Statistics for Spatial Data.

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

This paper reviews rock friction and the frictional properties of earthquake faults. The basis for rate- and state-dependent friction laws is reviewed. The friction state variable is discussed, including its interpretation as a measure of average asperity contact time and porosity within granular fault gouge. Data are summarized showing that friction evolves even during truly stationary contact, and the connection between modern friction laws and the concept of “static” friction is discussed. Measurements of frictional healing, as evidenced by increasing static friction during quasistationary contact, are reviewed, as are their implications for fault healing. Shear localization in fault gouge is discussed, and the relationship between microstructures and friction is reviewed. These data indicate differences in the behavior of bare rock surfaces as compared to shear within granular fault gouge that can be attributed to dilation within fault gouge. Physical models for the characteristic friction distance are discussed and related to the problem of scaling this parameter to seismic faults. Earthquake afterslip, its relation to laboratory friction data, and the inverse correlation between afterslip and shallow coseismic slip are discussed in the context of a model for afterslip. Recent observations of the absence of afterslip are predicted by the model.

/pdf/laboratory-derived-friction-laws-and-their-application-to-44s35v6won.pdf

Laboratory-derived friction laws and their application to seismic faulting

The eastern Tonale fault zone: a ‘natural laboratory’ for crystal plastic deformation of quartz over a temperature range from 250 to 700 °C

Dislocation creep regimes in quartz aggregates

Pseudotachylytes from a crustal scale shear zone in Central Australia have developed in a cyclical manner: once developed, an individual pseudotachylyte is deformed in a ductile manner, only to be overprinted at a later stage by a new generation of pseudotachylytes. Such cyclic generation and deformation of pseudotachylyte has been interpreted in the past as representing conditions at the brittleductile transition; a different interpretation, however, is presented here. It is proposed that psuedotachylytes and associated ultramylonites can develop entirely within the ductile regime as ductile instabilities. Such instabilities are different in nature to those previously discussed at length in the geophysical literature but are identical in principle with the instabilities that develop for velocity-weakening frictional behavior in spring-slider systems. At a given strain rate a critical temperature,T
c, is defined, at which the transient work hardening equals the product of stress relaxation due to a thermal fluctuation and the heat generated by shearing. A necessary condition for ductile instability at a given strain rate is that the temperature is belowT
c; then the rate of change of stress with respect to strain is negative. An additional requirement is that this rate of change exceeds, in magnitude, the effective elastic stiffness of the loading system. Ductile instabilities are marginally possible at geological strain rates in quartzites but are possible at mid-crustal temperatures in other rock types. On the basis of these observations a new interpretation is presented for the base of the seismogenic zone in crustal regions.

Earthquakes in the ductile regime

Abstract Material strain softening is commonly taken as a necessary and sufficient condition for localization in deforming rocks. However, there is a wide range of experimental and theoretical information which shows that localization can occur in sands, brittle rocks and ductile metals under strain-hardening conditions. This paper aims to bring these two contrasted views together. Three separate criteria are necessary in order to understand localization behaviour. The first involves the stability of the deforming system. The second determines whether a deforming system will undergo bifurcation so as to cease deforming in a homogeneous mode and instead deform in an inhomogeneous mode such as barrelling or localization. The stability and bifurcation criteria are independent of each other since barrelling is a stable mode whereas localization is unstable. The third criterion establishes if the unstable bifurcation mode is one of localization or of some other kind. Localization may arise from the presence of vertices on the yield surface (as in the case of pressure insensitive, rate dependent metals and in brittle rocks due to the development of preferred microfractures for slip) or from the constitutive relation being such that the plastic strain-rate vector is not normal to the yield surface (as in the cases of pressure sensitive, dilatant rocks, of materials deforming by crystal-plastic processes involving dislocation cross-slip and/or climb, and of visco-plastic materials in which voids are forming due to diffusive processes). It is important to distinguish between material and system softening (or hardening) behaviour. The theory for a kinematically unconstrained shortening experiment (that is, rigid, frictionless platens) indicates that localization can occur in strain-hardening materials but the system must strain-soften from then on; that is, localization occurs at peak stress for the system even though the material may continue to harden (or soften). However, the addition of kinematic constraints (such as friction at elastic platens, a constraint to deform in plane strain or at constant volume) means that localization may occur in a system that is monotonically strain hardening. Shear zones in naturally deformed rocks show ample evidence of dilatant behaviour in that evidence for the passage of large volumes of fluid during localization is common as is the development of dilatant vein systems. As such, since shear zones are strongly constrained by the elastic and (limited) plastic response of the relatively undeformed rocks surrounding the shear zones, strain-hardening behaviour of the system is to be expected as the norm, even if the rocks within the shear zones are undergoing material strain-softening.

