A Global Lightning Transients Detector
by
Charles Teng Wong
Submitted to the Department of Electrical Engineering
and Computer Science in partial fulfillment of the requirements for the degree of
Master of Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 8, 1996
© Massachusetts Institute of Technology, 199/3. All Rights Reserved.
Author .....
Department of Electrical Engineeinng aiComputer Science
Charles Teng Wong
C ertified by .......
,,
.................
.............
Associate Professor
Department of Civil Engineering
,esis Supervisor
ff,
A ccepted by .......... ........................... ..,
. .
--
.......
Paul L.Penfield
Department Head
Department of Electrical Engineering and Computer Science
A.•,u.SA,•SETTS
INS'7;'fiTE
OF TECHNOLOGY
JUN 111996
LIBRARIES
A Global Lightning Transients Detector
by
Charles Teng Wong
Submitted to the Department of Electrical Engineering and Computer Science on February 8, 1996, in partial fulfillment of the
requirements for the degree of Master of Engineering in Electrical
Engineering and Computer Science
and
Bachelor of Science in Electrical Engineering
Abstract
A new automated system was developed to analyse ELF transient signals. Quantitative
comparisons were made with the theoretical formulations describing the Earth's Schumann resonances and the experimental data. Agreement with theory was checked by
simultaneous measurements made by the National Lightning Data Network and the Optical Transients Detector.
Thesis Supervisor: Earle R. Williams
Title: Associate Professor
Table of Contents
1 Introduction ................................................................................................................ 11
... ... ... ...... . ... . ...
................... . . . .
1.1
What are Schumann Resonances? .................
11
1.2
Motivation for Studying ELF Transients from Individual Lightning Events..12
1.3
Brief History of Schumann Resonances .....................................
1.4
Description of Recording Site......................................
...... 13
................ 15
2 Background to Understanding ...................................................... 17
2.1
The Normal Mode Equations for Schumann Resonances ............................ 17
2.2
Legendre Polynomials ........................................................ 18
2.3
Discrete Fourier Transform (DFT) for Processing Transient Waveforms.......21
2.4
Spherical Geometry for Source Location .....................................
2.5
Lightning Terminology..............................................
..... 27
....................... 30
3 Theoretical Calculations for an Isotropic Cavity .....................................
.... 35
3.1
The Models of Wait and Jones..............................................35
3.2
Wave Impedance.....................................................
3.3
The Range-Frequency Curve ..........................................
3.4
The Lightning Source Term Ids(w) ............................................. 43
3.5
Source-Receiver Distance .............................................................................. 44
3.6
Sentm an M odel ................................................................................................
3.7
A Comparison of Models Used by Sentman and Jones ................................ 47
3.8
Q-values for the Earth-Ionosphere Cavity .....................................
3.9
Eigenvalues and Eigenfrequencies ........................................
.......................... 40
........
42
45
... 51
...... 55
4 Asymptotic Approximations of the Theory for an Isotropic Cavity ....................... 59
59
4.1
Theory vs Approxim ation .............................................................................
4.2
Nickolaenko's Approximation ....................................................................... 59
4.3
Ishaq and Jones' Approximation .......................................
........ 66
4.4
Ishaq and Jones vs Nickolaenko .........................................
....... 69
4.5
Sentm an's model...............................................
......................................... 69
5 Automation of Analysis on Global Location of Lightning Transients ................... 71
5.1
Digital Time Series Sequences of ELF Transients ..................................... 71
5.2
Windowing the Time Series of the ELF Transient ..................................... 76
5.3
Linearly Least Squares Fit to Magnetic Lissajous Plot ................................
5.4
Finding the Azimuthal Magnetic Field Hf ................................................. 83
5.5
Computing the Bearing from Receiver to Source..................................
5.6
Discrete Fourier Transform of Ez and Hf .....................................
5.7
Modulus and Argument of the Wave Impedance .....................................
5.8
Discrete Fourier Transform of the Modulus and Argument ......................... 93
5.9
Range vs Frequency Curve ...................................
