A model for grain dispersion and magnetic anisotropy in sedimentary rocks

Abstract

This paper is concerned with deriving the susceptibility ellipsoids for aggregates of small anisotropic magnetic grains dispersed thinly in a nonmagnetic matrix, given the individual grain susceptibilities. The statistical orientation of the magnetic grains is assumed to be represented by a Boltzmann distribution of their individual magnetic moments in thermal equilibrium with the earth‘s ambient magnetic field. This argument is similar to that used to describe a classical paramagnetic gas, in which it is assumed that magnetic grain interactions are negligible. Once the equilibrium distribution is reached, the aggregate is assumed to be cemented, and the anisotropy of the aggregate is calculated from the susceptibility parallel to and perpendicular to the preferred direction. Two types of grains are considered, grains with prolate and oblate susceptibility ellipsoids. The aggregate susceptibility is found to be prolate with both types of grains. The conclusion reached is that this should always be so unless factors other than thermodynamic equilibrium in the earth’s field affect individual magnetic grains during the accumulation and lithification of a sedimentary rock.