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

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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.

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Notes

  1. http://www.srl.caltech.edu/ACE/ASC/level2/index.html accessed on May 20, 2019.

  2. http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm accessed on May 20, 2019.

  3. https://wind.gsfc.nasa.gov/mfi/mag_cloud_pub1.html accessed on October 01, 2019.

  4. https://cdaweb.gsfc.nasa.gov/istp_public/ accessed on October 01, 2019.

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Acknowledgements

R.A. Rosa Oliveira thanks PROSUC-CAPES for the PhD scholarship in the Physics and Astronomy course at UNIVAP. A. Ojeda-González wishes to thank CNPq for financial support (grant 431396/2018-3). In addition, the authors would like to thank the ACE and Wind science team members for the data sets used in this work. V. De la Luz thanks to CONACyT Ciencia Básica (254497) support. We also wish to thank the anonymous referee.

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Authors and Affiliations

  1. Physics and Astronomy Laboratory, Universidade do Vale do Paraíba-UNIVAP, São José dos Campos, São Paulo, Brazil

    Rosemeire Aparecida Rosa Oliveira, Marcos William da Silva Oliveira & Arian Ojeda-González

  2. Federal Institute of Education, Science and Technology of São Paulo - IFSP, São José dos Campos, São Paulo, Brazil

    Marcos William da Silva Oliveira

  3. Escuela Nacional de Estudios Superiores, Unidad Morelia, Universidad Nacional Autónoma de México, 58190, Morelia, Michoacán, Mexico

    Victor De La Luz

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  1. Rosemeire Aparecida Rosa Oliveira
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Rosa Oliveira, R.A., da Silva Oliveira, M.W., Ojeda-González, A. et al. New Metric for Minimum Variance Analysis Validation in the Study of Interplanetary Magnetic Clouds. Sol Phys 295, 45 (2020). https://doi.org/10.1007/s11207-020-01610-6

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