Natural calcium carbonate minerals express a range of calcium isotope fractionations, with the precipitated mineral typically enriched in the lighter isotopes of calcium relative to source fluids. Experimental and theoretical evidence shows a strong dependence on precipitation rate, although this relationship has not been well quantified over the range of precipitation rates observed in natural settings. Endmember cases show that average marine carbonate precipitation expresses a large fractionation (${\delta }^{44/40}\mathrm{Ca}$ values lower than seawater by approximately 1‰), while diagenetic carbonate phases assumed to have precipitated or recrystallized at very slow rates show negligible fractionation. The limited examples of quantified precipitation rates in natural settings with measurable, non-zero fractionation represents a barrier for applying mechanistic models of calcium isotope fractionation to geological applications. This study examines a methane seep system in the northern Barents Sea south of Svalbard where authigenic carbonate minerals are precipitating, driven by anaerobic oxidation of methane, and where the apparent calcium isotope fractionation factor and precipitation rate can be constrained by measuring properties of the pore fluids. Pore fluid profiles are analyzed in two shallow cores, and authigenic carbonate nodules are analyzed in one of these cores. The pore fluid profiles point to a transitional, non-steady state which approximates a closed system, where the elevation of pore fluid calcium isotope ratios through carbonate precipitation can be modeled as a Rayleigh distillation system. The apparent fractionation factors for ⁴⁴Ca/⁴⁰Ca ratios at these sites are $\alpha$ = 0.99985 and 0.9996, although the carbonate nodules suggest a different calcium isotope fractionation factor may have been expressed under past conditions. Precipitation rates at the two sites are estimated to be 1.4 and 3.5 μmol/m²/h, intermediate between those of typical laboratory experiments and the much slower rates of marine diagenesis. Trace element analyses of the nodules (Mg/Ca and Sr/Ca ratios) suggest that both precipitation rate and mineralogy affect nodule composition. These results provide new constraints for the relationship between precipitation rate and calcium isotope fractionation and can inform modeling efforts leading towards mechanistic understanding of calcium isotope fractionation and trace element distributions in carbonate minerals.

天然碳酸钙矿物表达了一系列的钙同位素分馏，相对于源流体，沉淀的矿物通常富含较轻的钙同位素。尽管在自然环境中观察到的降水率范围内尚未很好地量化这种关系，但实验和理论证据显示出对降水率的强烈依赖性。最终成员的案例表明，平均海相碳酸盐降水表现出较大的分馏（${\delta }^{44/40}\mathrm{钙}$值比海水低约1‰），而假定以非常慢的速率沉淀或重结晶的成岩碳酸盐相的分馏可忽略不计。具有可测量的非零分馏的自然环境中定量降水速率的有限示例代表了将钙同位素分馏的机理模型应用于地质应用的障碍。这项研究研究了斯瓦尔巴德群岛南部巴伦支海北部的甲烷渗流系统，其中自生碳酸盐矿物正在沉淀，这是由甲烷的厌氧氧化驱动的，并且表观钙同位素分馏因子和沉淀速率可以通过测量孔隙流体的性质来约束。 。在两个浅层岩心中分析孔隙流体剖面，在这些岩心之一中分析了自生碳酸盐结核。孔隙流体剖面指向过渡的非稳态，近似于一个封闭的系统，其中通过碳酸盐沉淀得到的孔隙流体钙同位素比的升高可被建模为瑞利蒸馏系统。表观分馏因子为这些部位的⁴⁴ Ca / ⁴⁰ Ca比为$\alpha$= 0.99985和0.9996，尽管碳酸盐结节表明在过去条件下可能表达了不同的钙同位素分馏因子。据估计，这两个地点的降水速率分别为1.4和3.5μmol/ m ² / h，介于典型实验室实验的速率和海洋成岩速率要慢得多的速率之间。结核的微量元素分析（Mg / Ca和Sr / Ca比率）表明，沉淀速率和矿物学都会影响结核的组成。这些结果为降水速率与钙同位素分馏之间的关系提供了新的约束条件，并且可以为建模工作提供指导，从而有助于对碳同位素矿物中钙同位素分馏和微量元素分布的机械理解。