FinIrrSDA: A 3-D Model for Magnetic Shape and Distribution Anisotropy of Finite Irregular Arrangements of Particles With Different Sizes, Geometries, and Orientations

Abstract

The magnetic anisotropy carried by strongly magnetic particles such as magnetite or ferrofluid-filled pores is generally composed of shape anisotropy and distribution anisotropy. Their relative importance in rocks depends on numerous factors and has been discussed controversially. A major challenge in estimating their contributions so far has been that models for distribution anisotropy only exist for regular arrangements of equal particles along lines or in planes. Because magnetite grains or pores in rocks display wide ranges of orientations, shapes, and sizes in generally irregular arrangements, new models are needed to describe distribution anisotropy for more realistic grain and pore assemblies. The model presented in this study, FinIrrSDA, calculates shape and distribution anisotropy for finite irregular assemblies of unequal particles with different orientations. Input parameters are provided as a table with x, y, and z coordinates of the particle centers and the lengths and orientations of the major, intermediate, and minor axes of best fit ellipsoids. The model output consists of two susceptibility tensors: (1) the shape anisotropy tensor and (2) the total tensor combining shape and distribution anisotropies. FinIrrSDA can be applied to a wide range of input data sets, including known structures of synthetic samples, particle analyses from tomography data, and, subject to certain assumptions, 2-D images. The model will hopefully increase our understanding of the interplay between shape and distribution anisotropies in natural rocks and facilitate future interpretations of both the magnetic anisotropy carried by magnetite grains and magnetic pore fabrics.