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Castelnau, O, Blackman DK, Becker TW.  2009.  Numerical simulations of texture development and associated rheological anisotropy in regions of complex mantle flow. Geophysical Research Letters. 36   10.1029/2009gl038027   AbstractWebsite

The development of Lattice Preferred Orientations (LPO) within olivine aggregates under flow in the upper mantle leads to seismic and rheological (or viscoplastic) anisotropies. We compare predictions from different micromechanical models, applying several commonly used theoretical descriptions to an upwelling flow scenario representing a typical oceanic spreading center. Significant differences are obtained between models in terms of LPO and associated rheology, in particular in regions where the flow direction changes rapidly, with superior predictions for the recently proposed Second-Order approach. This highlights the limitations of ad hoc formulations. LPO-induced rheological anisotropy may have a large effect on actual flow patterns with 1-2 orders of magnitude variation in directional viscosities compared to the isotropic case. Citation: Castelnau, O., D. K. Blackman, and T. W. Becker (2009), Numerical simulations of texture development and associated rheological anisotropy in regions of complex mantle flow, Geophys. Res. Lett., 36, L12304, doi:10.1029/2009GL038027.

Castelnau, O, Blackman DK, Lebensohn RA, Castaneda PP.  2008.  Micromechanical modeling of the viscoplastic behavior of olivine. Journal of Geophysical Research-Solid Earth. 113   10.1029/2007jb005444   AbstractWebsite

Efforts to couple mantle flow models with rheological theories of mineral deformation typically ignore the effect of texture development on flow evolution. The fact that there are only three easy slip systems for dislocation glide in olivine crystals leads to strong mechanical interactions between the grains as the deformation proceeds, and subsequent development of large viscoplastic anisotropy in polycrystals exhibiting pronounced Lattice Preferred Orientations. Using full-field simulations for creep in dry polycrystalline olivine at high temperature and low pressure, it is shown that very large stress and strain rate intragranular heterogeneities can build up with deformation, which increase dramatically with the strength of the hard slip system (included for the purpose of enabling general deformations). Compared with earlier nonlinear extensions of the Self-Consistent mean-field theory to simulate polycrystal deformation, the "Second-Order'' method is the only one capable of accurately describing the effect of intraphase stress heterogeneities on the macroscopic flow stress, as well as on the local stress-and strain rate fluctuations in the material. In particular, this approach correctly predicts that olivine polycrystals can deform with only four independent slip systems. The resistance of the fourth system (or accommodation mechanism), which is likely provided by dislocation climb or grain boundary processes as has been observed experimentally, may essentially determine the flow stress of olivine polycrystals. We further show that the "tangent'' model, which had been used extensively in prior geophysical studies of the mantle, departs significantly from the full-field reference solutions.

Blackman, DK.  2007.  Use of mineral physics, with geodynamic modelling and seismology, to investigate flow in the Earth's mantle. Reports on Progress in Physics. 70:659-689.   10.1088/0034-4885/70/5/r01   AbstractWebsite

Seismologists and mineral physicists have known for decades that anisotropy inherent in mantle minerals could provide a means to relate surface seismic measurements to deformation patterns at great depth in the Earth, where direct geologic observations would never be possible. Prior to the past decade, only qualitative relationships or simple symmetry assumptions between mantle flow (deformation), mineral alignment and seismic anisotropy were possible. Recent numerical methods now allow quantitative incorporation of constraints from mineral physics to flow/deformation models and, thereby, direct estimates of the resulting pattern of seismic anisotropy can be made and compared with observed signatures. Numerical methods for simulating microstructural deformation within an aggregate of minerals subjected to an arbitrary stress field make it possible to quantitatively link crystal-scale processes with largescale Earth processes of mantle flow and seismic wave propagation, on regional (100s of kilometres) and even global scales. Such linked numerical investigations provide a rich field for exploring inter-dependences of micro and macro processes, as well as a means to determine the extents to which viable seismic experiments could discern between different models of Earth structure and dynamics. The aim of this review is to provide an overview of why and how linked numerical models are useful for exploring processes in the mantle and how they relate to surface tectonics. A brief introduction to the basic concepts of deformation of mantle minerals and the limits of knowledge currently available are designed to serve both the subsequent discussions in this review and as an entry point to more detailed literature for readers interested in pursuing the topic further. The reference list includes both primary sources and pertinent review articles on individual aspects of the combined subjects covered in the review. A series of flow/texturing models illustrate the differences that can arise when different methods or different flow parameters are employed. Representative seismic results illustrate the types of studies done to date and the inferences possible using their anisotropy measurements. Trade-offs involved in the modelling assumptions and seismic data processing methods are touched on. A final example illustrates the effects, relative to a 2D model of mantle flow near a subduction zone, that flow in a third dimension can have on anisotropy patterns.