78
85
.... 89
..............
91
95
5.10 Latitude and Longitude of the Source.................................
....... 96
5.11 Source Term Ids(w) .......................................................
..........
.......... 97
5.12 Autom ation .........................................................................
....................... 99
6 Application to Observed Transients.............................................
6.1
Introduction ........................................
6.2 The Sprites '95 Campaign ...........................................
6.3
103
103
........
103
Optical Transients Detector (OTD) ...............................................................
13
6.4
Large Amplitude ELF Events Sampled at 2k Hz.........................................
122
7 Conclusions.............................................................................................................. 133
7.1
Review of Analysis .......................................
7.2
Improvements ............................................................... 133
133
Acknowledgements
First, I would like to thank my thesis advisor Earle R. Williams for being patient.
This would not have been possible without your generous support and your encouragement. I also thank Bob Boldi for his always willingness to help me and to maintain our huge set of Schumann Resonance data. I also send my heart out to
Isabella, CoCo, Barney, and Big Foot whose friendships are undying. To Mary Ni,
you have made me the person that I am. Thanks coach. Finally, I give my family
thanks for their love and support and to my won bon Jennifer, you are the best.
To my father and mother,
Ta-Hsiung Wong
Shu-Jen Wong
Chapter 1
Introduction
1.1 What are Schumann Resonances?
Lightning is an extremely broad band radiator of electromagnetic energy. Some small
fraction of this energy finds itself in the frequency range 5-50 Hz where it resonates
within the Earth-ionosphere cavity. This phenomenon is called the Schumann
resonances. These Extremely Low Frequency (ELF) excitations are electromagnetic
transients of approximately 1 sec duration that propagate around the globe. The largest
most energetic lightnings produce vertical electric field and horizontal magnetic fields.
These electromagnetic fields can be measured above the background level of all the
smaller amplitude lightning events far from the source to study the nature of these
individual events. Because these waves travel long distances with respect to the Earth's
circumference, a single observation site can detect their presence on a global basis.
Worldwide thunderstorm lightning is the main contributor to the Schumann Resonances (Clayton and Polk, 1977; Sentman, 1995). Depending on the diurnal time and season, monitoring the level of Schumann Resonance can reveal locations of intense
thunderstorm activity. Balser and Wagner (1962) made observations around the globe and
determined that at approximately, 8, 14, and 20 GMT, the resonance energy is at a peak.
These peaks correspond to the late afternoon periods of deep tropical convection in the
Asian Maritime Continent, in Africa, and in America. Figure 1.1 shows the global diurnal
variation of lightning activity. It includes contributions from the three major convective
zones as observed by Balser and Wagner (1962).
Figure 1.1: Global Diurnal Variation of Lightning Activitty
Global Storm Diagram
Th
Ac
0
4
8
12
16
20
24
Time (UTC )20
1.2 Motivation for Studying ELF Transients from Individual Lightning
Events
Solar heating of the Earth's surface in these three regions creates conditions necessary
for deep convection of water particles accompanied by high velocity updrafts of many
meters/second. These water particles accumulate in the upper atmosphere where conditions reach freezing and ice particles can form. The large ice particles become preferentially charged as the cloud develops, leading to vertical charge separation. As the charge
separation continues, electric field intensity increases until the atmospheric breakdown
strength is exceeded and lightning discharges occur.
Williams (1992) measured wet bulb temperature and lightning frequency in Darwin,
Australia and showed a factor of 4-5 increase in light. ing frequency with about a 10 C
change in surface wet bulb temperature. He suggested that lightning and the global electri-
cal circuit may provide a sensitive temperature monitor. If ELF transients can be measured
and located on a global basis, then it is possible to make certain comparisons between
temperature and lightning activity in a certain region.
