pyUserCalc: A Revised Jupyter Notebook Calculator for Uranium‐Series Disequilibria in Basalts

Abstract

Abstract 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=∞). Access the full executable Jupyter notebook version of this manuscript here .

Keywords

• U‐series
• basalt
• melting
• modeling
• porous flow