This paper presents a theory for the anomalous magnetic gradient tensor due to a uniformly magnetised general triaxial ellipsoid. Expressions for the magnetic field vector and its gradient tensor are derived from expressions for the gravitational field or the gravity gradient tensor via an application of Poisson’s theorem. This theory provides increased capability in forward modelling, inversion and equivalent source applications in both magnetic and gravimetric exploration. It provides an accurate and computationally efficient means of modelling the magnetic gradient tensor of ellipsoidal bodies which may possess isotropic or anisotropic magnetic susceptibility, remanent magnetisation and, in the case of highly magnetic ellipsoids, may be subject to the effect of self-demagnetisation. This paper presents a novel method based on the eigenvector decomposition of the magnetic gradient tensor to provide estimates of the magnetisation direction over an ellipsoidal source. This includes an investigation of the influence of shape detail, observation height and inclination of magnetisation on the positioning of global maxima in normalised source strength and how this affects the problem of estimating magnetisation direction. This study confirms that magnetisation directions may be accurately estimated for extremely elongated ellipsoidal bodies where the ratio of smallest observation height to maximum elongation (in plan view) is greater than 1.

中文翻译：

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三轴椭球的磁梯度张量、其推导及其在确定磁化方向中的应用

本文提出了由均匀磁化的一般三轴椭球引起的异常磁梯度张量的理论。磁场矢量及其梯度张量的表达式是通过应用泊松定理从引力场或重力梯度张量的表达式导出的。该理论在磁和重力勘探中的正向建模、反演和等效源应用中提供了增强的能力。它提供了一种精确且计算效率高的方法来模拟椭球体的磁梯度张量，这些椭球体可能具有各向同性或各向异性的磁化率、剩磁，并且在高磁性椭球的情况下，可能会受到自退磁的影响。本文提出了一种基于磁梯度张量的特征向量分解的新方法，以提供对椭球源磁化方向的估计。这包括调查形状细节、观测高度和磁化倾角对归一化源强度中全局最大值定位的影响，以及这如何影响估计磁化方向的问题。这项研究证实，对于极细长的椭球体，可以准确估计磁化方向，其中最小观测高度与最大伸长率（在平面图中）的比率大于 1。观测高度和磁化倾角在归一化源强度中全局最大值的定位以及这如何影响估计磁化方向的问题。这项研究证实，对于极细长的椭球体，可以准确估计磁化方向，其中最小观测高度与最大伸长率（在平面图中）的比率大于 1。观测高度和磁化倾角在归一化源强度中全局最大值的定位以及这如何影响估计磁化方向的问题。这项研究证实，对于极细长的椭球体，可以准确估计磁化方向，其中最小观测高度与最大伸长率（在平面图中）的比率大于 1。