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• Király, Ágnes; Wang, Yijun; Conrad, Clinton P; Hansen, Lars N & Mather, Ben (2026). CPO2Hill: An Efficient Parametrisation to Infer Anisotropic Viscous Behaviour Directly from Olivine Texture Parameters. Geodynamica. 1(1). doi: 10.5070/f3.49008. Fulltekst i vitenarkiv Vis sammendrag

  Anisotropic viscosity is likely prevalent within the upper mantle, but is usually disregarded in geodynamics models. On a crystal scale, olivine’s intrinsic properties are such that dislocation creep occurs over an order of magnitude more easily along olivine’s [100] symmetry axis than along its [001] axis. However, deforming olivine aggregates generate crystallographic preferred orientations (CPO) with their own macroscopically effective anisotropic viscosities that have proven difficult to estimate from the microscopic anisotropies of individual olivine crystals. Here we present a simple method to derive anisotropic viscosity parameters directly from the CPO mean orientation tensors. To calibrate the method, we created a large database of textures likely to occur in geodynamic simulations. We tested our method within numerical simulations of simple shear with both constant and varying shear directions. Finally, we integrated our method into the geodynamic code ASPECT, where it can be used to explore the geodynamic importance of anisotropic viscosity.

• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips & Maupin, Valerie (2025). Mantle Flow and Anisotropy in Subduction Zones: Modeling and Clustering of Olivine Textures. Geochemistry Geophysics Geosystems. 26(7). doi: 10.1029/2025gc012160. Fulltekst i vitenarkiv Vis sammendrag

  The mantle near Earth's subduction zones endures intense deformation that generates anisotropic rock textures. These textures can be observed seismically and modeled geodynamically, but the complexity of this deformation makes analyses of these textures difficult. In this study, we apply time‐series clustering analysis to tracers within subduction models, allowing for the identification of regions in the subduction zone with common deformation histories and olivine crystallographic‐preferred orientation development. We compare olivine texture evolution predicted using different methods in both retreating and stationary‐trench settings. Our results reveal distinct variations in olivine texture, indicating that both seismic and viscous anisotropy can exhibit substantial heterogeneity within the mantle wedge, sub‐slab, and subducting plate regions. For retreating trenches, olivine textures are strongest in the mid‐depth mantle wedge region about 200 km away from the trench between 100 and 300 km depth. Our study shows that trench‐normal olivine a ‐axis orientations dominate in the center of subduction zones. Toroidal flow around slab edges generates a mix of trench‐normal, trench‐parallel, and oblique fast seismic directions. Textures and anisotropy are stronger for the retreating trench model than for the stationary trench model since more deformation has been accumulated due to trench motion. These findings provide insights for interpreting seismic anisotropy in subduction zones and highlight the importance of considering texture heterogeneity, as characterized by clustering algorithms, when analyzing both geodynamic models and seismic observations of subduction zones.

• Fraters, Menno RT; Billen, Magali; Gassmöller, Rene; Saxena, Arushi; Heister, Timo & Li, Haoyuan [Vis alle 10 forfattere av denne artikkelen] (2024). The Geodynamic World Builder: A planetary structure creator for the geosciences. Journal of Open Source Software (JOSS). 9(101). doi: 10.21105/joss.06671. Fulltekst i vitenarkiv Vis sammendrag

  Many Earth science applications require the discretization, parameterization, and/or visualization of complex geological features in a 3D geometry in global or regional settings. A prime example are geodynamic models that have to make assumptions about the Earth’s thermal and chemical structure and the geometry of different features such as plates, subducted slabs, or mantle plumes. This structure is needed in instantaneous models, as model initial conditions, or to test different hypotheses and compare model predictions to observations. Other examples are the creation of an Earth velocity structure for seismic forward modeling and hypothesis-testing, or the visualization of tectonic features in structural geology. The Geodynamic World Builder (GWB) has been designed to make the creation of complex parameterized models significantly easier. It can also be used to design simple synthetic models and it supports the use of several types of datasets to set up models. Besides setting up initial conditions for geodynamic models, the GWB can also visualize complex 3D geologic, tectonic, and geodynamic settings.

• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars & Fraters, Menno (2024). The Importance of Anisotropic Viscosity in Numerical Models, for Olivine Textures in Shear and Subduction Deformations. Tektonika. 2(1), s. 157–173. doi: 10.55575/tektonika2024.2.1.67. Fulltekst i vitenarkiv Vis sammendrag

  Olivine lattice preferred orientation (LPO), or texture, forms in relation to deformation mechanisms such as dislocation creep and can be observed in the upper mantle as seismic anisotropy. Olivine is also mechanically anisotropic, meaning that it responds to stresses differently depending on the direction of the stress. Understanding the interplay between anisotropic viscosity (AV) and LPO, and their role in deformation, is necessary for relating seismic anisotropy to mantle flow patterns. In this study, we employ three methods to predict olivine texture (D-Rex, MDM, and MDM+AV) in a shear box model and a subduction model. D-Rex and MDM are two representative texture development methods that have been compared before, and our results are in line with previous studies showing that textures computed by D-Rex develop faster and are stronger and more point-like than textures calculated with MDM. MDM+AV uses the same isotropic mantle stresses and particle paths as D-Rex and MDM but includes the effect of AV for texture predictions. MDM+AV predicts a texture similar to MDM with a distinct girdle-like orientation for simple shear deformation or at low strain in the subduction model. At larger strains, MDM+AV’s textures are more point-like and stronger compared to the other two methods. The effective viscosity for MDM+AV drops by up to 60% in a shear box model and can be either strengthened or weakened relative to isotropic viscosity for different regions of the subduction model experiencing different patterns of deformation. Our results emphasize the significant role of AV in olivine texture development, which could substantially affect geodynamic processes in the upper mantle.

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• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips & Maupin, Valerie (2025). Subduction dynamics and mantle anisotropy: modeling and clustering of olivine textures. Fulltekst i vitenarkiv Vis sammendrag

  The mantle near Earth's subduction zones experiences significant deformation, forming anisotropic rock textures. These textures can be detected using seismic methods and simulated in geodynamic models. This study employs time-series clustering to examine tracers in subduction models, identifying regions with similar deformation histories, olivine crystallographic-preferred orientation (CPO) development, and CPO-induced anisotropic viscosity. We compare the evolution of olivine textures predicted by various numerical methods (e.g. D-Rex, MDM, and MDM+AV) for both retreating and stationary trench subduction settings. Our modeling shows notable variations in olivine texture around the slab and as a function of subduction dynamics. These variations, which are illuminated by the clustering analysis, show that texture, seismic, and viscous anisotropy can vary greatly within the mantle wedge, sub-slab, and subducting plate regions of the upper mantle. In the retreating-trench model, the strongest textures are observed in the mid-depth mantle wedge region and beneath the slab at the 660 km transition zone. Trench-normal olivine a-axis orientations are predominant in the center of subduction zones, while toroidal flow around slab edges produces a mix of trench-normal, trench-parallel, and oblique fast seismic directions. On the other hand, in the stationary-trench model, the trench-normal signal in front of the slab is weaker while there are stronger trench-normal signals behind the slab at shallow depths between 100 and 300 km. At the edge of the slab, weak toroidal flow produces trench-oblique orientations while trench-parallel and trench-normal orientations are missing. In general, the retreating trench model exhibits stronger textures and anisotropy due to increased deformation from trench motion. These results provide valuable insights into seismic anisotropy in subduction zones and underscore the importance of considering texture heterogeneity when interpreting geodynamic models and seismic data. The use of time-series clustering algorithms highlights the intricate pattern of evolution and the relationship between deformation history, CPO, and CPO-induced viscous anisotropy occurring within subduction zones.

• Kiraly, Agnes; Wang, Yijun; Conrad, Clinton Phillips; Dannberg, Juliane; Fraters, Menno & Gassmoeller, Rene [Vis alle 7 forfattere av denne artikkelen] (2025). ANIMA the journey: how we model olivine CPO-related anisotropic viscosity. Fulltekst i vitenarkiv Vis sammendrag

  The long-term fluid-like movements in the Earth’s mantle largely depend on the rheological behaviour of olivine, the main rock-forming mineral in the upper mantle. Although the average viscosity of the mantle can be estimated from post-glacial rebound or geoid anomalies, the micromechanical mechanisms that facilitate the deformation of the solid mantle have been identified from rock mechanics experiments. Dislocation creep emerges as the predominant deformation mechanism in the uppermost mantle, aligning olivine crystals into a crystallographic preferred orientation (CPO) parallel to the flow, while this alignment of crystals also results in anisotropic viscous behaviour. Thus, anisotropic viscosity and CPO evolve hand in hand, and this interaction may impact many geodynamic processes. For example, beneath tectonic plates CPO evolves parallel to the plate motion direction, weakening the asthenosphere in that direction. However, if the plate motion direction changes, the asthenosphere will resist this change, leading to smaller velocities, less deformation and therefore a slow evolution of the CPO towards the new plate motion direction. In the ANIMA project, we aimed to find an efficient way of modelling CPO evolution and the related anisotropic viscosity in a fully coupled way within a geodynamic simulation. We developed a method that tracks CPO evolution on advected particles based on the D-REX method and utilizes the eigenvalues of the mean CPO orientation matrices to predict the anisotropic viscous parameters. These parameters allow us to calculate a tensor form of the viscosity, which we then feed back into our model solution. This method can be applied in combination with other rheologies, although with a cost of having to represent the viscosity as a tensor in the entire model domain, regardless of the dominant deformation mechanism. Despite an estimated increase in computational cost by up to an order of magnitude, incorporating anisotropic viscosity coupled to CPO evolution stands feasible for regional geodynamic models. This development will facilitate the study of a broad new range of geodynamics problems that involve olivine texture and anisotropic viscosity.

