An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites
An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites
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DOI：
10.1016/j.gca.2016.12.040
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发表时间：
2017-04-15
影响因子：
5
通讯作者：
Liang, Yan
中科院分区：
文献类型：
--
作者：
Liu, Boda;Liang, Yan
马尔可夫链蒙特卡罗(MCMC)模拟是解决逆问题的一种强有力的统计方法，具有广泛的应用前景。在地球科学中，MCMC模拟的应用主要是在地球物理领域。本研究的目的是将MCMC方法引入地幔熔融过程中与微量元素分馏有关的地球化学反问题。与最小二乘法相比，MCMC方法在解释玄武岩和地幔岩石中微量元素丰度的熔融过程中具有一定的优势。在这里，我们使用MCMC方法从中大西洋海脊、中印度洋海脊、西南印度洋海脊、Lena海槽和美洲-南极海脊的深海橄榄岩中单斜辉石中的稀土丰度来反演熔融程度、熔融过程中存在的熔体分数以及熔体和残余固体之间的化学不平衡程度。我们考虑了两种熔化模型：一种有精确的解析解，另一种没有。我们根据Metropolis-Hastings算法在熔化模型链中对后者进行数值求解。反演熔融参数的概率分布取决于物理模型的假设、地幔来源成分的知识以及来自REE数据的约束。MCMC反演的结果与基于非线性最小二乘反演的结果一致，并提供了更可靠的不确定度估计。结果表明，在大洋中脊扩张中心下方部分熔融过程中，化学不平衡可能对残余橄榄岩中LREE的分馏起重要作用。MCMC模拟非常适合于更复杂但物理上更现实的熔化问题，这些问题没有解析解。(C)2017爱思唯尔有限公司。保留所有权利。
Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions. (C) 2017 Elsevier Ltd. All rights reserved.