Instability, softening and localization of deformation

Adiabatic or catastrophic plastic shear has been reported in metals, polymers, and metallic glasses. The phenomenon is associated with rapid stress drops and audible pings or clicks as the material deforms in a plastic manner. The driving force for the plastic instability is the stored elastic strain energy of the loading system, and in many respects the behavior is reminiscent of the shear stress response arising from stick slip events during unstable frictional sliding, although the precise mechanism is different. It is shown here that adiabatic plastic shear is capable of explaining the detailed distribution of intermediate and deep focus earthquakes within subduction zones, the earthquake events being the result of instabilities in material undergoing plastic flow. It is argued that for a particular strain rate there exists a critical temperature, TC, which is depth dependent; for temperatures below TC the material is strain rate softening and, for a soft enough loading system, may undergo catastrophic plastic shear. For temperatures above TC the material is strain rate hardening and is always stable during plastic shear. The cutoff depth for deep focus earthquakes then corresponds to the transition from strain rate softening to strain rate hardening material, and for commonly accepted geothermal gradients within the slab corresponds to approximately 800 km. The precise distribution of earthquakes within the slab is a function of the subtle interplay between the geothermal gradient and the TC gradient. In particular, a decrease in seismic activity is to be expected below about 300 km in the slab with total stress drops decreasing from a maximum of 700 MPa above 300 km to a maximum of ≈ 50 MPa below 300 km. The differences in foci distribution between subduction zones such as Tonga, New Hebrides, and Peru result from minor differences in the geothermal gradients within the slabs. The model predicts the development of triple seismic zones high in the slab, double seismic zones down to approximately 300 km, and single seismic zones down to ≈ 800 km. Such a distribution is to be expected of relatively young, cool slabs; as the slab heats up, the seismic activity retreats up the slab. The paper only proposes a deformation mechanism for earthquake generation, it does not address the stress field within the slab but only the distribution of strength. Thus the distribution of focal plane mechanisms is not considered, only the locations where earthquakes due to plastic instabilities are possible. The absence of earthquakes does not necessarily mean that the slab does not exist, it only means that the slab is too hot to undergo plastic instability. This means that aseismic subduction is a distinct possibility in many regions of high geothermal gradient within the slab (i.e. > circa 3°C km−1).

Plastic instabilities: Implications for the origin of intermediate and deep focus earthquakes

The strength of the continental crust, detachment zones and the development of plastic instabilities

The chemical-dissolution front propagation problem exists ubiquitously in many scientific and engineering fields. To solve this problem, it is necessary to deal with a coupled system between porosity, pore-fluid pressure and reactive chemical-species transport in fluid-saturated porous media. Because there was confusion between the average linear velocity and the Darcy velocity in the previous study, the governing equations and related solutions of the problem are re-derived to correct this confusion in this paper. Owing to the morphological instability of a chemical-dissolution front, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve this problem. In order to verify the proposed numerical procedure, a set of analytical solutions has been derived for a benchmark problem under a special condition where the ratio of the equilibrium concentration to the solid molar density of the concerned chemical species is very small. Not only can the derived analytical solutions be used to verify any numerical method before it is used to solve this kind of chemical-dissolution front propagation problem but they can also be used to understand the fundamental mechanisms behind the morphological instability of a chemical-dissolution front during its propagation within fluid-saturated porous media. The related numerical examples have demonstrated the usefulness and applicability of the proposed numerical procedure for dealing with the chemical-dissolution front instability problem within a fluid-saturated porous medium. Copyright © 2007 John Wiley & Sons, Ltd.

Alison Ord

Papers

Earthquakes in the ductile regime

Instability, softening and localization of deformation

Plastic instabilities: Implications for the origin of intermediate and deep focus earthquakes

The strength of the continental crust, detachment zones and the development of plastic instabilities

Theoretical and numerical analyses of chemical‐dissolution front instability in fluid‐saturated porous rocks