Equation of state of hexagonal aluminous phase in basaltic composition to 63 GPa at 300 K

A laser-heated diamond-anvil cell that is capable of operating up to a pressure of 63 GPa, with X-ray diffraction facilities using a synchrotron radiation source at the SPring-8, has been developed to observe the compressibility of a hexagonal aluminous phase, [K_0.15Na_1.66Ca_0.11Mg_1.29Fe²⁺ _0.86Al_3.13Ti_0.09Si_1.98] _Σ9.27O₁₂. The hexagonal aluminous phase is a potassium host mineral from the subducted oceanic crust in the Earth's lower mantle. A sample was heated using a YAG laser at each pressure increment to relax the deviatoric stress in the sample. X-ray diffraction measurements were carried out at 300 K using an angle-dispersive technique. Pressure was measured using an internal platinum pressure calibrant. The observed unit-cell volumes were used to obtain a third-order Birch–Murnaghan equation of state: unit-cell volume V _o=185.94(±16) ų, density ρ _o=4.145 g/cm³, and bulk modulus K _o=198(±3) GPa when the first pressure is derivative of the bulk modulus K ^′ _o is fixed to 4. The density of hexagonal aluminous phase is lower than that of coexisting Mg-perovskite in the subducted oceanic crust.     

Ab initio elasticity of FeS2 pyrite from 0 to 135 GPa

Polynomial expressions for the elastic tensor coefficients, the bulk, the shear and Young’s moduli, the speed of sound for longitudinal and transverse waves, the equation of state and the x coordinate of the sulfur atom in pyrite are reported based on ab initio calculations in the range of 0–135 GPa. Comparison with published experimental data indicates good agreement for the equation of state and for values at 0 GPa as well as reasonable agreement for first derivatives. All modeling and interpretation was performed with Materials Toolkit v.2.0 and all ab initio computations with VASP.     

Compressibility of the calcium aluminosilicate, CAS, phase to 44 GPa

In situ X-ray diffraction measurements on a calcium aluminosilicate (CAS) phase have been carried out using a laser-heated diamond anvil cell up to a pressure of 44 GPa, employing a synchrotron radiation source. CAS is the major mineral formed from sediments subducted into the Earth's mantle. The sample was heated using a YAG laser after each pressure increment to relax the deviatoric stress in the sample. X-ray diffraction measurements were carried out at T = 300 K using an angle-dispersive technique. The pressure was calculated using an internal platinum metal pressure calibrant. The Birch–Murnaghan equation of state for the CAS phase obtained from the experimental unit cell parameters showed a density of ρ₀ = 3.888 g/cm³ and a bulk modulus of K₀ = 229 ± 9 GPa for K^′₀ = 4.7 ± 0.7. When the first pressure derivative of the bulk modulus was fixed at K^′₀ = 4, then the value of K₀ = 239 ± 2 GPa. From the experimental compressibility, the density of the CAS phase was observed to be lower than the density of co-existing Al-bearing stishovite, calcium perovskite, calcium ferrite-type phases, and (Fe,Al)-bearing Mg-perovskite in subducted sediments in the lower mantle. Therefore, the density of subducted sediments in the lower mantle decreases with increasing mineral proportion of the CAS phase.     

用Radon变换建立曲界面及其边界线方程

本文由接收到的一次反射纵波和横波的震相,利用Radon 变换理论和数学技巧,反演均匀各向同性的三维半无限介质中的曲界面及其边界曲线的方程。本文有一定实际背景,是理论性论文。     

Flue gas and pure CO2 sorption properties of coal: A comparative study

Presently many research projects focus on the reduction of anthropogenic CO₂ emissions. It is intended to apply underground storage techniques such as flue gas injection in unminable coal seams. In this context, an experimental study has been performed on the adsorption of pure CO₂ and preferential sorption behavior of flue gas. A coal sample from the Silesian Basin in Poland (0.68% V Rr), measured in the dry and wet state at 353 K has been chosen for this approach. The flue gas used was a custom class industrial flue gas with 10.9% of CO₂, 0.01% of CO, 9% of H₂, 3.01% of CH₄, 3.0% of O₂, 0.106% of SO₂ and nitrogen as balance.Adsorption isotherms of CO₂ and flue gas were measured upto a maximum of 11 MPa using a volumetric method. Total excess sorption capacities for CO₂ on dry and wet Silesia coal ranged between 1.9 and 1.3 mmol/g, respectively. Flue gas sorption capacities on dry and wet Silesia coal were much lower and ranged between 0.45 and 0.2 mmol/g, respectively, at pressures of 8 MPa. The low sorption capacity of wet coal has resulted from water occupying some of the more active adsorption sites and hence reducing the heterogeneity of adsorption sites relative to that of dry coal. Desorption tests with flue gas were conducted to study the degree of preferential sorption of the individual components. These experiments indicate that CO₂ is by far the prefered sorbing component under both wet and dry conditions. This is followed by CH₄. N₂ adsorbs very little on the coal in the presence of CO₂ and CH₄. It is also observed that the adsorption of CO₂ onto coal is not significantly hindered by the addition of other gases, other than dilution effect of the pressure.In addition to the sorption experiments, the density of the flue gas mixture has been determined up to 18 MPa at 318 K. A very good precision of these measurements were documented by volumetric methods.     

