MSAT: a new Matlab toolbox for the analysis and modelling of seismic anisotropy

<p>Poster presented at the 2011 Fall meeting of the AGU outlining MSAT, an open source Matlab toolbox designed to aid the analysis of seismic and elastic anisotropy.</p

Interpolation and Inversion – New Features in the Matlab Sesimic Anisotropy Toolbox

Poster presented at the 2015 AGU Fall Meeting (DI21A-2582)<br><br><b>Abstract<br><br></b>A key step in studies of seismic anisotropy in the mantle is often the creation of models designed to explain its physical origin. We previously released MSAT (the Matlab Seismic Anisotropy Toolbox), which includes a range of functions that can be used together to build these models and provide geological or geophysical insight given measurements of, for example, shear-wave splitting. Here we describe some of the new features of MSAT that will be included in a new release timed to coincide with the 2015 Fall Meeting.<p>A critical step in testing models of the origin of seismic anisotropy is the determination of the misfit between shear-wave splitting parameters predicted from a model and measured from seismic observations. Is a model that correctly reproduces the delay time "better" than a model that correctly reproduces the fast polarization? We have introduced several new methods that use both parameters to calculate the misfit in a meaningful way and these can be used as part of an inversion scheme in order to find a model that best matches measured shear wave splitting. Our preferred approach involves the creation, "splitting", and "unsplitting" of a test wavelet. A measure of the misfit is then provided by the normalized second eigenvalue of the covariance matrix of particle motion for the two wavelets in a way similar to that used to find splitting parameters from data. This can be used as part of an inverse scheme to find a model that can reproduce a set of shear-wave splitting observations.</p><p>A second challenge is the interpolation of elastic constants between two known points. Naive element-by-element interpolation can result in anomalous seismic velocities from the interpolated tensor. We introduce an interpolation technique involving both the orientation (defined in terms of the eigenvectors of the dilatational or Voigt stiffness tensor) and magnitude of the two end-member elastic tensors. This permits changes in symmetry between the end-members and removes anomalous intermediate velocity distributions.</p

Models of deformation and texture inheritance at the base of the mantle

<div>A poster presented at the 15th Symposium of the Study of the Earth's Deep Interior (SEDI 2016); 24-29th July, Nantes, France</div><div><b><br></b></div><div><b>Abstract</b></div><div><br></div><div>The profound changes in physical properties across the Earth’s core-mantle boundary makes this region key for the understanding of global-scale dynamics. As well as moderating any interaction between the metallic core and rocky mantle, the lowermost mantle also hosts the basal limb of mantle convection acting as a kind of inaccessible inverse lithosphere. In principle, knowledge of seismic anisotropy permits us to probe mantle flow in this region. However, in order to understand anisotropy in terms of flow, we need to know how the minerals present in the lowermost mantle deform and generate the textures that lead to bulk anisotropy. Previously, by combining predictions of mantle flow with the simulation of texture development in deforming post-perovskite aggregates, we have explored how different slip system activities give different predictions for the long-wavelength anisotropy in the lowermost mantle. By converting these results into models compatible with global scale radially anisotropic seismic tomography we have shown how different predictions correlate with tomographic inversions. We found that the most recent experimental indication of the active slip systems in post-perovksite, where dislocations gliding on (001) are most mobile, give predictions that were anti-correlated with results from tomography at long wavelengths. This means that it is difficult to explain the observed patterns of seismic anisotropy in the lowermost mantle as being due to the generation of lattice-preferred orientation in post-perovskite. A possible resolution to this difficulty is offered by experiments on analogues, which show that texture can be inherited during the perovskite to post-perovskite phase transition. Here we modify our previous approach to include this effect. This results in distributions of predicted seismic anisotropy that are in better agreement with tomography. In particular, we find that models where texture is generated by deformation of post-perovskite dominated by dislocations gliding on (001) followed by texture inheritance during the phase transition to perovskite driven by increasing temperature results in models that correlate with tomography at spherical harmonic degrees 1-5. In particular, texture inheritance in our models results in a better match to tomography in regions where the vertically polarised shear waves propagate more quickly than horizontally polarised shear waves.</div

