We present computational modeling outcomes for bilithologic (peridotite and pyroxenite) mantle melting in divergent environments, considering equilibrium and disequilibrium porous flow melting of 0–50 % pyroxenite in thermal equilibrium with peridotite, potential temperatures of 1300 and 1400 °C, upwelling rates from 1–50 cm yr−1, maximum porosities of 0.1–2.0 %, and four compositions that span pyroxenite melting behavior. Basalt-like pyroxenites (G2) uniquely produce low (226Ra/230Th) and (231Pa/235U) with high (230Th/238U), but quantities greater than ~10 % produce anomalously thick crust, restricting their global abundance. Silica-deficient pyroxenite (M7-16 and MIX1G) melts are more moderate, but require chemical re-equilibration during transport to resemble global basalts, while hybrid lithologies (KG1) produce melts similar to those of peridotites. Uranium-series disequilibria in partial melts can also be decoupled from trace elements by radioactive decay in two-dimensional regimes. The mantle must thus contain multiple types of pyroxenite on a global scale, with melts traveling by complex networks and experiencing heterogeneous extents of chemical re-equilibration.
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pyUserCalc: A Revised Jupyter Notebook Calculator for Uranium-Series Disequilibria in Basalts
Meaningful analysis of uranium-series isotopic disequilibria in basaltic lavas relies on the use
of complex forward numerical models like dynamic melting (McKenzie, 1985, https://doi.org/10.1016/0012- 821x(85)90001-9) and equilibrium porous flow (Spiegelman & Elliott, 1993, https://doi.org/10.1016/0012- 821x(93)90155-3). Historically, such models have either been solved analytically for simplified scenarios, such as constant melting rate or constant solid/melt trace element partitioning throughout the melting process, or have relied on incremental or numerical calculators with limited power to solve problems and/or restricted availability. The most public numerical solution to reactive porous flow, UserCalc (Spiegelman, 2000, https:// doi.org/10.1029/1999gc000030) was maintained on a private institutional server for nearly two decades, but that approach has been unsustainable in light of modern security concerns. Here, we present a more long-lasting solution to the problems of availability, model sophistication and flexibility, and long-term access in the form of a cloud-hosted, publicly available Jupyter notebook. Similar to UserCalc, the new notebook calculates U-series disequilibria during time-dependent, equilibrium partial melting in a one-dimensional porous flow regime where mass is conserved. In addition, we also provide a new disequilibrium transport model which has the same melt transport model as UserCalc, but approximates rate-limited diffusive exchange of nuclides between solid and melt using linear kinetics. The degree of disequilibrium during transport is controlled by a Damköhler number, allowing the full spectrum of equilibration models from complete fractional melting (Da = 0) to equilibrium transport (Da = ∞).
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- Award ID(s):
- 1658011
- PAR ID:
- 10317610
- Date Published:
- Journal Name:
- Earth and space science
- Volume:
- 8
- ISSN:
- 2333-5084
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract In the past decade, mounting evidence has pointed to complex, layered structure within and at the base of the mantle lithosphere of tectonically quiescent continental interiors. Sometimes referred to as negative velocity gradients or midlithospheric discontinuities (MLDs), the origin of intralithospheric layering has prompted considerable discussion, particularly as to how they may result from continent formation and/or evolution. Previous Sp receiver function analysis in Australia (Ford et al., 2010,
https://doi.org/10.1016/j.epsl.2010.10.007 ) found evidence for complex lithospheric layering beneath permanent stations located within the North, South, and West Australian Cratons and characterized these as MLDs. This study provides an update to the original study by Ford et al. (2010,https://doi.org/10.1016/j.epsl.2010.10.007 ). Sp receiver function results are presented for 34 permanent, broadband stations. We observe the lithosphere–asthenosphere boundary (LAB) on the eastern margin of the continent, at depths of 75–85 km. The cratonic core of Australia has discontinuities within the lithosphere, with no observable LAB. On the western margin of the continent, we observe several stations with an ambiguous phase that may correspond to an MLD or the LAB. We also observe multiple negative phases at most stations, suggesting a complex and heterogeneous lithosphere. Australian MLDs are likely linked to the presence of hydrous minerals in the midlithosphere and may result from ancient processes such as subduction, plume interaction, or melt infiltration from the paleo‐LAB. -
