Methods of calculating petrophysical properties from lattice preferred orientation data

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.