High-temperature anelasticity and elasticity of mantle peridotite     

H. Berckhemer  F. Auer  J. Drisler 《Physics of the Earth and Planetary Interiors》1979,20(1):48-59

An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q(ω) and of Young's modulus E(ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10^?5.The Q^?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?(t) = ?_u · [1 + 3.7 · q · {(1 + 50t)^0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to $\text{Q}{}^{\mathrm{?1}}\text{(ω, T) = 3 × 10}{}^3\text{· ω}{}^{\mathrm{<mtext>?0.27\; ·\; </mtext><mtext>exp</mtext>}}\text{(}\text{?30}\text{RT}\text{)}$E(ω) is related to Q(ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation $\text{?}\text{?}\text{= 3 × 10}{}^7\text{· δ}{}^{1.4}\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ indicative of grain boundary diffusion or superplasticity. At higher stresses a power law $\text{?}\text{?}\text{= 45 · δ}{}^4\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity η_f and Q of the form: $\text{log}\text{η}{}_{\mathrm{e??}}\text{=}\text{1}\text{α}\text{·}\text{log}\text{Q ? (n ? 1) ·}\text{log}\text{ω +}\text{log}\text{D}$ are derived, where α ～ 0.25, n is the power of σ, and D is a constant.  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   

Geothermal effects in the formation of electrically conducting zones and temperature distribution in the earth     

A. Ádám 《Physics of the Earth and Planetary Interiors》1978,17(2):P21-P28

Pollack and Chapman have shown that the surface heat flow in continental regions is dependent not only on the earth's crust below the observation site, but also on the upper mantle there. Therefore heat flow can be used to investigate the role of the thermal conditions in the creation of the electrically conductive zones in both the crust and mantle.Empirical exponential formulas describe the depth to the conductivity increase in the crust corresponding to granitization, the depth to the conductive zone at the top of the asthenosphere (SLVZ), as a function of heat flow. Comparing the latter with temperature estimations in the asthenosphere it is concluded that partial melting of the upper mantle occurs only where $\text{q ? 42}\text{m W m}{}^{\mathrm{?2}}\text{? 1}\text{HFU}$.The depth to the conductivity increase corresponding to the mineralogic phase transition in the upper mantle is increased with high temperatures. Such a conductive zone shows that the maximum temperature difference between stable platform areas and active zones is about 1000°C.  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   

Upper mantle plasticity from laboratory experiments     

Y. Gueguen  M. Darot 《Physics of the Earth and Planetary Interiors》1982,29(1):51-57

On the basis of two assumptions i.e. (1) plastic and anelastic behaviour of the upper mantle can be approximated by the behaviour of the dominant mineral olivine, and (2) the behaviour of natural olivine and synthetic forsterite are similar, we have investigated the flow laws and the flow microstructures of forsterite single crystals. The results obtained between 1400–1650°C and 10–100 MPa suggest a model of climb controlled creep in which the a edge dislocations are dominant. The activation energy measured in that regime is 4.7 eV, close to that of Si self-diffusion and the flow law is $\text{?}\text{?}\text{=10}{}^6\text{σ}{}^{2.6}\text{exp}\text{(?4.7}\text{eV/k}\text{T)}$, where σ is in MPa. Extrapolation of these results to the upper mantle would imply very low stresses (i.e. ?10 MPa) in the asthenosphere. However the effect of pressure and grain size are unknown and extrapolation to very low stresses is not straightforward.  相似文献   

An experimental study of magnetite-titanomagnetite interdiffusion     

R. Freer  Z. Hauptman 《Physics of the Earth and Planetary Interiors》1978,16(3):223-231

Interdiffusion experiments were performed between Fe₃O₄ (single crystal) and Fe_2.8Ti_0.2O₄ (powder), under self-buffering conditions (temperature range 600–1034°C), and for various oxygen potentials at 1400°C. Profiles of Fe and Ti were obtained by electronprobe microanalysis, and the interdiffusion coefficient $\text{D}$ was calculated by the Boltzmann-Matano method. Low-temperature data at 3 mole% Ti could be described by $\text{D}\text{= (3.85}{}_{\mathrm{?1.11}}{}^{\mathrm{+1.68}}\text{) × 10}{}^{\mathrm{?3}}\text{exp}\text{(2.23 ± 0.04}\text{eV}\text{/kT)}\text{cm}{}^2\text{/}\text{s}$. An estimate is given for the time to interdiffuse 2μm at various temperatures, and the results compared with recent experiments.  相似文献   

