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

板块构造描述了三种主要的板块边界类型：会聚、发散和变换。俯冲带是会聚边界的一个例子，在那里大洋板块冲回深地幔。俯冲过程总是与火山爆发有关；由于俯冲带环绕着太平洋，这也是世界上许多最危险的火山的所在地。为什么俯冲导致火山活动？科学家们只掌握了这个问题的答案的大致轮廓。我们知道，大洋沉积物、地壳和岩石圈的俯冲板块将海水输送到地幔100多公里深；我们知道，这些水最终从板块中释放出来，向上渗透到地幔并引发融化。我们知道，以这种方式产生的岩浆为俯冲带火山提供了食物。然而，除此之外，事情变得相当模糊。例如，在地幔内产生岩浆的压力和温度条件是未知的。这在很大程度上是由于一个系统的复杂性，在这个系统中，水、热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，但里面发生了什么仍然是一个谜。我们提议使用超级计算机，以及基于基本物理和化学的数学理论，来辨别隐藏在俯冲带黑匣子里的机械运作。一条可能包含有关俯冲带内发生的岩浆过程的有用信息的现有线索来自火山本身的位置。在地图上，火山呈弧形排列，位于俯冲板块上方。冰板内的地震使科学家能够确定冰板在火山弧下的深度。汇编世界上所有火山弧的深度，并将其与每个板块下降到地幔的速度进行比较，得出了一个惊人的趋势：较快的下降在板块上较浅的点上方产生弧形火山，而较慢的下降导致弧下较大的板块深度。最近发表了一种解释这一趋势的假说；它指出，火山形成的位置由下面地幔的温度结构和岩浆流动的细节决定。特别是，它提出了在俯冲带产生的最热的岩浆上升到地表，并创造了一个热管道，其他熔体跟随。弧形火山位于地表，就在管道的正上方。要验证这一假设，需要建立一个物理/数学模型，说明岩浆如何穿过地幔，以及它是如何输送热量的。以前的俯冲带模型没有包括岩浆流动，主要是因为它太难计算了。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。我们共同拥有创建新一代计算机模型的技能，该模型将描述俯冲带内的岩浆流动。这个模型将允许我们检验上述假设，以及其他相互竞争的假设。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。在这份提案中，我们详细介绍了一系列精心计划的任务，最终我们的最终目标是建立俯冲带岩浆作用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，希望他们能帮助我们改进它。在两名助手的帮助下，经过三年的工作，我们将有关于潜水的新知识，以及用于研究的新数学工具。

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.