Electrical and thermal investigations of rocks and minerals under extremep,T-conditions

Summary For the discussion of the physico-chemical state and the phase transitions in the earth interior it is necessary to compare the results of geophysical field measurements with geophysical solid state investigations in the laboratory under extremep,T-conditions. In correspondence with the theoretical studies about the behaviour of the materials in the deep earth we investigated two groups of materials: (I) different types of rocks with reference to their elastic and thermal behaviour under extreme conditions, (II) simple compounds of elements which belong possibly to the representatives of the deep mantle and the earth interior. The method for measurement of the thermal diffusivity and the influence of anisotropy on the propagation of elastic waves in different rocks is described. The results of the dependence of the electric resistivity on pressure and temperature on synthetic and natural chalkogenides of the 3d-transition metals are discussed.Publication No. 474 of the Central Earth Physics Institute, Academy of Sciences, 15 Potsdam, Telegrafenberg, GDR.     

Experimental study of the elasticity of single crystalline calcite under high pressure (the calcite I—calcite II transition at 14.6 kbar)

The length variations and the ultrasonic wave velocities were measured along principal single crystal calcite axes under high pressure.We have observed that six independent elastic constants undergo drastic changes at the calcite I—calcite II transition point at 14.6 kbar. Furthermore, we have determinated the length and volumetric variations in the phases I and II and during the I–II transition.These results allow us to deduce the following important points: influence of the planar CO₃ groups on the strong linear compressibility anisotropy in phase I; reciprocal relation between the decrease of elastic constants at the transition point and the anomaly of compressibility of the calcite II; compatibility of our data with the monoclinic structure of calcite II.     

Anisotropic thermal properties of talc under high temperature and pressure

The anisotropic thermal conductivity and diffusivity of talc were simultaneously measured up to 5.3 GPa and 900 K using the pulse transient method. Although significant anisotropy was observed in the thermal conductivity of talc, the average thermal conductivity is comparable to that of olivine and roughly three times greater than that of antigorite. From the ratio of the thermal conductivity to the thermal diffusivity, the heat capacity of talc was evaluated. The pressure derivative of heat capacity was found to be positive, which is related to the anomaly of thermal expansivity of talc above 50 °C at atmospheric pressure.     

The effect of anisotropic diffusivity on rotating magnetoconvection in the Earth's core

A thermal diffusive process in the Earth's core is principally enhanced by small-scale flows that are highly anisotropic because of the Earth's rapid rotation and a strong magnetic field. This means that a thermal eddy diffusivity should not be a scalar but a tensor. The effect of such anisotropic tensor diffusivity, which is to be prescribed, on dynamics in the Earth's core is investigated through numerical simulations of magnetoconvection in a rapidly rotating system. A certain degree of anisotropy has an insignificant effect on the character, like kinetic and magnetic energies, of magnetoconvection in a small region with periodic boundaries in the three directions. However, in a region with top and bottom rigid boundary surfaces, kinetic and magnetic energies of magnetoconvection can be altered by the same degree of anisotropy. This implies that anisotropic tensor diffusivity affects on dynamics in the core, in particular near the boundary surfaces.     

Effects of anisotropic diffusion on onset of rotating magnetoconvection in plane layer; stationary modes

ABSTRACT

Turbulence in the Earth's outer core not only increases all diffusive coefficients, but it can lead to their anisotropic properties. Therefore, the model of rotating magnetoconvection in horizontal plane layer rotating about vertical axis and permeated by homogeneous horizontal magnetic field, influenced by anisotropic diffusivities, viscosity and thermal diffusivity, is advanced by considering the magnetic diffusivity as anisotropic too. The case of full anisotropy, i.e. all coefficients anisotropic, is compared with both the case possessing isotropic diffusion coefficients and the case of partial anisotropy, i.e. mixed case with isotropic and anisotropic diffusive coefficients (viscosity and thermal diffusivity anisotropic and magnetic diffusivity isotropic). The existence and preference of instabilities is sensitive to all non-dimensional parameters, as well as on anisotropic parameter, the ratio of horizontal and vertical diffusivities. Two types of anisotropy, BM (introduced by Braginsky and Meytlis) and SA (stratification anisotropy) are studied. BM as well as SA were applied by ?oltis and Brestenský to the study of the partial anisotropy; this study is extended, in this paper, to full anisotropy cases (full SA and full BM) and it is shown that the style of convection given by the onset of stationary modes is more affected by anisotropic diffusivities in BM than in SA anisotropy. The important influence of strong anisotropies in the Earth's core dynamics is stressed.     

