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Geotail Studies of Low Frequency Waves in the Near Magnetotail Using the Wavelet Transform

K. Sigsbee and C. A. Cattell

Why Study Waves?

In 1992, the Geotail satellite was launched to study the Earth's magnetotail, a region of space behind the night side of Earth where the solar wind stretches the Earth's magnetic field out into a long tail. The physical processes occuring in the magnetotail are an important part of auroral substorms. During a typical substorm, electrical currents generated 60,000 km away from Earth in the magnetotail are diverted to the Earth's ionosphere where they produce the spectacular display of light known as the aurora borealis or northern lights. Electromagnetic waves and turbulence excited in the magnetotail are an essential part of many models attempting to explain how the magnetotail currents are disrupted during substorms(Lui et al., 1991; Huba et al., 1981). Studies of electromagnetic waves and turbulence in the magnetotail using data from Geotail have provided important information about the physical processes involved in the onset and growth of auroral substorms.

A New Analysis Technique

In order to study waves in the magnetotail, some method of decomposing the signals received by the spacecraft into different frequency components is needed. Traditionally, the fast Fourier transform (FFT) is the preferred technique. The FFT is based upon work that was done by the French mathematician Jean Baptiste Joseph Fourier in 1807. Fourier discovered that any function or signal could be represented as the sum of a series of sines and cosines with different frequencies. To analyze a signal by this method, the data is divided up into segments or "windows" of a fixed time span. The FFT is performed on each window, and the results are plotted on a grid in the time-frequency plane called a spectrogram. Although Fourier analysis is a very practical method, it does not work well for all types of signals. Information about low frequency parts of a signal can be lost if the size of the window is too small to contain one full oscillation cycle. Using a bigger window in time will help find these low frequency components, but it will cause information about how the signal evolves with time to be lost. As a result, Fourier analysis is not an ideal method for signals that vary unpredictably or change suddenly. To overcome the limitations of Fourier analysis, the method of wavelet analysis was developed in the early 1970s by French geophysicist Jean Morlet(Hubbard, 1996). In the wavelet transform, the width of the window is adjusted to the optimal size for each frequency, so the properties of the signal can be examined on different time scales. When the wavelet transform is plotted in the time-frequency plane, the result is an irregularly gridded picture of how the signal evolves called a "scalegram." Although the wavelet transform has been used extensively by geophysicists to analyze seismic data, it has not been used much in space physics until recently.

Preliminary Results

The two figures below show sample Morlet wavelet scalegrams of Geotail data for frequencies between 0.01 Hz and 0.16 Hz. Figure 1 shows a scalegram of 10 minutes of electric field data measured in the east-west direction starting at 07:50 on April 26, 1995. Figure 2 shows a scalegram of the magnetic field measured along the Earth-Sun direction for the same 10 minutes. Of particular interest is the intense white peak in the electric field scalegram starting around 07:51:40 which appears to glide upwards in frequency. Features like this provide interesting information about how the wave is propogating through space. These waves were observed in conjunction with some of the highest speed bulk flows of plasma towards Earth ever seen in this region of the magnetotail. During other events, low frequency oscillations of the electric and magnetic fields observed by Geotail are representative of standing wave oscillations in which the field lines vibrate like plucked violin strings. Similar oscillations have been observed by the GEOS-2 satellite(Holter et al., 1994).

Future Work

Ongoing studies of the waves observed by Geotail will involve a more careful examination of the timing of the waves relative to substorm onset and plasma flow bursts. Future work will also include correlative studies of data from Geotail and the FAST satellite, which was launched into a polar orbit in 1996. Conjunctions between FAST and Geotail in January and February of 1997 will allow comparisons between the waves observed in the magnetotail and the auroral zone. These events will provide valuable insight into the evolution of currents and plasma flows during substorms, and will facilitate new studies of the processes involved in coupling between the magnetotail and the ionosphere.

Click on the images to see the full size version.

Figure 1: Scalegram of EY GSE

Figure 2: Scalegram of BX GSE


Holter O., et al., Wavelet Analysis of Low Frequency Substorm Oscillations, Proceedings of the Second International Conference on Substorms ICS-2, Fairbanks, Alaska, 1994.

Huba, J. D., et al., On the Role of the Lower Hybrid Drift Instability in Substorm Dynamics, J. Geophys. Res., 86, 5881, 1981.

Hubbard, Barbara Burke, The World According to Wavelets, A. K. Peters, Ltd., Wellesley, MA, 1996.

Lui, A. T. Y., et al., A Cross-Field Current Instability for Substorm Expansions, J. Geophys. Res., 96, 11389, 1991.

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