Éditeur(s) : HAL CCSD Elsevier
Résumé : The dense hydrous magnesium silicate called the D phase is the most likely candidate to recycle hydrogen into the lower mantle in subduction zones. As seismology represents the preferred method to detect this mineral in subduction zones, the single crystal elastic tensor has been calculated using first principle methods. A triple cell (View the MathML source) was used to account for an ordered ideal composition of the D phase to lower mantle pressures. The elastic tensor of the mineral at ambient conditions is predicted to be C11 = 387.7, C33 = 287.7, C44 = 100.4, C12 = 108.0, C13 = 51.1, C14 = − 14.6 in GPa with bulk modulus at zero pressure Ko = 163 GPa and a statistical error of about 4.0 GPa for all constants. The pressure derivatives of the elastic constants have been determined to pressure of 80 GPa. Our tensor correctly predicts the published experimental measurements of linear compressibility along the a- and c-axes, the logarithmic pressure derivative of the c/a axial ratio and bulk modulus at zero pressure. It contradicts the experimentally measured elastic tensor reported by (Liu, L.-G., Okamoto, K., Yang, Y.-J., Chen, C.-C., Lin, C.-C., 2004. Elasticity of single-crystal phase D (a dense hydrous magnesium silicate) by Brillouin spectroscopy. Solid State Commun. 132, 517–520), which fails to reproduce the experimental compressibility data. Using the elastic constants and density predicted to 85 GPa, the seismic anisotropy of P- and S-waves has been calculated as a function of pressure. The single crystal has high P-wave velocities and shear wave splitting in the basal plane below 20 GPa. At high pressures, the maximum P-wave velocities have threefold symmetry normal to a-axes in the basal plane, whereas the maximum shear wave splitting is parallel to a-axes with twofold symmetry. The D phase has high Vp and Vs anisotropy at ambient pressure, 17.6% for Vp and 19.9% for Vs. The Vp anisotropy decreases with increasing pressure to about 30 GPa, while it remains constant at 8% from 30 to 85 GPa. The Vs anisotropy decreases to 17% at 20 GPa and then increases to 22% at 85 GPa. The isotropic velocity ratios of S to P (Rs/p), bulk sound to S (Rphi/s) and density to S (Rρ/s) are calculated as a function of pressure. The Rs/p shows very little variation with pressure with low value of 0.6, whereas both Rphi/s and Rρ/s increase with pressure to peak values of 2.8 and 2.0 respectively at about 60 GPa. The presence of the D phase in subducted horizontal ‘stagnant' plates in the circum Pacific could contribute to a number of seismic observations, such as the observed velocity heterogeneity at depths between 500 and 1000 km and the fast S-waves travelling horizontally with horizontal polarization in this depth range. Further the lower density of the D phase compared with anhydrous minerals could influence buoyancy of the hydrated ‘stagnant' slabs. The transformation of the D phase to perovskite plus ferripericlase during thermal annealing may be responsible for horizontal slab seismogenesis.
ISSN: 0012-821X

hal-00406379
https://hal.archives-ouvertes.fr/hal-00406379
DOI : 10.1016/j.epsl.2007.04.053

Éditeur(s) : HAL CCSD Oxford University Press (OUP): Policy F
Résumé : International audience
We discuss a property of distance-based measures that has not been addressed with regard to evaluating the geographic concentration of economic activities. The article focuses on the choice between a probability density function of point-pair distances or a cumulative function. We begin by introducing a new cumulative function, M, for evaluating the relative geographic concentration and the co-location of industries in a non-homogeneous spatial framework. Secondly, some rigorous comparisons are made with the leading probability density function of Duranton and Overman (2005), Kd. The merits of the simultaneous use of Kd and M is proved, underlining the complementary nature of the results they provide.
Journal of Economic Geography

hal-01094082
https://hal-agroparistech.archives-ouvertes.fr/hal-01094082
DOI : 10.1093/jeg/lbp056

