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

Laboratory measurements of rock strength provide limiting values of lithospheric stress, provided that one effective principal stress is known. Fracture strengths are too variable to be useful; however, rocks at shallow depth are probably fractured so that frictional strength may apply. A single linear friction law, termed Byerlee's law, holds for all materials except clays, to pressures of more than 1 GPa, to temperatures of 500°C, and over a wide range of strain rates. Byerlee's law, converted to maximum or minimum stress, is a good upper or lower bound to observed in situ stresses to 5 km, for pore pressure hydrostatic or subhydrostatic. Byerlee's law combined with the quartz or olivine flow law provides a maximum stress profile to about 25 or 50 km, respectively. For a temperature gradient of 15°K/km, stress will be close to zero at the surface and at 25 km (quartz) or 50 km (olivine) and reaches a maximum of 600 MPa (quartz) or 1100 MPa (olivine) for hydrostatic pore pressure. Some new permeability studies of crystalline rocks suggest that pore pressure will be low in the absence of a thick argillaceous cover.

Limits on lithospheric stress imposed by laboratory experiments

Rheological properties of the upper mantle of the Earth play an important role in the dynamics of the lithosphere and asthenosphere. However, such fundamental issues as the dominant mechanisms of flow have not been well resolved. A synthesis of laboratory studies and geophysical and geological observations shows that transitions between diffusion and dislocation creep likely occur in the Earth's upper mantle. The hot and shallow upper mantle flows by dislocation creep, whereas cold and shallow or deep upper mantle may flow by diffusion creep. When the stress increases, grain size is reduced and the upper mantle near the transition between these two regimes is weakened. Consequently, deformation is localized and the upper mantle is decoupled mechanically near these depths.

https://science.sciencemag.org/content/sci/260/5109/771.full.pdf

Rheology of the Upper Mantle: A Synthesis

The concept of strength envelopes, developed in the 1970s, allowed quantitative predictions of the strength of the lithosphere based on experimentally determined constitutive equations. Initial strength envelopes used an empirical relation for frictional sliding to describe deformation along brittle faults in the upper portion of the lithosphere and power law creep equations to estimate the plastic flow strength of rocks in the deeper part of the lithosphere. In the intervening decades, substantial progress has been made both in understanding the physical mechanisms involved in lithospheric deformation and in refining constitutive equations that describe these processes. The importance of a regime of semibrittle behavior is now recognized. Based on data from rocks without added pore fluids, the transition from brittle deformation to semibrittle flow can be estimated as the point at which the brittle fracture strength equals the peak stress to cause sliding. The transition from semibrittle deformation to plastic flow can be approximated as the stress at which the pressure exceeds the plastic flow strength. Current estimates of these stresses are on the order of a few hundred megapascals for relatively dry rocks. Knowledge of the stability of sliding along faults and of the onset of localization during brittle fracture has improved considerably. If the depth to the bottom of the seismogenic zone is determined by the transition to the stable frictional sliding regime, then that depth will be considerably more shallow than the depth of the transition to the plastic flow regime. Major questions concerning the strength of rocks remain. In particular, the effect of water on strength is critical to accurate predictions. Constitutive equations which include the effects of water fugacity and pore fluid pressure as well as temperature and strain rate are needed for both the brittle sliding and semibrittle flow regimes. Although the constitutive equations for dislocation creep and diffusional creep in single-phase aggregates are more robust, few data exist for plastic deformation in two-phase aggregates. Despite the fact that localization is ubiquitous in rocks deforming both in brittle and plastic regimes, only a limited amount of accurate experimental data are available to constrain predictions of this behavior. Accordingly, flow strengths now predicted from laboratory data probably overestimate the actual rock strength, perhaps by a significant amount. Still, the predictions are robust enough that uncertainties in geometry, mineralogy, loading conditions and thermodynamic state are probably the limiting factors in our understanding. Thus, experimentally determined rheologies can be applied to understand a broad range of topical problems in regional and global tectonics both on the Earth and on other planetary bodies.

Strength of the lithosphere: Constraints imposed by laboratory experiments

Topography extracted from swath profiles along the northern, southern, and eastern margins of the Tibetan Plateau show two end-member morphologies: steep, abrupt margins and longwavelength, low-gradient margins. Because the lack of significant upper crustal shortening across much of the eastern plateau margin implies that the crustal thickening occurs mainly in the deep crust, we compare regional topographic gradients surrounding the plateau to model results for flux of a Newtonian fluid through a lower crustal channel of uniform thickness. For an assumed 15-km-thick channel, we estimate a viscosity for the lower crust of 10 18 Pa·s beneath the low-gradient margins, 10 21 Pa·s beneath the steep margins, and an upper bound of 10 16 Pa·s beneath the plateau. These results indicate that the large-scale morphology of the eastern plateau reflects fluid flow within the underlying crust; crustal material flows around the strong crust of the Sichuan and Tarim Basins, creating broad, gentle margins, and “piles up” behind the basins creating narrow, steep margins. These results imply that this portion of the Eurasian crust was heterogeneous, but largely weak, even prior to construction of the Tibetan Plateau.