Physical constraints for the analysis of the geomagnetic secular variation     

Loren Shure  Kathy Whaler  David Gubbins  Bruce Hobbs 《Physics of the Earth and Planetary Interiors》1983,32(2):114-131

Slow changes in the magnetic field are believed to originate in the core of the Earth. Interpretation of these changes requires knowledge both of the vertical component of the field and of its rate of change at the core-mantle boundary (CMB). While various spherical harmonic models show some agreement for the field at the CMB, those for secular variation (SV) do not. SV models depend heavily on annual means at relatively few and poorly distributed magnetic observatories. In this paper, the SV at the CMB is modelled by fitting 15-year differences in the annual means of the X, Y and Z components (from 1959 to 1974). The model is made unique by imposing the constraint that $\text{?}{}_{\mathrm{CMB}}\text{B}\text{?}{}_{\mathrm{r}}{}^2\text{d}\text{S}$ be a minimum, using the method of Shure et al. (1982). If SV is attributed to motions of core fluid, then this model will yield, in some sense, the slowest core motions. The null space is determined by the distribution of observations, and therefore, to be consistent, only those observatories have been retained which recorded almost continuously throughout the interval 1959–1974.The method allows misfit between the model and the observations. The best value for the misfit can be derived from estimates of errors in the data, or alternatively, because larger misfit leads to smoother models (i.e., smaller $\text{?}\text{B}\text{?}{}_{\mathrm{r}}{}^2\text{d}\text{S}$), the best value can be estimated subjectively from the final appearance of the model. Both procedures have their counterparts in the conventional spherical harmonic expansion approach, when smoothing is achieved by lowering the truncation level. The new proposal made in this paper is to use objective criteria for determining the misfit, based on the assumption that diffusion is negligible, in which event all integrals $\text{∫}\text{B}\text{?}{}_{\mathrm{r}}{}^2\text{d}\text{S}$ will vanish when S_i is a region on the CMB bounded by a contour of zero vertical component of field. For the 1965 definitive model which is adopted here, and for most other contemporary models, there are six such areas, giving five independent integrals (the integrals over the six regions must sum to zero if ? · B = 0). Tabulating these integrals for various choices of the misfit gives minimum values near 2 nT y^?1. It is impossible to achieve this good a fit to the data using a reasonable model derived by truncating the spherical harmonic expansion. The value 2 nT y^?1 corresponds to errors of ～ 20 nT in individual annual means, which is rather larger than expected from the scatter in the data.  相似文献   

A confirmation of the correlation between hydrocarbons and chlorophyll a in the upper euphotic zone     

Adam Zsolnay 《Marine pollution bulletin》1979,10(4):107-108

The average hydrocarbon content found in 14 water samples from the euphotic zone off Northwest Africa was 4.4 μg l.^?1 with no extreme values. The average chlorophyll $\text{a}$ content was 1.9 μg l.^?1. The data fit a model proposed in a previous paper (Zsolnay, 1977). The resulting equation was $\text{HC}\text{= ?2.7 + 4.82}\text{Ch}\text{?0.942}\text{Ch}{}^2$ and could explain 59% of the variance in the hydrocarbon distribution. This indicates a correlation that is significant at the 0.002 level.  相似文献   

Rupture process of the Miyagi-Oki,Japan, earthquake of June 12, 1978     

Tetsuzo Seno  Kunihiko Shimazaki  Paul Somerville  Ken Sudo  Takao Eguchi 《Physics of the Earth and Planetary Interiors》1980,23(1):39-61