• Wang, Yijun; Kiraly, Agnes & Conrad, Clinton Phillips (2024). Implementation of anisotropic viscosity in ASPECT. Fulltekst i vitenarkiv
• Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars; Wang, Yijun & Mather, Ben (2024). Direct estimation of anisotropic viscosity parameters using texture scores of olivine polycrystals. Fulltekst i vitenarkiv
• Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars & Wang, Yijun (2023). Deriving anisotropic viscosity parameters directly from texture scores of olivine polycrystals. Fulltekst i vitenarkiv
• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Fraters, Menno & Hansen, Lars (2023). Anisotropic Viscosity in Subduction Models. Fulltekst i vitenarkiv
• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Hansen, Lars & Fraters, Menno (2023). Effect of olivine anisotropic viscosity in advancing and retreating subduction settings. Fulltekst i vitenarkiv Vis sammendrag

  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; Conrad, Clinton Phillips; Hansen, Lars N. & Mather, Ben (2023). Modelling anisotropic viscosity. Fulltekst i vitenarkiv Vis sammendrag

  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.

• 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. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Wang, Yijun; Kiraly, Agnes; Fraters, Menno; Gassmoeller, Rene; Dannberg, Juliane & Hansen, Lars [Vis alle 7 forfattere av denne artikkelen] (2022). Olivine texture evolution under a simple deformation scheme: Comparing different numerical methods of LPO calculations. Fulltekst i vitenarkiv
• Kiraly, Agnes; Wang, Yijun; Fraters, Menno; Gassmoeller, Rene; Dannberg, Juliane & Hansen, Lars [Vis alle 7 forfattere av denne artikkelen] (2022). Incorporating olivine CPO-related anisotropic viscosity into 3D geodynamics simulations. Fulltekst i vitenarkiv
• Wang, Yijun; Kiraly, Agnes; Conrad, Clinton Phillips; Fraters, Menno & Hansen, Lars (2022). Olivine texture evolution under simple deformation: Comparing different numerical methods for calculating LPO and anisotropic viscosity. Fulltekst i vitenarkiv
• Wang, Yijun; Kiraly, Agnes & Conrad, Clinton Phillips (2025). Texture evolution in subduction models, influenced by anisotropic viscosity. Simple tests, cluster analysis, and numerical implementation. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  The anisotropic viscosity of olivine plays a crucial role in mantle dynamics, influencing both large-scale geodynamic processes and texture evolution, and thus the resulting seismic anisotropy. While experimental studies have characterized the directional dependence in the viscosity of olivine, its integration into numerical geodynamic models remains limited. This thesis systematically investigates the effects of anisotropic viscosity during simple shear and during complex deformations in subduction zones, using a series of numerical methods implemented outside and within the geodynamic modeling software, ASPECT. As an initial step to estimate the effect of anisotropic viscosity, we compute olivine textures and texture-induced anisotropic viscosity as postprocessors based on deformation paths obtained from geodynamic models run in ASPECT. In these models, textures and Associated anisotropic viscosity do not modify deformations directly. We demonstrate that anisotropic viscosity has a limited impact during simple shear with a constant imposed velocity but can significantly alter texture development and the effective viscosity in a more dynamic subduction model. This is particularly the case in regions where accumulated strain is large, for example, in the mantle wedge region. Using time-series cluster analysis, we expand the analysis in subduction models to include more than 1000 particles located throughout the subduction zone covering the mantle wedge, sub-slab, and slab areas. We identify the spatial variability of mantle deformation, olivine texture, and anisotropic direction and strength, which are particularly pronounced in the retreating-trench model with large deformation. The clusters characterize the trench-normal orientations above and beneath the slab, as well as the trench-parallel orientations between 300 and 400 km depth behind the slab. These directions have also also observed in seismic anisotropy studies near subduction systems. To describe texture-induced anisotropic viscosity, we establish a quantitative relationship between olivine texture and anisotropic viscosity parameters, expressed as the Hill coefficients. This relationship is validated with textures both from experiments and numerical models. We then integrate this relationship into ASPECT, representing anisotropic viscosity with a tensor composed of the Hill coefficients and a stress-dependent scalar component. This implementation is tested under simple shear deformation, providing a framework for incorporating anisotropic viscosity into large-scale geodynamic simulations. Collectively, this research advances our understanding of how anisotropic viscosity influences olivine textures and mantle Dynamics and provides a computational methodology for integrating anisotropic viscosity into geodynamic models. The results emphasize the necessity of considering anisotropic viscosity in subduction zone modeling and offer new insights into the interpretation of seismic anisotropy in complex mantle flow environments.

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