Scales of mantle heterogeneity from 3D numerical models of mixing

这项研究涉及地球地幔的动力学，以便深入了解异质性的来源和规模以及地球深部内部的长期演化及其对地质过程的影响。 我们使用一种新的方法来计算拉伸和变薄的椭球示踪剂在三个正交方向的等粘，不可压缩的三维流动，结合新的方法可视化的三维对流和混合，以确定固定点，封闭的路径，和其他功能，发现在复杂的，三维数据产生的地幔对流模型。这些方法将在已建立的地幔对流程序中实现，以构建并分析具有大量粒子的时变地幔模型。该研究涉及三个基本主题：（1）地幔中混合三维时变对流的速率，以及可能导致观察到的非均匀性尺度的结构模式的形成和破坏（2）边界层中混合的结构和动力学，特别是在下地幔的D²层和（3）与地幔柱有关的混合。地球深部动力学的一个基本的开放性问题涉及地幔中观测到的不均匀性的尺度。地幔对流对非均匀性的发展和破坏反映了地球作为一颗行星的长期历史和热演化。为了确定地幔中不均匀性的起源、演化和持续性，需要了解地幔对流混合的物理学。这个问题一直是研究的主题，但由于科学家缺乏在3D中充分表征混合的手段，因此一直没有得到解决。我们的研究解决了这个问题，通过发展计算方法来研究混合在3D和应用这些方法的地幔对流的数值模拟。这些结果将有助于更好地解释所观察到的地幔各向异性和非均匀性的地震和地球化学观测。在研究过程中，我们将开发和实施新的方法来模拟粘性流体中的混合，这是多学科研究的重要领域，也是流动可视化的重要领域。所开发的方法将适用于工程中的计算流体动力学研究，以及具有应用到物理学。

This research addresses the dynamics of the Earth¹s mantle in order to provide insight into sources and scales of heterogeneity and the long-term evolution of the Earth¹s deep interior and its influence on geological processes. We use a new implementation of a method for computing the stretching and thinning of ellipsoidal tracers in three orthogonal directions in isoviscous, incompressible three-dimensional flows, combined with new methods for visualizing 3D convection and mixing to identify stationary points, closed paths, and other features, found within the complex, 3D data generated by mantle convection models. These methods are to be implemented in established mantle convection codes to construct and then analyze time-varying mantle models with a large number of particles. The research addresses three fundamental topics: (1) the rate of mixing 3D time-dependent convection in the mantle, and the formation and destruction of structural patterns that can lead to the observed scales of heterogeneity(2) the structure and dynamics of mixing in boundary layers, especially in the lower mantle¹s D² layer and (3) the mixing associated with mantle plumes.One of the fundamental open questions in dynamics of Earth¹s deep interior concerns the scales of the observed heterogeneity in the mantle. The development, and destruction, of heterogeneity by mantle convection reflects the long-term history and thermal evolution of the Earth as a planet. To determine the origins, evolution, and persistence of heterogeneity in the mantle requires understanding the physics of mixing by mantle convection.This problem has long been a topic of study, but it has not been resolved because scientists lacked the means to fully characterize mixing in 3D. Our research addresses this question by developing the computational methods to study mixing in 3D and applying these methods to numerical simulations of mantle convection. The results will enable improved interpretation of the observed seismic and geochemical observations of anisotropy and heterogeneity in the mantle. In the course of the research, we will develop and implement new methods for modeling mixing in viscous fluids, an important area of research across multiple disciplines, and for flow visualization. The methods developed will be applicable to computational fluid dynamics research in engineering as well as having applications to geophysics.