A dislocation model of microplate boundary ruptures n the presence of a viscoelastic asthenosphere

Summary. A microplate is modelled as an elastic plate with two long strike-slip boundaries, lying over a Maxwell-type viscoelastic asthenosphere. The microplate is subjected to a constant and uniform shear strain rate by the opposite motions of two adjoining larger plates. After the occurrence of an earthquake at one of the microplate boundaries, the time evolution of shear stress at the other boundary is studied. It is found that stress build-up at the second boundary is delayed due to stress diffusion governed by the asthenosphere relaxation. Earthquake occurrence at this latter boundary would be delayed depending upon both the microplate width and the ratio between the Maxwell relaxation time of the asthenosphere and a characteristic time required for tectonic strain to recover rupture conditions. It turns out that the parameters which determine the occurrence of seismic activity along the microplate boundaries are more strictly constrained in the presence of a viscoelastic asthenosphere than in the case of an elastic half-pace model.     

Late Triassic initial subduction of the Bangong‐Nujiang Ocean beneath Qiangtang revealed: stratigraphic and geochronological evidence from Gaize,Tibet

Sedimentological and geochronological studies along a north–south traverse across the Bangong‐Nujiang suture zone (BNSZ) in Gaize, Tibet provide evidence for a Late Triassic–Jurassic accretionary wedge accreted to the south margin of Qiangtang. This wedge, preserved as the Mugagangri Group (MG), records evidence for the northward subduction of the Bangong‐Nujiang Ocean (BNO) beneath Qiangtang. The MG strata comprise two coarser intervals (lower olistostromes and upper conglomerates) intercalated within sandy turbidites, which are consistent with timing and forearc stratigraphy during subduction initiation predicted by geodynamic modelling. Following the model, the northward subduction of the BNO beneath Qiangtang and subsequent arc‐magmatism are inferred to have begun, respectively, at ca. 220 Ma and ca. 210 Ma, with respect to depositional ages constrained by youngest detrital‐zircon ages. The initiation of arc‐magmatism is also supported by provenance transition reflected by sandstone detrital modes and age patterns of detrital zircons. Previously, evidence for an incipient arc was lacking, but the timing of Late Triassic BNO subduction and related arc‐magmatism is coincident with an important Late Triassic magmatic event in central Qiangtang that probably represents the ‘missing’ arc. Other Qiangtang events, such as exhumation of the Qiangtang metamorphic belt as a source area, and development of the Late Triassic Nadigangri deposits and bimodal volcanism, are more easily explained in the tectonic context of early northward subduction of the BNO beneath Qiangtang, beginning at about 220 Ma.     

Shallow earthquakes in a viscoelastic shear zone with depth-dependent friction and rheology

Summary. Most crustal earthquakes of the world are observed to occur within a seismogenic layer which extends from the Earth's surface to a depth of a few tens of kilometres at most. A model is proposed in which the shear zone along a transcurrent plate margin is represented as a viscoelastic medium with depth-dependent power-law rheology. A frictional resistance linearly increasing with depth is assumed on a vertical transcurrent fault within the shear zone. Such a model is able to reproduce a continuous transition from the brittle behaviour of the upper crust to the ductile behaviour at depth. Assuming that the shear zone is subjected to a constant strain rate from the opposite motions of the two adjacent plates, it is found that there exists a maximum depth H below which tectonic stress can never reach the frictional threshold: this may be identified as the maximum depth of earthquake nucleation. The value of H is consistent with observations for plausible values of the model parameters. The stress evolution in the shear zone is calculated in the linear approximation of the constitutive equation. A change in rigidity with depth, which is also introduced in the model, may reproduce the high vertical gradient of shear stress, which has been measured across the San Andreas fault, and the fact that most earthquakes are nucleated at some depth in the seismogenic layer. A crack which drops the ambient stress to the dynamic frictional level is then introduced in the model. To this aim, a crack solution is employed without a stress singularity at its edges, which is compatible with a frictional stress threshold criterion for fracture. A constraint on the vertical friction gradient is obtained if such cracks are assumed to be entirely confined within the seismogenic layer.     

