Ductile Flow Research Articles

Ductile flow in sub-volcanic carbonate basement as the main control for edifice stability: New experimental insights

Limestone in volcanic basements has been identified as a hazard in terms of edifice stability due to the propensity of calcite to decompose into lime and CO2 at high temperatures (>600 °C), causing a decrease in mechanical strength. To date, such hypotheses have been tested by experiments performed at ambient pressure. The present work determines the mechanical strength of limestone under sub-volcanic conditions of pressure and temperature and evaluates the effect of calcite decomposition. To this end, we use Mt. Etna as a case study, deforming sub-Etnean carbonate samples under triaxial compression using a Paterson deformation apparatus. We evaluate the effect of thermal decomposition of calcite on sample strength by comparing closed and open systems and measuring the permeability evolution under static conditions. Mechanical and micro-structural observations at a constant strain rate of 10−5 s−1 and at a confining pressure of 50 MPa indicate that the rocks are brittle up to and including 300 °C. At higher temperatures the deformation becomes macroscopically ductile, i.e., deformation is distributed throughout the sample. The brittle to ductile transition is accompanied by an irreversible permeability decrease from ∼10−17 to ∼10−19 m2 between 200 and 600 °C. We present new evidence that permanent change in permeability is due to ductile processes closing the initial pore space. Samples deformed at temperatures up to 900 °C do not contain any decarbonation products. At these temperatures, permeability is sufficiently low to permit CO2 pore pressures to increase, thereby increasing local CO2 fugacity, which in turn strongly limits the decarbonation reaction. We note that, for non-pure calcite rocks, permeability might be sufficient to allow decarbonation reactions to occur. As such, variability in lithologies may slightly influence the efficiency of decarbonation reactions. We conclude that, in a closed system, the instability of Mt. Etna is related to high temperature induced ductile flow of basement limestone rather than chemical/mineralogical changes. This may have important implication for the stability of volcanoes within carbonate-rich basement, as carbonates become significantly weak at high temperatures, which may increase the risk of sector collapse.

Structural glaciology of Austre Brøggerbreen, northwest Svalbard

ABSTRACTStructural glaciological maps can be used to study the structural evolution and past dynamics of glaciers. The map described here documents the glacier-wide structural characteristics of Austre Brøggerbreen, a c. 12 km2 predominantly cold-based valley glacier in northwest Svalbard. The structural map reveals that the glacier is dominated by deep-penetrating fractures that are now relict (crevasse traces). These structures indicate that, despite being relatively inactive at present, the glacier was once much more dynamic, presumably during its last advance in the Neoglacial (c. 1900 AD). Contemporary glacier structures (i.e. those that are actively forming) include primary stratification, longitudinal foliation and rare surface fracturing (crevasses and water-healed crevasses). Relict fracture sets become increasingly re-orientated and folded down-glacier as a result of ductile flow. Individual flow units show large differences in the evolution of structures, indicating that the flow units have been subject to different flow histories and dynamics. The map will also be useful for future change-detection studies on this rapidly receding glacier.

Eduction, extension, and exhumation of ultrahigh‐pressure rocks in metamorphic core complexes due to subduction initiation

AbstractThe controversy over the exhumation of ultrahigh‐pressure (UHP) rocks centers on whether it involves rising of pieces of crust detached from subducted continental lithosphere or an entire subducted plate that undergoes “eduction,” i.e., reverse subduction. We present a new thermomechanical model of continental subduction showing that these apparently contrasting mechanisms can occur together: crust subducted deep enough is heated and weakened, causing limited diapiric rise, while crust subducted to shallower depths retains strength and is exhumed only by eduction. The model also shows for the first time how eduction followed by seafloor spreading can occur in a zone of regional convergence. This occurs spontaneously when subduction of buoyant crust causes a subduction zone to “lock up” in one place causing a new subduction zone to form in another. The model is consistent with many features of the youngest region of UHP rock exhumation on earth: the D'Entrecasteaux Islands. UHP exhumation and the amount of regional extension, as well as the seismic structure around the islands, can be explained by eduction. Ductile flow fabrics, seen on the islands, would result from exhumation of the most deeply subducted crust heated enough to undergo partial melting. Reversal of motion on the north‐dipping continental subduction zone, required by this model, was likely triggered by initiation of the New Britain Trench, as suggested previously. Our model implies that the crust of Goodenough Basin, south of the islands, was exhumed by eduction in the last 5 Ma and this hypothesis can be tested by drilling.

