ANIMA – ANIsotropic Viscosity in MAntle Dynamics

• Gallo, Leandro Cesar; Domeier, Mathew Michael; Sapienza, F.; Swanson-Hysell, N. L.; Vaes, B. & Zhang, Y. [Show all 14 contributors for this article] (2023). Embracing Uncertainty to Resolve Polar Wander: A Case Study of Cenozoic North America. Geophysical Research Letters. ISSN 0094-8276. 50(11). doi: 10.1029/2023GL103436. Full text in Research Archive

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• Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars; Wang, Yijun & Mather, Ben (2024). Direct estimation of anisotropic viscosity parameters using texture scores of olivine polycrystals.
• Kiraly, Agnes; Wang, Yijun; Conrad, Clinton Phillips; Hansen, Lars N. & Mather, Ben (2023). Modelling anisotropic viscosity. Show summary

  Many of Earth’s layers – from the crust to the inner core – are mechanically anisotropic. Anisotropic (i.e. direction-dependent) behaviour of rocks can derive from intrinsic properties of rock forming minerals or from microscopic or macroscopic layering of rocks and/or melts with different composition (extrinsic anisotropy). The Earth Science community often discusses the phenomena of seismic anisotropy, which results from the direction dependent propagation of seismic waves. However, materials that are characterized by elastic (seismic) anisotropy often exhibit viscous anisotropy as well, which is less explored. In geodynamics we are primarily interested in anisotropic viscosity in the crust and the mantle, where both intrinsic and extrinsic anisotropy are present. To model anisotropic viscous behaviour, we have to handle the viscosity as a 4th order tensor while also thinking about the re-orientation of anisotropy (or evolution of texture) in time. In the upper mantle the main source of anisotropy derives from the lattice preferred orientation (LPO) of olivine. Under deformation olivine grains rotate into the deformation direction (we often refer to this as texture evolution), resulting in a texture where some – or many – olivine grains are aligned with each other. Furthermore, because single olivine crystals are mechanically anisotropic – which means they deform more easily along some slip systems than others – then LPO that is developed in the upper mantle will yield anisotropic viscosity on a macroscopic scale. The foundation of our modelling approach is the Modified Director Method, which includes texture evolution and micromechanical models, both deriving from rock mechanic laboratory experiments on olivine aggregates (Hansen et al., 2016a, 2016b). The micromechanical model allows us to calculate the stress needed to achieve a certain strain rate on an aggregate, while the texture evolution model calculates the rotation of grains under a given deformation. To integrate these models into a geodynamic code, or use it to model the evolution of texture and anisotropic viscosity under specific deformation paths, we have to characterize our texture with a rank 4 viscosity or fluidity tensor (Király et al., 2020). It has been shown that the anisotropy related to olivine textures can be characterized by the Hill coefficients (Hill, 1948; Signorelli et al., 2021). Here we show that by building a large database of different textures derived from geodynamic models, we can define a linear model between simple texture parameters and the Hill coefficients with a reasonable cost. This is advantageous for integrating anisotropic viscosity into 4D geodynamic models because it allows for a direct determination of the viscosity tensor from the evolving rock texture, saving a large amount of computational time.

• Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars & Wang, Yijun (2023). Deriving anisotropic viscosity parameters directly from texture scores of olivine polycrystals.
• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Fraters, Menno & Hansen, Lars (2023). Anisotropic Viscosity in Subduction Models.
• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars & Fraters, Menno (2023). Effect of olivine anisotropic viscosity in advancing and retreating subduction settings. Show summary