Blackman, DK, Kendall JM.  2002.  Seismic anisotropy in the upper mantle 2. Predictions for current plate boundary flow models. Geochemistry Geophysics Geosystems. 3   10.1029/2001gc000247   AbstractWebsite

[1] The anisotropic seismic structure due to flow-induced mineral alignment is investigated for a series of models designed to simulate deformation in the upper mantle within a few hundred kilometers of a plate boundary. The orientation distributions of olivine: enstatite aggregates evolve along streamlines of each flow model, based on each grains plastic response to the local stress/strain field. The effective elastic tensor for these textured aggregates provides predictions of P wave anisotropy and shear wave splitting throughout the model space. P and S travel time delay patterns and fast shear wave polarization angles are found to vary significantly with incidence angle for a given model. Comparison of predicted fast P direction for our method versus a finite-strain based estimate shows that agreement is acceptable for much of the model space, but notable differences occur in regions up to several tens of kilometers in size. Two-dimensional models of spreading center flow are presented for slow and fast rates and for several cases in which the ridge migrates over the deeper mantle. The effect of flow in the third dimension is addressed in a few calculations. For one comparison of flow in the mantle wedge at a subduction zone, the introduction of trench parallel flow causes significant changes in the predicted patterns of P wave anisotropy (magnitude, more than orientation) and SKS splitting.

Blackman, DK, Wenk HR, Kendall JM.  2002.  Seismic anisotropy of the upper mantle 1. Factors that affect mineral texture and effective elastic properties. Geochemistry Geophysics Geosystems. 3   10.1029/2001gc000248   AbstractWebsite

[1] Flow-induced mineral alignment in the Earth's mantle affects the nature of seismic wave propagation. Since measurements of seismic travel time and shear wave splitting are a key means by which the structure of the upper mantle can be imaged, it is important to understand the factors that contribute to variability in elastic properties. Seismic anisotropy associated with lattice-preferred orientations of minerals in peridotite is the focus of this study. One way to better understand anisotropy in a convecting upper mantle is to simulate texture evolution based on certain assumptions. Simulations of the development of olivine and orthopyroxene alignment along streamlines of a mantle flow field illustrate how continuously varying strain conditions affect the resulting orientation distribution. There are various uncertainties in rock texture simulations, and the aim here is to investigate how much model assumptions may influence the results. A model of upper mantle flow in the vicinity of an oceanic spreading center is used to illustrate these points. First we assess how sensitive results are on assumptions of different polycrystal plasticity models, specifically lower bounds and viscoplastic self-consistent approaches. We also investigate how recrystallization during deformation might affect the texture that develops along a streamline. The effects of grain growth and nucleation produce, as expected, textures that are different from the deformation-only case. However, the basic P wave structure of the predicted anisotropy is similar between models for streamlines in a slow-spreading, passive flow model as is commonly used for simulating flow near this type of plate boundary. Shear wave splitting patterns are more complex and differ somewhat more between the models in the off-axis region. We also compare predictions for texture development of olivine-only aggregates to that of mixed composition with 70% olivine and 30% orthopyroxene. Although we consider only one aspect of such polyphase deformation, i.e., plastic deformation on specified crystal slip systems, our results are consistent with field observations of the orientation distributions in ophiolitic peridotites. Finally, we determine how simplifying assumptions about the symmetry of the elastic anisotropy can bias interpretations of seismic travel time and shear wave splitting. Whereas a hexagonal approximation can lead to underestimates of the degree of anisotropy, an orthorhombic approximation is found to closely match the results predicted for a general elastic tensor corresponding to an orientation distribution whose symmetry is as low as monoclinic or triclinic.