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1.
J.Peter Watt Richard J. O&#x;Connell 《Physics of the Earth and Planetary Interiors》1980,21(4):359-370
Existing data supporting or disputing the validity of the Hashin-Shtrikman bounds on the elastic properties of multiphase aggregates often do not consider porosity, elastic anisotropy, or experimental errors. In this experiment, two-phase aggregates of KCl + (NH4Br, TlBr, CsCl, NaCl, Cu, and LiF) at every 20% volume fraction were vacuum hot-pressed and the compressional and shear velocities were measured with a computer-controlled ultrasonic interferometer to ±0.2%. The ratio of the shear moduli, μ, (phase 2/KCl) varied from about 1 to 5, producing a range of separations between the theoretical two-phase Hashin-Shtrikman bounds for the composites. Samples were generally 99% or better of the theoretical density, with less than 1% velocity anisotropy. Porosity corrections were applied assuming spherical pores, based on the observed velocity-pressure behaviour. Velocities agreed with the HS bounds calculated from the end-member single-crystal stiffnesses when anisotropy was taken into account.The velocity data were also used to estimate the bulk modulus, K, and shear modulus of the second phase by means of the matrix method — taking the K and μ of KCl as known and calculating the moduli of the other phase assuming that the measured velocities were the two-phase Hashin-Shtrikman bounds or the Voigt-Reuss-Hill average. A narrow range of moduli estimates results only if the μ's of both phases are fairly closely matched. For μ's mismatched by a factor of 5, the theoretical uncertainty in the estimates can be 10 times larger than the experimental uncertainty. Estimates using the VRH average can lie outside the HS-based results. 相似文献
2.
Geoffrey F. Davies 《Earth and Planetary Science Letters》1974,22(4):339-346
It is demonstrated that in many cases the ratio of elastic velocities of polymorphs of a material depends primarily on the crystal structures involved, and only secondarily on the composition. Crucial to this demonstration is the use of estimates, from the Hashin-Shtrikman bounds, of the elastic properties of mixtures of simple oxides isochemical to particular compounds. Normalization to the oxide mixture properties displays the interrelationships between the densities and velocities of different crystal structures. A wide range of velocity-density trends through possible phase transitions is found. Transitions involving increases of Si coordination from 4 to 6 tend to have lower slopes. Velocity-density correlations are reasonably consistent with the average trends through phase transitions.Comparison of models of the transition zone with the characteristics of the olivine-spinel-oxides transitions indicates that in some studies the lower mantle density may have been underestimated or the mean atomic weight of the lower mantle overestimated. The transition zone of Model B1 of Jordan and Anderson, which was derived entirely from seismic data, is consistent, overall, with the olivine-oxides transition and uniform composition, but the individual discontinuities are not consistent with the olivine-spinel and spinel-oxides transitions. 相似文献
3.
经典的微分等效介质(DEM)理论可用于确定多孔介质的弹性性质,但由于缺乏多重孔DEM方程,其估计的多重孔岩石的等效弹性模量依赖于包裹体(即不同孔隙纵横比的孔或缝)的添加顺序.本文首先从Kuster-Toksöz理论出发建立了Zimmermann和Norris两种形式的多重孔DEM方程.Norris形式的多重孔DEM方程预测的等效弹性模量总是位于Hashin-Shtrikman上下限内,而Zimmermann形式的多重孔DEM方程有时会越界.然后,通过使用干燥岩石模量比的解析近似式,对两个相互耦合的Norris形式DEM方程进行解耦得到干燥多重孔岩石的体积和剪切模量解析式.用全DEM方程的数值解对解析近似式的有效性进行了测试,解析公式的计算结果在整个孔隙度分布区间与数值解吻合良好.对实验室测量数据在假设岩石含有双重孔隙的情形下用双重孔DEM解析公式对岩石的弹性模量进行了预测,结果表明,解析式准确地预测了弹性模量随孔隙度的变化.双重孔(即软、硬孔)DEM解析模型可用来反演各孔隙类型的孔隙体积比,它可以通过实验室测量与理论预测之间的平方误差最小反演得到.砂岩样品的反演结果揭示,软孔的孔隙体积百分比与粘土含量没有明显的相关性. 相似文献
4.
