Pressure variations among rheologically heterogeneous elements in Earth's lithosphere: A micromechanics investigation

The total pressure a rock element is subjected to in Earth's lithosphere undergoing deformation may deviate from the lithostatic pressure. Despite many decades of research, the significance of this pressure deviation is still debated. Here, we apply the micromechanics approach based on the generalized Eshelby inclusion solutions for anisotropic power-law viscous materials to investigate the pressure deviation in rheologically heterogeneous rocks. We regard a rheologically distinct element (RDE) as a microscale heterogeneous inclusion which is embedded in and interacts with the heterogeneous macroscale medium. The latter is represented by a homogeneous-equivalent medium (HEM) with its effective rheology obtained self-consistently from the rheological properties of all constituent elements making up the ambient macroscale material embedding the RDE. Partitioning equations from the generalized Eshelby solutions and developed numerical implementations allow the pressure deviations inside and around the RDE to be calculated with quasi-analytical accuracy. We prove formally for limiting cases and demonstrate numerically that the maximum pressure deviation in and around any RDE is on the same order as the deviatoric stresses in the ambient medium or in the element for general power-law viscous materials, isotropic or anisotropic. The pressure deviation fields related to a RDE in an anisotropic HEM are lower than the pressure deviation fields related to the same RDE in an isotropic HEM. Pressure deviations due to an initial pressure anomaly are insignificant considering the viscoelastic interaction between an RDE and the HEM. Our results suggest that pressure deviations in Earth's lithosphere are insignificant for metamorphic processes if the differential stress in Earth's lithosphere is on a few hundred MPa level. Higher pressure deviations require correspondingly greater differential stresses in the lithosphere. They may be generated by short-term strong elastic interactions.