Structure of thinned continental crust across the Orphan Basin from a dense wide-angle seismic profile and gravity data

We present a 500-km long, 2-D P-wave velocity model across the Orphan Basin, offshore NE Newfoundland, Canada, from Flemish Cap to the Bonavista Platform, formed using refraction and wide-angle reflection data from 89 ocean-bottom seismometers. This layered model builds on a recent traveltime tomography result using additional constraints from coincident multichannel seismic reflection and gravity data plus borehole logs from three wells. The model shows (i) post-rift Tertiary (velocities ∼1.7–3.5 km s−1) and (ii) both post-rift and syn-rift, Cretaceous and Jurassic sediments (∼4–5 km s−1), deposited within an eastern and a western sub-basin that are separated by a major basement block. The existence of Jurassic sediments indicates a pre-Cretaceous rifting phase in the eastern sub-basin, and possibly in the western sub-basin. However, there is no evidence that Triassic sediments are widespread across the Orphan Basin. Two upper crustal sublayers and one lower crustal layer are defined by differences in velocities (5.4–6.1, 6.1–6.5 and 6.3–7.1 km s−1, respectively) and vertical velocity gradients (mean = 0.14, 0.10 and 0.05 s−1, respectively). Crustal thinning is asymmetric across the Orphan Basin. Within the eastern sub-basin, continental crust beneath Flemish Cap (∼32 km thick; β ∼ 1.1) thins westward into a 35-km-wide zone of hyperextended crust (<10 km thick; β > 3.4) beneath an 11-km-deep sedimentary basin. Within the western sub-basin, the Bonavista Platform crust (∼32 km thick) thins eastward into a 116-km-wide zone of hyperextended crust. Two zones of thicker crust (β = 2–3.5) exist within the central section, with muted topography within the eastern part and large basement highs in the western part, separated by the eastward dipping White Sail Fault (WSF). The zone to the east of the WSF displays higher velocities in the lower crust than to the west. This can only be explained by a lateral ductile flow across the zone boundary. By combining the two upper crustal sublayers into one, we define the full crustal thicknesses of the upper and lower crusts as 12 and 22 km, respectively. The extension and thinning factors of these two layers are calculated across the basin. Discrepancies between upper crustal thinning and lower crustal thinning are common but only produce a small mass deficit (∼7 per cent or 1.5 km) in the lower crust. Structural connections are shown between the Rockall Trough and the West Orphan Basin and between the Porcupine Basin and the East Orphan Basin in that a wider hyperextended western basin is paired with a narrower eastern basin by a middle zone of thicker crust. In contrast to the Rockall Trough and the Porcupine Basin, serpentinized mantle is not observed in the East Orphan Basin where hyperextended crust is observed (βmax ∼ 8.5). One possible cause is that the restricted size of the basin and its location adjacent to Flemish Cap may have permitted a heavier supply of sediment to cover the basement early during its extension. Such a cover would inhibit the flow of water into the crust and thus leave the mantle unchanged.

