The Achilles Heel of Normal Determinations via Minimum Variance Techniques: Worldline Dependencies

Details The Achilles Heel of Normal Determinations via Minimum Variance Techniques: Worldline Dependencies The Achilles Heel of Normal Determinations via Minimum Variance Techniques: Worldline Dependencies

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agufmsm11b0433m&link_type=abstract

American Geophysical Union, Fall Meeting 2002, abstract #SM11B-0433

Physics

2109 Discontinuities, 2411 Electric Fields (2712), 2748 Magnetotail Boundary Layers, 2794 Instruments And Techniques

Scientific paper

Time series of data collected across current layers are usually organized by divining coordinate transformations (as from minimum variance) that permits a geometrical interpretation for the data collected. Almost without exception the current layer geometry is inferred by supposing that the current carrying layer is locally planar. Only after this geometry is ``determined'' can the various quantities predicted by theory calculated. The precision of reconnection rated ``measured'' and the quantitative support for or against component reconnection be evaluated. This paper defines worldline traversals across fully resolved Hall two fluid models of reconnecting current sheets (with varying sizes of guide fields) and across a 2-D hybrid solution of a super critical shock layer. Along each worldline various variance techniques are used to infer current sheet normals based on the data observed along this worldline alone. We then contrast these inferred normals with those known from the overview of the fully resolved spatial pictures of the layer. Absolute errors of 20 degrees in the normal are quite commonplace, but errors of 40-90 deg are also implied, especially for worldlines that make more and more oblique angles to the true current sheet normal. These mistaken ``inferences'' are traceable to the degree that the data collected sample 2-D variations within these layers or not. While it is not surprising that these variance techniques give incorrect errors in the presence of layers that possess 2-D variations, it is illuminating that such large errors need not be signalled by the traditional error formulae for the error cones on normals that have been previously used to estimate the errors of normal choices. Frequently the absolute errors that depend on worldline path can be 10 times the random error that formulae would predict based on eigenvalues of the covariance matrix. A given time series cannot be associated in any a priori way with a specific worldline. Accordingly, the errors possible considering a variety of possible world lines is the only sure way to understand the imprecision of the normal from a given passage across a current sheet layer. Of course multiple spacecraft penetrating the same layer during an elapsed interval short to the evolution of the layer may help with this ambiguity. For a given crossing the remaining conservation laws beyond those exploited in minimum variance and Faraday Residue techniques may more constructively limit the error cone on the normal.

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