Incorporating history dependence and texture in models of mantle convection

<p><strong>Poster presented at AGU Fall Meeting 2012</strong></p> <p>The solid state deformation processes permitting convection of Earth's rocky mantle necessarily lead to strong feedbacks between the deformation history and the instantaneous flow field. Mechanisms leading to the history dependence include the alignment of mineral grains with the attendant generation of elastic and rheological anisotropy, as well as processes operating at larger and smaller length scales including phase sepa- ration, grain size reduction, changes to the defect chemistry and dislocation multiplication and entanglement. Despite their sophistication, current models of mantle dynamics frequently ignore history dependent rheologies, and the feedback between deformation, grain size, crystal orientation, chemistry and viscosity. These processes have huge effects on viscosity: in the crust, they lead to the development of shear-zones and highly localised deformation, whilst, in the mantle, they are nearly always ignored. Here, we describe an approach intended to introduce the consequences of history dependence into models of whole-mantle convection. We make use of existing technology that exists in several convection codes: the ability to track markers, or particles, through the evolving flow field. Tracers have previously been used to track attributes such as the bulk chemical composition or trace element ratios. Our modifica- tion is to use this technology to track a description of the current state of the texture and microstructure (encompassing an orientation distribution function, grain size parameters and dislocation density) such that we can advance models of polycrystalline deformation for many particles alongside and in sync with models of mantle convection. Our current implementation (called Theia coupling TERRA to DRex) is designed to allow the seismic anisotropy of the upper mantle to be studied, but in future we aim to extend the approach to allow a direct feedback between the development and evolution of microstructure, and the rheology used to advance the model of mantle convection.</p> <p>Abstract number <strong>T33G-2741</strong>.</p

Can global or regional scale seismic anisotropy in D″

<p>Slides for an invited talk at the 2011 Australian Academy of Science Elizabeth and Frederick White Research Conference "<strong>Minerals at extreme conditions – Integrating theory and experiment</strong>".</p

D" anisotropy derived from models of mantle flow: Predictions of elasticity and comparisons with seismic observations

<p><strong>Slides for invited talk at AGU 2011 Fall Meeting.</strong></p> <p><strong><br>Abstract number DI32A-02: <br></strong>We have developed an integrated model of the development of elastic anisotropy in the lowermost mantle by assuming mantle flow and deformation leads to the development of a lattice preferred orientation in post-perovskite. This texture development is simulated by tracing particles through a range of plausible mantle flow fields derived from the joint inversion of body wave travel times and geodynamic observations. Strain histories for the particles are extracted from the particle paths and these are used as the boundary conditions for polycrystalline models of texture development based on the visco-plastic self-constant approach. The resulting models of elastic anisotropy have been compared to global and regional scale observations of seismic anisotropy attributed to post-perovskite in D". At one extreme, we reduce the modelled anisotropy to one displaying vertical transverse isotropy. This is incompatible with some splitting measurements from ScS and SKS phases but permits a direct comparison with the results of global scale anisotropic tomography using S-waves. In order to assess the extent of azimuthal anisotropy in D" we make use of a global database of S-wave splitting measurements. These are also compared to the models of elastic anisotropy and provide further constraints on the degree to which lattice preferred orientation can be the explanation for anisotropy in D". On the regional scale we make comparisons with recent multi-azimuthal measurements of ScS splitting where the source side and receiver side upper-mantle anisotropy has been measured and removed. These measurements offer the most rigorous test of our predictions for the anisotropy of the lowermost mantle but also lead to difficulties in describing the frequency dependent effect of rapidly varying elasticity on the simulated seismic waveforms. Key findings are that uncertainty in the flow model is relatively insignificant compared to the current uncertainty in the single crystal plasticity, which can lead to model results which are anti-correlated to each other. In models where post-perovskite deformation is accommodated by dislocations moving on (010) or (100), patterns of anisotropy are approximately correlated with the results of tomographic inversions. On the other hand, in models where dislocations move on (001) patterns of anisotropy are nearly anti-correlated with tomographic inversions. If all the seismic anisotropy extracted from global anisotropic inversions is due to the presence of a lattice preferred orientation in post-perovskite in the lowermost mantle, and if the results of the tomographic inversions are not strongly biased by the sampling geometries, these results suggest that deformation of post-perovskite in the lowermost mantle may be accommodated by dislocations moving on (010) or (100)</p