The development of magnetic susceptibility anisotropy through crystallographic preferred orientation in a calcite rock

High-field torque-meter measurements of diamagnetic susceptibility anisotropy of a suite of samples of Carrara marble, axially shortened by amounts up to 50% at (1.5–3.0) · 10⁸ Pa confining pressure and at 20–500°C (mainly 400°C), have been compared with optical measurements of preferred crystallographic orientation. A revised value for the susceptibility anisotropy of calcite has been obtained from studies of single crystals, and it has been shown to be almost independent of the state of intracrystalline plastic strain. From the measured anisotropy of calcite, quantitative comparison of optical and magnetic fabric measurements is possible. It is found that these measurements agree and the implications of the observed progressive development of fabric intensity with strain are discussed.     

Experimental crystallization of gallium: ultrasonic measurements of elastic anisotropy and implications for the inner core

We present ultrasonic measurements of elastic anisotropy in gallium undergoing directional solidification in the presence of imposed thermal gradients, rotation, convection, turbulence, and magnetic fields. Simultaneous in situ measurements of temperature and compressional wave speed are used to track the crystallization front during solidification. We find that individual solidified gallium samples are always polycrystalline and elastically anisotropic, with grains elongated in the solidification direction. The measured compressional wave anisotropy in individual solid samples ranges from 20 to 80% of the single crystal values, depending on experimental conditions. We also find the amount of elastic anisotropy varies with position in an individual sample. Based on ensemble averages from multiple experiments made under similar environmental conditions, we find the direction of elastic anisotropy in the solid is sensitive to the thermal gradient direction, while the amount of anisotropy is most sensitive to the presence or absence of initial nucleation in the melt. Experiments that show average anisotropy have the ultrasonically fast axis aligned with gravity and the thermal gradient. Strongly anisotropic solids result when nucleation grains are present in the initial melt, whereas smaller or zero average anisotropy results when nucleation grains are initially absent. Other externally imposed factors we have examined, such as turbulence and magnetic fields, have either no measurable influence or tend to reduce the amount of anisotropy of the solid. Our results suggest that during crystallization of Earth’s inner core, the orientation of average anisotropy in the newly formed solid is controlled primarily by radial solidification, while the amount of anisotropy may be influenced by pre-existing inner core texture.     

Theoretical study of the elastic constants of calcite at the transition calcite I-calcite II

Sudden changes in the elastic stiffness constants of single crystalline calcite at the transition calcite I-calcite II (Vo Thanh and Lacam) are interpreted in terms of the interaction between pressure induced elastic strains and the rotational mode of CO₃⁼ groups. The latter is softened at the critical pressure, causing the transition.Our theoretical analysis explains qualitatively the experimental observations and data.     

The distribution of thermal diffusivity in the Earth's crust

Data in the literature and additional measurements on the thermal diffusivities of granites, granulites and ultrabasic rocks at temperatures up to 1000 K and pressures to 2 GPa, have been used to propose a new model for thermal diffusivity distribution in the crust and upper mantle.The laboratory measurements were made using a pulse method or the Angstroem method with cylindrical heat flow. After making particular assumptions about the pressure and temperature distribution within the top 60 km the pressure and temperature dependencies of diffusivity were transformed into a depth dependence.The model is characterised by a continuous decrease of diffusivity to a depth of ～30 km where there is a small but rapid increase to a nearly constant value of 7.3 × 10^?3 cm² s^?1.     

Classes of Anisotropic Media: A Tutorial

The purpose of the present article is to give a precise definition and analysis from first principals of anisotropy, as the term applies to elastic media, taking care to avoid unnecessary assumptions. Two fundamental concepts, material invariance and symmetry group of a material, are defined purely in terms of the stress-strain relation. The implications of material symmetry, or in other words, of anisotropy, for the structure of the stiffness tensor are then investigated. Using the reduced notation of Voigt, these results are presented as the well-known simplifications in the form taken by the six-by-six stiffness matrix that represents the material's stiffness tensor. A new, simple proof is given for the remarkable fact that an elastic medium cannot have rotational symmetry by an angle of less than 90° without being transversely isotropic. In addition, the mutual relation that the notions of elastic symmetry and crystal symmetry have with respect to the so-called orthogonal group is sketched. Despite the historical association between anisotropic elastic materials and the study of crystals, the given presentation shows that conceptually the notion of anisotropy in elastic media is entirely independent of that of crystal symmetry.     