The existence of Schumann Resonances allow for the capture of these ELF transients
as they propagate around the globe. Ogawa et al., (1966) classified ELF flashes from
lightning discharges into two types: N(noisy)-type and Q(quiet)-type. He observed that Ntype bursts have high frequency time series components preceding its onset whereas Qbursts have no VLF component but their amplitudes are larger than N-type bursts. He then
observed that these Q-type bursts exhibit a damped sinusoid type of oscillation with a frequency near 8 Hz and with longer duration than the N-type bursts. We will look at the signatures of these two types in the Schumann Resonance. However, before doing so, a brief
history of the theory and experiments for the Schumann Resonances is useful.
1.3 Brief History of Schumann Resonances
Schumann (1952) first conducted theoretical investigations of the electromagnetic
resonances produced by lightning. He noted that in the case of perfectly conducting
boundaries between the Earth's surface and its ionosphere, the resonant frequencies of
the electromagnetic waves were given by
f
n
speedoflight
n(n+ 1)
21t - (radious of Earth)
n, = 0,
1,
2,
3,
.....
(1.1)
where the radius of the Earth is 6.378x106 meters. However, in 1957, he improved on his
previous assumption of an infinite conductivity between the earth and its ionosphere with
a finite conductivity profile (Schumann, 1957). The first spectrum was presented by Balser
and Wagner (1960) who confirmed the existence of the Schumann Resonance modes.
They reported resonances at peaks of 8, 14, 20 and 26 Hz which were slight deviations
from Schumann's resonant frequencies based on an infinite conductivity model. Theoretical descriptions of the resonances which took into account diurnal variations and the inhomogeneous ionosphere were developed by Wait (1962). During this period, extensive
measurements of the Schumannn Resonance were made by Polk and Fitchen (1962),
Balser and Wagner (1962), Chapman and Jones (1964), Rycroft (1965), Madden (1965)
and Nelson (1967). Jones (1967) also conducted numerical experiments to determine the
conductivity profile of the ionosphere. Later, Ogawa et al. (1967) made measurements of
Q-type and N-type bursts and confirmed the global phenomenon of Schumann Resonance.
Jones and Kemp (1970) first used Wait's (1962) normal mode theory of Schumann
Resonance to determine source location of single stroke lightnings. They analyzed individual spectra of the electric and the magnetic field and compared them with theory in
order to estimate source location. Then Kemp and Jones(1971) developed the wave
impedance method which makes use of the ratio of the electric and the magnetic field
spectra and found a unique relationship with source-observer distance. Ishaq and Jones
(1977) first introduced an asymptotic approximation to the theory and showed good agreement with the earlier results.
Clayton and Polk (1977) demonstrated that global lightning activity could be monitored from a single station. A treatise on Schumann Resonances was published by Bliokh
et al. (1980). Later, Sentman (1987) discussed the effects of magnetic elliptical polariztion
on Schumann Resonance. Williams (1992) suggested that measuring the rate of lightning
discharges is a way of monitoring the global temperature. Then Nickolaenko(1993) provided modifications and new approaches to the asymptotic model Ishaq and Jones (1977)
first developed. Recently, Sentman (1996) derived a new model of the two-scale height
ionosphere and proposed new expressions for the electric and magnetic field. At the same
time, Boccippio et al. (1995) applied the Kemp and Jones impedance method for locating
large Q-bursts which are associated with sprites, an optical emission in the upper atmosphere.
Schumann Resonances have a rich history. This provides the theory and backbone to
much of the current research. We will discuss many of the various theories and measurements that have been made and see the new applications which arise as a result. Most
importantly, we will provide a new algorithm which examines the ELF transients efficiently and more comprehensively than previous studies. This will allow us to see global
behavior and help us to make certain educated assumptions about future research.
1.4 Description of Recording Site
The experiment is conducted in West Greenwich, Rhode Island on the Alton Jones Campus of the University of Rhode Island. The site was originally used by Dr. Charles Polk
when he first conducted experiments with the Schumann Resonances in the 1960's and
1970's. There are two magnetic coils and one electric pole on which a ball antenna sits.
