John F. Rudge

Uplift histories of Africa and Australia from linear inverse modeling of drainage inventories

This is the final version. It first appeared at http://onlinelibrary.wiley.com/wol1/doi/10.1002/2014JF003297/abstract.

Combined147,146Sm-143,142Nd constraints on the longevity and residence time of early terrestrial crust

Primordial silicate differentiation controlled the composition of Earths oldest crust. Inherited 142Nd anomalies in Archean rocks are vestiges of the mantle-crust differentiation before ca. 4300 Ma. Here we report new whole-rock 147,146Sm-143,142Nd data for the Acasta Gneiss Complex (AGC; Northwest Territories, Canada). Our 147Sm-143Nd data combined with literature data define an age of 3371 ± 141 Ma (2 SD) and yield an initial e143Nd of −5.6 ± 2.1. These results are at odds with the Acasta zircon U-Pb record, which comprises emplacement ages of 3920–3960 Ma. Ten of our thirteen samples show 142Nd deficits of −9.6 ± 4.8 ppm (2 SD) relative to the modern Earth. The discrepancy between 142Nd anomalies and a mid-Archean 147Sm-143Nd age can be reconciled with Nd isotope reequilibration of the AGC during metamorphic perturbations at ca. 3400 Ma. A model age of ca. 4310 Ma is derived for the early enrichment of the Acasta source. Two compositional end-members can be identified: a felsic component with 142Nd/144Nd identical to the modern Earth and a mafic component with 142Nd/144Nd as low as −14.1 ppm. The ca. 4310 Ma AGC source is ∼200 Myr younger than those estimated for Nuvvuagittuq (northern Quebec) and Isua (Itsaq Gneiss Complex, West Greenland). The AGC does not have the same decoupled Nd-Hf isotope systematics as these other two terranes, which have been attributed to the crystallization of an early magma ocean. The Acasta signature rather is ascribed to the formation of Hadean crust that was preserved for several hundred Myr. Its longevity can be linked to 142Nd evolution in the mantle and does not require slow mantle stirring times nor modification of its convective mode.

The energetics of melting fertile heterogeneities within the depleted mantle

To explore the consequences of mantle heterogeneity for primary melt production, we develop a mathematical model of energy conservation for an upwelling, melting body of recycled oceanic crust embedded in the depleted upper mantle. We consider the end‐member geometric cases of spherical blobs and tabular veins. The model predicts that thermal diffusion into the heterogeneity can cause a factor‐of‐ two increase in the degree of melting for bodies with minimum dimension smaller than ∼1 km, yielding melt fractions between 50 and 80%. The role of diffusion is quantified by an appropriately defined Peclet number, which represents the balance of diffusion‐driven and adiabatic melting. At intermediate Peclet number, we show that melting a heterogeneity can cool the ambient mantle by up to ∼20 K (spherical) or ∼60 K (tabular) within a distance of two times the characteristic size of the body. At small Peclet number, where heterogeneities are expected to be in thermal equilibrium with the ambient mantle, we calculate the energetic effect of pyroxenite melting on the surrounding peridotite; we find that each 5% of recycled oceanic crust diminishes the peridotite degree of melting by 1–2%. Injection of the magma from highly molten bodies of recycled oceanic crust into a melting region of depleted upper mantle may nucleate reactive‐dissolution channels that remain chemically isolated from the surrounding peridotite.

Compaction around a rigid, circular inclusion in partially molten rock

Conservation laws that describe the behavior of partially molten mantle rock have been established for several decades, but the associated rheology remains poorly understood. Constraints on the rheology may be obtained from recently published experiments involving deformation of partially molten rock around a rigid, spherical inclusion. These experiments give rise to patterns of melt segregation that exhibit the competing effects of pressure shadows and melt-rich bands. Such patterns provide an opportunity to infer rheological parameters through comparison with models based on the conservation laws and constitutive relations that hypothetically govern the system. To this end, we have developed software tools to simulate finite strain, two-phase flow around a circular inclusion in a configuration that mirrors the experiments. Simulations indicate that the evolution of porosity is predominantly controlled by the porosity-weakening exponent of the shear viscosity and the poorly known bulk viscosity. In two-dimensional simulations presented here, we find that the balance of pressure shadows and melt-rich bands observed in experiments only occurs for bulk-to-shear viscosity ratio of less than about five. However, the evolution of porosity in simulations with such low bulk viscosity exceeds physical bounds at unrealistically small strain due to the unchecked, exponential growth of the porosity variations. Processes that limit or balance porosity localization should be incorporated in the formulation of the model to produce results that are consistent with the porosity evolution in experiments.

Thermal impact of magmatism in subduction zones

Abstract Magmatism in subduction zones builds continental crust and causes most of Earths subaerial volcanism. The production rate and composition of magmas are controlled by the thermal structure of subduction zones. A range of geochemical and heat flow evidence has recently converged to indicate that subduction zones are hotter at lithospheric depths beneath the arc than predicted by canonical thermomechanical models, which neglect magmatism. We show that this discrepancy can be resolved by consideration of the heat transported by magma. In our one- and two-dimensional numerical models and scaling analysis, magmatic transport of sensible and latent heat locally alters the thermal structure of canonical models by ∼300 K, increasing predicted surface heat flow and mid-lithospheric temperatures to observed values. We find the advection of sensible heat to be larger than the deposition of latent heat. Based on these results we conclude that thermal transport by magma migration affects the chemistry and the location of arc volcanoes.

Textural equilibrium melt geometries around tetrakaidecahedral grains

In textural equilibrium, partially molten materials minimize the total surface energy bound up in grain boundaries and grain–melt interfaces. Here, numerical calculations of such textural equilibrium geometries are presented for a space-filling tessellation of grains with a tetrakaidecahedral (truncated octahedral) unit cell. Two parameters determine the nature of the geometries: the porosity and the dihedral angle. A variety of distinct melt topologies occur for different combinations of these two parameters, and the boundaries between different topologies have been determined. For small dihedral angles, wetting of grain boundaries occurs once the porosity has exceeded 11%. An exhaustive account is given of the main properties of the geometries: their energy, pressure, mean curvature, contiguity and areas on cross sections and faces. Their effective permeabilities have been calculated, and demonstrate a transition between a quadratic variation with porosity at low porosities to a cubic variation at high porosities.

Torsion of a cylinder of partially molten rock with a spherical inclusion: Theory and simulation

The processes that are involved in migration and extraction of melt from the mantle are not yet fully understood. Gaining a better understanding of material properties of partially molten rock could help shed light on the behavior of melt on larger scales in the mantle. In this study, we simulate three-dimensional torsional deformation of a partially molten rock that contains a rigid, spherical inclusion. We compare the computed porosity patterns to those found in recent laboratory experiments. The laboratory experiments show emergence of melt-rich bands throughout the rock sample, and pressure shadows around the inclusion. The numerical model displays similar melt-rich bands only for a small bulk-to-shear-viscosity ratio (five or less). The results are consistent with earlier two-dimensional numerical simulations; however, we show that it is easier to form melt-rich bands in three dimensions compared to two. The addition of strain-rate dependence of the viscosity causes a distinct change in the shape of pressure shadows around the inclusion. This change in shape presents an opportunity for experimentalists to identify the strain-rate dependence and therefore the dominant deformation mechanism in torsion experiments with inclusions.