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Abstract Cold, low‐density diapirs arising from hydrated mantle and/or subducted sediments on the top of subducting slabs have been invoked to transport key chemical signatures to the source region of arc magmas. However, to date there have been few quantitative models to constrain melting in such diapirs. Here we use a two‐phase Darcy‐Stokes‐energy model to investigate thermal evolution, melting, and depletion in a buoyant sediment diapir ascending through the mantle wedge. Using a simplified 2‐D circular geometry, we investigate diapir evolution in three scenarios with increasing complexity. In the first two scenarios we consider instantaneous heating of a diapir by thermal diffusion with and without the effect of the latent heat of melting. Then, these simplified calculations are compared to numerical simulations that include melting, melt segregation, and the influence of depletion on the sediment solidus along pressure‐temperature‐time (
P ‐T ‐t ) paths appropriate for ascent through the mantle wedge. The high boundary temperature induces a rim of high porosity, into which new melts are focused and then migrate upward. The rim thus acts like an annulus melt channel, while the effect of depletion buffers additional melt production. Solid matrix flow combined with recrystallization of melt pooled near the top of the diapir can result in large gradients in depletion across the diapir. These large depletion gradients can either be preserved if the diapir leaks melt during ascent, or rehomogenized in a sealed diapir. Overall our numerical simulations predict less melt production than the simplified thermal diffusion calculations. Specifically, we show that diapirs whose ascent paths favor melting beneath the volcanic arc will undergo no more than ~40–50% total melting. -
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Abstract Modeling convective air movement in unsaturated porous media requires appropriate characterization of the relative air permeability (RAP). Adopting Assouline et al. (1998,
https://doi.org/10.1029/97WR03039 ) water retention function that is based on the Weibull pore size distribution, this study was conducted to derive seven new predictive RAP models. These 7 new models, together with another 3 models developed by Assouline et al. (2016,https://doi.org/10.1002/2015WR018286 ), were then compared with data from 30 disturbed soil samples to investigate their predictive RAP performances. The model and data comparison results showed that the modified Burdine, modified Mualem, and modified Alexander and Skaggs relative permeability models proposed by Yang and Mohanty (2015,https://doi.org/10.1002/2014WR016190 ) had the highest accuracy for the RAP prediction among the 10 investigated models, which indicated that the tortuosity and connectivity exponent of water phase should be smaller than that of air phase for the disturbed soil samples. The modified Burdine, modified Mualem, and modified Alexander and Skaggs models were then the suggested RAP parameterizations for the subsurface multiphase flow numerical simulation. -
The transition from open-channel to surcharged flow creates problems for numerical modeling of stormwater systems. Mathematically, problems arise through a discrete shock at the boundary between the hyperbolic Saint-Venant equations and the elliptic incompressible flow equations at the surcharge transition. Physically, problems arise through trapping of air pockets, creation of bubbly flows, and cavitation in rapid emptying and filling that are difficult to correctly capture in one-dimensional (1D) models. Discussed herein are three approaches for modeling surcharged flow with hyperbolic 1D equations: (i) Preissmann Slot (PS), (ii) Two- component Pressure Approach (TPA) and (iii) Artificial Compressibility (AC). Each provides approximating terms that are controlled by model coefficients to alter the pressure wave celerity through the surcharged system. Commonly, the implementation of these models involve slowing the pressure celerity below physical values, which allows the numerical solution to dissipate the transition shock between the free surface and surcharged flows without resorting to extraordinarily small time-steps. The different methods provide different capabilities and numerical implementations that affect their behavior and suitability for different problems. https://doi.org/10.3850/IAHR-39WC2521711920221370more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1029/2020EA001619