Stress accumulation between volcanoes: an explanation for intra-arc earthquakes in Nicaragua?

Destructive upper crustal earthquakes in Central America are often located between active volcanic centres—a geometric relationship that we study using finite element Coulomb failure stress (CFS) models that incorporate the rheologically heterogeneous nature of the volcanic arc. Volcanoes are simulated as mechanically weak zones within a stronger crust. We find that deformation of the volcanic centres within a regional stress field dominated by dextral shear causes stress increases in surrounding crust, with a maximum CFS change between neighbouring volcanoes. This increase in CFS enhances the probability of fault slip on arc-normal faults that are located between volcanic centres; for example, the Tiscapa fault, which ruptured during the 1972 December 13,   M _s   6.2 Managua earthquake. The amount of stress increase due to long-term (100 yr) volcano shearing is on the order of 0.1–0.6 bars, similar to values estimated for subduction zone earthquakes.     

Stress and Flow beneath Island Arcs

Summary. The flow pattern, stress distribution, topography, and gravity anomalies were computed from numerical models having density and viscosity distributions resemblant to the Aleutian arc. The results were compatible with the hypothesis that the excess density of the slab drives its descent and that hydrodynamic forces are responsible for topographic and gravity highs over the outer rise seaward of the trench and the frontal arc and lows over the trench. In models with simple distributions of rheological parameters, the force from the slab was transmitted directly upward producing a negative gravity anomaly over the arc. Material with low resistance to flow was needed along the fault plane above the slab or within the crust of the frontal arc and within the wedge of asthenosphere above the slab to reduce that force and to allow the horizontal lithosphere to move with the slab. Models with the resistance to flow thus reduced had outer rises, deep trenches, horizontal tension seaward of the trench, horizontal compression under the trench, and downdip tension in the slab. Free air gravity anomalies, which are the sum of between deflections of the free surface due to hydrodynamic forces and direct attractions from the masses driving the flow, were not fit excellently by any of the models, in part because the coarse grid used precluded accurate representation of the fault zone above the slab and the frontal arc. An alternate to the hypothesis that about 5 kb of stress on the fault plane is needed to produce an outer rise is offered by these models. Shear stress between the slab and the island arc was always below 700 bars in the more successful models if the density distribution was scaled to match the topography of the trench. This is much less than the 2000 bars stresses needed if frictional heating causes island arc volcanism.     

State of stress within a bending spherical shell and its implications for subducting lithosphere

The state of stress within a bending spherical shell has some special features that are caused by sphericity. While most lithospheres are more like spherical shells than flat plates, our ideas of the state of stress have been dominated by flat-plate models. As a consequence, we might be missing some important aspects of the state of stress within subducting lithospheres. In order to examine this problem, we analyse spherical-shell bending problems from basic equations. We present two approaches to solve spherical-shell bending problems: one by the variational approach, which is suitable for global-scale problems, and the other by the asymptotic equation, which is valid to first order in h/R , where h is the thickness of the lithosphere and R is its curvature radius (i.e. under the assumption of small curvature). The form of the equation for displacement shows that wavelengths of deformation are determined by the spherical (elastic) effect and the gravitational buoyancy effect, for which only the latter effect is included in the usual flat-plate formulations. In the case of the Earth, the buoyancy force is dominant and, consequently, spherical effects are suppressed to a large extent; this explains why flat-plate models have been successful for Earth's lithospheric problems. On the other hand, the state of stress shows interesting spherical effects: while bending (fibre) stress along the subduction zone is always important, bending stress along the trench-strike direction can also be important, in particular when the subduction zone arc is small. Numerical results also indicate that compressive normal stress along the trench-strike direction is important when a subduction zone arc is large. These two stresses, the bending stress and the compressive normal stress, both along the trench-strike direction, may have important implications for intraplate earthquakes at subduction zones.     

