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 corrected
geomagnetic latitude or equivalently *L* = 3, and the other two
stations are both located at 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 ( 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 *i*th frequency band is denoted 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 *V*_{p}
and the magnetic field vector
are considered.
Also considered are the derived parameters, namely,
the IMF cone angle () and
the IMF clock angle (), which are defined as

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 falls with increasing frequency *f* as *f ^{-1.37}*.
This result is consistent with

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
and . It is especially clear that the distribution of
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
*P _{5}* and

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 *P _{6}*), 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