Experimental Investigation of Microcutting Mechanisms in Oxide Ceramic CM332 Grinding

The paper contains an experimental study of microcutting intended to help the optimization of the grinding process of the oxide ceramic CM332 (99.5% Al2O3) grinding. The need for investigating the mechanisms occurring between the abrasive material and the ceramic is imposed by the fact that grinding is the dominant technology used to achieve the required quality of the workpiece surface finish. The microcutting process was performed with a single diamond cone-shaped grain of tip radius of 0.2 mm at varying depths of cut. The investigations were carried out to determine the normal and tangential cutting forces, the critical penetration depth and the specific grinding energy as a function of the grain penetration speed and depth. The critical grain penetration depth separating ductile flow from brittle fracture falls within the 4–6 μm range. The values of the critical penetration depth are also consistent with the results of changes in the cutting forces and the specific grinding energy. The chip formation mechanism is associated with the presence of median/radial and lateral cracks, ductile flow, chipping along the groove, and crushing beneath the diamond grain, all this affecting the quality of the ceramic's machined surface.

Extensive normal faulting during exhumation revealed by the spatial variation of phengite K–Ar ages in the Sambagawa metamorphic rocks, central Shikoku, SW Japan

AbstractMetamorphic rocks experience change in the mode of deformation from ductile flow to brittle failure during their exhumation. We investigated the spatial variation of phengite K–Ar ages of pelitic schist of the Sambagawa metamorphic rocks (sensu lato) from the Saruta River area, central Shikoku, to evaluate if those ages are disturbed by faults or not. As a result, we found that these ages change by ca 5 my across the two boundaries between the lower‐garnet and albite–biotite, and the albite–biotite and upper‐garnet zones. These spatial changes in phengite K–Ar ages were perhaps caused by truncation of the metamorphic layers by large‐scale normal faulting at D2 phase under the brittle‐ductile transition conditions (ca 300°C) during exhumation, because an actinolite rock was formed along a fault near the former boundary. Assuming that the horizontal metamorphic layers and a previously estimated exhumation rate of 1 km/my before the D2 phase, the change of 5 my in phengite K–Ar ages is converted to a displacement of about 10 km along the north‐dipping, low‐angle normal fault documented in the previous study. Phengite 40Ar–39Ar ages (ca 85 to 78 Ma) in the actinolite rock could be reasonably comparable to the phengite K–Ar ages of the surrounding non‐faulted pelitic schist, because the K–Ar ages of pelitic schist could have been also reset at temperatures close to the brittle–ductile transition conditions far below the closure temperature for thermal retention of argon in phengite (about 500–600°C).

New insights into the generation of the 2013 Lushan Earthquake (Ms 7.0), China

AbstractGlobal seismic waveform inversion can provide information on where the 2013 Ms 7.0 Lushan earthquake occurred in Sichuan Province, China, and how its aftershock sequence expanded. To investigate the generation mechanism of the Lushan earthquake and its relation to the 2008 Wenchuan earthquake (Ms 8.0), 50 temporary seismic stations were installed in the source area following the Lushan earthquake. Crustal stress data were also collected along the Longmen‐Shan Fault zone (LMFZ) to reveal its influence on the generation of the Lushan earthquake. Seismic imaging and crustal stress analysis have revealed that the Lushan earthquake occurred in a distinct area with high velocity (Vp, Vs), low Poisson's ratio (σ), and high crustal stress. The high‐velocity zone at the Lushan source may reflect Precambrian metasedimentary or igneous rock in the seismogenic layer, which enables the accumulation of high crustal stress to generate large earthquakes. However, a sharply contrasting gap zone with low‐velocity, high‐σ anomalies is clearly imaged in the upper crust under the concatenated area between the Lushan and Wenchuan earthquakes. Seismic images indicate that the low‐velocity gap zone is associated with fluid‐bearing ductile flow from the lower crustal materials of Tibet being pushed into a weakened segment of the LMFZ. This study suggests that the 2013 Lushan earthquake may have been triggered by high crustal stress accumulation together with high coseismic stress further increased by the Wenchuan earthquake in the metamafic seismogenic layer. Contrasting rheological variations in the crust and crustal stress changes along the LMFZ control the rupture processes that generated the Lushan and Wenchuan earthquakes, as well as the generation of new earthquakes in the future.