Small-scale mantle flows and induced lithospheric stress near island arcs

Summary. This paper explores the middle ground between complex thermally-coupled viscous flow models and simple corner flow models of island arc environments. The calculation retains the density-driven nature of convection and relaxes the geometrical constraints of corner flow, yet still provides semianalytical solutions for velocity and stress. A novel aspect of the procedure is its allowance for a coupled elastic lithosphere on top of a Newtonian viscous mantle. Initially, simple box-like density drivers illustrate how vertical and horizontal forces are transmitted through the mantle and how the lithosphere responds by trench formation. The flexural strength of the lithosphere spatially broadens the surface topography and gravity anomalies relative to the functional form of the vertical flow stresses applied to the plate base. I find that drivers in the form of inclined subducting slabs cannot induce self-driven parallel flow; however, the necessary flow can be provided by supplying a basal drag of 1–5 MPa to the mantle from the oceanic lithosphere. These basal drag forces create regional lithospheric stress and they should be quantifiable through seismic observations of the neutral surface. The existence of a shallow elevated phase transition is suggested in two slab models of 300 km length where a maximum excess density of 0.2 g cm⁻³ was needed to generate an acceptable mantle flow. A North New Hebrides subduction model which satisfies flow requirements and reproduces general features of topography and gravity contains a high shear stress zone (75 MPa) around the upper slab surface to a depth of 150 km and a deviatoric tensional stress in the back arc to a depth of 70 km. The lithospheric stress state of this model suggests that slab detachment is possible through whole plate fracture.     

Stress and temperature in subduction shear zones: Tonga and Mariana

Summary. Because there is secondary sea-floor spreading in the Tonga and Mariana subduction systems, the island arcs are separate plates. Horizontal forces on the two sides of the arc must balance, and the maximum force on the back-arc side can be calculated from a lithostatic ridge model. This, in combination with gravity data, allows calculation of the average shear stress in the top 100 km of the subduction shear zone. Stress in Tonga is 220±100 bar, and in the Mariana it is 165±75 bar. These low stresses are probably made possible by a fluid pore pressure almost equal to the least compressive stress.
Knowledge of stress allows approximate calculation of temperature in the shear zone by integration of a single differential equation. These temperatures are too low to activate most dehydration reactions in the subducted crust. As it approaches the volcanic line, this crust is at 150–350°C in Tonga and 150–300°C in the Mariana. Shear melting of the crust is ruled out, and conductive melting of the slab by contact with the asthenosphere meets with geochemical objections. Magmas in these systems are probably produced by partial melting of asthenosphere, triggered by a sudden release of water from the slab.     

Tectonic control of facies architecture, sequence stratigraphy and drowning of a Liassic carbonate platform (Betic Cordillera, Southern Spain)

