The chemical composition of erupted basalts provides a record of the thermo-chemical state of their source region and the melting conditions that lead to their formation. Here we present the first probabilistic inversion framework capable of inverting both trace and major element data of mafic volcanic rocks to constrain mantle potential temperature, depth of melting, and major and trace element source composition. The inversion strategy is based on the combination of i) a two-phase multi-component reactive transport model, ii) a thermodynamic solver for the evolution of major elements and mineral/liquid phases, (iii) a disequilibrium model of trace element partitioning and iv) an adaptive Markov chain Monte Carlo algorithm. The mechanical and chemical evolution of melt and solid residue are therefore modelled in an internally- and thermodynamically-consistent manner.

We illustrate the inversion approach and its sensitivity to relevant model parameters with a series of numerical experiments with increasing level of complexity. We show the benefits and limitations of using major and trace element compositions separately before demonstrating the advantages of a joint inversion. We show that such joint inversion has great sensitivity to mantle temperature, pressure range of melting and composition of the source, even when realistic uncertainties are assigned to both data and predictions. We further test the reliability of the approach on a real dataset from a well-characterised region: the Rio Grande Rift in western North America. We obtain estimates of mantle potential temperature (∼ 1340 °C), lithospheric thickness (∼ 60 km) and source composition that are in excellent agreement with numerous independent geochemical and geophysical estimates. In particular, this study suggests that the basalts in this region originated from a moderately hot upwelling and include the contribution from a slightly depleted source that experienced a small degree of melt or fluid metasomatism. This component is likely associated with partial melting of the lower portions of the lithosphere. The flexibility of both the melting model and inversion scheme developed here makes the approach widely applicable to assessing the thermo-chemical structure and evolution of the lithosphere-asthenosphere system and paves the way for truly joint geochemical-geophysical inversions.

喷发玄武岩的化学成分记录了其源区的热化学状态和导致其形成的熔融条件。在这里，我们提出了第一个概率反演框架，能够反演基性火山岩的痕量和主量元素数据，以约束地幔势温、熔融深度以及主量和微量元素源组成。反演策略基于 i) 两相多组分反应输运模型，ii) 主要元素和矿物/液相演化的热力学求解器，(iii) 微量元素分配的不平衡模型和iv) 自适应马尔可夫链蒙特卡罗算法。

我们通过一系列复杂程度不断提高的数值实验来说明反演方法及其对相关模型参数的敏感性。在展示联合反演的优势之前，我们展示了分别使用主要和微量元素组成的好处和局限性。我们表明，这种联合反演对地幔温度、熔融压力范围和源成分具有很大的敏感性，即使在数据和预测都存在现实不确定性的情况下也是如此。我们进一步测试了该方法在来自一个特征明确的地区的真实数据集上的可靠性：北美西部的里奥格兰德裂谷。我们获得了地幔位温（~1340°C）的估计值，岩石圈厚度（约 60 公里）和源组成与许多独立的地球化学和地球物理估计非常一致。特别是，这项研究表明，该地区的玄武岩起源于中等热的上升流，包括来自经历了小程度熔融或流体交代作用的轻度枯竭源的贡献。该成分可能与岩石圈下部的部分熔化有关。这里开发的熔化模型和反演方案的灵活性使该方法广泛适用于评估岩石圈-软流圈系统的热化学结构和演化，并为真正联合地球化学-地球物理反演铺平了道路。这项研究表明，该地区的玄武岩起源于中等热的上升流，包括来自经历了小程度熔融或流体交代作用的轻度枯竭源的贡献。该成分可能与岩石圈下部的部分熔化有关。这里开发的熔化模型和反演方案的灵活性使该方法广泛适用于评估岩石圈-软流圈系统的热化学结构和演化，并为真正联合地球化学-地球物理反演铺平了道路。这项研究表明，该地区的玄武岩起源于中等热的上升流，包括来自经历了小程度熔融或流体交代作用的轻度枯竭源的贡献。该成分可能与岩石圈下部的部分熔化有关。这里开发的熔化模型和反演方案的灵活性使该方法广泛适用于评估岩石圈-软流圈系统的热化学结构和演化，并为真正联合地球化学-地球物理反演铺平了道路。该成分可能与岩石圈下部的部分熔化有关。这里开发的熔化模型和反演方案的灵活性使该方法广泛适用于评估岩石圈-软流圈系统的热化学结构和演化，并为真正联合地球化学-地球物理反演铺平了道路。该成分可能与岩石圈下部的部分熔化有关。这里开发的熔化模型和反演方案的灵活性使该方法广泛适用于评估岩石圈-软流圈系统的热化学结构和演化，并为真正联合地球化学-地球物理反演铺平了道路。