Harve S. Waff 《Surveys in Geophysics》1980,4(1-2):31-41
This paper examines the constraint placed by electrical conductivity on physical conditions existing within the mantle. Determination of bulk electrical conductivities of multiphase materials from knowledge of individual phase conductivities and their relative fractions is discussed in the light of recent studies of the equilibrium phase geometries of partial melts. It is concluded that existing models which are based on assumed geometries offer little refinement over Hashin-Shtrikman variational bounds. The possible effects of the gravitational field on phase geometry in partial melts and the resulting conductivity anisotropy are considered. At this time it appears that minimum melt fractions can be safely estimated from a knowledge of Earth conductivity combined with laboratory data on melt and crystalline conductivities and the Hashin-Shtrikman upper bound. The question of whether or not the asthenosphere corresponds to a zone of partial melting is also addressed. 相似文献
5.
研究青藏高原东缘地区的深部物质结构对于理解青藏高原的隆升及扩张机制具有重要的科学意义.本文将青藏高原东缘实测大地电磁测深剖面反演所得的岩石圈电性结构模型与高温高压岩石物理实验测得的上地幔矿物和熔融体导电性定量关系相结合,通过Hashin-Shtrikman(HS)边界条件建立上地幔电导率与温度、熔融百分比等参数的定量关系,在此基础上计算得到了青藏高原东缘上地幔热结构及熔融百分比分布模型.研究结果表明在青藏高原东缘地区通过大地电磁测深方法所探测到的上地幔低阻体可以解释为由高温作用所产生的局部熔融区域.其中,松潘—甘孜地块上地幔高导体对应的温度介于1300～1500℃之间,熔融百分比可高达10%,支持前人将松潘—甘孜地块内部的低阻体解释为局部熔融的观点.龙门山断裂带以东、四川盆地西缘的上地幔高导体温度介于1200～1400℃之间,熔融百分比介于1%～5%左右,表明扬子克拉通的西缘可能正在经历一定程度的活化作用.龙门山断裂带下方的上地幔高阻体温度介于1100℃附近,基本没有发生局部熔融,具有较冷的刚性块体特征,与该区域频发的地震活动相吻合.四川盆地东部的扬子上地幔温度介于800～900℃之间,没有发生局部熔融,符合古老稳定的克拉通块体的基本特征. 相似文献
6.
近年来围绕四川盆地侏罗系陆相致密砂岩已取得了勘探突破,其中川中—川西过渡带具备形成大气田的地质条件,但对该套致密砂岩弹性性质变化规律的研究还较少,致使利用地震方法进行"甜点"储层预测的精度不高.本文利用四川盆地侏罗系沙溪庙组32块样品开展了系统的声学测量,在此基础上,分析了样品弹性性质的变化规律.结合X射线衍射矿物组分分析、扫描电镜、铸体薄片和岩石薄片特征确定了不同成岩作用对岩石储集性能的影响.研究结果表明,研究区致密砂岩储层表现为孔隙型储层,受差异性成岩作用影响,黏土含量、钙质含量和硅质含量的差异以及它们分布特征之间的差异对岩石弹性性质造成了很大的影响.在研究区对岩石物性及弹性性质有明显影响的成岩作用包括早期的钙质胶结作用、压实作用和溶蚀作用,因此针对不同时期的成岩作用对岩石弹性及物性的影响,利用接触-胶结模型、微分等效模量模型和临界孔隙度校正的Hashin-Shtrikman上限模型建立了研究区致密砂岩的岩石物理模型. 相似文献
7.
Methods of calculating petrophysical properties from lattice preferred orientation data 总被引：13，自引：0，他引：13
We consider the theoretical problems of calculating the physical properties of an aggregate from the constituent crystal properties and the lattice preferred orientation. The notion of a macroscopically homogeneous sample with an internally varing distribution of stress and strain fields is introduced to explain why further efforts have to be made to improve on the physically based Voigt and Reuss bounds. It is shown that the Voigt and Reuss bounds become increasingly separated with inceasing anisotropy, emphasising the need for better methods. The problem of highly anisotropic minerals is illustrated with polycrystals of plagioclase feldspar and biotite. Biotite is used to illustrate the mean velocity, the geometric mean and the self-consistent methods. The self-consistent method, which is generally accepted to give the best estimate, is almost identical to geometric mean recently introduced by Matthies and Humbert (1993) and similar to the arithmetic mean of the Voigt and Reuss bounds (Hill, 1952). The geometric mean has the powerful physical condition that the aggregate mean is equal to the mean of the inverse property (e.g. mean elastic stiffness and compliance). Despite its lack of theoretical justification the Hill average remains a useful estimate. 相似文献
8.
