Transient and steady-state creep of pure forsterite at low stress     

W.B. Durham  C. Froidevaux  O. Jaoul 《Physics of the Earth and Planetary Interiors》1979,19(3):263-274

Thirty-one single crystals of synthetic forsterite, Fo₁₀₀, were deformed in 69 compressional creep tests in a 0.1-MPa confining atmosphere of H₂ + Ar. Temperature ranged from 1753 to 2023 K and stress σ (= σ₁ - σ₃) from 1.5 to 37.8 MPa. Steady-state creep under these conditions follows an empirical law of the form: strain rate $\text{?}\text{?}\text{= A}{}_{\mathrm{zigma;}}{}^{\mathrm{n}}\text{exp}\text{(}\text{?Q}\text{RT}\text{)}$ where A, n, and Q are constants. General characteristics of Fo₁₀₀ creep — uniformity of strain, shape change as a function of orientation of σ, relative deformation resistance of different orientations — match those of natural olivine single crystals of composition Fo₉₂. Specific constants in the flow law, however, are distinctly new: for σ oriented along [111]_c (equidistant from the three principal crystallographic axes), values for Fo₁₀₀ are n = 2.9 ± 0.2 and Q = 0.67 ± 0.03 MJ/mol (160 ± 7 kcal/mol). A single law covers the range 3 < σ < 30 MPa and 1753 < T < 1953 K. Steady-state deformation is preceded by a transient period of strain softening. High strain rates at σ ? 10 MPa render the transient barely resolvable; it apparently displaces the steady-state flow law by approximately ?0.5% in strain. At σ ? 7.8 MPa, the amount of strain imparted to a sample of the [101]_c orientation is typically <0.1% after one hour.  相似文献   

General relationships among sound speeds: II. Theory and discussion     

T.J. Shankland  D.H. Chung 《Physics of the Earth and Planetary Interiors》1974,8(2):121-129

The dependence of bulk sound speed V_φ upon mean atomic weight $\text{m}$ and density ρ can be expressed in a single equation: Here B is an empirically determined “universal” parameter equal to 1.42, $\text{m}{}_0\text{= 20.2}$, a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to $\text{γ ?}\text{1}\text{3}$ where γ is a Grüneisen parameter. The constant c = (? ln V_M/? ln $\text{m}\text{)}{}_{\mathrm{X}}$, where V_M is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use c_Fe = 0.14 for Fe²⁺Mg²⁺ and GeSi substitutions and c_Ca ? 1.3 for CaMg substitutional series. With these values it is pos to deduce from the above equation Birch's law, its modifications introduced by Simmons to account for Ca-bearing minerals, variations in the seismic equation of state observed by D.L. Anderson, and the apparent proportionality of bulk modulus K to V_M^?4.  相似文献   

Tides and mixing in the northwestern East China Sea,Part II: Near-bottom turbulence   总被引：1，自引：0，他引：1  

Iossif Lozovatsky  Zhiyu Liu  Hao Wei  H.J.S. Fernando 《Continental Shelf Research》2008

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Interionic repulsive force and compressibility of ions     

Yoshiaki Ida 《Physics of the Earth and Planetary Interiors》1976,13(2):97-104

The compressibility of an individual ion is examined, in comparison with a known set of data for the alkali halides. A simple extrapolation of ionic radius to high pressure is not acceptable, because the pressure derivative of ionic radius changes for different salts. According to the classical concept of an elastic ion, the repulsive potential energy between the ions i and j is specified by the nature of each ion as: as a function of the interionic distance r. In this expression, q_i and ρ_i are the ionic radius and ionic compressibility, respectively, in a suitably modified meaning. Such a form of the repulsive potential fits well to the data of lattice constants and bulk moduli. The parameters q_i and ρ_i are evaluated for alkali and halogen ions, and an anion turns out to be much more compressible than a cation. The present treatment may be usefully applied to the minerals in the Earth's mantle, which contain only a few major ions.  相似文献   

