Structural geology meets micromechanics: A self-consistent model for the multiscale deformation and fabric development in Earthʹs ductile lithosphere

Earthʹs lithosphere is made of rheologically heterogeneous elements of a wide range of characteristic lengths. A micromechanics-based self-consistent MultiOrder Power-Law Approach is presented to account for lithospheric deformations and the accompanying multiscale fabric development. The approach is principally based on the extended Eshelby theory for the motion of a power-law viscous ellipsoid in a power-law viscous matrix and the idea of embedding inhomogeneities within inhomogeneities. The extended theory provides a general means for investigating deformation partitioning in heterogeneous rocks. The “inhomogeneities within inhomogeneities” method allows multi-hierarchical levels of flow field partitioning and hence multiscale deformations to be investigated. Partitioned flow fields are used to investigate fabric development. Being based fully on micromechanics, the approach generates model predictions of both kinematic quantities (strain, strain rates, and vorticity) and stress histories. The former can be directly compared with field and laboratory structural observations while the latter can help to understand the physics of natural deformations. lf-consistent and multiscale approach is applied to a natural example of the Cascade Lake shear zone in the east Sierra Nevada of California. The modeling shows that the fabrics are most consistent with a steeply-dipping transpression zone with a convergence angle of 20° and a strike-slip displacement about 26 km. Further, the strength evolution of the model zone confirms that a transpression zone is a weakening system with respect to the simple shearing component and a hardening one for the pure-shearing component. This is consistent with slip partitioning in obliquely convergent plate boundaries: boundary-normal convergence tends to spread over a broad area whereas boundary-parallel shear tends to localize in major strike-slip zones.