This paper develops a tectono‐stratigraphic model for the evolution and drowning of Early Jurassic carbonate platforms. The model arises from outcrop analysis and Sr isotope dating of successions exposed in the Betic Cordillera in southeastern Spain. Here, an extensive Early Jurassic (Sinemurian) carbonate platform developed on the rifted Tethyan margin of the Iberian Plate. The platform was dissected by extensional faults in early jamesoni times (ca. 191 Ma) and again in late ibex times (ca.188 Ma) during the Pliensbachian stage. Extensional faults and fault block rotation are shown to control the formation of three sequence boundaries that divide the platform stratigraphy (the Gavilan Formation) into three depositional sequences. The last sequence boundary marks localised drowning of the platform and deposition of the deeper water Zegri Formation, whereas adjacent platforms remain exposed or continue as the site of shallow‐marine sediment accumulation. This study is based on mapping, facies analysis and dating of platform carbonates exposed in three tectonic units within the zone: Gabar, Ponce and Canteras. Facies analysis leads to the recognition of facies associations deposited in carbonate ramp environments and adjacent to synsedimentary, marine, fault scarps. Sr isotope dating enables us to correlate platform‐top carbonates from the different tectonic units at a precision equivalent to ammonite zones. A sequence stratigraphic analysis of sections from the three tectonic units is carried out using the facies models together with the Sr isotope dates. This analysis indicates a clear tectonic control on the development of the stratigraphy: depositional sequences vary in thickness, have wedge‐shaped geometries and vary in facies, internal geometries and systems tracts from one tectonic unit to another. Criteria characterising depositional sequences and sequence boundaries from the Gabar and Ponce units are used to establish a tectono‐stratigraphic model for carbonate platform depositional sequences and sequence boundaries in maritime rifts, which can be applied to other less well‐exposed or subsurface successions from other sedimentary basins. Onlapping transgressive and progradational highstand systems tracts are recognised on dip slope ramps. Falling stage and lowstand systems tracts are developed as thick breccia units in hangingwall areas adjacent to extensional faults. Sequence boundaries vary in character, amplitude and/or duration of sea‐level fall and persistence across the area. Some boundaries coalesce onto the Canteras unit, which remained as a relatively positive area throughout the early Pliensbachian (Carixian). The carbonate platform on the Ponce tectonic unit drowned in the latest Carixian (davoei biozone). However, the adjacent tectonic units remained emergent and developed a long‐lived sequence boundary, indicating tectonic subsidence as the major cause for platform drowning. The stratigraphic evolution of this area on the rifted southern Iberian margin indicates that a widespread restricted shallow‐water carbonate platform environment accumulating peritidal carbonates evolved with faulting to a more open‐marine setting. Sr dating indicates that this transition took place around the Sinemurian–Pliesbachian boundary and it was driven by local fault‐related subsidence together with likely post‐faulting regional subsidence.     

Aeolian shear stress ratio measurements within mesquite-dominated landscapes of the Chihuahuan Desert, New Mexico, USA

A field study was conducted to ascertain the amount of protection that mesquite-dominated communities provide to the surface from wind erosion. The dynamics of the locally accelerated evolution of a mesquite/coppice dune landscape and the undetermined spatial dependence of potential erosion by wind from a shear stress partition model were investigated. Sediment transport and dust emission processes are governed by the amount of protection that can be provided by roughness elements. Although shear stress partition models exist that can describe this, their accuracy has only been tested against a limited dataset because instrumentation has previously been unable to provide the necessary measurements. This study combines the use of meteorological towers and surface shear stress measurements with Irwin sensors to measure the partition of shear stress in situ. The surface shear stress within preferentially aligned vegetation (within coppice dune development) exhibited highly skewed distributions, while a more homogenous surface stress was recorded at a site with less developed coppice dunes. Above the vegetation, the logarithmic velocity profile deduced roughness length (based on 10-min averages) exhibited a distinct correlation with compass direction for the site with vegetation preferentially aligned, while the site with more homogenously distributed vegetation showed very little variation in the roughness length. This distribution in roughness length within an area, defines a distribution of a resolved shear stress partitioning model based on these measurements, ultimately providing potential closure to a previously uncorrelated model parameter.     

Two-dimensional modelling of subduction zone anisotropy with application to southwestern Japan

We present a series of 2-D numerical models of viscous flow in the mantle wedge induced by a subducting lithospheric plate. We use a kinematically defined slab geometry approximating the subduction of the Philippine Sea plate beneath Eurasia. Through finite element modelling we explore the effects of different rheological and thermal constraints (e.g. a low-viscosity region in the wedge corner, power law versus Newtonian rheology, the inclusion of thermal buoyancy forces and a temperature-dependent viscosity law) on the velocity and finite strain field in the mantle wedge. From the numerical flow models we construct models of anisotropy in the wedge by calculating the evolution of the finite strain ellipse and combining its geometry with appropriate elastic constants for effective transversely isotropic mantle material. We then predict shear wave splitting for stations located above the model domain using expressions derived from anisotropic perturbation theory, and compare the predictions to ∼500 previously published shear wave splitting measurements from seventeen stations of the broad-band F-net array located in southwestern Japan. Although the use of different model parameters can have a substantial effect on the character of the finite strain field, the effect on the average predicted splitting parameters is small. However, the variations with backazimuth and ray parameter of individual splitting intensity measurements at a given station for different models are often different, and rigorous analysis of details in the splitting patterns allows us to discriminate among different rheological models for flow in the mantle wedge. The splitting observed in southwestern Japan agrees well with the predictions of trench-perpendicular flow in the mantle wedge along with B-type olivine fabric dominating in a region from the wedge corner to about 125 km from the trench.     

