DETERMINATION OF ONSET TIMES OF LOW-LATITUDE Pi2 MAGNETIC PULSATIONS
Keiko FUKUYAMA[1], Tomoyuki Higuchi[3], Teiji Uozumi[2], Hideaki Kawano[1], Kiyohumi Yumoto[1,2]the CPMN Observation Group
Department of Earth and Planetary Sciences, Kyushu University, Japan[1]Space Environment Research Center, Kyushu University, Japan[2]The Institute of Statistical Mathmatics, Japan[3]02‑Jan‑2001

Until now, most people have used filtered data toidentify the Pi2 onset time ; however, the usage offiltered data tends to bias the onset time.(See Fig1)
Therefore, we have constructed two methods(Method-1 and -2 below ) which use raw data andcompared their results.

RAWGAM* One of the magnetic pulsations which occur in themagnetosphere.
* Wave period ranges from 40 to 150s.
* Waveform is irregular.

When isthe Pi2 onset ?

65
640?

(filtered data)

‑1

18:15

Determination of18:20
UTFig.1) Raw and bandpass filtered datawith Pi2 magnetic pulsation

Initial perturbation of Pi2

18:15* Its occurrence is believed to coincide with substorm
onset. → It has been known as a good indicator ofthe onset of substorm.

?

102‑Jan‑2001

GAM

RAW

66

BP[40‑150s]

In this study, to understand details of Pi2
and other related phenomena, we focus onPi2 onsets .

Pi2 magnetic pulsations

18:20

18:25

Pi2 magnetic pulsation
BP[40‑150]

Introduction

18:15

18:20
UT

18:25

Fig.2) Example of the Pi2 magnetic pulsation

Pi2 onset〜pt(=Pi2) starts with dH/dt > 0 in the middle or low latitude 〜(Saito,1961)

According to this definition, in the middle or low latitude, the Pi2 onset time of a raw H-componenttime-series data is defined as the point where differential values of adjacent data start to show apositive excresion. (In this study, we used differences instead of differential value.)

From our previous study, we are convinced that there exists a non-periodic fluctuation at
Pi2's initial stage, which we call an initial perturbation . (See Fig.7)

Study
1

<Method-1>
This method uses such assumption that Pi2 is described byperturbation+quasi-periodic oscillation.

13‑May‑2001

A smooth variation of the background magnetic field(tn)+ noisy component(wn)Model-1 + an oscillating component(qn=Pi2)
13‑May‑2001

RAW

Fit model-1

0.5

Fit model-2Pi2 onset !
qn(Pi2) component
starts here0

Initial perturbation
‑0.5

15:24

15:26
UT{

(Fig3.) Example of Method-2(* In this paper, we employ the following functional forms :: frequency of the Pi2 pulsation: sampling interval(=1): system noise which follows
a Gaussian distribution(Method-1's onset time - Method-2's one)

RAW0.20‑0.2

Trend component
0.20.1
0
‑0.1
15:23

15:25UT

15:27

The duration of this segment(L) is
set 1/6 of the wave period of pulsation
which is included in diff-trend data.
(The wave period is roughly estimatedfrom the auto-correlation function)

αL

3GAM

4

<Result>
15:24:50

Fig.6) The histogram in this analysis

Method-2's onset time isearlier than Method-1's one

161412Time lag = 2 s
0.2
0.1
0
‑0.1

4. We demonstrate these result by a histogram.
(See Fig.6)<Discussion & Conclusion>

Time0‑0.5

Differences

Pi2 onset !

Difftrend

0.5

RAW

2. For each event, we determined the Pi2 onset time with twomethods(Method-1 and -2).
3. We calculated the time lag between them.(See Fig.5)

Method‑1{Interval : Jan.2001-Dec.2002, LT19:00-04:00
Station : GAM(L=1.03,GMlat.=5.61[deg],GMlon=215.55[deg])

13‑May‑2001

Method‑2

1. We visually examined isolated Pi2 events, and found 61events.

12To be specific, we use a straight line segment(red line ;See the following figure) whoseoptimal inclination(α) is determined by a Bayesian inference.
We move the start time of this segment from the beginning to the end of the time-series,
and for each start time of the segment, we apply the line segment to fit the diff-trend data
for a determination of its inclination, and then calculates ABIC(Akaike BayesianInformation Criterion) which controls the trade-off between the degree of goodness offitting and the preference on a steeper slope ; finally, we choose the start time which
minimizes ABIC, and define it to be the Pi2 onset time.

The wave frequency is designed to gradually increase from fc/2(at the start of qn) up to fc(at the end of the first one cycle of qn).
→ qn can simulate the initial perturbation - then quasi-periodic oscillation .

<Analysis>

Pi2 onset !

14

In this method, we use the Bayesian statistical inference to estimate Pi2
onset more accurately and objectivity.

141216Fig.4) Example of Method-2

GAM

Optimal separation
point

16

qn

We divide raw H-component data into twosubintervals, fit Model-1 to the former subinterval, and fit Model-2 to the latter. The best
separation point which is determined by theAIC(Akaike Information Criterion) is regarded
as the optimal start point of qn=Pi2 component.
→ This time point is identified as the Pi2onset time. (See Fig.3)

First, we take differences of raw Hcomponent magnetic data and extract
its trend component(we call it diff-trend
data ; See Fig.4, middle panel).
Then, we search the time when thevariation of the diff-trend data turns
positive. The definition by Saito saysthat this is the Pi2 onset time.

GAM

18

DIFF‑trend DIFF&DIFF‑trend* We use the following two models in this Method-1 :[ Model-2 :2

The second procedure directly relies on the definition of the Pi2onset(Saito,1961) .

initialWe apply the time-series analysis which was introduced by Higuchi et al.[2002](Pi2 onset
time determination with information criterion), and determine the Pi2 onset time to be thetime where the oscillations start.

Model-1 :<Method-2>

15:24:48

15:24

15:26
UTFig.5) Example of this analysis
The top panel shows qn(Pi2) component
and the bottom shows diff-trend data

5

Although qn needs to be further improved, our results indicate that Pi2's

initial perturbation is veryimportant in determining the Pi2 onset. Therefore, we think that it could give us a clue to the trigger
mechanism of Pi2 and related phenomena, and it is our top priority to clarify characteristics of Pi2's initial
perturbation.

The time lag is centered around 0 second.
However, it shows a distribution from -10 to 20 s.

Summary
In this study, we have constructed two methods to determine the Pi2 onset time, and suggested the importance of Pi2'sresults.

initial perturbationfrom comparisons of their

There are two important aspects in our methodologies above : First, we used raw H-component data to avoid biases in the estimation of onset time due to characteristics of the filter itself. Second,
we employed the information criterion both in the Method-1(which is along the line of previous approach by Higuchi et al.[2002]) and in Method-2(which is based on the Bayesian statistical inference).
Therefore, we could make the estimation procedure more accurate and objective.

After this study, we plan to study the physical importance of Pi2's initial perturbation by statistically examining Pi2's at several stations(at wide range of latitudes).
Keiko Fukuyama : fucan@sb4.so-net.ne.jp