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41.
Chondrodite, a member of the humite group of minerals, forms by hydration of olivine and is stable over a range of temperatures
and pressures that includes a portion of the uppermost mantle. We have measured the single crystal elastic properties of a
natural chondrodite specimen at ambient conditions using Brillouin spectroscopy. The isotropic aggregate bulk (K) and shear
(μ) moduli calculated from the single-crystal elastic moduli, Cij, are: KS=118.4(16) GPa and μ=75.6(7) GPa. A comparison of the structures and elasticity of olivine and chondrodite indicate that the
replacement of O with (OH,F) in M2+O6 octahedra has a small effect on the elasticity of humite-group minerals. The slightly diminished elastic moduli of humite-group
minerals (as compared to olivine) are likely caused by a smaller ratio of strong structural elements (SiO4 tetrahedra) to weaker octahedra, and perhaps a more flexible geometry of edge-sharing MO4(O,OH,F)2 octahedra. In contrast to the humite-olivine group minerals, the incorporation of water into garnets and spineloids leads
to a more substantial decrease in the elastic properties of these minerals. This contrasting behavior is due to formation
of O4H4 tetrahedra and vacant hydroxyl-bearing octahedra in the garnets and spineloids, respectively. Therefore, the mechanism of
incorporation of H/OH into mineral phases, not only degree of hydration, should be taken into account when estimating the
effect of water on the elastic properties of minerals. The bulk elastic wave velocities of chondrodite and olivine are very
similar. If humite-like incorporation of OH is predominant in the upper mantle, then the reaction of OH with olivine will
have a minor or possibly no detectable effect on seismic velocities. Thus, it may be difficult to distinguish chondrodite-bearing
rocks from “anhydrous” mantle on the basis of seismically determined velocities for the Earth.
Received: 25 February 1998 / Revised, accepted: 18 August 1998 相似文献
42.
G. D. Gwanmesia J. Liu G. Chen S. Kesson S. M. Rigden R. C. Liebermann 《Physics and Chemistry of Minerals》2000,27(7):445-452
Dense isotropic polycrystalline specimens of majorite-rich garnets (Py100, Py62Mj38, Py50Mj50, Py21Mj79 and Mj100) along the pyrope (Mg3Al2Si3O12 = Py100)-majorite (MgSiO3 = Mj100) join were fabricated in a 2000-ton uniaxial split-sphere anvil apparatus (USSA-2000) at pressures from 10 to 18.5 GPa and
temperatures from 1200 to 1850 °C, within their stability fields in runs of 2–4-h duration, using hot-pressing techniques
developed by Gwanmesia et al. (1993). These specimens are single-phased, fine-grained (≤5 mm), free of microcracks, and have
bulk densities greater than 99% of the corresponding single-crystal X-ray density. Elastic compressional (P) and shear (S) wave velocities were determined at room pressure and temperature for these polycrystalline garnet specimens by phase comparison
ultrasonic interferometry. For Mj100, the P and S wave velocities are within 1% of the Hashin-Shtrikman averages calculated from the single crystal elastic moduli measured
by Brillouin spectroscopy. Both the elastic bulk modulus (K) and the shear modulus (G) decrease continuously with increasing majorite content from pyrope garnet (Py100) to pure majorite garnet (Mj100). The compositional dependence of K and G are given by K = 172.3 (40) − 0.085X, and G = 91.6 (10) − 0.038X, where X = mol% majorite), respectively, indicating that substitution of Si for Mg and Al decreases both K and G by about 5% along the solid solution series.
Received: 25 March 1999 / Accepted: 12 July 1999 相似文献
43.
Jennifer Kung Baosheng Li Yanbin Wang Robert C. Liebermann 《Physics of the Earth and Planetary Interiors》2004,147(1):27-44
Using acoustic measurement interfaced with a large volume multi-anvil apparatus in conjunction with in situ X-radiation techniques, we are able to measure the density and elastic wave velocities (VP and VS) for both ortho- and high-pressure clino-MgSiO3 polymorphs in the same experimental run. The elastic bulk and shear moduli of the unquenchable high-pressure clinoenstatite phase were measured within its stability field for the first time. The measured density contrast associated with the phase transition OEN → HP-CEN is 2.6-2.9% in the pressure of 7-9 GPa, and the corresponding velocity jumps are 3-4% for P waves and 5-6% for S waves. The elastic moduli of the HP-CEN phase are KS=156.7(8) GPa, G = 98.5(4) GPa and their pressure derivatives are KS′=5.5(3) and G′ = 1.5(1) at a pressure of 6.5 GPa, room temperature. In addition, we observed anomalous elastic behavior in orthoenstatite at pressure above 9 GPa at room temperature. Both elastic wave velocities exhibited softening between 9 and 13-14 GPa, which we suggest is associated with a transition to a metastable phase intermediate between OEN and HP-CEN. 相似文献
44.
