Computational tools for magma dynamics of subduction zones: finite element models and efficient solvers

俯冲带岩浆动力学计算工具：有限元模型和高效求解器

• 批准号: NE/I026995/1
• 负责人: Richard Katz
• 金额: $ 42.9万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=NE%2FI026995%2F1
• 关键词: Computational; tools; magma; dynamics; subduction

Plate tectonics describes three major plate-boundary types: convergent, divergent, and transform. A subduction zone is an example of a convergent boundary, in which an oceanic plate plunges back into the deep mantle. The subduction process is invariably associated with explosive volcanism; since subduction zones surround the Pacific ocean, this is also where many of the world's most dangerous volcanoes can be found. Why does subduction lead to volcanism? Scientists possess only the broad outlines of an answer to this question. We know that the subducting slab of oceanic sediments, crust, and lithosphere transports sea-water to 100+ kilometres depth in the mantle; we know that this water eventually is released from the slab, and that it percolates upward into the mantle and triggers melting. We know that the magma produced in this way feeds subduction-zone volcanoes. Beyond this, however, things become rather vague. The conditions of pressure and temperature under which magma is produced within the mantle, for example, are not known. This is largely due to the complexity of a system in which water, heat, and mantle rock are combined at inaccessible depths. The subduction zone is like a "black box"---we know the inputs and the outputs, but what happens inside remains a mystery. We are proposing to use supercomputers, and mathematical theory based on fundamental physics and chemistry, to discern the mechanical workings hidden within the black box of a subduction zone.One available clue that may contain useful information about the magmatic processes that occur within a subduction zone comes from the position of the volcanoes themselves. In map view, the volcanoes are arrayed in arcs that sit above the subducting slab. Earthquakes within the slab have allowed scientists to determine the depth of the slab beneath the arc of volcanoes. Compiling this depth for all the world's volcanic arcs, and comparing it with the rate of descent of each slab into the mantle produces a striking trend: faster descent produces arc volcanoes over a shallower point on the slab, while slower descent leads to large slab-depths beneath the arc. A hypothesis to explain this trend was recently published; it states that the volcanoes form at a position determined by the temperature structure of the mantle beneath, and by the details of magmatic flow. In particular, it proposes that the hottest magmas that are produced in the subduction zone rise toward the surface, and create a hot conduit that other melts follow. The arc volcanoes are found on the surface, directly above the conduit.Testing this hypothesis requires a physical/mathematical model of how magma moves through the mantle, and how it transports heat. Previous models of subduction zones have not included the flow of magma, mostly because it was too challenging to compute. To overcome this challenge, we have assembled a team of four scientists with complementary expertise in software engineering, mathematical modelling, fluid dynamics, and geophysics. Together we have the skills to create a new generation of computer model that will describe the flow of magma within a subduction zone. This model will allow us to test the hypothesis described above, as well as other, competing hypotheses. Developing the model will require a multi-stage assembly process, in which each component of the software is designed, written, and tested separately. In this proposal we detail a carefully planned series of tasks that culminate in our ultimate goal of a model of subduction zone magmatism and the position of volcanic arcs. Along the way, we intend to make our software available to other scientists for their use, with the hope that they might help us to improve it. After three years of work with help from two assistants, we'll have new knowledge about subduction, and new mathematical tools for research.

