Magnetic fabrics and petrofabrics: their orientation distributions and anisotropies

Magnetic-fabric and other petrofabric anisotropies may be described by second-rank tensors represented by ellipsoids. For a homogeneous petrofabric that is adequately sampled, a stereoplot of the orientation-distribution of the tensors' principal axes (maximum, intermediate and minimum) should show three orthogonal concentrations. The concentrations form some combination of shapes from circular clusters through partial girdles to full girdles. The concentrations' elliptical eccentricities are constrained by the symmetry of the sample-orientation-distribution (i.e. L, L > S, L = S etc.) as well as the individual sample-anisotropies. The mean orientations of principal axes must be orthogonal, just as with individual sample-tensors. This requires tensor-statistics for their calculation (Jelinek, 1978). Furthermore, elliptical confidence cones for the means should parallel principal planes, preserving overall orthorhombic symmetry. However, in practice, sub-orthorhombic symmetry may arise from unrepresentative sampling but it may also be a useful indicator of multiple or heterogeneous petrofabrics. In the case of magnetic fabrics, the wide range in average susceptibility values and variation in magnetic mineralogy permit small numbers of high-susceptibility samples to deflect the orientation of the tensor-mean away from the majority of samples. Normalizing the samples by their bulk susceptibility overcomes this, but the orientation of high-susceptibility outliers may signify an event or subfabric of importance that we should not discard. Therefore, stereoplots of both normalized and non-normalized orientation-distributions should be compared, preferably also identifying the outliers. It is important to distinguish the shape of the orientation distribution ellipsoid from the shape of the individual magnetic fabric ellipsoids. (The qualitative L-S nomenclature is best replaced by Tj where Tj = + 1 = oblate; Tj = - 1 = prolate (Jelinek, 1981).) Invariably, the orientation distribution is described by an ellipsoid whose shape is more spherical than that of the individual sample-anisotropy ellipsoids because the latter have scattered orientations. Furthermore, the shape of the orientation-distribution ellipsoid need bear no relation to the shape of individual sample-ellipsoid anisotropies. The concepts are illustrated with 1119 measurements of anisotropy of magnetic susceptibility (AMS) from seven areas and with 188 measurements of anisotropy of anhysteretic remanence (AARM) from two areas. (C) 2001 Elsevier Science Ltd. All rights reserved.