Yu-Qian Guo Hong-Da Ma Kai-Bo Shi Hong Cao Lu-Zhong Huang Feng-Chang Yao Tian-Yue Hu 《应用地球物理》2013,10(4):411-422
Most of the carbonates in the Tarim Basin in northwest China are low-porosity and low-permeability rocks. Owing to the complexity of porosity in carbonates, conventional rockphysics models do not describe the relation between velocity and porosity for the Tarim Basin carbonates well. We propose the porous-grain-upper-boundary (PGU) model for estimating the relation between velocity and porosity for low-porosity carbonates. In this model, the carbonate sediments are treated as packed media of porous elastic grains, and the carbonate pores are divided into isolated and connected pores The PGU model is modified from the porous-grain-stiff-sand (PGST) model by replacing the critical porosity with the more practical isolated porosity. In the implementation, the effective elastic constants of the porous grains are calculated by using the differential effective medium (DEM) model. Then, the elastic constants of connected porous grains in dry rocks are calculated by using the modified upper Hashin-Shtrikman bound. The application to the Tarim carbonates shows that relative to other conventional effective medium models the PGU model matches the well log data well. 相似文献
9.
基于Ｍａｘｗｅｌｌ和Ｋｅｌｖｉｎ流变模型，以延续时间与松弛期的比值，即松弛数，作为衡量指标，对地壳、上地幔不同层次的变形属性进行了判别。结果表明，除软流圈地幔主要为粘性流动外，其上各层的情况是：在漫长的地质过程中，不仅岩石圈地幔和下地壳属于粘性，上地壳也有可能处于粘性流动状态；在延续数十年的情况下，上地壳以及岩石圈地幔都可能呈弹性状态；延续时间介乎二者，通常上地壳为弹性，下地壳和岩石圈地幔为粘性或滞弹粘性。此外，还结合变形属性的判别，就岩石圈地幔的流动和板内的驱动力远程传递等问题进行了讨论 相似文献
10.
This activation volume ΔV for creep may be derived from Keyes's elastic strain energy model or from Weertman's empirical relationship between viscosity and the melting temperature. These formulations are shown to be equivalent if the anharmonic Grüneisen parameters γ of all acoustic modes are equal and if the pressure dependence of the melting temperature follows Lindemann's law, both of which assumptions are valid for the close-packed mineral structure of the lower mantle. The pressure derivative of ΔV depends only on the bulk modulus and the acoustic γ, both of which are directly available from seismic models. Using the data of Brown and Shankland, we show that ΔV decreases by almost 50% between the top and the bottom of the lower mantle, which makes it easier to maintain a constant viscosity in this region. The isoviscous temperature profile can be adiabatic in the deep lower mantle only below 1700 km depth; it is super-adiabatic in the top 1000 km of the lower mantle. 相似文献
11.
The traditional view of the rheology of the continental lithosphere, sometimes known as the “jelly sandwich model”, consists of a strong upper crust, a weak lower crust, and a strong upper lithospheric mantle. Some authors argue, however, that the lithospheric mantle is weak and contributes little to the total strength and the effective elastic thickness of the lithosphere; this weakness is claimed to be due to the mantle being wet or subjected to temperatures higher than usually believed. This paper uses the relationship between rheology of the lithosphere and heat flow to calculate theoretical effective elastic thicknesses for three regions of the central Iberian Peninsula (the Duero Basin, the Spanish Central System and the Tajo Basin), taking into account the contribution of the crust and the lithospheric mantle, for dry and wet rheologies. We found that a wet peridotite rheology for the lithospheric mantle is generally consistent with independent (based on Bouguer coherence or flexural modeling) estimates of the effective elastic thickness for the study area, whereas a dry peridotite rheology cannot be reconciled with them. Moreover, the contribution of the mantle to the bending moment of the lithosphere, and therefore to both the effective elastic thickness and the total strength of the lithosphere, is important, and it may even be the dominant contribution. Therefore, the jelly sandwich model may be considered valid for the central Iberian Peninsula. 相似文献
12.
