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Philosophical Transactions of the Royal Society of London. for the Year Mdcccxxvii. Part I. Volume Cxvii:355–388, 1827

Large amounts of data, like one or more time series from some spacecraft carried instruments, have to be reduced and presented in understandable quantities. As physical theories and models often are formulated in terms of frequency rather than time, it is often useful to transform the data from the time domain into the frequency domain. The transformation to frequency domain and application of statistics on the result is known as spectral analysis. The literature on spectral analysis is voluminous. In most cases, it is written by experts in signal processing, which means that there are many texts available outlining the fundamental mathematics and elaborating the fine points. However, this is not the only background needed for a space physicist who is put to the task of actually analysing spacecraft plasma data. Simple questions on normalisation, physical interpretation, and how to actually use the methods in practical situations are sometimes forgotten in spectral analysis texts. This chapter aims at conveying some information of that sort, offering a complement to the textbooks rather than a substitute for them. The discussion is illustrated with idealised examples as well as real satellite data. In order not to expand the chapter into a book in itself, we concentrate on the application of basic Fourier and wavelet methods, not treating interesting topics in time series analysis like stationarity tests, filtering, correlation functions, and nonlinear analysis methods. Higher order methods like bispectral analysis are also neglected. Fundamentals of such items are covered by many of the references to this chapter, and methods particularly suited for multipoint measurements are of course found throughout this book. Other introductions with multi-spacecraft applications in mind can be found in the paper by Glassmeier and Motschmann [1995] and in other papers in the same publication. The disposition of the chapter is as follows. First, we introduce the basic concepts in Section1.2, where we also discuss time-frequency methods for the analysis of nonstationary signals. The practical implementation of classical Fourier techniques is treated in Section1.3, while the implementation of Morlet wavelet analysis is discussed in Section 1.4. In Section1.5, we turn to the simultaneous analysis of two or more signals by the cross spectrum technique, particularly relevant for the analysis of multipoint measurements. Finally, we touch upon the use of parametric spectral methods in Section 1.6.

Analysis methods for multi-spacecraft data

The Cluster mission provides a new opportunity to study plasma processes and structures in the near-Earth plasma environment Four-point measurements of the magnetic field will enable the analysis of the three dimensional structure and dynamics of a range of phenomena which shape the macroscopic properties of the magnetosphere Difference measurements of the magnetic field data will be combined to derive a range of parameters, such as the current density vector, wave vectors, and discontinuity normals and curvatures, using classical time series analysis techniques iteratively with physical models and simulation of the phenomena encountered along the Cluster orbit The control and understanding of error sources which affect the four-point measurements are integral parts of the analysis techniques to be used The flight instrumentation consists of two, tri-axial fluxgate magnetometers and an on-board data-processing unit on each spacecraft, built using a highly fault-tolerant architecture High vector sample rates (up to 67 vectors s-1) at high resolution (up to 8 pT) are combined with on-board event detection software and a burst memory to capture the signature of a range of dynamic phenomena Data-processing plans are designed to ensure rapid dissemination of magnetic-field data to underpin the collaborative analysis of magnetospheric phenomena encountered by Cluster

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The cluster magnetic field investigation

[1] For the first time, the Cluster spacecraft have collected 3-D information on magnetic field structures at small to medium scales in the Earth's dayside magnetosphere. We focus here on the first application of the Curlometer (direct estimation of the electric current density from curl(B), using measured spatial gradients of the magnetic field) analysis technique. The applicability of this multipoint technique is tested, for selected events within the data set, in the context of various mission constraints (such as position, timing, and experimental accuracy). For the Curlometer, nonconstant spatial gradients over the spacecraft volume, time dependence, and measurement errors can degrade the quality of the estimate. The estimated divergence of the magnetic field can be used to monitor (indirectly) the effect of nonconstant gradients in the case of many magnetic field structures. For others, and at highly distorted spacecraft configurations, this test may not reflect the quality of the Curlometer well. The relative scales and relative geometry between the spacecraft array and the structures present, as well as measurement errors, all are critical to the quality of the calculation. We demonstrate that even when instrumental and other errors are known to contribute to the uncertainty in the estimate of the current, a number of current signatures within the magnetosphere can be plausibly determined in direction, if not absolute size. A number of examples show consistent currents at the magnetopause, both separate from, and nearby or in the cusp region. Field-aligned currents near the polar cap boundary are also estimated reliably. We also demonstrate one example of an anomalous current arising from the effect of a highly distorted spacecraft configuration.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001JA005088

Four‐point Cluster application of magnetic field analysis tools: The Curlometer

Abstract Geomagnetic disturbances have affected electrical systems on the ground for over 150 years. The first effects were noted on the early telegraph in the 1840s and in this century magnetic storms have caused power system blackouts and phone system outages. Affected systems include all those that use electrical conductors: whether for transmission of power or signals or where the conducting properties are incidental to their use such as with pipelines and railway tracks. In power systems geomagnetically induced currents cause partial saturation of power transformers producing transformer heating and distortion of the ac waveform leading to misoperation of relays and other equipment. On pipelines, induced currents may contribute to corrosion but also present a problem with the electrical surveys of the pipe performed to monitor the corrosion prevention systems. Severity of these effects depends on disturbance size, proximity to the auroral zone, and the conductivity structure of the Earth. Also significant are system parameters such as the use of higher resistance coatings on pipelines and the linking of power systems into larger networks. In this paper we have attempted to catalogue all the published reports of geomagnetic effects on electrical systems and show their occurrence in the context of the solar cycle and geomagnetic activity variations for the years 1844 to 1996.