http://basin.earth.ncu.edu.tw/Course/SeminarII/abstract2014_1/2014.10.02_Sun,%20Yuan-Cheng/Topographic%20ooze%20building%20the%20eastern%20margin%20fo%20Tibet%20by%20low%20crustal%20flow.pdf

Topographic ooze: Building the eastern margin of Tibet by lower crustal flow

Summary. Previous attempts to deduce the stress distribution in the bending lithosphere near a consuming plate margin have relied on the observed bathymetry and an assumed constitutive relation for lithospheric behaviour, eg. perfectly elastic, viscous/perfectly plastic, or elastic perfectly plastic. From the point of view of rock mechanics, each of these approximations fails to describe one or more of several basic phenomena, including brittle failure of rock, temperature dependence of elasticity, and temperature and/or strain rate dependence of ductile behaviour. In order to formulate a more realistic constitutive relation, a limiting yield strength curve, which is primarily a function of temperature, is constructed from data from brittle failure and ductile flow experiments. The moments which can be supported by plates with this constitutive behaviour are compared to the moments calculated from bathymetric profiles. The comparison indicates that moments required by the bathymetric data are consistent with moments supported by plates with experimentally determined constitutive laws as extrapolated to geo- logically reasonable temperatures and strain rates. The stresses developed in such models are required to reach values greater than 100 MPat in the depth range 25-45 km. Geotherms necessary for strength curves consistent with moments calculated from the bathymetric data match those derived from heat flow data for the Aleutian, Bonin, Mariana and Tonga trenches. Of the trenches studied, only the geotherm inferred from the Kuril trench data is significantly different, perhaps implying that the Kuril plate is weaker than the others. The strength curves show that as a first approximation it is better to assume that bending moment is independent of curvature of the plate than to assume that bending moment and curvature are linearly related.

Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics

Gem quality single crystals of dry olivine were plastically deformed in compression at differential stresses between 50 and 1500 bars, with zero confining pressure, and at temperatures between 1428° and 1650°C. When these new data are combined with existing creep data for dry olivine-bearing rock, a flow law of the form e˙ = ƒ(σ) exp (−Q/RT) is obtained, whereƒ(σ) is an empirical function that is not simply proportional to σn for constant n and Q is equal to 125 ± 5 kcal/mol. The flow law covers the stress range 50–10,000 bars and the temperature range 1100°–1700°C and is consistent with all published data to 1 decade in strain rate.

Low-stress high-temperature creep in olivine single crystals

The variation of hardness with temperature was measured for olivine on a number of crystal faces by the Vickers diamond pyramid technique (up to 800°C) and by a mutual indentation technique (for temperatures up to 1500°C). A comparative review of hardness data and compressive creep measurements obtained under large confining pressures confirms the hypothesis of Rice [1971] that single-crystal hardness measurements, corrected for elastic effects, can be correlated to the fully ductile yielding of a polycrystal by intragranular dislocation mechanisms, including dislocation climb and glide. The computed differential yield stresses, σ (in gigapascals), which empirically correspond to a strain rate of 10−5 s−1, were well represented by an equation of the form σ = 9.1(±0.3) - 0.23(±0.01)T2, where T is the absolute temperature (in degrees Kelvin), and the quoted variances are for 1 standard deviation. The olivine data therefore predict a high-stress polycrystalline flow law that may be expressed as = 1.3 × 1012exp - [(60×103)/T][1 - (σ/9.1)]2 where is the strain rate in s−1. A similar functional dependence of strain rate on stress is indicated for Al2O3 for temperatures below 900°C but is contraindicated for MgO and NaCl. Using a semiempirical method of dislocation rosette analysis, the critical resolved shear stress on the {110} [001] slip system was estimated (to 20%) over the temperature range 20°C to 780°C as 1.2 GPa and 0.3 GPa, respectively. These data are useful in providing an upper bound to the yield stress in a region of stress and temperature space not easily accessible by other experimental methods.

The temperature variation of hardness of olivine and its implication for polycrystalline yield stress

A total of 41 selectively oriented single crystals of olivine (Fo92) were deformed under uniaxial stresses of 100–1800 bars in the temperature range 1150°–1600°C. Under uniform stress no strain inhomogeneities were observed. For all orientations both strain rate and dislocation structure stabilized after 1–2% strain and remained stable to the highest strains achieved (40%). For all orientations, creep could be represented by a power law of the form = Aσ3.6 where A varied with orientation by a factor of 50. Shape change and crystallographic rotation data for some orientations could only be accounted for by a substantial dislocation climb contribution to the strain rate. All specimens were decorated to show the dislocation structure.

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Plastic flow of oriented single crystals of olivine: 1. Mechanical data

The variation of hardness with temperature was measured for olivine on a number of crystal faces by the Vickers diamond pyramid technique (up to 800oC) and by a mutual indenta- tion technique (for temperatures up to 1500oC). A comparative review of hardness data and com-

C. Goetze

Papers

Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics

Low-stress high-temperature creep in olivine single crystals

The temperature variation of hardness of olivine and its implication for polycrystalline yield stress

Plastic flow of oriented single crystals of olivine: 1. Mechanical data

The temperature variation of hardness of olivine and its implication