Orthogonality of spherical harmonic coefficients     

Malcolm G. McLeod 《Physics of the Earth and Planetary Interiors》1980,23(2):P1-P4

An essentially arbitrary function V(θ, λ) defined on the surface of a sphere can be expressed in terms of spherical harmonics $\text{V(θ, Λ) = a}\text{∑}\text{n=1}\text{∞}\text{∑}\text{m=0}\text{n}\text{p}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{(cos θ) (g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{cos mΛ + h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{sin mΛ)}$ where the P_n^m are the seminormalized associated Legendre polynomials used in geomagnetism, normalized so that $\text{〈[P}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{(cos θ) cos mΛ]〉}{}^2\text{=1/}\text{(2n+1)}$ The angular brackets denote an average over the sphere. The class of functions V(θ, λ) under consideration is that normally of interest in physics and engineering. If we consider an ensemble of all possible orientations of our coordinate system relative to the sphere, then the coefficients g_n^m and h_n^m will be functions of the particular coordinate system orientation, but $\text{〈:(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{〉) = 〈(h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{=}\text{S}{}_{\mathrm{n}}\text{/}\text{(2n=1)}$ where $\text{S}{}_{\mathrm{n}}\text{=}\text{∑}\text{m=0}\text{n}\text{[(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{+ (h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{]}$ for any orientation of the coordinate system (S_n is invariant under rotation of the coordinate system). The averages are over all orientations of the system relative to the sphere. It is also shown that 〈g^m_ng^l_p〉 = 〈h^m_nh^l_p〉 = 0 for l ≠ m or p ≠ n and 〈g^m_nh^l_p〉 = 0 fro all n, m, p, l.  相似文献   

A coupled lattice Boltzmann model for advection and anisotropic dispersion problem in shallow water     

Yineng Li  Ping Huang   《Advances in water resources》2008,31(12):1719-1730

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Using dispersivity values to quantify the effects of pore-scale flow focusing on enhanced reaction along a transverse mixing zone     

Thomas Willingham  Changyong Zhang  Charles J. Werth  Albert J. Valocchi  Mart Oostrom  Thomas W. Wietsma 《Advances in water resources》2010

A key challenge for predictive modeling of transverse mixing and reaction of solutes in groundwater is to determine values of transverse dispersivity (_αT)$({\alpha }_T)$ in heterogeneous flow fields that accurately describe mixing and reaction at the pore scale. We evaluated the effects of flow focusing in high permeability zones on mixing enhancement using experimental micromodel flow cells and pore-scale lattice-Boltzmann-finite-volume model (LB-FVM) simulations. Micromodel results were directly compared to LB-FVM simulations using two different pore structures, and excellent agreement was obtained. Six different flow focusing pore structures were then systematically tested using LB-FVM, and both analytical solutions and a two-dimensional (2D) continuum-scale model were used to fit _αT${\alpha }_T$ values to pore-scale results. Pore-scale results indicate that the overall rate of mixing-limited reaction increased by up to 40% when flow focusing occurred, and it was greater in pore structures with longer flow focusing regions and greater porosity contrast. For each pore structure, _αT${\alpha }_T$ values from analytical solutions of transverse concentration profiles or total product at a given longitudinal location showed good agreement for nonreactive and reactive solutes, and values determined in flow focusing zones were always smaller than those downgradient after the flow focusing zone. Transverse dispersivity values from the 2D continuum model were between values within and downgradient from the flow focusing zone determined from analytical solutions. Also, total product and transverse concentration profiles along the entire pore structure from the 2D continuum model matched pore scale results. These results indicate that accurate quantification of pore-scale flow focusing with transverse dispersion coefficients is possible only when the entire flow and concentration fields are considered.  相似文献   

Variation of the magnetic properties in a basaltic dyke with concentric cooling zones     

B.M Smith  M Prévot 《Physics of the Earth and Planetary Interiors》1977,14(2):120-136

The effects of the variation of magnetic grain size on the magnetic properties of rocks have been studied throughout a reversely magnetized basaltic dyke with concentric cooling zones.Except in a few tachylites in which the magnetic mineral is a Ti-rich titanomagnetite, in the bulk of the dyke the magnetization is carried by almost pure magnetite grains. Although the percentage p of these magnetic oxides varies slightly, the large changes in the various magnetic parameters observed across the dyke are essentially attributable to large variations in the grain size of the magnetic particles.From the outer scoria region, where the magnetic grains are a mixture of single-domain (SD) and superparamagnetic (SP) grains, to the tachylite zone with finely crystallized basaltic glass containing interacting elongated SD particles, one observes an increase of both the ratio of the saturation remanent magnetization and the saturation induced magnetization J_rs/J_is, the bulk coercive force H_c, the median destructive field MDF, the intensity of the remanent magnetization J_r, and the Koenigsberger ratio Q. In the tachylites these parameters reach unusually high values, for subaerial basalts: These parameters decrease in the basalt toward the centre of the dyke where pseudo-single-domain (pseudo-SD) particles coexist together with multidomain (MD) grains. The susceptibility remains approximately constant from the inner basalt to the tachylite, but increases in the scoria up to values 10 times higher owing to the presence of SP particles. The magnetic viscosity increases also drastically toward the margin of the dyke due to an increase of the fraction of the SD particles just above the superparamagnetic threshold.  相似文献   

