A MICROMECHANICAL APPROACH FOR HETEROGENEOUS DEFORMATION AND MULTISCALE FABRIC DEVELOPMENT IN EARTH'S LITHOSPHERE

Earth’s lithosphere is made of rheologically heterogeneous rock masses on a wide range of observation scales. When subjected to a tectonic boundary condition such as in a deforming zone between two converging lithospheric plates or blocks, the incurred flow field in the deforming zone is heterogeneous from one rheologically distinct element to another. In any individual element, the flow field also varies with time. Multi-scale structures and fabrics develop as a result of both the deformation of the constituent elements and the flow fields inside these elements which control the formation of smaller-scale fabrics inside these elements. Single-scale kinematic and mechanical models cannot capture these characteristics of lithospheric deformation. We need an effective approach to address flow field partitioning, so that flow field heterogeneity can be considered, and to track the histories of partitioned flow fields so that multi-scale fabric development can be considered. From a physical point of view, flow field partitioning occurs because of mechanical interactions between a rheologically distinct element and the surrounding medium. A micromechanical approach has been developed which is based on Eshelby’s inhomogeneity formalism extended for general power-law viscous materials and the self-consistent method that determines the effective rheological properties of the surrounding medium. The approach has been applied to a natural example of the Cascade Lake shear zone by considering the progressive deformation on three different scales. On the macroscopic scale, representing the average assemblage of rock units at a point, the rock masses are regarded as a continuum made of many first-order elements. The progressive deformation of first-order elements in the macroscopic flow field leads to tectonic transposition. On the scale of an individual first-order element, it is regarded as an Eshelby inhomogeneity embedded in a poly-element continuum. The model predicts lineation patterns observed in natural high-strain zones that have remained unexplained by single-scale models. The micromechanical approach is likely a powerful means for tackling flow partitioning in natural deformations and the accompanying multi-scale development of structures and fabrics.