The magnetic coils are aligned perpendicular to each other running from East to West and
North to South. The Magnetic coils are sleeved with solonoidal windings for accurate
absolute calibration. The electric pole is Polk's original sensor and extends ten meters
above the ground. Three double shielded wires run from the coils and the pole to a hut 200
yards away. There, the signals are converted digitally with a 12-bit Data Translation A-toD board and finally are fed into two IBM compatible 486 personal computers. One computer calculates a running sum of the Fourier Transform Spectrum every 12 seconds. After
a running total of 60 transforms, the spectrum is time stamped with a GPS clock and
stored after which the sum starts over. The second computer is devoted to the recording of
transient events and triggers off a threshold voltage value of the electric channel. Signals
which exceed this value are stored for later analysis. Each event has a duration of 500 ms
of which 100 ms is prior to the event and 400 ms is the actual event itself. Either computer
can also be used to record in continuous time series mode in which every data point for
each of three signals is saved. Originally, the sampling rate of the system was 350Hz interleaved every 1/1050 seconds. Later, a sampling rate of 2000Hz was used in order to avoid
the phase offset of the two magnetic signals due to interleaved sampling. The signals are
notch-filtered at 60Hz with an overall bandwidth from 3 to 120Hz.
Chapter 2
Background to Understanding
2.1 The Normal Mode Equations for Schumann Resonances
The normal mode equations for Schumann Resonances were described by Wait
(1962). The radial electric field is
E(o) = i.
Ids(co) v (v + 1)P (-cos)
.)
2
4a2 Eoohsin (xv)
(2.1)
and the azimuthal magnetic field is
H (co) =
-Ids (o) P i (-cosO)
4ah sin (Eiv)
(2.2)
where Pvo and Pv 1 are Legendre functions. These two formulaes become the backbone of
a theory which Jones later uses to interpret observations. In looking at the two field equations, we see that the Legendre functions are of order 0 and 1 with a new subscript v. This
v is the complex eigenvalue. The fundamental zonal harmonic expansion of these Legendre Functions is
(_COS,+
P(-cos) = (-1)
s)inv)
(2n + 1sini
Pm (cos 0)
(2+)P(2.3)
S
n (n + 1) -v (v + 1)
n=0
We see that equation 2.3 is an infinite sum of Legendre Polynomials. Each of the polynomials describes a mode which is part of the Schumann Resonance spectrum. Therefore,
the summation of all these modes gives us the total Schumann Resonance.
2.2 Legendre Polynomials
The Legendre Polynomials are the key ingredients to understanding the theory behind
the Schumann Resonances. The general equation for the Legendre polynomials is
(n - m) Pm (x) = (2n - 1) xP,_ (x) - (n + m - 1) P-2 (x)
(2.4)
where only order m = 0 or 1 is needed in our calculations and n is arbitrary.
Other relations include
d[(1
P0(x) = 2nn! dx
x 2)
P0 (x) = -P (x)
(2.5)
(2.6)
These three equations will allow us to generate infinite number of n modes of order 0
or 1. When we substitute cos 0 for x, we get mode distribution as a function of the cosine
of theta. Figures 2.1 and 2.2 show the first three modes for the Legendre Polynomials of
order 0 and 1. These modes are the discrete Schumann Resonance modes. Legendre polynomials of order 0 correspond to the radial electric field and polynomials of order 1 correspond to the azimuthal magnetic field. The polar angle is the displacement from the source
to the receiver. In the electric field, the first mode structure for a point source at due east
shows the greatest contribution at the source (polar angle is zero) and at the antipode, or
due west (polar angle is 180 degrees). On the other hand, the magnetic field's first mode is
minimum when the electric field is maximum and vice versa. As the modes change, so do
the sizes of the lobes which contribute to the Schumann Resonance. In essence, the
Figure 2.1: Electric Field
First Three Modes of Legendre Polynomials of Degree 0
mode 3 = -.
mode 2 = :
mode 1 = -
Figure 2.2: Magnetic Field
First Three Modes of Legendre Polynomials of Degree 1
mode 1l=-
mode 2=:
mode 3=-.
total Schumann Resonance of the electric and magnetic field is the summation of all
modes described by these Legendre Polynomials.
