Application of Kriging Interpolation for Glacier Mass Balance Computations

In order to compute the specific mass balance of a glacier, point measurements of mass balance need to be integrated and thus interpolated over the entire glacier. In this study kriging was applied as interpolation technique to mass balance data of Storglaciren, a 3 km² valley glacier, focusing on the sensitivity of results to the choice of some kriging parameters. Although the spatial means varied only little in most cases, the spatial distribution of the mass balance quantities was sensitive to the assumption on kriging parameters, suggesting that the kriging parameters need to be carefully optimized for each case if the spatial distribution is of interest.     

Weakening and strain localization produced by syn-deformational reaction of plagioclase

There are many observations in naturally deformed rocks on the effects of mineral reactions on deformation, but few experimental data. In order to study the effects of chemical disequilibrium on deformation we have investigated the hydration reaction plagioclase + H₂OM more albitic plagioclase + zoisite + kyanite + quartz. We utilized fine-grained (2-6 µm) plagioclase aggregates of two compositions (An54 and An60), both dried and with 0.1-0.4 wt% H₂O present, in shear deformation experiments at two sets of conditions: 900 °C, 1.0 GPa (in the plagioclase stability field) and 750 °C, 1.5 GPa (in the zoisite stability field). Dry samples and those deformed in the plagioclase stability field underwent homogeneous shearing by dislocation creep, but samples with 0.1 to 0.4 wt% water deformed in the zoisite stability field showed extreme strain localization into very narrow (~1-3 µm) shear bands after low shear strain. In these samples the microstructures of reaction products in the matrix differ from those in the shear bands. In the matrix, large (up to 400 µm) zoisite crystals grew in the direction of finite extension, and relict plagioclase grains are surrounded by rims of recrystallized grains that are more albitic. In the shear bands, the reaction products albitic plagioclase, zoisite, white mica, and traces of kyanite form polyphase aggregates of very fine-grained (<0.1 µm) dislocation-free grains. Most of the sample strain after % ~2 has occurred within the shear bands, within which the dominant deformation mechanism is inferred to be diffusion-accommodated grain boundary sliding (DAGBS). The switch from dislocation creep in dry samples deformed without reaction to DAGBS in reacted samples is associated with a decrease in flow stress from ~800 to <200 MPa. These experiments demonstrate that heterogeneous nucleation driven in part by chemical disequilibrium can produce an extremely fine-grained polyphase assemblage, leading to a switch in deformation mechanism and significant weakening. Thus, localization of deformation in polyphase rocks may occur on any pressure (P),temperature (T)-path where the equilibrium composition of the constituent minerals changes.     

A stabilized extended finite element framework for hydraulic fracturing simulations

We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

“Wet” low angle subduction: a possible mechanism below the Tanzania craton 2 Ga ago

The hypothesis that much of the lithosphere of the Archaean Tanzania Craton was hydrated, by the dehydration of a buoyant subduction 2 Ga ago is presented in this study. Buoyant subduction is a potential mechanism for thermal erosion and metasomatism of extensive regions of the cold overlying continental lithosphere. This hypothesis could explain why the Tanzania Craton forms an undeformed island within the intensely deformed mobile belts. Furthermore, it would explain the formation of the eclogite and lherzolite bearing kimberlites within the Tanzania Craton far away from the trench. A buoyant, slow subduction is required because this would provide sufficient cooling from the overlying cratonic lithosphere and therefore the dipping slab could retain hydrous minerals such as antigorite in hydrated aureoles in peridotites. To test this hypothesis, the release of water during prograde metamorphism of a flat-subducting plate was modeled. It is shown that water can be transported ～800 km laterally, inboard of the trench, which is close to the north-south extension of the Archaean Tanzania Craton.     

Differentiation and crystallization conditions of basalts from the Kerguelen large igneous province: an experimental study

Phase relations of basalts from the Kerguelen large igneous province have been investigated experimentally to understand the effect of temperature, fO₂, and fugacity of volatiles (e.g., H₂O and CO₂) on the differentiation path of LIP basalts. The starting rock samples were a tholeiitic basalt from the Northern Kerguelen Plateau (ODP Leg 183 Site 1140) and mildly alkalic basalt evolved from the Kerguelen Archipelago (Mt. Crozier on the Courbet Peninsula), representing different differentiation stages of basalts related to the Kerguelen mantle plume. The influence of temperature, water and oxygen fugacity on phase stability and composition was investigated at 500 MPa and all experiments were fluid-saturated. Crystallization experiments were performed at temperatures between 900 and 1,160°C under oxidizing (log fO₂ ~ ΔQFM + 4) and reducing conditions (log fO₂ ~ QFM) in an internally heated gas-pressure vessel equipped with a rapid quench device and a Pt-Membrane for monitoring the fH₂. In all experiments, a significant influence of the fO₂ on the composition and stability of the Mg/Fe-bearing mineral phases could be observed. Under reducing conditions, the residual melts follow a tholeiitic differentiation trend. In contrast, melts have high Mg# [Mg²⁺/(Mg²⁺ + Fe²⁺)] and follow a calk-alkalic differentiation trend at oxidizing conditions. The comparison of the natural phenocryst assemblages with the experimental products allows us to constrain the differentiation and pre-eruptive conditions of these magmas. The pre-eruptive temperature of the alkalic basalt was about 950–1,050°C. The water content of the melt was below 2.5 wt% H₂O and strongly oxidizing conditions (log fO₂ ~ ΔQFM + 2) were prevailing in the magma chamber prior to eruption. The temperature of the tholeiitic melt was above 1,060°C, with a water content below 2 wt% H₂O and a log fO₂ ~ ΔQFM + 1. Early fractionation of clinopyroxene is a crucial step resulting in the generation of silica-poor and alkali-rich residual melts (e.g., alkali basalt). The enrichment of alkalis in residual melts is enhanced at high fO₂ and low aH₂O.     

Hydrating laterally extensive regions of continental lithosphere by flat subduction: A pilot study from the North American Cordillera

It has been suggested that much of the lithopheric mantle beneath the Colorado Plateau was hydrated by the dehydration of the Farallon plate when it was undergoing low angle subduction during the Laramide orogeny. If correct, low angle subduction could be a viable mechanism for weakening laterally extensive regions of continental lithosphere, allowing such lithosphere potentially to be recycled back into the Earth's interior and into the asthenospheric mantle wedge. To test this hypothesis, we model the release of water during prograde metamorphism of a flat-subducting Farallon plate by considering a thermal model for flat subduction and tracking open-system metamorphic phase equilibria. Our model indicates that significant amounts of water can be laterally transported ∼700 km inboard of the trench, close to the width of the North American Cordillera. The amount of water released is shown here to have been large enough to influence the rheology of the overriding North American lithosphere and the potential for melting at its base. Anomalously high S-velocities in the lithospheric mantle supports our modeled calculations of laterally extensive weakening at the base of the continental lithosphere.