120oW
60oW
60oE
120oE
BLK
50oN
o
0o
MOS
RID
06
25 N 07
180oW
o
SHL
17
50oN
25 N
14
0
o
01
03
04
02
o
25 S
24
23
22
2021 18
19
16
21
2422 1912
20 23 09 08
1513
1411
1701 1816
05
02
05
04
09
08
11
130715 03
06
10
10
0
o
o
25 S
12
50oS
50oS
SYO
120oW
60oW
0o
60oE
120oE
180oW
Figure 1. BLK = Belsk, Poland; MOS = Moshiri, Japan; RID = Rhode Island, USA; SHL = Shillong,
India, and SYO = a Japanese-team-operated station in Antarctica
2A
EW : MOS , 090101 , Period # 003
1000
500
0
0
1
2
3 4 5 6 7 8 9 10 11 12
Time within Period, Min
NS : MOS , 090101 , Period # 003
1000
500
0
-500
-1000
0
1
2
3 4 5 6 7 8 9 10 11 12
Time within Period, Min
2B
MOS: 090101 #003<00:24-36UT> MOS: 090101 #003<00:24-36UT>
0.6
1.5
0.4
1
0.2
0.5
0
5
8 11 14 17 20 23 26 29
0
5
EW
NS
30
30
20
20
10
10
0
0
30.8 61.6 92.4 123.2 154
EC [5-29 Hz], pT**2/Hz
8 11 14 17 20 23 26 29
0
0
64.6 129.2 193.8 258.4 323
EC [5-29 Hz], pT**2/Hz
Figure 2. An example of observational material:
A: the 12-min time series of the EW and NS magnetic components;
B, upper panels: the rectified spectra of the above time series;
B, lower panels: the sampling distributions of the energy contents of 5-sec segments within the 12min period.
3A
EW : SYO , 090101 , Per # 003
0.3
Median-Filtered Spectrum
I-LOR Approximations
0.25
0.2
0.15
0.1
0.05
0
5
8
11
14
17
20
Frequency, Hz
23
26
29
NS : SYO , 090101 , Per # 003
Median-Filtered Spectrum
I-LOR Approximations
0.12
0.1
0.08
0.06
0.04
0.02
0
5
8
11
14
17
20
Frequency, Hz
23
26
29
3B
Per #003
:
fn
Qn
Pn
7.33
3.48
0.29
SR#2 :
13.72
4.50
SR#3 :
SR#4 :
20.53
26.28
4.62
3.84
SR#1 : EW :
fn
Qn
Pn
7.74
4.44
0.13
0.16
14.09
4.79
0.05
0.12
0.08
19.50
25.81
4.88
4.44
0.03
0.02
NS :
Figure 3. An example of processed observational material:
A: the 12-min median-filtered spectra of the EW / NS magnetic components and their I-Lor
approximations;
B: the MATLAB protocol of the I-Lor procedure for this period.
4A
EW : BLK , 0901
8
Day 1
Day 2
Day 3
f1, Hz
7.8
7.6
7.4
7.2
7
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
4B
NS : BLK , 0901
8.1
8
f1, Hz
7.9
7.8
7.7
Day 1
Day 2
Day 3
7.6
7.5
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
Figure 4. Examples of the day-to-day stability (A) / variability (B)
of the I-Lor modal EW / NS frequencies at the same station.
EW : BLK , 0901
1.2
Day 1
Day 2
Day 3
0.8
2
P1, pT /Hz
1
0.6
0.4
0.2
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
5A
EW : BLK , 0901
0.7
Day 1
Day 2
Day 3
0.5
2
P2, pT /Hz
0.6
0.4
0.3
0.2
0.1
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
5B
NS : BLK , 0901
0.8
Day 1
Day 2
Day 3
0.7
2
P1, pT /Hz
0.6
0.5
0.4
0.3
0.2
0.1
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
5C
NS : BLK , 0901
0.4
Day 1
Day 2
Day 3
0.35
2
P2, pT /Hz
0.3
0.25
0.2
0.15
0.1
0.05
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
5D
Figure 5. Examples of the day-to-day variability of the I-LOR modal EW/NS intensities in the EW (A,
B) and NS (C, D) components.