However, the Legendre Polynomials do not alone define Schumann Resonance. Properties of the Earth-ionosphere cavity, such as attenuation and wave propagation, must be
accounted for in formulating an expression for the radial electric and the azimuthal magnetic field of Schumann resonance modes.
Jones and Joyce (1989) realized that for the values of v appropriate for the electromagnetic wave computations, a few hundred Legendre polynomical modes are needed to compute Pv ° and thousands of terms to compute Pv1. Though poorly convergent, the above
equation is a much simpler formulae. For this reason, ways to develop alternative and
more convergent expansion formulae involving the zonal harmonics were developed by
Jones (1989). From the work of Erdelyi et al (1953), the relations between successive Legendre functions are
(2v + 1) SP1 (-C) = v (v + 1) [P.
(-C) - P,(-C)]
(2v + 1) SPo (-C) = -[P+,(-C) - P_, (-C)]
(2.7)
(2.8)
in which S=sin 0 and C=cos 8 and m=O or 1 as indicated. Using equation 2.6, 2.7, and
2.8, he developed faster convergent formulae for the Legendre functions which are
.
4
(sine)
(2n + 1) •N
P•0 (cos0)
n =(2
N 1 = [n(n + 1) + (v - 1) (v + 2)]
(2.10)
DI = [n (n + 1) - (v - 2) (v - 1)] [n(n + 1) -v(v + 1)] [n(n + 1) - (v + 2) (v + 3)]
(2.11)
and
16
(-cos= (-1) sinvv
PV P(-Cos.0),=n(-I)
7
(2n + 1) - N 2 P0 (cos0)
3D
(sin O)3
D2
n(2.12)
N 2 = [2n(n + 1) + (v - 2) (v + 3)]
D2 = [n(n + )-(v-3) (v-2)] [n(n+l)-v(v-1)] x
(2.13)
(2.14)
[n(n + 1)- (v+ 1)(v+2)] [n(n + ) - (v+3) (v+4)]
In Section 3.1, we will use these zonal harmonic expansions of the Legendre Function
expressions to calculate the field associated with electric and azimuthal field components
of a lightning source.
2.3 Discrete Fourier Transform (DFT) for Processing Transient Waveforms
In analysing ELF transients and their signatures in the Schumann Resonances, knowledge of the frequency content of these lightning events allows their classification and their
range from the receiver. The frequency representation of a discrete time series event is
realized with the Discrete Fourier Transform. Given a discrete time series x[n], the Discrete Fourier Transform is defined as
N-1
X[k] =
-x[n]
e
-j( 2 N)k
n
(2.15)
n=O
whose Inverse Fourier Transform is
N-1
x[n] =
-
j( 2)kn
X[k] e
(2.16)
k=0
where N is the period of the time series sequence and k is the index of the Discrete Fourier
Transform. Therefore, the number of points in the Discrete Fourier Transform must be less
than or equal to the period of the time series. Because the DFT is a complex series, we can
specify two quantities associated with the DFT - the magnitude or modulus and the argument, where
magnitude = IX [k] =
real (X k ]]) 2+ imag (X [k]) 2
(2.17)
( imag (X [k]))
argument = X [k] = atan(
(X[k]) )
(2.18)
Figure 2.3 and 2.4 show a time sequence and its corresponding DFT magnitude and
argument. We see that the x-axis of the DFT is in terms of the index number k which
ranges from 0 to the number of DFT points specified by the user. In order to convert to a
frequency label, we must first know the sampling rate and the number of points in the
Figure 2.3: Discrete Time Series Waveform
6
Figure 2.4: Magnitude and Argument of the Discrete Fourier Transform
Magnitude of the Discrete Fourier Transform
20
15
0
2
4
10
k index number
k index number
12
14
DFT. This ratio of the sampling rate and the number of DFT points gives us the frequency
spacing between DFT points.