华北克拉通破坏动力机制研究导致了全球动力系统及“板块动力模型”研究.板块运动最有可能的动力是地幔物质流动,但由于地幔物质流动的成因至今尚未查明,所以板块构造学说研究仍处于“运动模型”阶段,而没有进入“动力模型”阶段.如果地幔密度异常是驱动地幔物质流动的成因,那么就有可能基于重力学方法以“板块动力模型”的形式建立地幔密度异常驱动模式;软流圈中可能存在着动力特性不同的区块,地幔密度正异常代表物质盈余、区块内的物质要向区块外移动,地幔密度负异常代表物质亏损、区块外的物质要向区块内移动.本项目采用重力和地震资料相结合研究地球的整体分层,根据重力大地水准面联合地震波速度结构反演求解地幔密度异常,再根据地球正常密度假说和板块运动重力学机制的观点并与现有“板块运动模型”相结合,分析地幔密度异常动力区块,初步建立“基于重力学机制的板块动力模型”;为最终建立多学科机制的“全球板块动力模型”,迈出重要一步. 相似文献
13.
T. J. Shankland 《Surveys in Geophysics》1977,3(1):69-100
The observed systematic relations between velocities, density, and crystal structure in minerals are viewed as part of the general problem of the interactions of ions and electrons in solids. A complete explanation of these systematics would result from an adequate physical model of interactions between atoms in a crystal. For ionic models, understanding such interactions mainly requires knowledge of inter-ionic repulsive forces, which can be calculated from solutions for the electronic energy levels. The main forms of systematics developed in the last few years can be classed either as bulk modulus-molar volume (K-V
M
) or, equivalently, velocity-density (v-p) relations. Isostructural and isochemical (having constant mean atomic weight
) trends exist, and for both classes of systematics it is possible to produce semi-empirical universal expressions with the ability to predict elastic properties to a few percent. The best estimates of composition of the Earth's interior come from comparisons of mineral elastic properties with seismic data. On the basis of current velocity profiles of the Earth, the mantle appears to be chemically homogeneous. 相似文献
14.
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. 相似文献
15.
16.
—A seismological characterization of crust and upper mantle can refer to large-scale averages of seismic velocities or to fluctuations of elastic parameters. Large is understood here relative to the wavelength used to probe the earth.¶In this paper we try to characterize crust and upper mantle by the fluctuations in media properties rather than by their average velocities. As such it becomes evident that different scales of heterogeneities prevail in different layers of crust and mantle. Although we cannot provide final models and an explanation of why these different scales exist, we believe that scales of inhomogeneities carry significant information regarding the tectonic processes that have affected the lower crust, the lithospheric and the sublithospheric upper mantle.¶We focus on four different types of small-scale inhomogeneities (1) the characteristics of the lower crust, (2) velocity fluctuations in the uppermost mantle, (3) scattering in the lowermost lithosphere and on (4) heterogeneities in the mantle transition zone. 相似文献
17.
Ashley E. Medin Robert L. Parker Steven Constable 《Physics of the Earth and Planetary Interiors》2007,160(1):51-59
We examine the nonlinear inverse problem of electromagnetic induction to recover electrical conductivity. As this is an ill-posed problem based on inaccurate data, there is a critical need to find the reliable features of the models of electrical conductivity. We present a method for obtaining bounds on Earth’s average conductivity that all conductivity profiles must obey. Our method is based completely on optimization theory for an all-at-once approach to inverting frequency-domain electromagnetic data. The forward modeling equations are constraints in an optimization problem solving for the electric fields and the conductivity simultaneously. There is no regularization required to solve the problem. The computational framework easily allows additional inequality constraints to be imposed, allowing us to further narrow the bounds. We draw conclusions from a global geomagnetic depth sounding data set and compare with laboratory results, inferring temperature and water content through published Boltzmann-Arrhenius conductivity models. If the upper mantle is assumed to be volatile free we find it has an average temperature of 1409-1539 ° C. For the top 1000 km of the lower mantle, we find an average temperature of 1849-2008 ° C. These are in agreement with generally accepted mantle temperatures. Our conclusions about water content of the transition zone disagree with previous research. With our bounds on conductivity, we calculate a transition zone consisting entirely of Wadsleyite has <0.27 wt.% water and as we add in a fraction of Ringwoodite, the upper bound on water content decreases proportionally. This water content is less than the 0.4 wt.% water required for melt or pooling at the 410 km seismic discontinuity. 相似文献
18.