Simulating the seismic signal of phase transtions in the deepest mantle

<p><strong>Slides for invited talk at AGU 2013 Fall Meeting.</strong></p> <p><strong>Abstract number DI34A-02:</strong> The discovery of the perovskite to post­perovskite phase transition in (Mg,Fe)SiO3 explains many of the seismic observations of the lowermost mantle including the presence of multiple seismic discontinuities and significant seismic anisotropy. However, the explanations of many detailed features remain elusive. The recent discovery of a topotactic relationship between the orientation of perovskite and post­perovskite crystals in a partially transformed analogue opens the possibility of texture inheritance through the phase transition [1]. This effect must be captured in simulations designed to explain the seismic anisotropy of the lowermost mantle, especially those which link mantle dynamics with seismic observations.</p> <p><br>We have extended our previous work linking models of flow in the lowermost mantle with simulations of texture development and predictions of seismic anisotropy [2] in order to account for the topotaxy between perovskite and post­perovskite. In particular, we compare four cases: (1) As in [2], anisotropy is only generated in post­perovskite by dislocation mediated deformation dominated by one of a number of slip systems, phase transitions destroy texture and ferropericlase and perovskite dominated rocks are isotropic. (2) Although phase transitions destroy texture, ferropericlase and/or perovskite deform by dislocation motion permitting the generation of seismic anisotropy in warmer regions of the mantle where post­perovskite is unstable. We account for the possibility of the inversion of slip­system activities in ferropericlase at high pressure as suggested by models of dislocation motion based on atomic scale simulations [3]. (3) Allow texture development by dislocation motion in perovskite and post­perovskite and texture inheritance through phase transitions by the mechanism described in [1]. However, we assume that the bulk of the lower mantle deforms by a mechanism that does not lead to the development of texture and so begin the simulation from a random distribution of crystal orientations the first time the post­perovskite stability field is encountered for downward migrating packages of mantle material. (4) Allow the bulk of the lower mantle to deform by dislocation creep such that material entering the lowermost mantle for the first time is already textured, allow this texture to be inherited and further modified by strain and phase transitions.</p> <p><br>These calculations show clear differences in global and local scale elastic anisotropy in the lowermost mantle between cases where texture is allowed to persist through the phase transitions and those where it is not. On a global scale and when radial anisotropy is imposed<br>the inclusion of topotaxy results in a dramatic decrease in the strength of the degree two signal and better agreement between observations and the model for post­perovskite deformation where dislocations moving on (001) dominate. On a smaller scale we see potential signs of reflectors generated by a change in anisotropy between perovskite that has inherited a strong starting texture from post­perovskite and overlaying perovskite that has never undergone the phase transition. These observations suggest that the incorporation of texture inheritance will be an important feature of future models of anisotropy in the lowermost mantle.</p> <p><br>[1] Dobson et al. 2013 Nature Geosci. 6:575–578 [2] Walker et al. 2011 Geochem. Geophys. Geosys. 12:Q10006 [3] Cordier et al. 2012 Nature 481:177­180</p

Modelling the Tectonics of the Lowermost Mantle

<p>Poster outlining method for and recent results of texture modelling from flow in the lowermost mantle. Presented at a meeting in June 2013. Includes textures from the deformation of post-perovskite, perovskite and periclase as well as the possibility of texture inheritance (topotaxy) for retrograde post-perovskite to perovskite transition.</p

Anisotropy: A cause of heat flux variation at the CMB?

<p>Slide deck for talk at Goldschmidt 2013 (session 04b "Earth's Heat: Where, Why, Whence, and How Much?", Tuesday). Abstract: Walker A, Ammann M, Stackhouse S, Wookey J, Brodholt J & Dobson D (2013) Mineralogical Magazine, 77(5) 2438.</p