Methods of calculating petrophysical properties from lattice preferred orientation data
Methods of calculating petrophysical properties from lattice preferred orientation data
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DOI：
10.1007/bf00690175
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发表时间：
1994-09
影响因子：
4.6
通讯作者：
D. Mainprice;M. Humbert
中科院分区：
文献类型：
--
作者：
D. Mainprice;M. Humbert
我们考虑从组成晶体性质和晶格择优取向计算聚集体物理性质的理论问题。引入了具有内部变化的应力和应变场分布的宏观均匀样本的概念，以解释为什么必须做出进一步的努力来改进基于物理的 Voigt 和 Reuss 边界。结果表明，随着各向异性的不断增加，Voigt 和 Reuss 边界变得越来越分离，强调需要更好的方法。斜长石和黑云母的多晶说明了高度各向异性矿物的问题。用黑云母来说明平均速度、几何平均和自洽方法。自洽方法被普遍认为可以给出最佳估计，它几乎与 Matthies 和 Humbert (1993) 最近引入的几何平均相同，并且类似于 Voigt 和 Reuss 界限的算术平均 (Hill, 1952)。几何平均值具有强大的物理条件，即聚合平均值等于逆属性（例如平均弹性刚度和柔度）的平均值。尽管缺乏理论依据，希尔平均值仍然是一个有用的估计。
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.