Éditeur(s) : HAL CCSD Elsevier
Résumé : We have studied the phase transformation of forsterite to wadsleyite under shear stress at the Earth's transition zone pressure and temperature conditions. Two-step experiments were performed using a multi-anvil press. First, we hot pressed iron-free forsterite at 6 or 11 GPa and 1100 degrees C. Then we deformed a slab of this starting material using a direct simple shear assembly at 16 GPa and 1400 degrees C for 1, 15, 35, 40, or 60 min. Both the starting material and the deformed samples were characterized using optical and scanning electron microscopy including measurements of crystal preferred orientations (CPO) by electron back scattered diffraction (EBSD), transmission electron microscopy (TEM), and Fourier transform infrared spectroscopy (FTIR). The phase transformation occurs very rapidly, in less than 1 min, and metastable forsterite relics are not observed after deformation. The grain size of wadsleyite is slightly smaller than the forsterite starting material. The water contents obtained from FTIR analyses in forsterite and wadsleyite are 65-124 wt ppm H2O and 114-736 wt ppm H2O, respectively, which are well below water solubility at similar conditions in the presence of free water. Wadsleyite aggregates display weak CPO patterns with [1 0 0] axes concentrated at low angle to the shear direction, [0 1 0] axes perpendicular to the shear plane and nearly random [0 0 1] axes. Only a few dislocations were observed in wadsleyite with TEM. This observation is consistent with the assumption that most dislocations formed during the initial high-stress stages of these stress-relaxation experiments, were consumed in the phase transformation, probably enhancing the transformation rate. CPO patterns vary as a function of the water content: with increasing water content the density of [1 0 0] axes parallel to the shear direction decreases, and the density of [0 0 1] axes increases. Viscoplastic self-consistent modeling of CPO evolution using previously reported glide systems for wadsleyite, i.e., [1 0 0]{0 k 1} and 1/2 (1 1 1){1 0 1}, cannot reproduce the measured CPO, unless the [0 0 1](0 1 0) system, for which dislocations have not been observed by TEM, is also activated. In addition, wadsleyite grain growth suggests the participation of diffusion-assisted processes in deformation. Calculated anisotropies for P and S-waves using measured CPO are always below 1%. This very low anisotropy is due to both the low finite strain achieved in the experiments, which leads to weak wadsleyite CPO, and to the diluting effect of added majorite. The present experiments emphasize the importance of stress, grain size evolution and water content in the forsterite to wadsleyite phase transformation and subsequent deformation in the transition zone.
ISSN: 0031-9201

hal-00617430
https://hal.archives-ouvertes.fr/hal-00617430
DOI : 10.1016/j.pepi.2010.11.001

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : International audience
Anisotropy of low-field magnetic susceptibility (AMS) of basaltic lava flows can give some clues about post-emplacement tilting occurring in volcanic sequences. Such a study has been carried out on a sequence of 19 successive lava flows from Kerguelen Archipelago. Surprisingly, two different patterns were observed. The first one - herein called normal fabric - is consistent with the lava-flow direction inferred from geological observations, whereas the second one observed for about 70 per cent of the analysed samples - herein called abnormal fabric - appears to be unrelated to the shear history of the lava flows during their emplacements. These abnormal fabrics are not strictly inverse fabric but seem to have a more complex origin. The unusual nature of these abnormal fabrics has been confirmed by lattice preferred orientation of plagioclases obtained from high-resolution electron backscattered diffraction measurements. The aim of this study is to propose a physical interpretation of these fabrics. A first step in our understanding was to clearly identify the nature and the magnetic properties of the Fe-Ti oxides assemblage. Thus, we present a comprehensive rock magnetic analysis relying on low- and high-temperature thermomagnetic curves (K-T), crossover diagrams, first-order reversal curves, ore-microscopy, Mössbauer measurements and electron backscattered images. We found that in the present case the abnormal fabrics are probably linked to a mixture of prevailing single domain (SD) strongly interacting grains population and a subsidiary multidomain grains population. SD grains are identified as small magnetite crystallized within the interstitial glass in globular aggregates along the silicate framework. Then a question arises: to what extent such SD interacting grains in globular aggregates can affect the magnetic susceptibility and its anisotropy? To answer this question, we developed a physical model in which the total energy density of an SD grain with an uniaxial anisotropy is minimized. In this model, the distribution function of the direction of the magnetic interaction field is comprised between two boundary states. It is either isotropic, which formally corresponds to the thermal demagnetized state, or it is ordered, which formally corresponds to the Alternative Field demagnetized state. We show that in both cases the degree of anisotropy decreases as the interaction field increases. Thus, we conclude that the abnormal fabric encountered in this study can be simply explained by strong magnetostatic interactions that would explain the large scattering of AMS often observed in basaltic lava flows.
ISSN: 0956-540X

hal-00716449
https://hal.archives-ouvertes.fr/hal-00716449
https://hal.archives-ouvertes.fr/hal-00716449/document
https://hal.archives-ouvertes.fr/hal-00716449/file/gji-S-12-HAL.pdf
DOI : 10.1111/J.1365-246X.2012.05421.X

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
We predict the IR-TO, IR-LO and Raman modes (wave numbers and intensities) of magnesite (MgCO3) up to 50 GPa, at T = 0 K, using the density-functional perturbation theory up to a third order perturbation, under the harmonic assumption. The predicted IR-TO and Raman mode wave numbers, the mode Grüneisen parameters and the Davydov splittings are systematically compared with experimental data for all modes up to the pressures of 10-30 GPa and for some modes up to 50 GPa. Existing experiments allow extending this comparison only to IR-LO wave numbers of the E u (ν3) asymmetric-stretch mode, confirming the odd experimental behavior of this mode at very high pressures. Predicted IR-TO, IR-LO and Raman intensities up to 50 GPa are just tabulated, but data are missing for their comparison with precise experiments. However, the generally good agreement observed between numerical results and experimental data, when their comparison is possible, suggests that first-principles methods are a major help to predict the entire spectrum up to very high pressures.
ISSN: 0342-1791

hal-00527834
https://hal.archives-ouvertes.fr/hal-00527834
DOI : 10.1007/s00269-010-0395-y