The faulting mechanism and multiple rupture process of the M = 7.4 Miyagi-Oki earthquake are studied using surface and body wave data from local and worldwide stations. The main results are as follows. (1) P-wave first motion data and radiation patterns of long-period surface waves indicate a predominantly thrust mechanism with strike N10° E, dip 20°W, and slip angle 76°. The seismic moment is 3.1 × 10²⁷ dyne-cm. (2) Farfield SH waveforms and local seismograms suggest that the rupture occurred in two stages, being concordant with the two zones of aftershock activity revealed by the microearthquake network of Tohoku University. The upper and lower zones, located along the westward-dipping plate interface, are separated by a gap at a depth of 35 km and have dimensions of 37 × 34 and 24 × 34 km², respectively. Rupture initiated at the southern end of the upper aftershock zone and propagated at N20°W subparallel to the trench axis. About 11 s later, the second shock, which was located 30 km landward (westward) of the first, initiated at the upper corner of the lower aftershock zone and propagated down-dip N80°W. Using Haskell modelling for this rupture process, synthetic seismograms were computed for teleseismic SH waves and nearfield body waves. Other parameters determined are: seismic moment $\text{M}{}_0\text{= 1.7 × 10}{}^{27}\text{dyne-cm, slip dislocation}\text{u}\text{= 1.9}\text{m}\text{, Δσ = 95}\text{bar, rupture velocity}\text{ν = 3.2}\text{km s}{}^{\mathrm{?1}}\text{,}\text{rise time}\text{τ = 2}\text{s}$, for the first event; $\text{M}{}_0\text{= 1.4 × 10}{}^{27}\text{dyne-cm}\text{,}\text{u}\text{= 2.4}\text{m}\text{, Δσ = 145}\text{bar}$, for the second event; and time separation between the two shocks ΔT = 11 s. The above two-segment model does not explain well the sharp onsets of the body waves at near-source stations. An initial break of a small subsegment on the upper zone, which propagated down-dip, was hypothesized to explain the observed near-source seismograms. (3) The multiple rupture of the event and the absence of aftershocks between the two fault zones suggests that the frictional and/or sliding characteristics along the plate interface are not uniform. The rupture of the first event was arrested, presumably by a region of high fracture strength between the two zones. The fracture energy of the barrier was estimated to be 10¹⁰ erg cm^?2. (4) The possible occurrence of a large earthquake has been noted for the region adjacent to and seaward of the area that ruptured during the 1978 event. The 1978 event does not appear to reduce the likelihood of occurrence of this expected earthquake.  相似文献   

Are anharmonicity corrections needed for temperature-profile calculations of interiors of terrestrial planets?     

Orson L. Anderson 《Physics of the Earth and Planetary Interiors》1982,29(1):91-104

It is shown that there is linearity between the thermal pressure P_TH and T between the Debye temperature θ and some high temperature $\text{T}{}^1$. $\text{T}{}^1$ has been measured at 1 atm and is reported for several minerals including, for example, MgO (1300 K) and forsterite (1200 K). The change in thermal pressure from room temperature for five solids, so far measured, indicate striking linearity with T at high temperatures.It is further shown that the value of $\text{T}{}^1$ increases greatly as the pressure increases. It is therefore concluded that P_TH is probably linear with T for mantle minerals under mantle conditions. The proportionality constant is derived from the measurements of thermal expansivity and bulk modulus at high temperature and zero pressure.The argument is then reversed. Assuming that the thermal pressure is in fact linear with T for the various shells in a planet, the resulting density and temperature profile of the planet is derived. The resulting density profile of the Earth compares favorably with corresponding values of recent seismic profiles.  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   

Anelastic degradation of acoustic pulses in rock     

M.T. Gladwin  F.D. Stacey 《Physics of the Earth and Planetary Interiors》1974,8(4):332-336

Measurements on acoustic pulses propagating in massive rock lead to a simple empirical relationship between the pulse rise time, τ and the time of propagation of a pulse, t: where τ₀ is the initial rise time (at t = 0), Q is the anelastic parameter which may be expressed in terms of the fractional loss of energy per cycle of a sinusoidal wave, Q = 2π(ΔE/E)^?1, and is assumed to be essentially independent of frequency, and C is a constant whose value we estimate experimentally to be 0.53 ± 0.04. Of the linear theories of seismic pulse attenuation, model 2 of Azimi et al. (1968) is favoured. Pulse shapes computed from equations of Futterman (1962) also give C = 0.5, but the pulse arrives earlier than in a non-attenuating medium with the same elasticity and density. Pulse shapes calculated using Strick's (1967, 1970, 1971) theory give values of C incompatible with our results. The observations suggest that a method of estimating the Q-structure of the earth from seismic pulse rise times may have a particular advantage over the spectral ratio method.  相似文献   

Creep response of the lunar crust in mare regions from an analysis of crater deformation     

A.W. Gerhard Kunze 《Physics of the Earth and Planetary Interiors》1974,8(4):375-387