6A
EW : BLK : 090101 <3x MedFilt>
14.7
14.6
f2, Hz
14.5
14.4
14.3
14.2
14.1
14
13.9
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
EW : RID : 090101 <3x MedFilt>
14.6
f2, Hz
14.4
14.2
14
13.8
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
6B
NS : BLK : 090101 <3x MedFilt>
14.6
f2, Hz
14.4
14.2
14
13.8
13.6
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
NS : RID : 090101 <3x MedFilt>
14.2
14.1
f2, Hz
14
13.9
13.8
13.7
13.6
13.5
13.4
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
Figure 6. Examples of the inversion’s input data (modal frequencies):
one-hour mean values and standard deviations for the EW (A) and NS (B) magnetic components at
two geographically remote stations
7A
EW : SYO : 090101 <3x MedFilt>
0.4
P4/P1
0.35
0.3
0.25
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
EW : RID : 090101 <3x MedFilt>
0.65
0.6
P4/P1
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
7B
NS : SYO : 090101 <3x MedFilt>
0.35
P2/P1
0.3
0.25
0.2
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
NS : RID : 090101 <3x MedFilt>
1.2
P2/P1
1
0.8
0.6
0.4
0
2
4
6
8 10 12 14 16 18 20 22 24
UT, Hrs
Figure 7. Examples of the inversion’s input data (relative intensities):
one-hour mean values and standard deviations for the EW (A) and NS (B) magnetic components at
two geographically remote stations
1
0.9
ASIA
AFRICA
AMERICA
Relative Activity
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Universal Time, Hrs
Figure 8. The average diurnal variations of the relative activities
of three global thunderstorm “chimneys”
(modeled from the summary of geophysical data)
090101, 14UT: Nelson"s Inversions, Africa
0
Latitude, Deg
-5
African Initial # 1
African Initial # 2
African Initial # 3
African Initial # 4
-10
-15
-20
-25
20
25
30
35
Longitude, Deg
9A
40
45
090101, 14UT: Nelson"s Inversions, Maritime
5
Latitude, Deg
0
-5
-10
-15
-20
African Initial # 1
African Initial # 2
African Initial # 3
African Initial # 4
100
110
120
130
Longitude, Deg
9B
140
150
090101, 14UT: Nelson"s Inversions, Africa & Maritime
Function of Maximum Likelihood
0
-500
-1000
-1500
-2000
-2500
African Initial # 1
African Initial # 2
African Initial # 3
African Initial # 4
-3000
-3500
1
2
3
4
5
6
7
8
9
10
Number of Iteration
9C
Figure 9. Testing Nelson’s inversion algorithm:
A: the African inversion trajectories (open circles) for four different initial locations (double circles)
of African “chimney” with a fixed initial location of the American chimney
(the final African locations are shown by filled circles).
B: the American inversion trajectories (open circles) for four different initial locations of African
“chimney”
(the final American locations are shown by filled circles).
C: The dynamics of the function of maximum likelihood.
(NOTE: This function has been used here ONLY as an indicator of the inversion’s progress to be
compared with Goltzman’s algorithm,
but not as an inversion instrument.)
090101, 14UT: Goltzman"s Inversions, Africa
10
5
African Initial # 1
African Initial # 2
African Initial # 3
African Initial # 4
Latitude, Deg
0
-5
-10
-15
-20
-25
-30
10
15
20
25
30
35
Longitude, Deg
10A
40
45
090101, 14UT: Goltzman"s Inversions, Maritime
30
25
African Initial # 1
African Initial # 2
African Initial # 3
African Initial # 4
Latitude, Deg
20
15
10
5
0
-5
-10
-15
100
110
120
130
140
Longitude, Deg
10B
150
160
170
090101, 14UT: Goltzman"s Inversions, Africa & Maritime
Function of Maximum Likelihood
0
-500
-1000
-1500
-2000
-2500
African Initial # 1
African Initial # 2
African Initial # 3
African Initial # 4
-3000
-3500
1
2
3
4
5
6
7
8
9
10
Number of Iteration
10C
Figure 10. Testing Goltzman’s inversion algorithm:
A: the African inversion trajectories (open circles) for four different initial locations (double circles)
of African “chimney” with a fixed initial location of the American chimney
(the final African locations are shown by filled circles).
B: the American inversion trajectories (open circles) for four different initial locations of African
“chimney”
(the final American locations are shown by filled circles).
C: The dynamics of the function of maximum likelihood.
090101: Goltzman"s Inversions for Maritime Chimney
15
14
10
Latitude, Deg
5
0
05
-5
-10
04
08
09
11
13
03
15
07
-15
06
10
-20
-25
130
140
150
160
Longitude, Deg
11A
170
180
090101: Goltzman"s Inversions for African Chimney
5
21
24
0
Latitude, Deg
-5
22
23
19
08
20
12
09
11
-10
15
-15
17
18
13
14
16
01
10
-20
-25
02
-30
-10
0
10
20
30
Longitude, Deg
11B
40
50
090101: Goltzman"s Inversions for American Chimney
30
Latitude, Deg
20
06
17
07
10
24
23
22
20 21
0
-10
03 01
04 02
18
19
16
-20
05
-30
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
Longitude, Deg
11C
Figure 11. The hour-to-hour results of the inversion procedure
for January 01, 2009 in three continental areas:
(A) Maritime “continent”, (B) Africa, and (C) America.
(Goltzman’s algorithm; 5 stations; modal frequencies 1 to 4;
relative intensities P2/P1 to P4/P1)