On the reliability of the AMS ellipsoid by statistical methods

• Analyzing the reliability of Hext and bootstrap methods to estimate the AMS ellipsoid.
• Using different configurations of errors, AMS parameters and number of measurements.
• Methods are not reliable when the eigenvalues are too close.
• Increasing number of measurements provide smaller errors and better reliability.

Weak magnetic materials whose susceptibility values are close to the instrument's accuracy show very large errors in the direct evaluation of their ellipsoid parameters. This may lead to misinterpretation of the magnetic fabric, which is often used as a geological indicator. In order to estimate the measurement uncertainties, several statistical methods have been proposed. Within the available statistical methods, the Linear Perturbation Analysis (Hext, 1963) and the non-parametric bootstrap (Constable and Tauxe, 1990) technique have been widely used. In this paper, we make a complete study about these methods to estimate their limitations when applied to n measurements of a single sample. We will analyze which method is better in terms of uncertainties, we will determine when the methods do not provide reliable results and we will establish a measuring protocol. For that, we run simulations for the Linear Perturbation Analysis and the non-parametric bootstrap varying i) the number of measurements, ii) the instrumental error and iii) the shape parameter and the anisotropy degree of the AMS ellipsoid. The results show that both methods are not reliable when the difference between eigenvalues is too close in relation to the instrumental error, but increasing the number of measurements can improve the results.

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