New Metric for Minimum Variance Analysis Validation in the Study of Interplanetary Magnetic Clouds

Abstract

The aim of this article is to study the minimum variance analysis (MVA) degeneration problem based on the variance space geometry. We propose a mathematical metric to evaluate the separation of the eigenvalues. In the MVA method, a variance space is obtained geometrically using an ellipsoid where the axes are equal to the square root of the eigenvalues of the covariance matrix. The metric is defined as the product between the geometric flattening of the ellipsoid with respect to the three axes. In this article, we present a statistical analysis applied to the distribution of the eigenvalue ratios and the mathematical metric focussed on the study of several interplanetary coronal mass ejections with and without magnetic clouds (MCs). The results show the non-applicability of the ratio between the intermediate and minimum eigenvalues, as well as that around $90\%$ of MC events have values in the $[4.5,19.5]$ range for the defined metric. Our metric is compared with others and we show its robustness in indicating the usefulness of the MVA method to identify the axes of MCs.