Thermal diffusivity of seasonal snow determined from temperature profiles

Thermal diffusivity of snow is an important thermodynamic property associated with key hydrological phenomena such as snow melt and heat and water vapor exchange with the atmosphere. Direct determination of snow thermal diffusivity requires coupled point measurements of thermal conductivity and density, which continually change due to snow metamorphism. Traditional methods for determining these two quantities are generally limited by temporal resolution. In this study we present a method to determine the thermal diffusivity of snow with high temporal resolution using snow temperature profile measurements. High resolution (between 2.5 and 10 cm at 1 min) temperature measurements from the seasonal snow pack at the Plaine-Morte glacier in Switzerland are used as initial conditions and Neumann (heat flux) boundary conditions to numerically solve the one-dimensional heat equation and iteratively optimize for thermal diffusivity. The implementation of Neumann boundary conditions and a t-test, ensuring statistical significance between solutions of varied thermal diffusivity, are important to help constrain thermal diffusivity such that spurious high and low values as seen with Dirichlet (temperature) boundary conditions are reduced. The results show that time resolved thermal diffusivity can be determined from temperature measurements of seasonal snow and support density-based empirical parameterizations for thermal conductivity.     

低孔隙度泥页岩应力依赖的各向异性裂纹演化特性研究

本文在实验室对所获取的东营地区层理发育的低孔隙度页岩和泥岩的各向异性裂纹演化特性进行了研究,获得了各向同性条件下泥页岩的力学与超声波响应特性,分析了应力幅度对于页岩声波速度和各向异性的影响.主要结论包括:(1)泥页岩在循环载荷下存在滞后效应,表明其经历了去压实或油气产生导致的超压;(2)泥岩和页岩具有不同程度的各向异性,随着各向同性压力的增高微裂隙逐渐闭合,样品的各向异性程度减弱;(3)分析了岩石韧度和裂纹损伤参数随压力的变化特征,相比泥岩,页岩各向异性程度更高,随压力变化更明显,其裂纹导致的附加各向异性更强;(4)分析了各向异性岩石的动态弹性模量特征,由于软裂隙空间的闭合,动态弹性模量在低压条件下都随着围压的增加有硬化趋势.     

Temperature and Pressure Dependencies of Thermal Transport Properties of Rocks: Implications for Uncertainties in Thermal Lithosphere Models and new Laboratory Measurements of High-Grade Rocks in the Central Fennoscandian Shield

Measurements on thermal conductivity and diffusivity as functions of temperature (up to 1150 K) and pressure (up to 1000 MPa) are presented for Archaean and Proterozoic mafic high-grade rocks metamorphosed in middle and lower crustal pressures, and situated in eastern Finland, central Fennoscandian Shield. Decrease of 12–20% in conductivity and 40–55% in diffusivity was recorded between room temperature and 1150 K, which can be considered as typical of phonon conductivity. Radiative heat transfer effects were not detected in these samples. Pressure dependencies of the samples are weak if compared to crystalline rocks in general, but relatively typical for mafic rocks.The temperature and pressure dependencies of thermal transport properties (data from literature and the present study) were applied in an uncertainty analysis of lithospheric conductive thermal modellings with random (Monte Carlo) simulations using a 4-layer model representative of shield lithosphere. Model parameters were varied according to predetermined probability functions and standard deviations were calculated for lithospheric temperature and heat flow density after 1500 independent simulations. The results suggest that the variations (uncertainties) in calculated temperature and heat flow density values due to variations in the temperature and pressure dependencies of conductivity are minor in comparison to the effects produced by typical variations in the room temperature value of conductivity, heat production rate or lower boundary condition values.     

