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1.
The thermodynamic properties of the lower mantle are determined from the seismic profile, where the primary thermodynamic variables are the bulk modulus K and density ρ. It is shown that the Bullen law (K ∝ P) holds in the lower mantle with a high correlation coefficient for the seismic parametric Earth model (PEM). Using this law produces no ambiguity or trade-off between ρ0 and K0, since both K0 and K′0 are exactly determined by applying a linear K?ρ relationship to the data. On the other hand, extrapolating the velocity data to zero pressure using a Birch-Murnaghan equation of state (EOS) results in an ambiguous answer because there are three unknown adjustable parameters (ρ0, K0, K′0) in the EOS.From the PEM data, K = 232.4 + 3.19 P (GPa). The PEM yields a hot uncompressed density of 3.999 ± 0.0026 g cm?3 for material decompressed from all parts of the lower mantle. Even if the hot uncompressed density were uniform for all depths in the lower mantle, the cold uncompressed mantle would be inhomogeneous because the decompression given by the Bullen law crosses isotherms; for example, the temperature is different at different depths. To calculate the density distribution correctly, an isothermal EOS must be used along an isotherm, and temperature corrections must be placed in the thermal pressure PTH.The thermodynamic parameters of the lower mantle are found by iteration. Values of the three uncompressed anharmonic parameters are first arbitrarily selected: α0 (hot), the coefficient of thermal expansion; γ0, the Grüneisen parameter; and δ, the second Grüneisen parameter. Using γ0 and the measured ρ0 (hot) and K0 (hot), the values of θ0 (Debye temperature) and q = dlnγ/dlnρ are found from the measured seismic velocities. Then from (αKT)0 and q the thermal pressure PTH at all high temperatures is found. Correlating PTH against T to the geotherm for the lower mantle, PTH is found at all depths Z. The isothermal pressure, along the 0 K isotherm, at every Z is found by subtracting PTH from the measured P given by the seismic model. Using the isothermal pressure at depth Z, the solution for the cold uncompressed density ρ0C and the cold uncompressed bulk modulus, KT0 is found as a trace in the KT0?ρ0C plane. A narrow band of solutions is then found for ρ0C and KT0 at all depths.The thermal expansion at all T is found from [ρ0C ? ρ0 (hot)/ρ0C. From Suzuki's formula, the best fit to the thermal expansion determines γ0 and α0 (hot). When the values of these two parameters do not agree with the original assumptions, the calculation is repeated until they do agree. In this way all the important thermodynamic parameters are found as a self-consistent set subject only to the assumptions behind the equations used. 相似文献
2.
Kyu Han Kim Keisuke Nagao Hirochika Sumino Tsuyoshi Tanaka Takamasa Hayashi Toshio Nakamura Jong Ik Lee 《Chemical Geology》2008,253(3-4):180-195
We report analyses of noble gases and Nd–Sr isotopes in mineral separates and whole rocks of late Pleistocene (< 0.2 Ma) monzonites from Ulleungdo, South Korea, a volcanic island within the back arc basin of the Japan island arc. A Rb–Sr mineral isochron age for the monzonites is 0.12 ± 0.01 Ma. K–Ar biotite ages from the same samples gave relatively concordant ages of 0.19 ± 0.01and 0.22 ± 0.01 Ma. 40Ar/39Ar yields a similar age of 0.29 ± 0.09 Ma. Geochemical characteristics of the felsic plutonic rocks, which are silica oversaturated alkali felsic rocks (av., 12.5 wt% in K2O + Na2O), are similar to those of 30 alkali volcanics from Ulleungdo in terms of concentrations of major, trace and REE elements. The initial Nd–Sr isotopic ratios of the monzonites (87Sr/86Sr = 0.70454–0.71264, 143Nd/144Nd = 0.512528–0.512577) are comparable with those of the alkali volcanics (87Sr/86Sr = 0.70466–0.70892, 143Nd/144Nd = 0.512521–0.512615) erupted in Stage 3 of Ulleungdo volcanism (0.24–0.47 Ma). The high initial 87Sr/86Sr values of the monzonites imply that seawater and crustally contaminated pre-existing trachytes may have been melted or assimilated during differentiation of the alkali basaltic magma.A mantle helium component (3He/4He ratio of up to 6.5 RA) associated with excess argon was found in the monzonites. Feldspar and biotite have preferentially lost helium during slow cooling at depth and/or during their transportation to the surface in a hot host magma. The source magma noble gas isotopic features are well preserved in fluid inclusions in hornblende, and indicate that the magma may be directly derived from subcontinental lithospheric mantle metasomatized by an ancient subduction process, or may have formed as a mixture of MORB-like mantle and crustal components. The radiometric ages, geochemical and Nd–Sr isotopic signatures of the Ulleungdo monzonites as well as the presence of mantle-derived helium and argon, suggests that these felsic plutonic rocks evolved from alkali basaltic magma that formed by partial melting of subcontinental lithospheric mantle beneath the back arc basin located along the active continental margin of the southeastern part of the Eurasian plate. 相似文献
3.
Vladislav Babuška Jiří Fiala Mineo Kumazawa Ichiro Ohno Yoshio Sumino 《Physics of the Earth and Planetary Interiors》1978,16(2):157-176
The elastic constants of sixteen garnet specimens of wide variety in chemical composition are accurately determined by means of the rectangular parallelpiped resonance method. The dependence of the elastic properties on chemical composition is analyzed using the present data and those for seven garnets investigated by other authors. The property Xi of a garnet solid solution i is given by a linear addition law in terms of the mole fraction nij of component j; Xi = ΣnijXj where the Xj's are the properties of the end-members j (j = pyrope, almandine, spessartine, grossular and andradite). The Xj's are determined for density ρ, bulk modulus K, and shear moduli Cs = (C11 ? C12)/2 and C44. No systematic deviation is observed from the linear addition law for the elastic moduli nor for other quantities such as the elastic wave velocities. The extrapolated elastic moduli (Mbar) of the end-members are:
Almandine | Pyrope | Spessartine | Grossular | Andradite | |
1.779 ± 0.008 | 1.730 ± 0.009 | 1.742 ± 0.009 | 1.691 ± 0.008 | 1.379 ± 0.017 | |
0.981 ± 0.004 | 0.925 ± 0.004 | 0.964 ± 0.004 | 1.106 ± 0.004 | 0.979 ± 0.007 | |
0.958 ± 0.005 | 0.919 ± 0.005 | 0.937 ± 0.005 | 1.017 ± 0.006 | 0.827 ± 0.010 |