  Lattice preferred orientation (LPO) of olivine crystals occurs due to deformation in the mantle. Different parts of the upper mantle can undergo a large variety of deformation paths. During simple processes, such as simple shearing below oceans due to the movement of tectonic plates, the LPO will reflect the direction of the movement of tectonic plates. On the other hand, in areas, such as around subduction zones, the mantle undergoes more complex deformation paths, resulting in a less easily predictable LPO. Seismic anisotropy has been used as a proxy for mantle flows and the LPO formed in the mantle. To interpret the seismic anisotropy observations more accurately, we need to understand how LPO forms in different regions of subduction. LPO has been implemented in many numerical modelling tools to predict seismic anisotropy, which places constraints on mantle dynamics. However, a few recent studies have linked olivine texture development to viscous anisotropy, resulted from the summed effect of individual crystals that are deforming anisotropically. Anisotropic viscosity can affect deformation and in turn the resulting LPO. To study the effect of anisotropic viscosity (AV) and LPO evolution in geodynamics processes, it is important to know the role of AV on LPO and the differences between the numerical methods that calculate them. We choose three methods of olivine texture development to examine in this study. D-Rex is a polycrystal LPO model that is relatively balanced in computational efficiency and accuracy. From previous studies, D-Rex has been shown to produce faster texture development and stronger texture compared to other methods, including our second choice, the modified director method (MDM). The MDM parameterizes the olivine LPO formation as relative rotation rates along the slip systems that participate in the rotation of olivine grains due to finite deformation. We also couple the MDM with a micromechanical model for olivine AV (which makes our third choice MDM+AV), to allow the anisotropic texture to modify the viscosity and in turn affect the formation of LPO. Here we compare the LPO evolution under subduction settings with a slowly advancing trench and a retreating trench, with and without the effect of AV. Since the mantle flow pattern in subduction zones is not homogeneous, different particles experience a variety of deformation paths. We place 60 particles in each subduction model around the slab to track the deformation and resulting olivine texture. We compute olivine texture using the above-mentioned three different methods (D-Rex, MDM, MDM+AV). With the particles, we can identify characteristic textures developed in key regions such as the mantle wedge, sub-slab area, and lateral slab edge. We then run a statistical analysis on the texture parameter and anisotropic properties of the particles from both retreating and advancing subduction models, to study where anisotropic viscosity has the largest effect on the mantle flow. We expect AV to have a larger effect in a retreating slab setting since the mantle flows feeding material to the sub-slab region is more intensive.

• Kiraly, Agnes; Wang, Yijun; Fraters, Menno; Gassmoeller, Rene; Dannberg, Juliane & Hansen, Lars [Show all 7 contributors for this article] (2022). Incorporating olivine CPO-related anisotropic viscosity into 3D geodynamics simulations.
• Wang, Yijun; Kiraly, Agnes; Fraters, Menno; Gassmoeller, Rene; Dannberg, Juliane & Hansen, Lars [Show all 7 contributors for this article] (2022). Olivine texture evolution under a simple deformation scheme: Comparing different numerical methods of LPO calculations.
• Kiraly, Agnes; Fraters, Menno & Gassmoeller, Rene (2022). Implementing 3D anisotropic viscosity calculations into ASPECT. Show summary

  Olivine, the main rock-forming mineral of Earth's mantle, responds to tectonic stress by deforming viscously over millions of years. This deformation creates an anisotropic (direction-dependent) texture that typically aligns with the mantle flow direction. According to laboratory experiments on olivine, we expect this texture to also exhibit anisotropic viscosity (AV), with deformation occurring more easily when it is parallel to, rather than across, the texture. However, the direction dependency of lithospheric and asthenospheric viscosity is rarely addressed in geodynamic models. The open-source modeling package ASPECT can address AV in a 2D setting using the director method, where AV is present due to shape preferred orientation created by dike intrusions (Perry-Houts and Karlstrom, 2019). We have adapted this implementation for current versions of ASPECT and benchmarked it against similar Rayleigh-Taylor instability models by Lev and Hager (2008). Unfortunately, a 2D method is inappropriate to address AV related to olivine crystallographic preferred orientation (CPO or texture), as, by default, olivine has three independent slip systems on which deformation can occur. Integrating anisotropic viscosity into 3D models would also allow us to use the actual laboratory-based parametrizations of the olivine slip system activities and texture parameters when describing the evolution of CPO and AV. One of the biggest challenges in addressing AV in a 3D setting is to find the full, rank 4, viscosity tensor, which can be done with a method similar to the one for the fluidity tensor in Király et al., (2021). Here, we present the initial results of simple geodynamic setups (shear box, corner flow), where 3D olivine CPO develops, based on the D-Rex method (Fraters and Billen, 2021), and this CPO creates AV based on the micromechanical model described in Hansen et al., (2016). Our goal is to create a tool within ASPECT that allows for CPO to develop and affect the asthenospheric or lithospheric mantle’s viscosity to improve modeling a wide range of geodynamic problems.

• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars N. & Fraters, Menno (2022). Olivine texture evolution under simple deformation: Comparing different numerical methods for calculating LPO and anisotropic viscosity. Show summary

  The development of olivine texture, or lattice preferred orientation (LPO), has been implemented in many numerical modelling tools to predict seismic anisotropy, which places constraints on mantle dynamics. However, a few recent studies have linked olivine texture development to its mechanical anisotropy, which in turn can affect deformation rates and also the resulting texture. To study the effect of anisotropic viscosity (AV) and LPO evolution in geodynamics processes, it is important to know the role of AV and LPO and the differences between the numerical methods that calculate them. The modified director method parameterizes the olivine LPO formation as relative rotation rates along the slip systems that participate in the rotation of olivine grains due to finite deformation. When it is coupled with a micromechanical model for olivine AV, it allows the anisotropic texture to modify the viscosity. We compare the olivine textures predicted by the modified director method both with and without a coupled micromechanical model and textures predicted by the D-Rex LPO evolution model. To do this, we recalculate the texture observed in simple 3D models such as a shear box model and two other well-understood models: a corner flow model and a subduction model. In general, we observed that the D-Rex models predict a stronger anisotropic texture compared to the texture predicted by the modified director method both with and without the micromechanical model, in agreement with previous studies. When including the micromechanical model, the anisotropic texture changes the observed strain rates, which allows for a slightly faster texture evolution that is more similar to the D-Rex predictions than it is to those produced by the modified director method alone. We found that even for the simplest settings there is an increase of 10~15% in strain rate during deformation until a strain of 2.5. When shearing the asthenosphere over ~10 Myr, such anisotropy could modify the effective viscosity of the mantle,causing an up to 40% increase in plate velocity for the same applied stress. The anisotropy can also induce deformation in planes other than the initial shear plane, which can change the direction of the primary deformation. Our ultimate goal is to understand the role of AV and LPO evolution in geodynamic processes by looking at deformation paths predicted by geodynamic models in ASPECTWith this initial test, we will gain a basic understanding of olivine AV behavior and LPO evolution under different deformation settings calculated with different numerical methods, which we will carry onto our next step of implementing anisotropic viscosity of olivine in 3D into ASPECT. How to cite: Wang, Y., Király, Á., Conrad, C. P., Hansen, L., and Fraters, M.: Olivine texture evolution under simple deformation: Comparing different numerical methods for calculating LPO and anisotropic viscosity, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-7201, https://doi.org/10.5194/egusphere-egu22-7201, 2022.

• Kiraly, Agnes (2021). Dynamic interactions between subduction zones. Show summary

  Fundamental properties of subducting slabs, such as their buoyancy, the dip direction and the rheology of the slab and the surrounding mantle, determine the first order motions and geometries of subduction zones. Due to the horizontal migration of slabs n the mantle, subduction zones often “approach” each other, altering the dynamics of single subductions. In this presentation, I will summarize the dynamics of subduction zone interactions in four simple geometries, that are most commonly used to describe the geodynamic history of tectonically complex areas. Using data from geological and geophysical observations and the results of many geodynamics models, we can conclude some common features of subduction zones interactions, such as: changing slab dips, reduced trench migration rates, complex flow patterns in the mantle, and strong rotations of lithospheric blocks. These features are resulted from the stress transfer between neighboring slabs which ultimately changes the force balance of individual subduction zones. Understanding the dynamics of such complex systems can help to interpret geological and geophysical data, and to reconstruct the tectonic history of areas, where multiple subduction zones are/were active simultaneously. A great example for such a tectonically complex area is the Central Mediterranean, which I will discuss in the light of the conclusions we make about the dynamics of subduction zones interactions.

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