Small-Scale Mineralogical Heterogeneity from Variations in Phase Assemblages in the Transition Zone and D" Layer Predicted by Convection Modelling

Small-scale heterogeneity in the deep mantle is concentrated in the upper-mantle transition zone （TZ）, in the depth range 410-660 km and also at the bottom 250 km D＂ region. This encourages a more detailed investigation of the potential for seismic reflectivity imaging by modelling heterogeneous structures in mantle convection models including phase transitions of the TZ and D＂ regions. We applied finite elements with variable spacing near the boundary layers in 2-D cylindrical geometry that allow for sufficient spatial resolution. We investigated several models including an extended Boussinesq （EBA） model, focused on the D＂ region, and a compressible （ALA） model for the TZ region. The results for the D＂ region show typical lens-shaped structures of post-perovskite （PPV） embedded in the perovskite （PV） background mantle, where the thickness of the lenses, at 200-400 km, strongly depends on the Clapeyron slope of the PV-PPV transition. A second phase transition （double crossing） occurs in case the core temperature is higher than the intercept temperature Ti. Our phase-dependent rheology results in contrasting effective viscosity between PV and PPV. Our model results reveal a distinctly clear mechanical weakening of the PPV lenses with about an order of magnitude lower viscosity. The shear wave-speed distributions computed from our convection results are strongly correlated with the heterogeneous distribution of the mineral phase. Gradients in the seismic wave-speed that are the target of seismological reflectivity imaging are clearly revealed. The wave-speed results show a clear resolution of the top and bottom interfaces of the PPV lenses. Our ALA model for the TZ is based on a thermodynamical model for the magnesium end- member of an olivine-pyroxene mantle. The model predicts a much more complex distribution of mineral phases, compared to our D＂ results, in agreement with the greater number of mineral phases involved in the olivine-pyroxene phase diagram for the P, T conditions of the transition zone. Near cold downwelling flows representing subducting lithospheric slabs, where the local geotherm can differ by up to 1 000 K from the horizontal average, and small-scale lateral variations in the mineral phases can occur.

Frequency Extrapolation through Sparse Sums of Lorentzians

Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are as- signed： translation and scale. These parameters can be found by using a method for complex fre- quency detection in the frequency domain. This method is based on an alternating projection scheme between Hankel matrices and finite rank operators, and have the advantage that it can be done in weighted spaces. The weighted spaces can be used to partially revoke the effect of finite band-width filters. Apart from frequency extrapolation the method provides a way of estimating discontinuity locations.