Scales of mantle heterogeneity from 3D numerical models of mixing

本研究解决了地球地幔的动力学问题，以便深入了解非均质性的来源和规模，以及地球深层内部的长期演化及其对地质过程的影响。我们使用了一种新的实现方法来计算椭球面示踪剂在等粘性、不可压缩的三维流动中在三个正交方向上的拉伸和变薄，并结合了3D对流和混合可视化的新方法，以识别地幔对流模型生成的复杂3D数据中的固定性点、封闭路径和其他特征。这些方法需要在已建立的地幔对流代码中实现，以构建并分析具有大量粒子的时变地幔模型。本研究涉及三个基本主题：(1)地幔中三维随时间对流的混合速率，以及导致观测到的非均质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¹s D²层中；(3)与地幔柱相关的混合。地球深部动力学中一个基本的开放性问题涉及到观测到的地幔非均质性的尺度。地幔对流对非均质性的发展和破坏反映了地球作为一个行星的长期历史和热演化。为了确定地幔中非均质性的起源、演化和持续，需要了解地幔对流混合的物理学。这个问题长期以来一直是一个研究课题，但由于科学家缺乏充分表征3D混合的手段，因此一直没有得到解决。我们的研究通过开发研究三维混合的计算方法并将这些方法应用于地幔对流的数值模拟来解决这个问题。这些结果将有助于改进对观测到的地震和地球化学观测到的地幔各向异性和非均质性的解释。在研究过程中，我们将开发和实施粘性流体混合建模的新方法，这是一个跨多学科研究的重要领域，以及流动可视化。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对地球物理学的应用。

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.