S = sampling frequency
P = number of DFT points
(2.19)
S = frequency interval between points (Hz)
P
(2.20)
X_
magnitude = Xjfl =
SI(qrealJX[k2)+imag(X[
=X[real(X--_)_+imagXP
9
Jsampling frequency
sampling frequency
We have normalized the magnitude by dividing by the square root of our sampling frequency. Figure 2.5 shows each index number k being multiplied by this frequency ratio
and the magnitude normalized by a sampling frequency of 10 samples per second.
Figure 2.5: Frequency Magnitude and Argument of the Time Series Waveform
Magnitude of the Discrete Fourier Transform
Argument of the Discrete Fourier Transform
ISO
Transform
Argument of the Dlsorele Fourier
//7
100o
t
°
-SO.
-100
-160
S3
ai
,
a
o
10
-2 0
frequency (Hz)
Now the two spectra are in terms of frequency from 0 to the S Hz. We have connected
the points defined at the discrete frequencies to approximate the frequencies in between
the points. The magnitude spectrum illustrates the relative frequency strength whereas the
argument spectrum shows the phase characteristic of the time series signal at each frequency. The value of the Magnitude at the point f = 0 is the average level of the time
series waveform. Notice that the magnitude spectrum from 0 to 1 S Hz is reflected from
S to S Hz and the argument spectrum is oddly reflected. This is due to the fact that the
time series sequence is real. Because the sampling rate is S, we can resolve only frequencies from 0 to S. This is a consequence of the Nyquist theorem which states that the sampling frequency must be at least twice the frequency band of the time series signal.
Figure 2.6: Zero-padded DFT
Magnitude of the Discrete Fourier Transform
25
20 -
15TF
O810
o
SO
:Pk
i
Ti
in
-h
~
20
3 u40
indexn
umber
50
so
50
60o
Argument of the Discrete Founer Transform
t
10oo0
50 -100-
-200
10
200
o0
k index number
40
The magnitude and argument spectra of the time series sequence in Figure 2.5 seem to
be jagged and lacking in smoothness. There are methods in which we can interpolate
points between the DFT points and thereby smooth the Discrete Fourier Transform. This
is the method of zero-padding (Oppenheim and Shafer, 1989). The fundamental theory
behind zero-padding lies in the convolution of two time series. It is a general fact that
when two time series signals convolve, their frequency domain representation is the product of each individual DFT. We first look at the forward problem of interpolating points in
the time domain. Then by using the same concept, we apply it in the frequency domain.
To interpolate in the time domain, we take the DFT of the time series as illustrated in
Figure 2.4. Lets now extend the number of points from N= 14 to 4N = 56 by putting zeros
Figure 2.7: Inverse Discrete Fourier Transform of Zero-padded DFT
n sample points
at the end of the original DFT as shown in Figure 2.6. Then we take the Inverse Discrete
Fourier Transform (IDFT) of our zero-padded DFT to recover our original time sequence.
Remember that because the number of points has increased to 56, we must multiply by a
factor of 4 in the IDFT in order to match the original amplitude of
1
in equation 2.16. Fig-
ure 2.7 shows a 56-point IDFT of our zero-padded DFT. We now see our 56-point time
series. This is the original time series interpolated with 3 data points in between each sample. Thus if we take every fourth point of this 56-point time series, we will recover our
original time series.
Figure 2.8: Aligned Interpolated Time Series with Original Time Series
S-------
3-
Interpolated
Original
-2
-o
S-4
0
2
4
6
8
n sample points
10
12
14
Figure 2.9: Original ,4N, and 10N Lowpass Interpolated Times Series
ON Interpolated
--4
r
3
r
2
I
~
I
1
o
0
I
I
/,
i
\\
--1
--2
-- 3
0
2
4
6
8
10
12
14
n sample points
This method is called lowpass interpolation. We now align the two time series together
in Figure 2.8. We now can see the interpolated points between the original time series.
These points have in effect smoothed the original time series. Figure 2.9 shows interpolating of 10N aligned with the original time series. It is clear that now the time series is quite
smooth as compared to the previous two time series.
