Methods of calculating petrophysical properties from lattice preferred orientation data

Abstract

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.

From crystal to crustal: petrofabric-derived seismic modelling of regional tectonics

“…Mainprice 1990;Barruol & Mainprice 1993;Mainprice & Humbert 1994;Lloyd & Kendall 2005). The crystal orientation of each mineral grain in a sample is measured automatically via SEM/EBSD (e.g.…”

Calculating anisotropic physical properties from texture data using the MTEX open-source package

“…Let T i1,...,ir be a tensor of rank r. It is well known (cf. Kneer 1965;Bunge 1968;Ganster & Geiss 1985;Humbert & Diz 1991;Mainprice & Humbert 1994;Morris 2006) that the rotated tensor T i1,...,ir (g) has an expansion into generalized spherical harmonics up to order r,…”

Seismic properties of the upper mantle beneath Lanzarote (Canary Islands): Model predictions based on texture measurements by EBSD

“…As lineation was never observed in these samples, the orientation data were then rotated within the foliation plane assuming olivine [100] (for the samples with a normal foliation) or [010] (for those with anomalous foliation) pole maxima (eigenvectors) as lineation indicators placed in the projection plane towards X or Z, respectively. (2) Orientation data Mainprice and Humbert, 1994;Mainprice, 1998, Pera et al, 2003) was calculated for olivine, orthopyroxene and clinopyroxene after rotation in the common reference frame. Averages were obtained by merging all the orientations of a given phase, each measurement having the same weight independently of the size of the scan.…”