We investigate in this paper various approaches to correct gravity changes for the effect of atmospheric pressure changes. Two specific locations are considered: Strasbourg (France) as mid-latitude station, where regular pressure fronts occur and Djougou (Benin) as equatorial station with large thermally driven S1 and S2 waves of planetary extent. We first review the classical approaches based on a constant or frequency-dependent admittance using only local pressure and gravity data. We consider then a model of atmospheric loading and show the barometric admittance in terms of elastic, Newtonian and total load, as a function of the distance from the station. We consider both a 2D pressure model (surface loading) and a 2.5D model, where the density decreases with height (standard atmosphere). Assuming horizontal advection in the atmospheric dynamics, we convert this spatially dependent admittance into a frequency-dependent admittance. Using global pressure data from European Centre for Medium-Range Weather Forecasts (ECMWF) at about 12 km spatial resolution and 3 h sampling, we compute the model-predicted pressure admittance for Djougou and Strasbourg and we simulate the frequency dependence inferred from gravity and pressure observations below 4 cycle per day. A long gravity and pressure data set (1996–2013) from Strasbourg is used to investigate the low frequency part of the pressure admittance while a common 2.5 year data set (August 2010–February 2013) for Strasbourg and Djougou is then analyzed to investigate the high frequency part of the admittance. In both cases, our results are in close agreement with the predictions inferred from an atmospheric 2.5D loading model with a distance–time relationship due to horizontal advection. The frequency dependence of the barometric admittance is explained by the competing contributions of Newtonian attraction and elastic surface deformation according to the distance from the gravimeter. In the far field (low frequencies), the magnitude of the admittance decreases with frequency because of the combined elasticity effect and Newtonian attraction (when the atmosphere is below the horizon) while, on the contrary, in the near field (high frequencies), elasticity becomes negligible and the pressure admittance mainly decreases with increasing frequency because of the decreasing attraction effect of the atmospheric masses inside the cylindrical pressure cell centered on the sensor location of decreasing radius. In the last part, we show that there is variability in time in the pressure admittance for both stations. 相似文献
45.
Numerous experimental studies indicate that as a result of shear stress, the elastic behavior of granular media becomes both non-linear and anisotropic. This paper presents a simple constitutive model for sands with respect to anisotropic elasticity. To this aim, using the concept of second order fabric tensor, a simplified elasticity theory is presented which is capable of considering the effect of induced anisotropy on the elastic response. SANISAND is the name used for a family of simple anisotropic sand models developed in the framework of critical state soil mechanics and bounding surface plasticity. An existing SANISAND model is modified in order to include the proposed anisotropic elasticity. The modified model simulations are compared with those obtained from the other members of this family. It is shown that considering anisotropic elasticity can take part in explanation of drastic loss of mean principal stress when sand is subjected to reverse loading in dilative branch of behavior and as a result, improve the liquefaction simulations. 相似文献
46.
We perform analytical and numerical studies of scaling relations of earthquakes and partition of elastic strain energy between seismic and aseismic components using a thermodynamically based continuum damage model. Brittle instabilities occur in the model at critical damage level associated with loss of convexity of the strain energy function. A new procedure is developed for calculating stress drop and plastic strain in regions sustaining brittle instabilities. The formulation connects the damage rheology parameters with dynamic friction of simpler frameworks, and the plastic strain accumulation is governed by a procedure that is equivalent to Drucker–Prager plasticity. The numerical simulations use variable boundary forces proportional to the slip-deficit between the assumed far field plate motion and displacement of the boundary nodes. These boundary conditions account for the evolution of elastic properties and plastic strain in the model region. 3-D simulations of earthquakes in a model with a large strike-slip fault produce scaling relations between the scalar seismic potency, rupture area, and stress drop values that are in good agreement with observations and other theoretical studies. The area and potency of the simulated earthquakes generally follow a linear log–log relation with a slope of 2/3, and are associated with stress drop values between 1 and 10 MPa. A parameter-space study shows that the area-potency scaling is shifted to higher stress drops in simulations with parameters corresponding to lower dynamic friction, more efficient healing, and higher degree of seismic coupling. 相似文献
47.
Mathieu Dumberry 《Geophysical Journal International》2008,172(3):903-920
A decadal polar motion with an amplitude of approximately 25 milliarcsecs (mas) is observed over the last century, a motion known as the Markowitz wobble. The origin of this motion remains unknown. In this paper, we investigate the possibility that a time-dependent axial misalignment between the density structures of the inner core and mantle can explain this signal. The longitudinal displacement of the inner core density structure leads to a change in the global moment of inertia of the Earth. In addition, as a result of the density misalignment, a gravitational equatorial torque leads to a tilt of the oblate geometric figure of the inner core, causing a further change in the global moment of inertia. To conserve angular momentum, an adjustment of the rotation vector must occur, leading to a polar motion. We develop theoretical expressions for the change in the moment of inertia and the gravitational torque in terms of the angle of longitudinal misalignment and the density structure of the mantle. A model to compute the polar motion in response to time-dependent axial inner core rotations is also presented. We show that the polar motion produced by this mechanism can be polarized about a longitudinal axis and is expected to have decadal periodicities, two general characteristics of the Markowitz wobble. The amplitude of the polar motion depends primarily on the Y 1 2 spherical harmonic component of mantle density, on the longitudinal misalignment between the inner core and mantle, and on the bulk viscosity of the inner core. We establish constraints on the first two of these quantities from considerations of the axial component of this gravitational torque and from observed changes in length of day. These constraints suggest that the maximum polar motion from this mechanism is smaller than 1 mas, and too small to explain the Markowitz wobble. 相似文献
48.
Klaus Helbig 《Geophysical Prospecting》2013,61(1):1-20
One hundred and fifty five years ago, Kelvin published the first part of a fundamental analysis of the elastic tensor, in which he proposed a coordinate‐free representation through its eigensystem. His thoughts were apparently far ahead of his time, since it took 125 years before the paper elicited a positive reaction (it is now accessible through several modern reviews). Science not only lost track for 125 years of the original paper but also lost the ideas Kelvin might have proposed in the second part, a publication that was never put to paper, presumably in view of the lack of appreciation of the first part. In an attempt to establish what might have been on Kelvin's mind for a second part, one has to ‘forget’ the progress of mathematical physics in the intervening time and base all arguments strictly on the content of the first part and on the state of science in the second half of the 19thcentury. The theory of elasticity would certainly have developed faster, had Kelvin's paper peen appreciated by his ‘peers’. But a theory based on Kelvin's ideas would be fruitful even today. 相似文献