sediment supply, eustasy, etc.) may be tectonically controlled and that with improved three-dimensional imaging of rift basins these effects may be recognized.

Implications of fault array evolution for synrift depocentre development: insights from a numerical fault growth model

Constraining slip rates and spacings for active normal faults

Fault tip displacement gradients and process zone dimensions

A statistical physics model is used to simulate antiplane shear deformation and rupture of a tectonic plate with heterogeneous material properties. Rupture occurs when the chosen state variable reaches a threshold value. After rupture, broken elements are instantaneously healed and retain the original material properties. We document the spatiotemporal evolution of the rupture pattern in response to a constant velocity boundary condition. A fundamental feature of this model is that ruptures become strongly correlated in space and time, leading to the development of complex fractal structures. These structures, or “faults,” are simply defined by the loci where deformation accumulates. Repeated rupture of a fault occurs in events (“earthquakes”) which themselves exhibit both spatial and temporal clustering. Furthermore, we observe that a fault may be active for long periods of time until the locus of activity spontaneously switches to a different fault. The formation of the faults and the temporal variation of rupture activity is due to a complex interplay between the random small-scale structure, long-range elastic interactions, and the threshold nature of rupture physics. The characteristics of this scalar model suggest that spontaneous self-organization of active tectonics does not result solely from the tensorial nature of crustal deformation; that is, kinematic compatibility is not required for complex fault pattern formation. Furthermore, the localization of the deformation is a dynamical effect rather than a consequence of preexisting structure or preferential weakening of faults compared to the surrounding medium. We present an analysis of scaling relationships exhibited by the fault pattern and the earthquakes in this model.

Patience A. Cowie

Papers

A conceptual model for the origin of fault damage zone structures in high-porosity sandstone

Implications of fault array evolution for synrift depocentre development: insights from a numerical fault growth model

Constraining slip rates and spacings for active normal faults

Fault tip displacement gradients and process zone dimensions

Statistical physics model for the spatiotemporal evolution of faults