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Data

The wave power data of BS1 are derived from the magnetic field measured by the Air Force Geophysics Laboratory (AFGL) Magnetometer Network [Knecht, 1985], which consists of seven stations in the contiguous United States. The stations operated from 1978 through 1983. Five of the seven stations form a line roughly at $55\deg$ corrected geomagnetic latitude or equivalently L = 3, and the other two stations are both located at $40\deg$ corrected geomagnetic latitude. The instrumentation at all sites was essentially identical. However, for the same pulsation event, the observed wave amplitude may vary from station to station because of the difference in local time and the conductivity structures underneath the stations [Chi et al., 1996]. Later in this section, it will be seen that the instrumental noise limits the selection of wave events, particularly for those at high frequencies; thus it is preferrable to use the station which has the greatest signal to noise ratio. In this study, we use the data from Mount Clemens station (MCL, L = 3) since on average it observes the strongest signals among all the AFGL stations [Chi et al., 1996].

The observations were made by a three-axis fluxgate magnetometer built by the University of California, Los Angeles. The magnetometer has a basic analog (fine-scale) range of -64 to +64 nT; it is kept on scale by applying to the sensor a precise (coarse-scale) nulling field of an integral multiple of 64 nT to cover the full range of approximately -65,000 to +65,000 nT. The fine-scale output is digitized by an 11-bit analog-to-digital converter, with the least significant bit representing 1/16 nT. The instrument was sampled once per second.

The wave power database of BS1 consists of successive power spectral densities from a 512-point discrete Fourier transform (DFT). The calculation is carried every 512 s ($ \simeq 8.5$ min), and integrated wave power is calculated in progressively doubled bands: (1) 2-4 mHz, (2) 4-8 mHz, (3) 8-16 mHz, (4) 16-32 mHz, (5) 32-64 mHz, and (6) 64-128 mHz. The wave power for the ith frequency band is denoted $P_i (i = 1,2, \ldots , 6)$hereafter. Table 1 shows the corresponding Pc frequencies that are traditionally used in the pulsation literature for these six frequency bands. Detailed description regarding the processing and properties of the wave power data can be found in BS1.

An example of the wave power data recorded by station MCL on August 19-20 (day 231-232), 1978, is shown in Figure 1. It should be noted that the vertical scales vary with frequency bands. The two spectrum-like diagrams on the bottom of Figure 1 show the wave power of six frequency bands at two particular times. At 1109 UT, there was an enhancement in frequency band 3, whereas at 1853 UT the enhancement was in frequency band 4. Since we found that the wave power in the X component (magnetically north) was generally larger than that in the Y component (magnetically east), we will concentrate on the X component only.

Figure 1. An example of the power-spectral-density data from Bloom and Singer [1995]. The diagrams on the bottom show the observed wave power at two particular times.

Solar wind data are recorded by the IMP 8 spacecraft. Basic physical quantities for the solar wind such as the proton velocity Vp and the magnetic field vector $\mathbf{B}$ are considered. Also considered are the derived parameters, namely, the IMF cone angle ($\theta_{BX}$) and the IMF clock angle ($\phi$), which are defined as

\begin{displaymath}
\theta_{BX} = \cos^{-1}(B_x/B_t) \\ \end{displaymath}

\begin{displaymath}
\phi = \left\{
 \begin{array}
{lll}
 \tan^{-1}(B_y/B_z)-\pi ...
 ...
 \mbox{$B_y \geq 0$\space and $B_z < 0$.}
 \end{array} \right.\end{displaymath}

where Bx, By, and Bz are in the GSM coordinates and $ B_t = \vert\mathbf{B}\vert $.Local time (LT) is another parameter considered in the analysis. We will concentrate on the dayside region since it is where most of the wave power was observed [Bloom and Singer, 1995]. All the parameters described above as well as the integrated wave power in the six frequency bands are averaged every 20min.

To provide an overview of the properties of the wave power data, we first examine the distributions of the wave power at all frequency bands. Figure 2 presents such distributions on the same scale. In each distribution, the central box shows the data between the first and the third quartiles, with the median represented by a line. The dotted line extends to the extremes of the data. If we consider the median values for all the six frequency bands, we see a consistent decrease of wave power toward higher frequencies. It can be shown that the magnetic field amplitude spectrum in units of $\rm fT/\!\sqrt{Hz}$falls with increasing frequency f as f-1.37. This result is consistent with Lanzerotti et al. [1990], who reported a frequency dependence of the average spectrum ranging between $ \sim\!f^{-1} $ and $ \sim\!f^{-1.5} $in the band 10-5 - 105 Hz.

Figure 2. Distribution of wave power data. For each frequency band, the central box shows the data between the first and third quartiles, with the median represented by a line, and the dotted line extends to the extremes of the data.

Figure 3 shows the histograms and the normal probability quantile-quantile plots (or Q-Q plots) of the same wave power data. A Q-Q plot is a plot of the ordered values of data versus the corresponding quantiles of a standard normal distribution, that is, a normal distribution with mean zero and standard deviation 1. Here we follow the custom that the horizontal axis, the quantile, is in the unit of standard deviations. Using a Q-Q plot is one of the best ways to compare the distribution of data with a known distribution [Venables and Ripley, 1994]. If the normal probability Q-Q plot is fairly linear, the data are reasonably Gaussian. In Figure 3, the histograms of wave power on a logarithmic scale are symmetrical and Gaussian-like except for $\log(P_5)$ and $\log(P_6)$. It is especially clear that the distribution of $\log(P_6)$ is skewed right and has a long tail. The normal probability Q-Q plots in Figure 3 further confirm the Gaussian distribution of logarithmic wave power. For the first through the third frequency bands, the Q-Q plots show rather linear structures, which indicate that the distributions of logarithmic wave powers are reasonably Gaussian. For the fourth and the fifth frequency bands, there exist two distinct components, one with stronger power and the other with weaker power. Both of the components appear to have a Gaussian-like distribution. For the sixth frequency band, the weaker-power component becomes the major part of the distribution although the stronger-power component still occupies about 30% of the data points. The weaker-power component also has a narrower spread that leads to a short tail on the left side and a skew in the histograms for P5 and P6.

Figure 3. Histograms and quantile-quantile plots (Q-Q plots) for the wave power (in logarithmic scale) of six frequency bands.

The stronger-power component contains most of the data points (except for P6), and it is expected to be environmental. The weaker-power component seems to have an upper limit for its magnitude since it does not appear in P1, P2, and P3, which have larger magnitudes due to stronger environmental wave activity. In addition, the weaker-power component is usually less than $10^{-3}\,\mathrm{nT^{2}}$,equivalent to a wave amplitude smaller than 0.03nT, which is close to the instrument threshold for the magnetometer to measure. Therefore the weaker-power component appears to be instrument noise. Hereafter the stronger-power component and weaker-power component are termed the ``wave'' component and the ``noise'' component, respectively.


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