The settling trends of 318 lunar mare craters are compared with predictions of numerical finite-element models in order to determine the creep response of the upper lunar mare crust. No settling is evident in craters smaller than 5 km in diameter. Settling rates of larger craters increase as function of crater size in a manner suggesting a non-linear lunar creep response corresponding to the power law $\text{ε}\text{?}\text{= 8.3 · 10}{}^{\mathrm{?34}}\text{σ}{}^2$ where ε&#x0301; is the strain rate and σ is the differential stress. However, the observed nonlinearity is probably an apparent nonlinearity resulting from the temperature induced viscosity decrease with depth due to a lunar crustal temperature gradient of 3° C/km and a creep activation energy of 20 kcal/mole. It is concluded that creep in the lunar medium is essentially Newtonian, and that the effective viscosity of the upper lunar mare crust is (1.6 ± 0.3) · 10²⁵ poise.  相似文献   

Présence d'eaux anciennes dans les eaux du forage de N'Tarla,région de Koutiala (république du mali)     

Claude Jusserand 《Journal of Hydrology》1976,30(3):287-292

The N'Tarla bore-hole groundwaters show an ${}^{18}\text{O}{}^{16}\text{O}$ isotopic composition different from the mean weighted value of precipitations in this region. On the basis of ¹⁴C bicarbonate activity and tritium content, a mixing process of recent and ancient waters is assessed.  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   

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   

Helium and carbon isotopic compositions of hot spring gases in the Tibetan Plateau     

《Journal of Volcanology and Geothermal Research》1999,88(1-2):99-107

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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   

Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro     

P.G. Meredith  B.K. Atkinson 《Physics of the Earth and Planetary Interiors》1985,39(1):33-51

The double torsion testing method has been used to determine catastrophic and subcritical crack propagation parameters for pre-cracked specimens of Westerly granite and Black gabbro under a number of environmental conditions.The critical stress intensity factor for catastrophic crack propagation (fracture toughness) of granite and gabbro has been measured at temperatures from 20 to 400°C, in a vacuum. At 20°C, the fracture toughness of Westerly granite was $\text{1.79 ± 0.02}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and for two blocks of Black gabbro it was $\text{3.03 ± 0.08}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{2.71 ± 0.15}\text{MPa}\text{·}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, respectively. These values are very close to those reported by other investigators for tests conducted in air of ambient humidity at room temperature. For both rocks, fracture toughness at first increased slightly, and then decreased steadily on raising the temperature above ambient conditions. This behaviour is explained in terms of the density and distribution of thermally induced microcracks, as determined by quantitative optical microscopy.Subcritical crack growth behaviour has been studied at temperatures up to 300°C, and under water vapour at pressures of 0.6 to 15 kPa. Both the load relaxation and incremental constant displacement rate forms of the double torsion testing method were utilised to generate stress intensity factor/crack velocity diagrams. Crack growth was measured over the velocity range 5 × 10^?3 to 10^?7 m · s^?1. Increasing both temperature and water vapour pressure resulted in substantially higher crack growth rates. The overall effect of raising the temperature over the range studied here (20–300°C) was to increase the crack growth rate in granite and gabbro by ～5 and 7 orders of magnitude, respectively, at constant stress intensity factor and vapour pressure of water. For both rocks, the slopes of stress intensity factor/crack velocity curves were sensitive to changes in both temperature and water vapour pressure at low values of the latter parameter. Slopes fell substantially on raising the water vapour pressure, but were relatively insensitive to changes in temperature at these higher pressures. No subcritical crack growth limit was encountered.Estimates of the uncertainty in our experimental data are given. From the results of multiple load relaxation experiments on Westerly granite specimens, we estimate the uncertainty in position of stress intensity factor/crack velocity curves along the stress intensity axis to be c. 10% of the fracture toughness, and the uncertainty in slope of such curves to be c. 12%.Problems associated with the extrapolation of our experimental data to regions of higher effective confining pressure in the Earth's crust are discussed.  相似文献   

Gamma emitting fission products in surface sediments of the Ravenglass estuary     

S.R Aston  D.A Stanners 《Marine pollution bulletin》1982,13(4):135-138

The occurrence of some fission products from the Sellafield (formerly Windscale) nuclear fuel reprocessing facility has been determined for surface sediments from forty locations in the Ravenglass estuary, North-west England. The influence of the silt-sized fraction in the sediments on the geographic distribution of ¹³⁷Cs is clearly important, and to a lesser extent also influences the distributions of ¹⁰⁶Ru, ${}^{134}\text{Cs}\text{+}{}^{95}\text{Zr}\text{Nb}$ and ¹⁴⁴Ce. The data are compared with recently published results reported by the Ministry of Agriculture, Fisheries and Food for a monitoring site in this estuary.  相似文献