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

板块构造理论不能解释在大陆板块边界带内观测到的运动，那里的变形是扩散的，空间上复杂的，并跨越多个断层。块状形变模型和连续形变模型的研究在复制大陆地区的GPS数据方面同样成功，因此突出了非唯一性。因此，为了更好地理解大陆岩石圈变形的本质，我们建议应用极场理论来模拟这些区域。极场理论是经典连续介质力学的推广，允许有子结构的粘性流动。这一建议的目的是：(1)检验大陆变形岩石圈是否可以模拟为微极流体中的相干结构，其运动是由刚性构造板块相对运动产生的应力场边界条件驱动的；(2)识别可以通过统计力学形式在平均场意义上获得的相干(块体)结构；(3)使用投影算符工具来研究相干结构和相关现象的松弛；以了解大陆变形的本质。板块构造理论解释刚性球帽或板块相对运动的能力倾向于沿着板块的大陆边界崩溃，在那里，板块的相对运动在许多断层上占据了100至1000公里的范围。大陆板块边界的这种弥漫性质导致研究人员将大陆岩石圈模拟为连续的粘性流体，其中地表单个断层的影响在整个板块边界的长度范围内积分。其他人则认为，单个断层的脆性性质就像是一个迷你的板块边界，并将正在变形的大陆岩石圈模拟为有限数量的旋转的刚性块体，这些块体由大型走滑断层相互滑动隔开，形成一个“迷你板块构造”系统。最近对这两类模型的研究表明，观测值的解是不唯一的。在现实中，大陆岩石圈的行为并不是单一的端元情况，变形的大陆岩石圈的确切性质仍然没有得到充分的了解。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、颗粒等)之间的离散尺度分离。以及“材料”颗粒(例如，流体颗粒)。然而，有一大部分物质不能被经典的连续介质力学充分模拟，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而得到充分的模拟，这种理论被称为极连续介质力学。在这一建议中，我们提出了大陆岩石圈是极地连续体的又一个例子的假设，并建议应用极地理论，该理论自然可以同时考虑板内变形和狭窄的变形集中带，以充分了解大陆变形的性质。

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.