Effect of oxygen partial pressure on the dislocation recovery in olivine: a new constraint on creep mechanisms     

Shun-ichiro Karato  Hiroki Sato 《Physics of the Earth and Planetary Interiors》1982,28(4):312-319

The dislocation annihilation rate in experimentally deformed olivine single crystals was measured as a function of oxygen partial pressure (P_O2). It was shown that the dislocation annihilation rate decreased with increasing P_O2. This result is inconsistent with the reported P_O2 dependence of creep rate () in single olivine crystals, thus indicating that the creep in single olivine crystals is not rate-controlled by recovery, under the experimentally investigated conditions.  相似文献   

Anisotropic effective medium solutions of head and velocity variance to quantify flow connectivity     

C.C. Frippiat  T.H. Illangasekare  G.A. Zyvoloski 《Advances in water resources》2009

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Spatial power spectra of the crustal geomagnetic field and core geomagnetic field     

Malcolm G. McLeod  Paul J. Coleman 《Physics of the Earth and Planetary Interiors》1980,23(2):P5-P19

Lowes (1966, 1974) has introduced the function R_n defined by $\text{R}{}^{\mathrm{n}}\text{=(n + 1)}\text{∑}\text{m=0}\text{∞}\text{[(g}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{+ (h}{}^{\mathrm{m}}{}_{\mathrm{n}}\text{)}{}^2\text{]}\text{where}\text{g}{}_{\mathrm{n}}{}^{\mathrm{m}}\text{and}\text{h}{}_{\mathrm{n}}{}^{\mathrm{m}}$ are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = ??V on a sphere of radius r > α is given by $\text{〈}\text{B}\text{·〉 =}\text{∑}\text{n=1}\text{∞}\text{R}{}^{\mathrm{n}}\text{(}\text{a/}\text{r}\text{)}{}^{\mathrm{2n=4}}\text{where}\text{a}$ is the Earth's radius. We refer to R_n as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rⁿ = R^M_n = R^C_n where the components R_n^M due to the main (or core) field and R_n^C due to the crustal field are given approximately by $\text{R}{}^{\mathrm{M}}{}_{\mathrm{n}}\text{= [}\text{(n =1)/}\text{(n + 2)}\text{](1.142 × 10}{}^9\text{)(0.288}{}^{\mathrm{n}}\text{Λ}{}^2\text{R}{}^{\mathrm{C}}{}_{\mathrm{n}}\text{= [}\text{(n =1){[1 — exp(-n/290)]/}\text{(n/290)} 0.52 Λ}{}^2\text{where}\text{Iγ = 1 nT}$. The two components are approximately equal for n = 15.Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.Equations relating average great circle power spectra of the geomagnetic field components to R_n are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the R_n for celestial bodies from average great circle power spectra of the magnetic field components.  相似文献   

Temperature extremes reduce seagrass growth and induce mortality     

C.J. Collier  M. Waycott 《Marine pollution bulletin》2014

Extreme heating (up to 43 °C measured from five-year temperature records) occurs in shallow coastal seagrass meadows of the Great Barrier Reef at low tide. We measured effective quantum yield (_?PSII${?}_{\text{PSII}}$), growth, senescence and mortality in four tropical seagrasses to experimental short-duration (2.5 h) spikes in water temperature to 35 °C, 40 °C and 43 °C, for 6 days followed by one day at ambient temperature. Increasing temperature to 35 °C had positive effects on _?PSII${?}_{\text{PSII}}$ (the magnitude varied between days and was highly correlated with PPFD), with no effects on growth or mortality. 40 °C represented a critical threshold as there were strong species differences and there was a large impact on growth and mortality. At 43 °C there was complete mortality after 2–3 days. These findings indicate that increasing duration (more days in a row) of thermal events above 40 °C is likely to affect the ecological function of tropical seagrass meadows.  相似文献   

