Laboratory measurements of the viscous anisotropy of olivine aggregates

Extrinsic Anisotropy of Two-Phase Newtonian Aggregates: Fabric Characterization and Parameterization

Rocks of the Earth's crust and mantle commonly consist of different minerals with contrasting mechanical properties. During progressive, high-temperature (ductile) deformation, these rocks develop extrinsic mechanical anisotropy linked to strain partitioning between different minerals, amount of accumulated strain, and bulk strain geometry. Extrinsic anisotropy plays an important role in a wide range of geodynamic processes up to the scale of mantle convection. However, the evolution of grain- and rock-scale fabrics causing this anisotropy cannot be directly simulated in large-scale numerical simulations. For two-phase aggregates-a good rheological approximation of most Earth's rocks-we propose a method to indirectly approximate the extrinsic viscous anisotropy by combining (a) 3D mechanical models of rock fabrics, and (b) analytical effective medium theories. Our results confirm that weak inclusions induce substantial weakening by forming a network of weak thin layers with limited lateral connectivity. Consequently, even when the inclusion phase is extremely weak, structural weakening is not larger than 30-60%, less than in previous estimates. On the other hand, the presence of strong inclusions does not have a profound impact on the effective strength of the aggregate, and lineated fabrics only develop at relatively low viscosity contrasts. When rigid inclusions become clogged, however, the aggregate viscosity can increase over the theoretical upper bound. We show that the modeled grain-scale fabrics can be parameterized as a function of the bulk deformation and material phase properties and combined with analytical solutions to approximate the anisotropic viscous tensor.

Green's functions for geophysics: a review

The Green's function (GF) method, which makes use of GFs, is an important and elegant tool for solving a given boundary-value problem for the differential equation from a real engineering or physical field. Under a concentrated source, the solution of a differential equation is called a GF, which is singular at the source location, yet is very fundamental and powerful. When looking at the GFs from different physical and/or engineering fields, i.e. assigning the involved functions to real physical/engineering quantities, the GFs can be scaled and applied to large-scale problems such as those involved in Earth sciences as well as to nano-scale problems associated with quantum nanostructures. GFs are ubiquitous and everywhere: they can describe heat, water pressure, fluid flow potential, electromagnetic (EM) and gravitational potentials, and the surface tension of soap film. In the undergraduate courses Mechanics of Solids and Structural Analysis, a GF is the simple influence line or singular function. Dropping a pebble in the pond, it is the circular ripple traveling on and on. It is the wave generated by a moving ship in the opening ocean or the atom vibrating on a nanoscale sheet induced by the atomic force microscopy. In Earth science, while various GFs have been derived, a comprehensive review is missing. Thus, this article provides a relatively complete review on GFs for geophysics. In section 1, the George Green's potential functions, GF definition, as well as related theorems and basic relations are briefly presented. In section 2, the boundary-value problems for elastic and viscoelastic materials are provided. Section 3 is on the GFs in full- and half-spaces (planes). The GFs of concentrated forces and dislocations in horizontally layered half-spaces (planes) are derived in section 4 in terms of both Cartesian and cylindrical systems of vector functions. The corresponding GFs in a self-gravitating and layered spherical Earth are presented in section 5 in terms of the spherical system of vector functions. The singularity and infinity associated with GFs in layered systems are analyzed in section 6 along with a brief review of various layer matrix methods. Various associated mathematical preliminaries are listed in appendix, along with the three sets of vector function systems. It should be further emphasized that, while this review is targeted at geophysics, most of the GFs and solution methods can be equally applied to other engineering and science fields. Actually, many GFs and solutions methods reviewed in this article are derived by engineers and scientists from allied fields besides geophysics. As such, the updated approaches of constructing and deriving the GFs reviewed here should be very beneficial to any reader.

Role of orthopyroxene in rheological weakening of the lithosphere via dynamic recrystallization

For plate tectonics to operate on a terrestrial planet, the surface layer (the lithosphere) must have a modest strength (Earth, ≤ 200 MPa), but a standard strength profile based on olivine far exceeds this threshold value. Consequently, it is essential to identify mechanisms that reduce the strength of the lithosphere on Earth. Here we report results of high-strain laboratory deformation experiments on a representative olivine-orthopyroxene composition that show the addition of orthopyroxene substantially reduces the strength in the ductile regime within a certain temperature window. The reduction in strength is associated with the formation of small orthopyroxene and olivine grains. Our samples show heterogeneous microstructures similar to those observed in natural peridotites in shear zones: fine-grained regions containing both orthopyroxene and olivine that form interconnected bands where a large fraction of strain is accommodated. A model is developed to apply these results to geological conditions. Such a model, combined with our experimental observations, suggests that orthopyroxene may play a key role in the plastic deformation of the lithosphere in a critical temperature range, leading to long-term weakening associated with strain localization in the lithosphere.