Deformation of peridotite caused by mantle flow beneath an oceanic spreading centre can result in the development of seismic anisotropy. Traveltime anomalies and shearwave splitting will develop as seismic energy propagates through such an anisotropic region, thus providing a signature of the deformation field at depth. In this study we investigate the nature of deformation associated with mantle upwelling for two models of flow in the upper 100 km of the mantle. The finite-strain fields of the passive upwelling model versus the buoyancy-enhanced upwelling model are quite different. This suggests that mineral aggregates deform differently in the two models, thus developing seismic signatures that are distinguishable. Numerical estimates of the corresponding mineral textures are made using polycrystal theory for olivine with four operative slip systems. The activation of a slip system is determined for each grain on the basis of the local critical resolved shear stress. The computed grain deformation reflects a balance between stress equilibrium, for the aggregate as a whole, and strain continuity between neighbouring grains within the aggregate. This approach enables a direct link to be made between the model flow fields and the resulting texture development. Given these mineral orientation distributions, elastic parameters are calculated and wavefronts are propagated through the anisotropic structure. Traveltimes for teleseismic body waves are computed using ray theory, and amplitudes are estimated for an across-axis profile extending 100 km from the ridge axis. Relative P-wave residuals of up to 1 s are predicted for the buoyant model with on-axis arrivals being earliest, since near-vertical velocities are fastest beneath the axis. On-axis P-wave arrivals for the passive model are half a second earlier than arrivals 60 km off-axis, and relative delays continue to increase slowly as distance from the ridge increases. S-wave splitting of almost a second is predicted for the buoyant model, whereas less than a half-second of splitting is determined for the passive model.

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An optimization-based method for pole-figure (PF) inversion that utilizes the orientation distribution function (ODF) gradient for conditional control of the solution is presented. The novel PF inversion method, coined the hybrid H 1seminorm minimization (HHSM), is empirically shown to be versatile, general and robust in the presence of simulated experimental errors. Finite elements (FE) and Rodrigues space are used for the representation and parameterization of the orientation space throughout. The versatility of the FE representation is significantly enhanced from previous implementations by introducing a method for obtaining discrete approximations to spherical harmonic modes from the local FE basis functions. A comparative study with similar implementations of the basic WIMV algorithm and the maximum entropy method is undertaken using several model ODFs of varying sharpness and symmetry. Randomly distributed noise is added to the synthetic PFs to simulate experimental errors and assess the stability of each method. Solution consistency is assessed by inverting two sets of measured PFs, one complete, one incomplete, using several meshes on the orientation space with an increasing number of degrees of freedom. The HHSM method is shown to compare favorably in tests with both the WIMV method and the maximum entropy method. research papers 698 Joel V. Bernier et al. Pole-figure inversion method

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.