High-pressure recovery of olivine: implications for creep mechanisms and creep activation volume     

S. Karato  M. Ogawa 《Physics of the Earth and Planetary Interiors》1982,28(2):102-117

High-temperature and high-pressure recovery experiments were made on experimentally deformed olivines at temperatures of 1613–1788 K and pressures of 0.1 MPa to 2.0 GPa. In the high-pressure experiments, a piston cylinder apparatus was used with BN and NaCl powder as the pressure medium, and the hydrostatic condition of the pressure was checked by test runs with low dislocation density samples. No dislocation multiplication was observed. The kinetics of the dislocation annihilation process were examined by different initial dislocation density runs and shown to be of second order, i.e. where ρ is the dislocation density, k₀ is a constant, $\text{E}{}^1\text{and}\text{V}{}^1$ are the activation energy and volume respectively, and P, R and T are pressure, gas constant and temperature, respectively. Activation energy and volume were estimated from the temperature and pressure dependence of the dislocation annihilation rate as $\text{E}{}^1\text{=389±59}\text{kJ mol}{}^{\mathrm{?1}}$ and $\text{V}{}^1\text{=14±2}\text{cm}{}^3\text{mol}{}^{\mathrm{?1}}$, respectively.The diffusion constants relevant to the dislocation annihilation process were estimated from a theoretical relation k=αD where $\text{k=k}{}_0\text{exp}\text{[?(E}{}^1\text{+ PV}{}^1\text{)/RT], D}$ is the diffusion constant and α is a non-dimensional constant of ca. 300. The results agree well with the self-diffusion constant of oxygen in olivine. This suggests that the dislocation annihilation is rate-controlled by the (oxygen) diffusion-controlled dislocation climb.The mechanisms of creep in olivine and dry dunite are examined by using the experimental data of static recovery. It is suggested that the creep of dry dunite is rate-controlled by recovery at cell walls or at grain boundaries which is rate-controlled by oxygen diffusion. Creep activation volume is estimated to be 16±3 cm³ mol^?1.  相似文献   

Melting temperature distribution and fractionation in the lower mantle     

Eiji Ohtani 《Physics of the Earth and Planetary Interiors》1983,33(1):12-25

The melting curve of perovskite MgSiO₃ and the liquidus and solidus curves of the lower mantle were estimated from thermodynamic data and the results of experiments on phase changes and melting in silicates.The initial slope of the melting curve of perovskite MgSiO₃ was obtained as $\text{d}\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{/}\text{d}\text{P?77}\text{K}\text{GPa}{}^{\mathrm{?1}}$ at 23 GPa. The melting curve of perovskite was expressed by the Kraut-Kennedy equation as $\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{(}\text{K}\text{)=917(}\text{1+29.6ΔV}\text{V}{}_0\text{)}$, where T_m?2900 K and P?23 GPa; and by the Simon equation, $\text{P(}\text{GPa}\text{)?23=21.2[}\text{(T}{}_{\mathrm{<mtext>m</mtext>}}\text{(}\text{K}\text{)}\text{2900)}{}^{1.75}\text{?1}\text{]}$.The liquidus curve of the lower mantle was estimated as $\text{T}{}_{\mathrm{<mtext>liq</mtext>}}\text{? 0.9 T}{}_{\mathrm{<mtext>m</mtext>}}$ (perovskite) and this gives the liquidus temperature T_liq=7000 ±500 K at the mantle-core boundary. The solidus curve of the lower mantle was also estimated by extrapolating the solidus curve of dry peridotite using the slope of the solidus curve of magnesiowüstite at high pressures. The solidus temperature is ～ 5000 K at the base of the lower mantle. If the temperature distribution of the mantle was 1.5 times higher than that given by the present geotherm in the early stage of the Earth's history, partial melting would have proceeded into the deep interior of the lower mantle.Estimation of the density of melts in the MgOFeOSiO₂ system for lower mantle conditions indicates that the initial melt formed by partial fusion of the lower mantle would be denser than the residual solid because of high concentration of iron into the melt. Thus, the melt generated in the lower mantle would tend to move downward toward the mantle-core boundary. This downward transportation of the melt in the lower mantle might have affected the chemistry of the lower mantle, such as in the D″ layer, and the distribution of the radioactive elements between mantle and core.  相似文献   

