The main goal of the Cluster mission, consisting of four identical spacecraft, is the spatial resolution of plasma structures. For the determination of the wave vectors of a wave field from four positions, classical Fourier analysis is inappropriate. We develop a generalized minimum variance technique which gives a high wave vector resolution though the spatial grid is restricted to only a few sampling positions. This technique uses the amplitude and phase information of the magnetic field from the four satellite positions and determines the optimum wave field corresponding to the measured data. The components of the magnetic field are assumed to be normally distributed. The divergence-free nature of the magnetic field is used as a constraint. Using the magnetic data measured at four positions allows up to seven different wave vectors at one frequency to be uniquely resolved.

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The advent of missions comprised of phased arrays of spacecraft, with separation distances ranging down to at least mesoscales, provides the scienti®c community with an opportunity to accurately analyse the spatial and temporal dependencies of structures in space plasmas. Exploitation of the multi-point data sets, giving vastly more information than in previous missions, thereby allows unique study of their small-scale physics. It remains an outstanding problem, however, to understand in what way comparative information across spacecraft is best built into any analysis of the combined data. Dierent investigations appear to demand dierent methods of data co-ordination. Of the various multispacecraft data analysis techniques developed to aect this exploitation, the discontinuity analyser has been designed to investigate the macroscopic properties (topology and motion) of boundaries, revealed by multi-spacecraft magnetometer data, where the possibility of at least mesoscale structure is considered. It has been found that the analysis of planar structures is more straightforward than the analysis of non-planar boundaries, where the eects of topology and motion become interwoven in the data, and we argue here that it becomes necessary to customise the analysis for non-planar events to the type of structure at hand. One issue central to the discontinuity analyser, for instance, is the calculation of normal vectors to the structure. In the case of planar and`thin' non-planar structures, the method of normal determination is well-de®ned, although subject to uncertainties arising from unwanted signatures. In the case of`thick', non-planar structures, however, the method of determination becomes particularly sensitive to the type of physical sampling that is present. It is the purpose of this article to ®rstly review the discontinuity analyser technique and secondly, to discuss the analysis of the normals to thick non-planar structures detected in magnetometer data.

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Abstract. The advent of missions comprised of phased arrays of spacecraft, with separation distances ranging down to at least mesoscales, provides the scienti®c community with an opportunity to accurately analyse the spatial and temporal dependencies of structures in space plasmas. Exploitation of the multi-point data sets, giving vastly more information than in previous missions, thereby allows unique study of their small-scale physics. It remains an outstanding problem, however, to understand in what way comparative information across spacecraft is best built into any analysis of the combined data. Di erent investigations appear to demand di erent methods of data co-ordination. Of the various multispacecraft data analysis techniques developed to a ect this exploitation, the discontinuity analyser has been designed to investigate the macroscopic properties (topology and motion) of boundaries, revealed by multi-spacecraft magnetometer data, where the possibility of at least mesoscale structure is considered. It has been found that the analysis of planar structures is more straightforward than the analysis of non-planar boundaries, where the e ects of topology and motion become interwoven in the data, and we argue here that it becomes necessary to customise the analysis for non-planar events to the type of structure at hand. One issue central to the discontinuity analyser, for instance, is the calculation of normal vectors to the structure. In the case of planar and`thin' non-planar structures, the method of normal determination is wellde®ned, although subject to uncertainties arising from unwanted signatures. In the case of`thick', non-planar structures, however, the method of determination becomes particularly sensitive to the type of physical sampling that is present. It is the purpose of this article to ®rstly review the discontinuity analyser technique and secondly, to discuss the analysis of the normals to thick non-planar structures detected in magnetometer data.

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