高温高压下红河断裂带断层泥力学性质的研究

断层泥在室温高压下的应力-应变曲线呈非线性、线性等阶段性变形,在高温高压下则呈非线性变形,两者均表现出渐进破坏。含水量、矿物成分和温压条件对变形特征和破坏强度有重要影响。曲线的初始弹性模量小于有效弹性模量。断层泥在温度T≥400℃和σ_3≥300MPa时发生岩化,据此岩化温压条件可估计出未岩化断层泥存在深度将不超过10—15km。由于断层泥具渐进破坏特征,故在高温高压条件下断层泥有利于断层活动呈现稳滑     

The impact of different clay minerals on the anisotropy of clay matrix in shale

Although clay is composed of disconnected anisotropic clay platelets, many rock physics models treat the clay platelets in shale as interconnected. However, the clay matrix in shales can be modelled as anisotropic clay platelets embedded within a soft isotropic interplatelet region, allowing the influence of disconnected clay platelets on the elastic properties of the clay matrix to be analysed. In this model, properties of the interplatelet region are governed by its effective bulk and shear moduli, whereas the effective properties of the clay platelets are governed by their volume fraction, aspect ratio and elastic stiffness tensor. Together, these parameters implicitly account for variations in clay and fluid properties, as well as fluid saturation. Elastic stiffnesses of clay platelets are obtained from the literature, including both experimental measurements and first-principles calculations of the full anisotropic (monoclinic or triclinic) elastic stiffness tensors of layered silicates. These published elastic stiffness tensors are used to compile a database of equivalent transverse isotropic elastic stiffness tensors, and other physical properties, for eight common varieties of layered silicates. Clay matrix anisotropy is then investigated by examining the influence of these different elastic stiffnesses, and of varying model parameters, upon the effective transverse isotropic elastic stiffness tensor of the clay matrix. The relationship between the different clay minerals and their associated anisotropy parameters is studied, and their impact on the resulting anisotropy of the clay matrix is analysed.     

利用三维孔隙弹性模型探讨紫坪铺水库对汶川地震的影响

本文基于三维孔隙弹性理论,建立了紫坪铺水库及周边地区的有限元模型.根据紫坪铺水库开始蓄水到汶川地震发震时刻的水位变化情况,计算了整个区域的孔隙压力和库仑应力.详细讨论了断层及周围地层的弹性模量和扩散系数对计算结果的影响.计算结果表明:从弹性角度看,断层的弹性模量对汶川地震震源处的库仑应力影响很小;震源处的库仑应力随着断层和周围地层的扩散系数增大而增大.当给定弹性模量和扩散系数代表性值的时候,计算结果表明在汶川地震发震时刻,震源处的库仑应力变化量为+1 kPa左右,这表明紫坪铺水库使得汶川地震发震断层更加危险.是否这个量级的库仑应力就能够触发汶川地震还需要进一步探讨.通过分析库区周边小震的分布,发现小震分布区域均是库仑应力增加的地区,因此紫坪铺水库周边的小震应该与紫坪铺水库蓄水有直接关系.     

不同围压和流体饱和状态下致密砂岩弹性各向异性特征

为研究致密砂岩声波速度及其各向异性随围压的变化规律以及不同流体饱和状态下的弹性各向异性特征,钻取了不同方向的岩心并在实验室超声波频率下对致密砂岩的声学特性进行了测量,分别给出干燥和饱和水状态下,不同方向样品纵横波速度、刚性系数以及各向异性系数随围压的变化规律,并对实验结果进行了分析讨论.实验结果表明致密砂岩纵横波速度、纵横波速度比以及刚性系数均随围压增加而增加,但其在不同饱和状态下的变化率却截然不同;纵横波速度比、各向异性系数在饱和水状态下变化规律不明显,表明孔隙流体的存在对于岩石物理性质有着非常重要的影响.这方面的实验工作不但对于考察不同流体性质对致密岩石弹性各向异性影响是必要的,而且有助于致密砂岩油水和气层的识别.     

