Textural evolutiona plate boundary problem

Plate tectonics is a first order feature of our planet that is integral to the geosciences. Yet despite its importance, our understanding remains 'kinematic' rather than 'dynamic'. In order to produce plates, strain needs to be localised into thin boundaries allowing the plate interior to remain approximately rigid. Modelling approaches have demonstrated that the power-law rheologies associated with deformation mechanisms are insufficient to localise strain. Consequently, more exotic physics is required to understand plate tectonics.
More recently, non-linear feedbacks associated with fabric elements such as grain-size, crystallographic preferred orientation (CPO) and melt preferred orientation (MPO) have been proposed as key mechanisms of generating strain localisation. The grain-size feedback operates in a heterogeneous microstructure, where large grains generate small grains as they strain which are then able to readily deform through diffusion creep. The positive feedback between increasing strain and increasing strain rate generates an instability which can cause strain to localise. The CPO and MPO feedback occurs due to viscous anisotropy associated with preferred orientation: rocks which are favourably orientated deform much more readily than rocks in other orientations. Since both CPO and MPO form and strengthen with increasing strain, there is the potential for a feedback which localises deformation.
However, each of these fabric elements have problems when applied to the plate tectonic problem. The small grain sizes associated with the grain size feedback are not thought to be long lived enough to explain the reactivation of old plate boundary scars. The potential for CPO based strain localisation may be limited due to the progressive rotation of crystallographic axis from their optimal orientation with increasing strain. In addition, CPO is generally thought to form in the dislocation creep regime, so if the grain size is too small due to the grain size feedback, CPO may be unable to form. Recent experiments have also demonstrated an interaction between CPO and MPO termed the 'a-c' switch. Clearly an integrated approach which considers the dynamical interaction of grain-size, CPO and MPO together is needed to assess the potential role of these fabric elements and their respective feedbacks in the formation and operation of plate boundaries.
To assess the role of each fabric element, models must be developed which describe the evolution of each element as a function of time and other variables such as strain rate. Models exist for each of these fabric elements but are problematic when applied to the problem of plate boundaries. For example, grain size evolution models typically parameterise grain size as a single scalar variable and so cannot model the microstructural heterogeneity needed to develop the grain size feedback. Although a model for MPO development exists, it too parameterises the strength of MPO as a single scalar variable, and in the parameterisation of the model important physics is missing such as a treatment of the reduction in strength of MPO as strain rate decreases.
Despite these challenges, new approaches to modelling these fabric elements have opened new avenues for addressing the problem. A recent model of CPO evolution has tackled the issue of olivine not fulfilling the von Mises criterion by seeking a best fit solution instead of the more technical approaches used in the past. This approach has both improved the accuracy and significantly decreased the complexity of CPO modelling. A yet unpublished model of grain size approaches the problem through constraints on the rate of dissipation of entropy.