5. Discussion and Summary

Although it seems mathematically trivial, Equation (1.2) is one of the most important results in our review. It describes all physical effects on the measured magnetic field and provides a rigorous theoretical foundation for minimum variance analyses of the magnetic field. It shows that the minimum variance analyses are based on a one-dimensional assumption but do not require a steady state. If the minimum variance analyses also depended on the steady state assumption as many people perceived since it was first developed to analyze discontinuity, it would not have been applicable to wave analysis.

Another fundamental result is the derivation of Equation (4.6) which provides a unified theory for correlation analyses. Every existing correlation analysis technique can be found to be a special case of this equation. This expression specifies clearly the assumptions upon which each technique is based. In developing data analysis methods for Cluster missions, one needs to compare the methods against this expression in order to identify the effects that are neglected in the methods and justify for the simplification. We emphasize that at the practical level there has not yet been sufficient analysis of multiple satellites data to test and refine many of the techniques discussed herein.

On one hand, discontinuity analysis is, among time series data analysis methods, best understood and its computer programs are most user-friendly. It is widely used. However on the other hand, the errors of the analysis have not been recognized as widely as it should. Occasionally, one may see in publication a discontinuity is presented in boundary normal coordinates with an unequal normal magnetic field across it.

Multiple parameter best fits are often used to determine unmeasured shock parameters. As we now know that this method in practice usually has a large uncertainty and may provide a large range of solutions with a small difference in input parameters. Here we again urge caution in using this method.

In wave analysis, a common trend is that fewer and fewer people actually analyze the time series data itself, and more and more people rely on dynamic spectrograms. Occasionally, one sees that a field rotation is interpreted as broadband emission that last for a period of the window length. Here we strongly urge analysts to examine the original time series data. On the other hand, there is a significant room for further improving the techniques of wave analysis.

In addition to mastering the various analysis methods, an analyst has to possess adequate knowledge of the data set he/she is using. From our experience, direct collaboration with an builder of the instrument is an effective way to ensure that the data is utilized correctly. However this is still no substitute for the proper documentation of the instruments and the data stream.

Acknowledgments. This work was supported by NASA under research grants NAGW-3948, NAGW-3974, NAG5-4066 and NAG5-3880 to UCLA, and by National Science Foundation/Office of Naval Research under research grant NSF-ATM 9713492. The authors are grateful to Bengt Sonnerup for useful discussions.

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