Ductile shear zones: some aspects of constant slip velocity and constant shear stress models

Summary The thermomechanical differential equations governing deformation in viscous shear zones have been solved for both constant velocity and constant stress boundary conditions. The solutions show that the inertial term in these equations can be neglected everywhere.
The starting condition of the constant velocity model has been shown to be a constant velocity gradient and not a Heaviside function. The temperature anomaly produced by shear heating at the centre of the shear zone is shown to increase gradually and continuously with time, not reaching an asymptotic value. Conclusions for the constant velocity boundary condition are otherwise generally similar to those presented by Yuen et al , and agree with Fleitout & Froidevaux. The temperatures reached by constant velocity shears are sufficient for partial melting.
Constant stress boundary condition shear zone models show an initially broad shear zone with uniform shear velocity gradient. Depending on the level of applied shear stress and ambient temperature, localized intense shear heating may develop followed by thermal runaway. At lower ambient temperatures relatively high stresses are required to produce thermal runaway.
The broadening of the constant velocity shear zone proceeds more rapidly with increased ambient temperature. This can be used to show that shear zones broaden with depth. The merging of parallel shear zone pairs has been investigated and shear zones separated by distances of less than 10km coalesce to form a single shear zone within 3 Myr. Only shear zones separated by 50km or more remain distinct over periods of tens of millions of years.     

Depositional wedge tops: interaction between low basal friction external orogenic wedges and flexural foreland basins

Growth structures develop mainly across depositional wedge tops where the top of the distal orogenic wedge lies below local base level within the flexural foreland basin. Documented examples indicate that optimum conditions for the development of a depositional wedge top occur when the dip of the upper surface of the outer orogenic wedge (α) is low (0–1°), regardless of the taper angle (α+β), where β is the inclination of the base of the wedge. Low α angles are associated with the presence of low friction décollements, usually salt. Therefore, depositional wedge tops develop most commonly on low basal friction wedges. In natural examples such as the northern Apennines, the South Central Pyrenees and the Zagros, it is shown that whereas α is consistently low, β can vary considerably (1–9°), being principally controlled by flexure of the lower plate. In addition, the distribution of deformation in the wedge is complex. The applicability of the critical wedge model to low basal friction external orogenic zones is examined. Neither taper angles, nor the complex distribution of internal deformation nor the often associated forward slip of the whole wedge, can be satisfactorily explained by the established critical wedge model. As weak detachments such as salt cannot support any significant topography, it follows that low basal friction wedges cannot attain a critical state and, therefore, the critical wedge model cannot be satisfactorily applied to these external orogenic systems. This model, however, explains well the behaviour of external orogenic wedges with high basal friction. In the analysis of orogenic wedges, separate analysis of the angles α and β proves more useful than the critical taper angle α+β.     

Influence of the mechanical behaviour of brittle–ductile fold–thrust belts on the development of foreland basins

