Mathematical Model of Anisotropy of  Magnetic Susceptibility (AMS)

William W. Guo

doi:10.4236/jamp.2015.34050

Abstract

Magnetic susceptibility of natural rocks and ores is important in many applications. In a few rock types magnetic susceptibility is independent of the direction in which a weak magnetic field is applied. Such rocks are magnetically isotropic. In most rock types, however, the magnitude of magnetic susceptibility in a constant weak field depends on the orientation of the magnetic field applied. Such rocks are magnetically anisotropic and such directional variation in magnetic susceptibility with these rocks is termed as anisotropy of magnetic susceptibility (AMS). Although attempts have been made on describing AMS using mathematical models, there is still a need to present a more consistent and united mathematical process for AMS. This paper presents a united AMS model by rationalizing the existing pieces of different AMS models through a consistent approach. A few examples of AMS from some types of natural rocks and ores are also presented to substantiate this united AMS model.

Highlights

Magnetic susceptibility of natural rocks and ores plays important roles either directly or indirectly in many applications, such as oil and mineral explorations [1]-[3], geology [4], climate change and environment assessment [5] [6], mining and metallurgy [7] [8], and archeology [9]
Such directional variation in magnetic susceptibility with some rocks and ores is termed as anisotropy of magnetic susceptibility (AMS)
This indicates that the three principal susceptibilities are parallel to their corresponding populations of magnetic field, and no interactions occur among the three orthogonal populations

Summary

Introduction

Magnetic susceptibility of natural rocks and ores plays important roles either directly or indirectly in many applications, such as oil and mineral explorations [1]-[3], geology [4], climate change and environment assessment [5] [6], mining and metallurgy [7] [8], and archeology [9]. In a few rock types the induced magnetization in symmetrically shaped specimens is independent of the direction in which a weak magnetic field is applied. By Equations (1) and (4), in the new coordinates, the populations of induced magnetization are expressed as This indicates that the three principal susceptibilities are parallel to their corresponding populations of magnetic field, and no interactions occur among the three orthogonal populations. For an anisotropic material, assuming there is an angle θ between the induced magnetization J and the applied field H , and the projection of J to H , or the directional magnetization JH can be expressed as. The minimum susceptibility axis is normal to the magnetic foliation plane so it can be regarded as the pole to the foliation plane (Figure 1)

Examples of AMS of Rocks and Iron Ores

Conclusion