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.