A two‐dimensional mathematical model considering coupling between a deforming elasto‐visco‐plastic fold–thrust belt, flexural subsidence and diffusional surface processes is solved using the Finite Element Method to investigate how the mechanical behaviour of brittle–ductile wedges influences the development of foreland basins. Results show that, depending mainly on the strength of the basal décollement, two end‐member types of foreland basin are possible. When the basal detachment is relatively strong, the foreland basin system is characterised by: (1) Highly asymmetrical orogen formed by thrusts concentrated in the incoming pro‐wedge. (2) Sedimentation on retro‐side takes place in one major foredeep basin which grows throughout orogen evolution. (3) Deposition on the pro‐side occurs initially in the foredeep, and continues in the wedge‐top before isolated basins are advected towards the orogen core where they become uplifted and exhumed. (4) Most pro‐wedge basins show an upward progression from low altitude, foredeep deposits at the base to high altitude, wedge‐top deposits near the surface. In contrast, when the basal detachment behaves weakly due to the presence of low viscosity material such as salt, the foreland basin system is characterised by (1) Broad, low relief orogen showing little preferential vergence and predominance of folding relative to faulting. (2) Deposition mainly in wedge‐top basins showing growth strata. (3) Many basins are initiated contemporaneously but form discontinuously due to the locus of active deformation jumping back and forth between different structures. Model results successfully reproduce first order observations of deforming brittle–ductile wedges and foreland basins. Moreover, the results support and provide a framework for understanding the existence of two main end‐member foreland basin types, simple and complex, associated with fold–thrust belts whose detachments are relatively strong and weak, respectively.     

Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus

Plates are an integral part of the convection system in the fluid mantle, but plate boundaries are the product of brittle faulting and plate motions are strongly influenced by the existence of such faults. The conditions for plate tectonics are studied by considering brittle behaviour, using Byerlee's law to limit the maximum stress in the lithosphere, in a mantle convection model with temperature-dependent viscosity.
When the yield stress is high, convection is confined below a thick, stagnant lithosphere. At low yield stress, brittle deformation mobilizes the lithosphere which becomes a part of the overall circulation; surface deformation occurs in localized regions close to upwellings and downwellings in the system. At intermediate levels of the yield stress, there is a cycling between these two states: thick lithosphere episodically mobilizes and collapses into the interior before reforming.
The mobile-lid regime resembles convection of a fluid with temperature-dependent viscosity and the boundary-layer scalings are found to be analogous. This regime has a well defined Nusselt number–Rayleigh number relationship which is in good agreement with scaling theory. The surface velocity is nearly independent of the yield stress, indicating that the 'plate' motion is resisted by viscous stresses in the mantle.
Analysis suggests that mobilization of the Earth's lithosphere can occur if the friction coefficient in the lithosphere is less than 0.03–0.13—lower than laboratory values but consistent with seismic field studies. On Venus, the friction coefficient may be high as a result of the dry conditions, and brittle mobilization of the lithosphere would then be episodic and catastrophic.     

Dynamic rupture and stress change in a normal faulting earthquake in the subducting Cocos plate

A large nearly vertical, normal faulting earthquake ( M _w = 7.1) took place in 1997 in the Cocos plate, just beneath the ruptured fault zone of the great 1985 Michoacan thrust event ( M _w = 8.1). Dynamic rupture and resultant stress change during the 1997 earthquake have been investigated on the basis of near-source strong-motion records together with a 3-D dynamic model.
Dynamically consistent waveform inversion reveals a highly heterogeneous distribution of stress drop, including patch-like asperities and negative stress-drop zones. Zones of high stress drop are mainly confined to the deeper, southeastern section of the vertical fault, where the maximum dynamic stress drop reaches 280 bars (28 MPa). The dynamically generated source time function varies with location on the fault, and yields a short slip duration, which is caused by a short scalelength of stress-drop heterogeneities. The synthetic seismograms calculated from the dynamic model are generally consistent with the strong-motion velocity records in the frequency range lower than 0.5 Hz.
The pattern of stress-drop distribution appears, in some sense, to be consistent with that of coseismic changes in shear stress resulting from the 1985 thrust event. This consistency suggests that the stress transfer from the 1985 event to the subducting plate could be one of the possible mechanisms that increased the chance of the occurrence of the 1997 earthquake.     