Seismic Anisotropy in the Deep Mantle, Boundary Layers and the Geometry of Mantle Convection

—An attempt is made to explore the geodynamical significance of seismic anisotropy in the deep mantle on the basis of mineral physics. The mineral physics observations used include the effects of deformation mechanisms on lattice and shape preferred orientation, the effects of pressure on elastic anisotropy and the nature of lattice preferred orientation in deep mantle minerals in dislocation creep regime. Many of these issues are still poorly constrained, but a review of recent results shows that it is possible to interpret deep mantle seismic anisotropy in a unified fashion, based on the solid state processes without invoking partial melting. The key notions are (i) the likely regional variation in the magnitude of anisotropy as deformation mechanisms change from dislocation to diffusion creep (or superplasticity), associated with a change in the stress level and/or grain-size in the convecting mantle with a high Rayleigh number, and (ii) the change in elastic anisotropy with pressure in major mantle minerals, particularly in (Mg, Fe)O. The results provide the following constraints on the style of mantle convection (i) the SH > SV anisotropy in the bottom transition zone and the SV > SH anisotropy in the top lower mantle can be attributed to anisotropy structures (lattice preferred orientation and/or laminated structures) caused by the horizontal flow in this depth range, suggesting the presence of a mid-mantle boundary layer due to (partially) layered convection, (ii) the observed no significant seismic anisotropy in the deep mantle near subduction zones implies that deformation associated with subducting slabs is due mostly to diffusion creep (or superplasticity) and therefore slabs are weak in the deep mantle and hence easily deformed when encountered with resistance forces, and (iii) the SH > SV anisotropy in the cold thick portions of the D" layer is likely to be due to horizontally aligned shape preferred orientation in perovskite plus magnesiowüstite aggregates formed by strong horizontal shear motion in the recent past.     

Quantifying Damage, Saturation and Anisotropy in Cracked Rocks by Inverting Elastic Wave Velocities

Crack damage results in a decrease of elastic wave velocities and in the development of anisotropy. Using non-interactive crack effective medium theory as a fundamental tool, we calculate dry and wet elastic properties of cracked rocks in terms of a crack density tensor, average crack aspect ratio and mean crack fabric orientation from the solid grains and fluid elastic properties. Using this same tool, we show that both the anisotropy and shear-wave splitting of elastic waves can be derived. Two simple crack distributions are considered for which the predicted anisotropy depends strongly on the saturation, reaching up to 60% in the dry case. Comparison with experimental data on two granites, a basalt and a marble, shows that the range of validity of the non-interactive effective medium theory model extends to a total crack density of approximately 0.5, considering symmetries up to orthorhombic. In the isotropic case, Kachanov's (1994) non-interactive effective medium model was used in order to invert elastic wave velocities and infer both crack density and aspect ratio evolutions. Inversions are stable and give coherent results in terms of crack density and aperture evolution. Crack density variations can be interpreted in terms of crack growth and/or changes of the crack surface contact areas as cracks are being closed or opened respectively. More importantly, the recovered evolution of aspect ratio shows an exponentially decreasing aspect ratio (and therefore aperture) with pressure, which has broader geophysical implications, in particular on fluid flow. The recovered evolution of aspect ratio is also consistent with current mechanical theories of crack closure. In the anisotropic cases—both transverse isotropic and orthorhombic symmetries were considered—anisotropy and saturation patterns were well reproduced by the modelling, and mean crack fabric orientations we recovered are consistent with in situ geophysical imaging. Our results point out that: (1) It is possible to predict damage, anisotropy and saturation in terms of a crack density tensor and mean crack aspect ratio and orientation; (2) using well constrained wave velocity data, it is possible to extrapolate the contemporaneous evolution of crack density, anisotropy and saturation using wave velocity inversion as a tool; 3) using such an inversion tool opens the door in linking elastic properties, variations to permeability.     

不同温压条件下蛇纹岩和角闪岩中波速与衰减的各向异性

在实验室中研究了蛇纹岩和角闪岩样品在不同温压条件下的纵、横波速度和Q值．这两种岩样对应的主要组成矿物叶蛇纹石和普通角闪石都具有很强的晶格优选方位（LPO）．随着围压的增加,波速和Q值均增大,但是在相互正交的三个方向上（垂直或平行于层理面及线理方向）增大的速度并不相同,这与微裂隙的逐渐闭合密切相关．在600MPa的围压下升高温度直到600℃以上,由于微裂隙的热扩张受到约束,波速和Q值下降幅度很小．观测到的波速和Q值的各向异性具有不同的机理,波速各向异性主要与定向分布的微裂隙和主要矿物的LPO等构造因素有关;高围压下纵波Q值各向异性与速度各向异性正好相反,可能是由于形成层理面的定向排列的平板状矿物晶体沿不同方向边界之间接触程度不同造成的．