Climate changes control offshore crustal structure at South China Sea continental margin

Rifted continental lithosphere subsides as a consequence of combined crustal thinning and mantle lithosphere cooling yet basins on some continental margins experience anomalous subsidence events that postdate active extension. Deep basins on the northern margin of the South China Sea, notably the Baiyun Sag, show basement subsidence accelerating after ∼21 Ma, postdating extension by several million years. We combine geophysical observations and numerical forward modeling to show that loading of the offshore basins by increased sediment flux caused by faster onshore erosion following Early Miocene monsoon intensification is a viable trigger for ductile flow after the cessation of active extension. This illustrates that offshore basin dynamics at continental margins with weak crust can be controlled by onshore surface processes in a newly recognized form of climate–tectonic coupling.

Two crustal low-velocity channels beneath SE Tibet revealed by joint inversion of Rayleigh wave dispersion and receiver functions

Competing geodynamic models, such as rigid-block extrusion, continuous deformation, and the mid-lower crustal flow, have been proposed to describe the growth and expansion of eastern Tibet. However, the dynamic processes responsible for plateau evolution and deformation remain poorly understood partly due to resolution limitations of previous models of lithospheric structure. On the basis of joint inversion of Rayleigh wave dispersion and receiver functions using data from a newly deployed seismic array, we have obtained a high-resolution 3D image that reveals the distribution of low-velocity zones (LVZs) with unprecedented clarity. The prominent feature of our model is two low-velocity channels that bound major strike-slip faults in SE Tibet and wrap around the Eastern Himalaya Syntaxis, consistent with the clockwise movement of crustal material in this region. Most large earthquakes in this region occurred in the boundaries of the LVZs. We propose that ductile flow within these channels, in addition to shear motion along strike-slip faults, played a significant role in accommodating intensive lithospheric deformation during the eastward expansion of Tibet in the Cenozoic.

Deformation events in the Gridino zone, Belomorian Province, Fennoscandian Shield: relationships between mafic dike swarms and eclogite-bearing mélange

Relationships between reference mafic dikes and deformations in the Gridino zone, Belomorian province, Fennoscandian Shield, make it possible to subdivide the deformations into three groups: pre-dike, synmagmatic, and post-dike. The Neoarchaean eclogite-bearing mélange was formed by disintegration of large eclogite slices in the course of ductile flow, which was associated with synkinematic granitoid magmatism and metamorphism varying from the granulite to amphibolite facies. Exotic blocks, including those of eclogites, are distributed in the TTG gneisses as layers and lenses, whose thicknesses range from a few to a few hundred metres and which are conformable with the foliation. Ductile flow brought the rock complexes to the depth level where brittle–ductile deformations were possible. As a result, certain parts of the mélange were deformed in a more rigid setting. A number of mafic dike swarms were emplaced into relatively cold rocks in an extensional environment in the earliest Palaeoproterozoic. The dikes cut across all earlier structures and are thus an important benchmark for distinguishing Neoarchaean and Palaeoproterozoic processes. Post-dike (~1.9 Ga) tectonic activity was associated with local deformations and discrete metamorphic retrogression to amphibolite facies. None of them significantly affected the pre-existing regional structure.

Postseismic deformation after 2008 Wenchuan Earthquake

Apparent postseismic deformation was observed after the 2008 Wenchuan earthquake, China. The displacement in the direction normal to the fault decays to nearly zero after 2013, but the significant dextral movement did not decay obviously during our observation of up to May 2013. It indicates that the stress paralleled to the fault in the southern part of the rupture zone was not relaxed during the coseismic slip. The unrelaxed stress transfers northward after the earthquake and continues after 2013. The postseismic deformation may be dominated by afterslip or stress readjustment, but the effects of the viscoelastic relaxation also cannot be ignored. The low velocity zone under the Bayan Har block, which is velocity strengthening, may greatly affect the postseismic deformation and makes it possible that the lower crust ductile flow and the shortening of the crust both contribute to the uplift of the Longmen Shan. The viscoelastic coefficients of the low velocity zone and the lower crust should be larger than 3×1018 Pa.s which is optimised with our observations by using the single viscoelastic relaxation model.

