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. Plain Language Summary Models are helpful when we aim at understanding and interpreting measured data, provided that they are applicable to reality. This paper presents a new model to predict magnetic properties and their directional dependence (anisotropy) of strongly magnetic particles (e.g., magnetite or pores filled with strongly magnetic fluid) in rock samples. This model is applicable to irregular assemblies of particles of various sizes and orientations and thus helps close the gap between existing models and reality. The model helps us understand the sources of magnetic anisotropy and thus makes magnetic anisotropy an even more valuable tool to investigate preferred alignment of magnetite or pores in rocks.

Explaining the large variability in empirical relationships between magnetic pore fabrics and pore space properties

“…All D.T. samples apart from the (a) series possess both shape and distribution anisotropy, and their expected directional susceptibilities were computed using the FinIrrSDA code (Biedermann, 2020).…”

“…All data is reported in the paper and supplementary materials. The FinIrrSDA model used here for the predictions has been previously published (Biedermann, 2020), and the code is available on https://zenodo.org/record/4040785.…”

“…Rocks contain numerous pores in a complex and irregular three-dimensional network, and distribution anisotropy, arising from magnetostatic interaction of the ferrofluid in different pores, also contributes to the measured anisotropy (Biedermann, 2019, Biedermann, 2020. Distribution anisotropy has been extensively investigated for magnetite grains in rocks (Grégoire et al, 1998, Grégoire et al, 1995, Hargraves et al, 1991, Cañón-Tapia, 1996, Cañón-Tapia, 2001, Stephenson, 1994, and is described in a similar way for MPFs (Biedermann, 2019, Biedermann, 2020. Thus, the MPF depends not only on the pores' shape preferred orientation as proposed initially, but also on the distribution of the pores throughout the rock.…”

Ferrofluid Impregnation Efficiency and Its Spatial Variability in Natural and Synthetic Porous Media: Implications for Magnetic Pore Fabric Studies

“…While large efforts have been made to study empirical correlations between MPFs and pore shapes or other anisotropic properties, or to improve our understanding of how MPFs arise (Benson et al 2003 ; Biedermann, 2019 , 2020 ; Biedermann et al 2021 ; Hailwood et al 1999 ; Hrouda et al 2000 ; Jezek and Hrouda 2007 ; Jones et al 2006 ; Louis et al 2005 ; Pfleiderer and Halls, 1993 , 1994 ; Robion et al 2014 ), relatively little is known about the ferrofluid impregnation process itself. Valuable insights on this process and its evolution over time were obtained here from impregnating transparent TEOS and agarose gel samples.…”

Decrypting Magnetic Fabrics (AMS, AARM, AIRM) Through the Analysis of Mineral Shape Fabrics and Distribution Anisotropy

“…SPO analyses have also been conducted using high-resolution X-ray micro-computed tomography imaging (µXCT), which offers the opportunity to obtain 3D grain shape and location data on the same sample as analyzed with AMS (Schöpa et al, 2015;Zhu et al, 2017). However, unlike experimental and theoretical approaches (Biedermann, 2019(Biedermann, , 2020bGaillot et al, 2006;Grégoire et al, 1995;Hargraves et al, 1991;Stephenson, 1994), petrofabric studies on natural rocks have so far not been able to show a close relationship between DA and the AMS ellipsoid axes orientation and shape. The large center to center spacing that occurs between ferrimagnetic grains in many rock types likely rendered magnetic interactions largely negligible (Grégoire et al, 1998;Schöpa et al, 2015).…”