THE INVERSE PROBLEM OF KLEIN-GORDON EQUATION BOUNDARY VALUE PROBLEM AND ITS APPLICATION IN DATA ASSIMILATION

Since the solution of elliptic partial differential equations continuously depends on the boundary condition, the Euler equation derived from variational method cannot be solved without boundary condition. It is often difficult to provide the exact boundary condition in the practical use of variational method. However, in some application problems such as the remote sensing data assimilation, the values can be easily obtained in the inner region of the domain. In this paper, the boundary condition is tried to be retrieved by using part solutions in the inner area. Firstly, the variational problem of remote sensing data assimilation within a circular area is established. The Klein-Gordon elliptic equation is derived from the Euler method of variational problems with assumed boundary condition. Secondly, a computer-friendly Green function is constructed for the Dirichlet problem of two-dimensional Klein-Gordon equation, with the formal solution according to Green formula. Thirdly, boundary values are retrieved by solving the optimal problem which is constructed according to the best approximation between formal solutions and high-accuracy measurements in the interior of the domain. Finally, the assimilation problem is solved on substituting the retrieved boundary values into the Klein-Gordon equation. It is a type of inverse problem in mathematics. The advantage of this method lies in that it overcomes the inherent instability of the inverse problem of Fredholm integral equation and alleviates the error introduced by artificial boundary condition in data fusion using variational method in the past.     

Hydrostatic compression of galenobismutite (PbBi<Subscript>2</Subscript>S<Subscript>4</Subscript>): elastic properties and high-pressure crystal chemistry

A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F₀| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V ₀ = 700.6(2) ų, K ₀ = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe₂O₄ (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi₂S₄ attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.     

Post-stack impedance blocky inversion based on analytic solution of viscous acoustic wave equation

The conventional impedance inversion method ignores the attenuation effect, transmission loss and inter-layer multiple waves; the smooth-like regularization approach makes the corresponding impedance solution excessively smooth. Both fundamentally limit the resolution of impedance result and lead to the inadequate ability of boundary characterization. Therefore, a post-stack impedance blocky inversion method based on the analytic solution of viscous acoustic equation is proposed. Based on the derived recursive formula of reflections, the 1D viscous acoustic wave equation is solved analytically to obtain zero-offset full-wave field response. Applying chain rule, the analytical expression of the Fréchet derivative is derived for gradient-descent non-linear inversion. Combined with smooth constraints, the blocky constraints can be introduced into the Bayesian inference framework to obtain stable and well-defined inversion results. According to the above theory, we firstly use model data to analyse the influence of incompleteness of forward method on seismic response, and further verify the effectiveness of the proposed method. Then the Q-value sensitivity analysis of seismic trace is carried out to reduce the difficulty of Q-value estimation. Finally, the real data from Lower Congo Basin in West Africa indicate that the proposed approach provide the high-resolution and well-defined impedance result. As a supplement and development of linear impedance inversion method, the non-linear viscous inversion could recover more realistic and reliable impedance profiles.     

基于结构方程模型的中国县域人口老龄化影响机制

利用2000年和2010年分县人口普查数据,分析中国县域人口老龄化的空间格局及变化,采用结构方程模型拟合人口老龄化影响因子之间的路径关系,探讨中国县域人口老龄化的影响机制。结果表明:内蒙古包头至云南腾冲是中国县域人口老龄化较为清晰的空间分界线,其东南部老龄化高值县区连片集中,低值县区夹杂其间;西北全域老龄化率普遍较低,仅在北缘横亘一条中值县区连绵带。结构方程模型的拟合结果很好地解释了中国县域人口老龄化空间差异的影响机制。迁移率、预期寿命和生育率是人口老龄化进程的内生因素,其中,预期寿命对县域人口老龄化有正向效应,迁移率和生育率则对县域人口老龄化有负向效应。社会经济、家庭状况和自然环境等因素是人口老龄化进程的外生因素,对中国县域人口老龄化有显著的直接和间接效应。收入增加、社会发展、居住条件改善以及环境舒适性提高等推高县域人口老龄化水平,城镇化水平提高则降低县域人口老龄化水平。     

P-V-T equation of state of lawsonite

A pressure-volume-temperature data set has been obtained for lawsonite [CaAl₂Si₂O₇(OH)₂.H₂O], using synchrotron X-ray diffraction and an externally heated diamond anvil cell. Unit-cell volumes were measured to 9.4 GPa and 767 K by angle dispersive X-ray diffraction using imaging plates. Phase changes were not observed within this pressure-temperature range, and lawsonite compressed almost isotropically at constant temperature. The P-V-T data have been analyzed using a Birch- Murnaghan equation of state and a linear equation of state expressed as β=–1/V₀ (∂V/∂P) _T . At room temperature, the derived equation of state parameters are: K ₀=124.1 (18) GPa K'₀ set to 4) and β^–1=142.0(24) GPa, respectively. Our results are intermediate between previously reported measurements. The high-temperature data show that the incompressibility of lawsonite decreases with increasing temperature to ∼500 K and then increases above. Hence, the second order temperature derivative of the bulk modulus is taken into account in the equation of state; a fit of the volume data yields K ₀=123.9(18) GPa, (∂K/∂T)_P=–0.111(3) GPa K^–1, (∂² K/∂T ²)_P=0.28(6) 10^–3 GPa K^–2, α₀=3.1(2) 10^–5 K^–1, assuming K'₀=4. Received: 2 June 1998 / Revised, accepted: 12 Ocotber 1998