板块构造学描述了三种主要的板块边界类型：收敛型、发散型和转换型。俯冲带是汇聚边界的一个例子，在这里大洋板块俯冲回地幔深处。俯冲过程总是与爆炸性火山作用相联系；由于俯冲带环绕着太平洋，这里也是世界上许多最危险的火山的所在地。为什么俯冲作用会导致火山活动？对于这个问题，科学家们只掌握了大致的答案。我们知道，由海洋沉积物、地壳和岩石圈组成的俯冲板块将海水输送到地幔100多公里深的地方；我们知道，这些水最终会从板块中释放出来，并向上渗透到地幔中，引发融化。我们知道，以这种方式产生的岩浆为俯冲带火山提供了能量。然而，除此之外，事情就变得相当模糊了。例如，地幔中岩浆产生的压力和温度条件是未知的。这主要是由于一个系统的复杂性，在这个系统中，水、热量和地幔岩石在难以到达的深处结合在一起。俯冲带就像一个“黑匣子”——我们知道输入和输出，但内部发生的事情仍然是个谜。我们建议使用超级计算机，以及基于基础物理和化学的数学理论，来辨别隐藏在俯冲带黑盒子里的机械运作。关于发生在俯冲带内的岩浆过程，一个可能包含有用信息的可用线索来自火山本身的位置。从地图上看，火山呈弧形排列，位于俯冲板块上方。板块内的地震使科学家能够确定火山弧下板块的深度。将世界上所有火山弧的深度汇总起来，并将其与每个板块向地幔下降的速度进行比较，可以得出一个惊人的趋势：快速下降会在板块较浅的一点上产生弧状火山，而缓慢下降则会在弧下形成较大的板块深度。最近发表了一个解释这一趋势的假设；它指出，火山形成的位置是由地幔的温度结构和岩浆流动的细节决定的。特别是，它提出，在俯冲带产生的最热的岩浆向地表上升，并形成一个热管道，其他的熔体紧随其后。弧状火山位于地表，就在导管的正上方。要验证这一假设，需要建立一个物理/数学模型，说明岩浆如何在地幔中运动，以及它如何传递热量。以前的俯冲带模型没有包括岩浆流，主要是因为计算起来太困难了。为了克服这一挑战，我们组建了一个由四名科学家组成的团队，他们在软件工程、数学建模、流体动力学和地球物理学方面具有互补的专业知识。我们有能力共同创造新一代的计算机模型来描述俯冲带内岩浆的流动。这个模型将允许我们测试上述假设，以及其他竞争性假设。开发模型将需要一个多阶段的组装过程，在这个过程中，软件的每个组件都是单独设计、编写和测试的。在这个建议中，我们详细介绍了一系列精心策划的任务，最终目标是建立一个俯冲带岩浆活动和火山弧位置的模型。在此过程中，我们打算将我们的软件提供给其他科学家使用，希望他们可以帮助我们改进它。在两位助手的帮助下，经过三年的工作，我们将获得关于俯冲的新知识，以及用于研究的新数学工具。

项目成果

Frazil-ice growth rate and dynamics in mixed layers and sub-ice-shelf plumes

混合层和冰架下羽流中的碎冰生长速率和动态

• DOI: 10.5194/tc-2017-155
• 发表时间: 2017
• 作者: Rees Jones D

Three-Field Block Preconditioners for Models of Coupled Magma/Mantle Dynamics

岩浆/地幔耦合动力学模型的三场块预处理器

• DOI: 10.1137/14099718x
• 发表时间: 2015
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Rhebergen S

Compaction around a rigid, circular inclusion in partially molten rock

部分熔融岩石中刚性圆形包裹体周围的压实

• DOI: 10.1002/2013jb010906
• 发表时间: 2014
• 期刊: Solid Earth
• 影响因子: 3.4
• 作者: Alisic L

Consequences of glacial cycles for magmatism and carbon transport at mid-ocean ridges

• DOI: 10.1016/j.epsl.2019.115845
• 发表时间: 2019-12-15
• 期刊: EARTH AND PLANETARY SCIENCE LETTERS
• 影响因子: 5.3
• 作者: Cerpa, Nestor G.;Jones, David W. Rees;Katz, Richard F.
• 通讯作者: Katz, Richard F.

Pipe Poiseuille flow of viscously anisotropic, partially molten rock

• DOI: 10.1093/gji/ggu345
• 发表时间: 2014-04
• 期刊: Geophysical Journal International
• 影响因子: 2.8
• 作者: J. Allwright;R. Katz