Open AccessGeometry of magnetosonic shocks and plane‐polarized waves: Coplanarity Variance Analysis (CVA)
Author(s) -
Scudder J. D.
Publication year - 2005
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2004ja010660
Subject(s) - coplanarity , classification of discontinuities , physics , plane (geometry) , covariance matrix , wavenumber , eigenvalues and eigenvectors , geometry , mathematical analysis , mathematics , optics , algorithm , quantum mechanics
Minimum Variance Analysis (MVA) is frequently used for the geometrical organization of a time series of vectors. The Coplanarity Variance Analysis (CVA) developed in this paper reproduces the layer geometry involving coplanar magnetosonic shocks or plane‐polarized wave trains (including normals and coplanarity directions) 300 times more precisely (<0.1°) than MVA using the same input data. The CVA technique exploits the eigenvalue degeneracy of the covariance matrix present at planar structures to find a consistent normal to the coplanarity plane of the fluctuations. Although Tangential Discontinuities (TDs) have a coplanarity plane, the eigenvalues of their covariance matrix are usually not degenerate; accordingly, CVA does not misdiagnose TDs as shocks or plane‐polarized waves. Together CVA and MVA may be used to sort between the hypotheses that the time series is caused by a one‐dimensional current layer that has magnetic disturbances that are (1) coplanar, linearly polarized (shocks/plane waves), (2) intrinsically helical (rotational/tangential discontinuities), or (3) neither 1 nor 2.