An efficient,high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media     

G. Lin  A.M. Tartakovsky 《Advances in water resources》2009

In this study, a probabilistic collocation method (PCM) on sparse grids is used to solve stochastic equations describing flow and transport in three-dimensional, saturated, randomly heterogeneous porous media. The Karhunen–Loève decomposition is used to represent log hydraulic conductivity Y=ln_Ks$Y=\ln K_s$. The hydraulic head h   and average pore-velocity v$\mathbf{v}$ are obtained by solving the continuity equation coupled with Darcy’s law with random hydraulic conductivity field. The concentration is computed by solving a stochastic advection–dispersion equation with stochastic average pore-velocity v$\mathbf{v}$ computed from Darcy’s law. The PCM approach is an extension of the generalized polynomial chaos (gPC) that couples gPC with probabilistic collocation. By using sparse grid points in sample space rather than standard grids based on full tensor products, the PCM approach becomes much more efficient when applied to random processes with a large number of random dimensions. Monte Carlo (MC) simulations have also been conducted to verify accuracy of the PCM approach and to demonstrate that the PCM approach is computationally more efficient than MC simulations. The numerical examples demonstrate that the PCM approach on sparse grids can efficiently simulate solute transport in randomly heterogeneous porous media with large variances.  相似文献   

Two leaks isolation in a pipeline by transient response     

Cristina Verde  Nancy Visairo  Sylviane Gentil 《Advances in water resources》2007

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Synthesis of a new high-pressure ohase of tin dioxide and some geophysical implications     

Lin-Gun Liu 《Physics of the Earth and Planetary Interiors》1974,9(4):338-343

Tin dioxide (SnO₂) in the rutile structure as starting material has been found to transform to the orthorhombic α-PbO₂ structure (S.G. Pbcn) at about 155 kbar and 1000–1400°C when compressed in a diamond-anvil cell and heated by irradiation with a YAG laser. The lattice parameters at room temperature and 1 bar are $\text{a}{}_{\mathrm{<mtext>o</mtext>}}\text{= 4.719 ± 0.002, b}{}_{\mathrm{<mtext>o</mtext>}}\text{= 5.714 ± 0.002,}\text{and}\text{c}{}_{\mathrm{<mtext>o</mtext>}}\text{= 5.228 ± 0.002}\text{A}\text{?}\text{with}\text{Z = 4}$ for the orthorhombic form of SnO₂, which is 1.5% more dense than the rutile form. Crystal-chemical arguments suggest that stishovite (SiO₂) may also transform to the α-PbO₂ structure at elevated pressure and temperature with an increase in zero-pressure density of about 2–3%. Mineral assemblages containing the orthorhombic SiO₂ are unstable relative to those containing the perovskite MgSiO₃ under lower-mantle conditions.  相似文献   

Applications of liquid state physics to the Earth's core     

D.J. Stevenson 《Physics of the Earth and Planetary Interiors》1980,22(1):42-52

By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) dK/$\text{d}\text{P ? 5 ? 5. 6P}$/K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of dK/dP proposed by Birch (1939) and Bullen (1949). (2) dlnT_M/dlnρ = (γC_V ? 1)/($\text{C}{}_{\mathrm{<mtext>V</mtext>}}\text{?}\text{3}\text{2}\text{),}\text{where}\text{T}{}_{\mathrm{<mtext>M</mtext>}}$ is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and C_V the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for C_V = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if $\text{γ <}\text{2}\text{3}$. However, it is shown that $\text{γ <}\text{2}\text{3}\text{? ∫}{}^{\mathrm{\infty }}{}_0\text{(?g/?T)}{}_{\mathrm{\rho }}\text{r(}\text{d}\text{/}\text{d}\text{r)(r}{}^2\text{φ)}\text{d}\text{r > 0}$, which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that $\text{γ >}\text{2}\text{3}$ and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ～ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory.  相似文献   

Approach to saturation analysis of hysteresis measurements in rock magnetism and evidence for stress dominated magnetic anisotropy in young mid-ocean ridge basalt     

《Physics of the Earth and Planetary Interiors》2006,154(3-4):299-307

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AVO-A response of an anisotropic half-space bounded by a dipping surface for P–P,P–SV and P–SH data     

《Journal of Applied Geophysics》2001,46(1):1-29

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