A “slice-and-view” (FIB–SEM) study of clay gouge from the SAFOD creeping section of the San Andreas Fault at ∼2.7 km depth

The San Andreas Fault is one of the most studied earthquake-generating structures on Earth, but the reason that some sections are anomalously weak, and creep without apparent seismicity, remains poorly understood. Here, we present results from nanoscale (FIB–SEM) 3D microstructural observations of weak (friction coefficient of 0.095) SAFOD clay fault gouge containing serpentinite clasts, recovered from the active Central Deforming Zone at ∼2.7 km vertical depth. Our nanoscale observations confirm that frictional slip and extreme weakness occur via deformation of smectite clay that forms a shear fabric within the fault zone. We infer that creep initiates by fracture-controlled, substrate growth of oriented Mg-smectite on R, P and Y shears, followed by clay smearing and ductile flow of an evolving and expanding clay matrix. At the crystal-scale, pervasive sliding occurs along hydrated smectite interlayers and surfaces occupied by exchangeable Mg- and Ca-ions, with slip typically spaced at 3–5 lattice layers apart. We conclude that the strength and seismic behaviour of major tectonic faults at shallow crustal levels evolves as clay fabric develops with accumulated fault slip.

Structure and composition of mantle peridotites at the boundary with crustal complexes of ophiolites in the Syumkeu massif, Polar Urals

Intense viscous-ductile deformations with multiorder flow folds and thin banding have been established in lherzolite and harzburgite of the Syumkeu massif 1.0–1.5 km below the boundary with crustal complexes. Intense shear deformation of mantle restites is traced along the entire boundary zone. The mineral composition of lherzolite and harzburgite in this zone occupies a transitional position between peridotite restites and olivine websterite from the lower part of the banded dunite-wehrlite-pyroxenite-gabbro complex. This implies that the mantle rocks from the crust-mantle transition zone were substantially transformed under transpressional intense shear stress settings along with a high-temperature ductile flow of mantle restites interacting with the supplied melt at a depth of more than 10 km. This type of transition zones differs from those known elsewhere in the Urals and supplements our knowledge on modes of mantle restite juxtaposition with crustal plutonic rocks.

Rheological profile across the NE Japan interplate megathrust in the source region of the 2011 Mw9.0 Tohoku-oki earthquake

A strength profile across the NE Japan interplate megathrust was constructed in the source region of the 2011 Tohoku-oki earthquake (Mw9.0) using friction, fracturing, and ductile flow data of the oceanic crustal materials obtained from laboratory experiments. The depth-dependent changes in pressure, temperature, and pore fluid pressure were incorporated into a model. The large tsunamigenic slips during the M9 event can be explained by a large gradient in fault strength on the up-dip side of the M9 hypocenter, which was located 17 to 18 km beneath sea level. A large stress drop (approximately 80 MPa) induced by the collapse of a subducted seamount possibly triggered the M9 earthquake. In the deep (>35 km) part of the thrust fault, where M7-class Miyagi-oki earthquakes have repeatedly occurred, plastic deformation occurs in siliceous rocks but not in gabbroic rocks. Thus, the asperity associated with the M7-class earthquakes was most likely a gabbroic body, such as a broken seamount, surrounded by siliceous sedimentary rocks. The conditionally stable nature of the surrounding region can be explained by the frictional behavior of wet quartz in the brittle-ductile transition zone. In contrast to the deep M7-class asperity, the M9 asperity (i.e., a region that was strongly coupled before the M9 Tohoku-oki earthquake) extended to a large area of the plate interface because shear strength is relatively insensitive to lithological variation at intermediate depths. However, the along-arc extension of the M9 asperity was constrained by fluid-rich regions on the plate interface.

Room temperature homogeneous ductility of micrometer-sized metallic glass.

Homogeneous ductile flow of metallic glasses is observed at the micrometer scale. It is shown that this unusual deformation mode of an otherwise brittle material depends on both specimen size and applied loading rate. The results are explained by intrinsic length-scale effects of nanometer-sized defects, and provide a rationale for the long term debated brittle-to-ductile transition of amorphous metals.