The Effects of Geomagnetic Disturbances on Electrical Systems at the Earth's Surface - An Update

Analysis of multipoint magnetometer data

Accuracy of Current Density Determination

A magnetic reconnection event detected by Cluster is analyzed using three methods: Single-spacecraft Inference based on Flow-reversal Sequence (SIFS), Multispacecraft Inference based on Timing a Structure (MITS), and the First-Order Taylor Expansion (FOTE). Using the SIFS method, we find that the reconnection structure is an X line; while using the MITS and FOTE methods, we find it is a magnetic island (O line). We compare the efficiency and accuracy of these three methods and find that the most efficient and accurate approach to identify a reconnection event is FOTE. In both the guide and nonguide field reconnection regimes, the FOTE method is equally applicable. This study for the first time demonstrates the capability of FOTE in identifying magnetic reconnection events; it would be useful to the forthcoming Magnetospheric Multiscale (MMS) mission.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2015JA021701

Identifying magnetic reconnection events using the FOTE method

We studied energetic electron bursts (EEBs) (40-250keV) in the plasma sheet (PS) and their relation to bursty bulk flows (BBFs) using the data recorded by Cluster from 2001 to 2009. The EEBs in the PS can be classified into four types. Three types of EEBs are dispersionless, including EEBs accompanied with BBFs (V>250km/s) but without dipolarization front (DF); EEBs accompanied with both dipolarization front (DF) and BBF; and EEBs accompanied with DF and fast flow with V<250km/s. One type of EEB, i.e., EEBs not accompanied with BBFs and DFs, is dispersed. The energetic electrons (40-130keV) can be easily transported earthward by BBFs due to the strong dawn-dusk electric field embedded in BBFs. The DFs in BBFs can produce energetic electrons (40 to 250keV). For the EEBs with DF and BBFs, the superposed epoch analyses show that the increase of energetic electron flux has two phases: gradual increase phase before DF and rapid increase phase concurrent with DF. In the PS around x=-18 R-E, 60%-70% of EEBs are accompanied with BBFs, indicating that although hitherto there have been various acceleration mechanisms of energetic electrons, most of the energetic electrons in the PS are related with magnetic reconnection, and they are produced either directly by magnetic reconnection or indirectly by the DFs within BBFs. In the BBF's braking region of -12 R-E<x<-10 R-E, 20% of EEBs are accompanied with BBFs. The corresponding ratio between EEBs and BBFs shows a dawn-dusk asymmetry.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014JA020169

Energetic electron bursts in the plasma sheet and their relation with BBFs

In the analysis of in-situ space plasma and field data, an establishment of the coordinate system and the frame of reference, helps us greatly simplify a given problem and provides the framework that enables a clear understanding of physical processes by ordering the experimental data. For example, one of the most important tasks of space data analysis is to compare the data with simulations and theory, which is facilitated by an appropriate choice of coordinate system and reference frame. While in simulations and theoretical work the establishment of the coordinate system (generally based on the dimensionality or dimension number of the field quantities being studied) and the reference frame (normally moving with the structure of interest) is often straightforward, in space data analysis these are not defined a priori, and need to be deduced from an analysis of the data itself. Although various ways of building a dimensionality-based (D-based) coordinate system (i.e., one that takes account of the dimensionality, e.g., 1-D, 2-D, or 3-D, of the observed system/field), and a reference frame moving along with the structure have been used in space plasma data analysis for several decades, in recent years some noteworthy approaches have been proposed. In this paper, we will review the past and recent approaches in space data analysis for the determination of a structure’s dimensionality and the building of D-based coordinate system and a proper moving frame, from which one can directly compare with simulations and theory. Along with the determination of such coordinate systems and proper frame, the variant axis/normal of 1-D (or planar) structures, and the invariant axis of 2-D structures are determined and the proper frame velocity for moving structures is found. These are found either directly or indirectly through the definition of dimensionality. We therefore emphasize that the determination of dimensionality of a structure is crucial for choosing the most appropriate analysis approach, and failure to do so might lead to misinterpretation of the data. Ways of building various kinds of coordinate systems and reference frames are summarized and compared here, to provide a comprehensive understanding of these analysis tools. In addition, the method of building these systems and frames is shown not only to be useful in space data analysis, but also may have the potential ability for simulation/laboratory data analysis and some practical applications.

/pdf/dimensionality-coordinate-system-and-reference-frame-for-38bievpv7b.pdf

Malcolm Dunlop

Papers

Analysis of multipoint magnetometer data

Accuracy of Current Density Determination

Identifying magnetic reconnection events using the FOTE method

Energetic electron bursts in the plasma sheet and their relation with BBFs

Dimensionality, Coordinate System and Reference Frame for Analysis of In-Situ Space Plasma and Field Data