M. S. Molodenskii 《Izvestiya Physics of the Solid Earth》2009,45(9):832-837
The paper presents the results of analytical and numerical model calculations of elastic surface displacements caused by earthquakes
and the processes of earthquake nucleation. The analytical calculations are focused on the model of a homogeneous elastic
space; the numerical calculations also cover models of radially inhomogeneous distributions of elastic moduli in the crust
and upper mantle described by the PREM model. 相似文献
19.
Long period Rayleigh wave and Love wave dispersion data, particularly for oceanic areas, have not been simultaneously satisfied by an isotropic structure. In this paper available phase and group velocity data are inverted by a procedure which includes the effects of transverse anisotropy, anelastic dispersion, sphericity, and gravity. We assume that the surface wave data represents an azimuthal average of actual velocities. Thus, we can treat the mantle as transversely isotropic. The resulting models for average Earth, average ocean, and oceanic regions divided according to the age of the ocean floor, are quite different from previous results which ignore the above effects. The models show a low-velocity zone with age dependent anisotropy and velocities higher than derived in previous surface wave studies. The correspondence between the anisotropy variation with age and a physical model based on flow aligned olivine is suggestive. For most of the Earth SH > SV in the vicinity of the low-velocity zone. Neat the East Pacific Rise, however, SV > SH at depth, consistent with ascending flow. Anisotropy is as important as temperature in causing radial and lateral variations in velocity. The models have a high velocity nearly isotropic layer at the top of the mantle that thickens with age. This layer defines the LID, or seismic lithosphere. In the Pacific, the LID thickens with age to a maximum thickness of ～50 km. This thickness is comparable to the thickness of the elastic lithosphere. The LID thickness is thinner than derived using isotropic or pseudo-isotropic procedures. A new model for average Earth is obtained which includes a thin LID. This model extends the fit of a PREM, type model to shorter period surface waves. 相似文献
20.
The shape and location of clay within sandstones have a large impact on the P‐wave and S‐wave velocities of the rock. They also have a large effect on reservoir properties and the interpretation of those properties from seismic data and well logs. Numerical models of different distributions of clay – structural, laminar and dispersed clay – can lead to an understanding of these effects. Clay which is located between quartz grains, structural clay, will reduce the P‐wave and S‐wave velocities of the rock. If the clay particles become aligned or form layers, the velocities perpendicular to the alignment will be reduced further. S‐wave velocities decrease more rapidly than P‐wave velocities with increasing clay content, and therefore Poisson's ratios will increase as the velocities decrease. These effects are more pronounced for compacted sandstones. Small amounts of clay that are located in the pore space will have little effect on the P‐wave velocity due to the competing influence of the density effect and pore‐fluid stiffening. The S‐wave velocity will decrease due to the density effect and thus the Poisson's ratio will increase. When there is sufficient clay to bridge the gaps between the quartz grains, P‐wave and S‐wave velocities rise rapidly and the Poisson's ratios decrease. These effects are more pronounced for under‐compacted sandstones. These general results are only slightly modified when the intrinsic anisotropy of the clay material is taken into account. Numerical models indicate that there is a strong, nearly linear relationship between P‐wave and S‐wave velocity which is almost independent of clay distribution. S‐wave velocities can be predicted reasonably accurately from P‐wave velocities based on empirical relationships. However, this does not provide any connection between the elastic and petrophysical properties of the rocks. Numerical modelling offers this connection but requires the inclusion of clay distribution and anisotropy to provide a model that is consistent with both the elastic and petrophysical properties. If clay distribution is ignored, predicting porosities from P‐wave or S‐wave data, for example, can result in large errors. Estimation of the clay distribution from P‐wave and S‐wave velocities requires good estimates of the porosity and clay volume and verification from petrographic analyses of core or cuttings. For a real data example, numerical models of the elastic properties suggest the predominance of dispersed clay in a fluvial sand from matching P‐wave and S‐wave velocity well log data using log‐based estimates of the clay volume and porosity. This is consistent with an interpretation of other log data. 相似文献