Gridino melange zone of the Belomorian eclogite province: Succession of tectonic events and structural position of mafic dyke swarms

Based on relationships between Paleoproterozoic mafic dykes, lithotectonic complexes, and tectonic structures of the Gridino Zone in the Belomorian eclogite province of the Fennoscandian Shield, deformations have been divided into groups differing in age and the succession of tectonic events has been reconstructed. The formation of Neoarchean eclogite-bearing melange was related to disintegration of large eclogite sheets in the course of near-horizontal ductile flow accompanied by syntectonic granitoid magmatism, multiple migmatization, and granulite-to amphibolite-facies metamorphism. The exotic blocks, including eclogites, were incorporated into TTG gneisses as sheets and lenses up to a few hundreds of meters in thickness and oriented conformably with gneissic banding. As a result of ductile flow, the lithotectonic complexes were transported at the level of discrete brittle-ductile deformations expressed as strike-slip faults and associated folds. Under conditions of a relatively rigid medium, individual structural elements underwent rotation approximately through 90° in plan view. Under the extension regime in the Early Paleoproterozoic, several swarms of mafic dykes were injected into the already cold framework rocks, as is evident from dyke morphology. The dykes crosscut all predated structures, included turned blocks, and are therefore important reference points for subdivision of Neoarchean and Paleoproterozoic processes. The Svecofennian postdyke tectonic activity was accompanied by local shearing and boudinage of metabasic rocks, development of quartz and pegmatite veins along tension cracks, disharmonic folding, and discrete retrograde metamorphism up to amphibolite-facies conditions. The postdyke deformations did not exert a substantial effect on the previously formed regional structure.

Studies on Ductile Damage and Flow Instabilities during Hot Deformation of a Multiphase γ-TiAl Alloy

Gamma titanium aluminides are promising alloys for low-pressure turbine blades. A significant disadvantage of such intermetallic alloys is failure induced during forming processes due to ductile damage and flow instabilities. Previous investigations on a gamma titanium aluminide alloy (TNM), have shown ductile damage due to tensile stress components and instabilities such as shear bands, pores and micro-cracks at low temperatures and high strain rates. The main part of the current work is to delineate damage and unstable regions in the low temperature region. Hot deformation experiments are conducted on a Gleeble®3800 thermomechanical treatment simulator to obtain flow curves to be implemented in a finite element method (FEM) code. Instabilities in the material are described by existing instability criteria as proposed by Semiatin and Jonas and implemented into FEM code DEFORMTM 2D. Predictions of ductile damage models and the instability parameter are validated through detailed microstructural studies of deformed specimens analysed by light optical- and scanning electron microscopy.

Carbonatite-hosted niobium deposit at Aley, northern British Columbia (Canada): Mineralogy, geochemistry and petrogenesis

The Aley Nb deposit in northern British Columbia, Canada, is hosted by metamorphosed calcite and dolomite carbonatites of anorogenic affinity emplaced in Lower Paleozoic sedimentary carbonate rocks in the Devonian. Primary Nb mineralization consists of pyrochlore (commonly comprising a U–Ta-rich and F-poor core) and ferrocolumbite developed as discrete crystals and replacement products after the pyrochlore. These phases and associated heavy minerals (apatite±magnetite±zircon±baddeleyite) precipitated early in the magmatic history and probably formed laterally extensive cumulate layers up to at least 1.5m in thickness. Fractionation of copious amounts of pyrochlore is reflected in the chemical composition of the carbonatites and their constituent minerals, which show large variations in Nb/Ta value, but a near-chondritic Zr/Hf ratio. Alkali-rich metasomatic rocks (in particular, fenites and glimmerites) associated with the carbonatites are barren; the bulk of Nb in these rocks is contained in rutile, phlogopite and, to a much lesser extent, amphibole. When the passive margin of North America became the zone of plate convergence in the Cretaceous, the host carbonatites were strongly deformed, which is manifested in structures and textures indicative of grain comminution, ductile flow, folding and, locally, brecciation. The structure and continuity of the cumulate units enriched in Nb minerals were profoundly affected by these processes. Interaction of the carbonatites with crustal fluids of complex chemistry resulted in extensive dolomitization, replacement of the pyrochlore and ferrocolumbite by fersmite, and development of hydrothermal parageneses consistent with the lower greenschist-facies conditions. At these late evolutionary stages, Nb was mobilized only to a very limited extent and sequestered in a variety of minerals (fersmite, euxenite, Mg-rich ferrocolumbite and Nb-bearing rutile) typically occurring as scarce minute crystals associated with hydrothermal dolomite, quartz and chlorite. Progressive enrichment of the deformed dolomite carbonatites in heavy C and O isotopes relative to primary calcite, coupled with changes in the trace-element composition of Nb phases, indicate that the fluids were equilibrated with the wall-rock sedimentary rocks hosting the Aley deposit and were capable of transporting F−, (PO4)3−, U, Th and rare-earth elements, but not Nb.