Scales of boundary resistance in coarse-grained channels: turbulent velocity profiles and implications

Gravel-bed surfaces are characterized by morphological features occurring at different roughness scales. The total shear stress generated by the flow above such surfaces is balanced by the sum of friction drag (grain stress) and form drag components (created by bed forms). To facilitate a better understanding of total resistance and bed load transport processes, there is a need to mathematically separate shear stress into its component parts. One way to do so is to examine the properties of vertical velocity profiles above such surfaces. These profiles are characterized by an inner layer that reflects grain resistance and an outer layer that reflects total resistance. A flume-based project was conducted to address these concerns through systematically comparing different roughness scales to ascertain how increased roughness affects the properties of vertical velocity profiles. Great care was taken to create natural roughness features and to obtain flow data at a high spatial and temporal resolution using an Acoustic Doppler Velocimeter.Average vertical velocity profiles above each roughness scale were clearly segmented. The vertical extent of the inner flow region was directly related to the scale of roughness present on the bed (and independent of flow depth), increasing with increased roughness. On a rough but rather uniform “plane” bed made of heterogeneous coarse sediments (with no bed forms), the shape of the velocity profile was clearly dominated by the local variations in grain characteristics. When pebble clusters were superimposed, the average shear stress in the outer flow region increased by 100% from the plane bed conditions. The ratio of inner grain shear stress to outer total shear stress for this pebble cluster experiment was 0.18 under shallow flow conditions and 0.3 under deep flow conditions. The grain stress component that should be used in bed load transport equations therefore appears to vary in these experiments between 15% and 30% of the total channel stress, increasing with decreased resistance. Roughness height (K_s/D₅₀) values at the grain scale for the plane bed and pebble cluster experiments were 0.73 and 0.63, respectively. These are values that should be used in flow resistance equations to predict grain resistance and grain stress for bed load transport modeling.     

Plate generation and two-phase damage theory in a model of mantle convection

The formation of narrow, rapidly deforming plate boundaries separating strong plate interiors are integral components of the generation of plate tectonics from mantle convection. The development of narrow plate boundaries requires the interaction of a non-linear rheology and convection. One such non-linear rheology is two-phase damage theory which employs a non-equilibrium relation between interfacial surface energy, pressure and viscous deformation, thereby forming a theoretical model for void generation. Two-phase damage theory was recently extended to allow for deformational work to increase the fineness (reduce the grain size) of the matrix phase. We present results testing two-phase damage theory in a 2-D convectively driven system where we allow for (1) pure void-generating damage, (2) pure fineness-generating damage and (3) combined void- and fineness-generating damage. Pure void-generating damage is found to be unsuccessful at producing plate-like features. Fineness-generating damage is successful at inducing plate-like behaviour in certain circumstances, including increasing viscosity sensitivity to fineness and certain regimes of damage input and healing rate. Cases with combined void- and fineness-generating damage produce significantly more localization than the end-members due to the apparent increase of deformational work input into fineness generation. The interaction of microcracks and grain size reduction in two-phase damage theory suggests a rheological model for shear localization necessary for the formation of plate tectonic boundaries.     

Orogenic volcanism caused by thermal runaways?

Summary. Quartz eclogite as source rock seems capable of explaining the chemistry of calc-alkaline volcanics. This model requires partial melting of quartz eclogite in the depth range 100–200 km. Shear heating of the subducting crust is one of the most debated models. The problem may be treated with two different boundary conditions: constant strain rate or constant shear stress. In the former case an increase in temperature tends to reduce the heat production thus stabilizing the shear flow; the result is a moderate increase in temperature which will remain constant during flow. The latter case may lead to a thermal feedback instability and thus temperature and strain rate may suddenly grow to very high values. This phenomenon is termed a runaway and will be discussed in this paper using an adiabatic approximation. It is shown that for a runaway to occur the local energy density must amount to a common value independent of the rheology. In contrast to the constant strain rate case, shear heating is negligible until just before the instability occurs. When the melting point is reached shear stress will break down but the stored local energy will be set free and supply the latent heat of melting. The possibility of a runaway occurring is strongly dependent on the ambient temperature. In subduction shear zones neither shear stress nor strain rate are likely to be constant throughout, but if the former is constant or changes little on a 1–10 km scale a runaway is liable to occur at a depth of around 150 km thus possibly being the cause of calcalkaline volcanism.