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1.
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.
dρdt= ?p2K0exp[?(E1+PV1RT]
where ρ is the dislocation density, k0 is a constant, E1and V1 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 E1=389±59 kJ mol?1 and V1=14±2 cm3mol?1, respectively.The diffusion constants relevant to the dislocation annihilation process were estimated from a theoretical relation k=αD where k=k0 exp[?(E1 + PV1)/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   

2.
The N'Tarla bore-hole groundwaters show an 18O16O 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   

3.
An essentially arbitrary function V(θ, λ) defined on the surface of a sphere can be expressed in terms of spherical harmonics V(θ, Λ) = a n=1m=0npmn (cos θ) (gmn cos mΛ + hmn sin mΛ) where the Pnm are the seminormalized associated Legendre polynomials used in geomagnetism, normalized so that 〈[Pmn(cos θ) cos mΛ]〉2 =1/(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 gnm and hnm will be functions of the particular coordinate system orientation, but 〈:(gmn)2〉) = 〈(hmn)2 = Sn/(2n=1) where Sn =m=0n [(gmn)2 + (hmn)2] for any orientation of the coordinate system (Sn 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 〈gmnglp〉 = 〈hmnhlp〉 = 0 for lm or pn and 〈gmnhlp〉 = 0 fro all n, m, p, l.  相似文献   

4.
Lowes (1966, 1974) has introduced the function Rn defined by Rn =(n + 1) m=0 [(gmn)2 + (hmn)2] where gnmand hnm 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 B ·〉 =n=1 Rn(a/r)2n=4where a is the Earth's radius. We refer to Rn as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rn = RMn = RCn where the components RnM due to the main (or core) field and RnC due to the crustal field are given approximately by RMn = [(n =1)/(n + 2)](1.142 × 109)(0.288n Λ2 RCn = [(n =1){[1 — exp(-n/290)]/(n/290)} 0.52 Λ2where 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 Rn 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 Rn for celestial bodies from average great circle power spectra of the magnetic field components.  相似文献   

5.
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 a content was 1.9 μg l.?1. The data fit a model proposed in a previous paper (Zsolnay, 1977). The resulting equation was HC = ?2.7 + 4.82 Ch?0.942 Ch2 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   

6.
The dependence of bulk sound speed Vφ upon mean atomic weight m and density ρ can be expressed in a single equation:
Vφ=Bρλ(m0m[12+λ(1?c)](km/sec)
Here B is an empirically determined “universal” parameter equal to 1.42, m0 = 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 γ ? 13 where γ is a Grüneisen parameter. The constant c = (? ln VM/? ln m)X, where VM is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use cFe = 0.14 for Fe2+Mg2+ and GeSi substitutions and cCa ? 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 VM?4.  相似文献   

7.
8.
Source parameters of 27 major shallow earthquakes in the magnitude range 7.0–8.6, which occurred during 1906–1969, are used to establish dimensionless invariants involving the fault dimensions, average slip, and the rise time. It is found that these entities are expressible as simple functions of the subsonic shear Mach number (M) and the cube root of the seismic potency, (US)13. Moreover, a new principle is suggested according to which all dimensionless numbers which can be constructed from the basic fault elements are simple powers of the contraction factor (1-M2)?12 with coefficients of the order unity. The laws of dynamical similarity thus found are those appropriate for subsonic rupture in which the Mach number is very close to unity and the radiation efficiency is between 16 and 13. The empirical similarity laws are shown to be compatible with a source model in which the fault plane is simulated by a flexible membrane with additional restoring stiffness forces provided by an elastic medium attached to it on one side. Results suggest the possibility that earthquake rupture, together with the radiation of seismic waves, terminates at the moment that Mach 1 is reached.  相似文献   

9.
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 ?CMBB?r2dS 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 ? B?r2dS), 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 B?r2dS will vanish when Si 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   

10.
An approximate expression is developed for the relationship between the hydraulic gradient (J), the specific discharge (q) and fluid and porous matrix properties in the case of saturated, steady and uniform (macroscopic) flow of a Newtonian liquid at high Reynolds numbers through a homogeneous anisotropic porous medium:
gJ=(vw(2)+B(4):qq/q+C(3)·qq
In this expression, the tensors w(2), B(4) and C(3) denote properties of the solid matrix only. The tensors W(2), and C(3) are symmetrical; the tensor B(4) is symmetrical only in the first and last pairs of indices. It seems that no mathematical expression with a finite number of parameters exists, which can serve as a universal exact expression for the sought relationship between J and q.  相似文献   

11.
It is shown that there is linearity between the thermal pressure PTH and T between the Debye temperature θ and some high temperature T1. T1 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 T1 increases greatly as the pressure increases. It is therefore concluded that PTH 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   

12.
Interdiffusion experiments were performed between Fe3O4 (single crystal) and Fe2.8Ti0.2O4 (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 D was calculated by the Boltzmann-Matano method. Low-temperature data at 3 mole% Ti could be described by D = (3.85?1.11+1.68) × 10?3exp(2.23 ± 0.04 eV/kT) cm2/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   

13.
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 ε? = 8.3 · 10 ?34 σ2 where έ 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   

14.
15.
By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, ??, can be related to the mantle-derived heat flux, Q?. If cell size is independent of Q?2 then ??Q?. (If cell size varies with Q?, then a different power law prevails, but the essential conclusions are unaffected.) Then the factthat for constant thermodynamic efficiency of mantle convection, the mechanical power dissipation is proportionalto Q?, gives convective stress σ ∝ Q??1, i.e. the stress increases as the convection slows. This means an increasing viscosityor stiffness of the mantle which can be identified with a cooling rate in terms of a temperature-dependent creep law. If we suppose that the mantle was at or close to its melting point within 1 or 2 × 108 years of accretionof the Earth, the whole scale of cooling is fixed. The present rate of cooling is estimated to be about 4.6 × 10?8 deg y?1 for the average mantle temperature, assumed to be 2500 K, but this very slow cooling rate represents a loss ofresidual mantle heat of 7 × 1012 W, about 30% of the total mantle-derived heat flux. This conclusion requires theEarth to be deficient in radioactive heat, relative to carbonaceous chondrites. A consideration of mantle outgassing and atmospheric argon leads to the conclusion that the deficiency is due to depletion of potassium, and that the K/U ratio of the mantle is only about 2500, much less than either the crustal or carbonaceous chondritic values. Thetotal terrestrial potassium is estimated to be about 6 × 1020 kg. Acceptance of the cooling of the Earth removes the necessity for potassium in the core.  相似文献   

16.
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 Q?1(ω, T) = 3 × 103 · ω?0.27 · exp(?30RT)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 ?? = 3 × 107 · δ1.4 · exp(?125RT) indicative of grain boundary diffusion or superplasticity. At higher stresses a power law ?? = 45 · δ4 · exp(?125RT) 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 ηf and Q of the form: logηe?? = 1α · logQ ? (n ? 1) · log ω + log D are derived, where α ~ 0.25, n is the power of σ, and D is a constant.  相似文献   

17.
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 M0 = 1.7 × 1027dyne-cm, slip dislocationu = 1.9 m, Δσ = 95 bar, rupture velocity ν = 3.2 km s?1, rise time τ = 2 s, for the first event; M0 = 1.4 × 1027dyne-cm, u = 2.4 m, Δσ = 145 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   

18.
19.
20.
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 1.79 ± 0.02 MPa · m12, and for two blocks of Black gabbro it was 3.03 ± 0.08 MPa · m12 and 2.71 ± 0.15 MPa ·m12, 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   

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