A parameter for estimating the degree of magnetic susceptibility anisotropy

Abstract

Confusion has existed in the literature over the use of the term "degree of magnetic susceptibility anisotropy". Previous parameters proposed as estimators of the anisotropy degree have no physical basis, and their motivation has been mainly operational. The low-field susceptibility can be approximated by a symmetric tensor of second rank. The tensor for isotropic susceptibility is represented as a sphere and for anisotropic susceptibility as an ellipsoid. The anisotropy degree therefore increases as the ellipsoid departes from sphericity. Thus, it seems logical that the degree of anisotropy can be estimated from the degree of departure from sphericity and measured by comparing the ellipsoids (anisotropy) with the sphere (isotropy). For this purpose we define a parameter based on the argument that solids of equal surface areas but of different volumes have different shapes and express it as the ratio of the volume of a sphere, of the same surface areas as the ellipsoid, to the volume of the ellipsoid. Simple expressions for estimating the anisotropy degree for the cases of oblate spheroids are derived. Finally, approximate expressions for estimating the degree of magnetic susceptibility anisotropy of rocks are proposed.