Probing the lithospheric rheology across the eastern margin of the Tibetan Plateau

The fundamental geological structure, geodynamics, and rheology of the Tibetan Plateau have been debated for decades. Two end-member models have been proposed: (1) the deformation of Tibet is broadly distributed and associated with ductile flow in the mantle and middle or lower crust, (2) the Tibetan Plateau formed during interactions between rigid lithospheric blocks with localization of deformation along major faults. The nature and distribution of continental deformation are governed by the varying rheology of rocks and faults in the lithosphere. Insights into lithospheric rheology can be gained from observations of postseismic deformation, which represents the response of the Earth's interior to coseismic stress changes. Here we use up to 2 years of InSAR and GPS measurements to investigate postseismic displacements following the 2008 Mw 7.9 Wenchuan earthquake in eastern Tibet and probe the differences in rheological properties across the edge of the Plateau. We find that near-field displacements can be explained by shallow afterslip on the Beichuan Fault, which is anti-correlated with the coseismic slip distribution. Far-field displacements cannot be explained by a homogeneous rheology, but instead require a viscoelastic lower crust (from 45 to 60 km depth) beneath Tibet with an initial effective viscosity of 4.4×1017 Pas and a long-term viscosity of 1018 Pas, whereas the Sichuan Basin block has a high-viscosity upper mantle (>1020 Pa s) underlying an elastic 35-km-thick crust. The inferred strong contrast in lithospheric rheologies between the Tibetan Plateau and the Sichuan Basin is consistent with models of ductile lower crustal flow that predict maximum topographic gradients across the Plateau margins where viscosity differences are greatest.

The Minimized Power Geometric model: An analytical mixing model for calculating polyphase rock viscosities consistent with experimental data

AbstractHere we introduce the Minimized Power Geometric (MPG) model which predicts the viscosity of any polyphase rocks deformed during ductile flow. The volumetric fractions and power law parameters of the constituting phases are the only model inputs required. The model is based on a minimization of the mechanical power dissipated in the rock during deformation. In contrast to existing mixing models based on minimization, we use the Lagrange multipliers method and constraints of strain rate and stress geometric averaging. This allows us to determine analytical expressions for the polyphase rock viscosity, its power law parameters, and the partitioning of strain rate and stress between the phases. The power law bulk behavior is a consequence of our model and not an assumption. Comparison of model results with 15 published experimental data sets on two‐phase aggregates shows that the MPG model reproduces accurately both experimental viscosities and creep parameters, even where large viscosity contrasts are present. In detail, the ratio between experimental and MPG‐predicted viscosities averages 1.6. Deviations from the experimental values are likely to be due to microstructural processes (strain localization and coeval other deformation mechanisms) that are neglected by the model. Existing models that are not based on geometric averaging show a poorer fit with the experimental data. As long as the limitations of the mixing models are kept in mind, the MPG model offers great potential for applications in structural geology and numerical modeling.