CMG RESEARCH: The Application of Polar Field Theories to Large-Scale Continental Deformation

板块构造理论不能解释大陆板块边界带内观测到的运动，在那里变形是分散的，空间复杂的，并容纳在多个断层。 块体和连续变形模型的研究在再现大陆区域的全球定位系统数据方面同样成功，从而突出了非唯一性。 因此，为了更好地理解大陆岩石圈变形的性质，我们建议应用极性场理论，经典连续介质力学的推广，允许粘性流与子结构，模拟这些地区。 本文的目的是：（1）检验大陆变形岩石圈是否可以用微极流体中的相干结构来模拟，微极流体的运动是由刚性构造板块的相对运动所产生的应力场边界条件所驱动的;（2）用统计力学的形式主义来识别平均场意义下的相干（块体）结构;（3）利用投影算子工具研究弛豫到相干结构及相关现象，以了解大陆变形的本质。板块构造理论解释刚性球冠或板块相对运动的能力，倾向于沿着沿着板块的大陆边界破裂，在那里，相对板块运动在无数断层上持续了100到1000公里。大陆板块边界的这种扩散性质使研究人员将大陆岩石圈建模为连续的粘性流体，其中在整个板块边界的长度尺度上整合了表面单个断层的影响。 其他人则认为，脆性性质的单个断层充当了“迷你”板块边界，并将变形的大陆岩石圈建模为有限数量的旋转刚性块体，这些块体被大型走滑断层分开，在“迷你板块构造”系统中相互滑动。 最近对这两类模型的研究表明，观测值的解是非唯一的。事实上，大陆岩石圈的行为并不是一个单一的端元的情况下，变形大陆岩石圈的确切性质仍然没有完全理解。 在经典的连续介质力学中，有一个隐含的假设，即“物理”粒子（原子、分子、晶体、晶粒等）之间存在离散的尺度分离。和“物质”颗粒（例如流体颗粒）。 然而，有一个很大的物质子集不能用经典连续介质力学充分建模，因为不存在这样的离散尺度分离。然而，这种材料通常可以通过经典连续介质理论的推广（称为极性连续介质力学）来充分建模。在这一提议中，我们提出了大陆岩石圈是极地连续体的另一个例子的假设，并建议应用极地理论，它可以自然地允许板内变形和狭窄的集中变形区，以充分理解大陆变形的性质。

Plate tectonics theory cannot account for the observed motions occurring within continental plate boundary zones, where deformation is diffuse, spatially complex, and accommodated over multiple faults. Studies of block and continuous deformation models are equally successful at reproducing GPS data in continental regions, thus highlighting non-uniqueness. Therefore, in order to better understand the nature of deforming continental lithosphere we propose to apply polar field theories, a generalization of classical continuum mechanics that allows for viscous flow with substructure, to model these regions. The goal of this proposal is to (1) test if continental deforming lithosphere can be modeled as coherent structures in a micropolar fluid whose motion is driven by the stress field boundary conditions resulting from the relative motions of rigid tectonic plates; (2) identify coherent (block) structures that can be obtained in a mean field sense by a statistical mechanical formalism; (3) use projection operator tools to examine relaxation to coherent structures and related phenomena; in order to understand the nature of continental deformation. The ability of plate tectonics theory to explain the motion of rigid spherical caps or plates with respect to each other tends to break down along continental boundaries of plates where relative plate motions are taken up over 100s to 1000s of km over numerous faults. This diffuse nature of continental plate boundaries have led researchers to model continental lithosphere as a continuous viscous fluid where the effect of individual faults at the surface are integrated over the length scale of the entire plate boundary. Others have argued that the brittle nature individual faults act as 'mini' plate boundaries and have modeled deforming continental lithosphere as a finite number of rotating rigid blocks separated by large strike-slip faults sliding past each other in a 'mini plate tectonics' system. Recent studies of both classes of models show that solutions to observations are non-unique. In reality, the behavior of the continental lithosphere is not a single end member case and the exact nature of the deforming continental lithosphere is still not fully understood. In classical continuum mechanics there is an implicit assumption of a discrete scale separation between the 'physical' particles (atoms, molecules, crystals, grains, etc.) and the 'material' particles (e.g. fluid particles). However, there is a large subset of matter that cannot be adequately modeled by classical continuum mechanics, because no such discrete scale separation exists. Such materials can often, however, be adequately modeled by a generalization of classical continuum theories, known as polar continuum mechanics. In this proposal we put forward the hypothesis that the continental lithosphere is yet another example of a polar continuum and propose to apply polar theories, which can naturally allow for both intra-plate deformation and narrow concentrated zones of deformation to fully understand the nature of continental deformation.