Figure 2.10: 10N Lowpass Interpolation of the DFT
4
Argument of the Discrete Fourier Transform
200
ISO50
-100
2000
2
4
68
k index number
10
12
14
Therefore to interpolate in the frequency domain, we zero pad the time series sequence
and then take the DFT. Here we do not have to worry about amplitude scaling due to the
increase in the number of DFT points (equation 2.15). This has the effect of interpolating
points between the original frequency samples. Figure 2.10 shows the interpolation of the
original DFT in Figure 2.5 by 10N. The new DFT in solid lines connects the original DFT
points. Here again we see significant improvement in smoothness. It should be noted that
zero-padding does have a limit in that there is a point at which no further smoothing
improvement to the spectrum can be achieved. This is seen in Figure 2.9 where the 4N and
10N interpolated time series are nearly identical. Computationally, this is important for we
do not want to waste time calculating a 1000-point DFT which has no more information
than a 500-point DFT.
2.4 Spherical Geometry for Source Location
North Pole
,Source
Receiver
Figure 2.11:
In solving the lightning event source location problem, some knowledge of spherical
geometry is necessary and a consideration of the spherical triangle in Figure 2.1 is most
useful. Wave equation (equations 2.1 and 2.2) solutions return a source bearing and a
range estimation. The bearing defines the great circle path connecting the source and the
receiver and is defined from the receiver. Therefore travelling a range specified by the
solutions on that great circle path leads to the lightning source. Given the bearing and
range, we must derive the longitude and latitude coordinates associated with the source.
Figure 2.1 shows the physical picture involved in solving this problem. Side a is the range
on the circle path, side b is the colatitude of observation site, and angle C is the bearing
defining the cirle path, all of which are known. Side c is the colatitude of the source and
angle A is the source longitude relative to the observation site, both of which are
unknown.
From Napier's analogies,
1
sin (a-b)
1
tan (A-B)
S1
sin (a + b)
1
cot C
2
1
cos (a-b)
cos
1
(a + b)
tan
1
(2.21)
(A+B)
1
cot C
1
(2.22)
We want to solve for the unknown A and after carefully rearranging of the two analogies in equations 2.19 and 2.20, we get
(A(A
- B) 2
22
atanB
otI sin (a-b)
(2.23)
smý (a + b)
- atan
c - ...
cos2 (a + b)
1
(2.24)
To solve for A, we sum the above two equations to get a single equation with known
quantities.
A = atan
cotC) sin
sin
(a - b)
+ atan
cot(C
(a + b)
cos
1
(a - b)
(2.25)
cos- (a + b)
where atan is the four-quadrant arctangent function. Because A is the source longitude relative to that of the observer, it is the difference of these two longitudes.
A = (source longitude - receiver longitude)
(2.26)
Now, in order to find the latitude of the source, we use the law of sines.
sinb =sinc
B
C
(2.27)
. sinC\
c = asin (sinasinA
(2.28)
sina
A
Therefore,
where asin is the arcsine function. The integrand of the arcsin function is always positive
ranging from 0 to 1. However, the arcsin function cannot distinguish an angle greater than
90 degrees. These angles greater than 90 degrees correspond to the negative latitudes and
they are going to be mapped as (180-actual colatitude) degrees by the arcsin function. In
order to test if the latitude and longitude are correct values for the range and bearing, we
use the law of cosines for sides.
cosa = cosb - cosc + sinb - sinc. cosA
If both sides of the equality are the same, the colatitude c has the correct value and
therefore, the latitude is
c = 90 - source latitude =- source latitude = 90 - c
(2.29)
Otherwise, the equality is not satisfied, in which case
c = 180 - actual colatitude =- actual colatitude = 180 - c
(2.30)
source latitude = 90 - actual colatitude =- source latitude = 90 - (180 - c)
(2.31)
In essence, all the lightning source data will be converted from range and bearing values to latitude and longitude coordinates on the globe thereby allowing simple plotting
procedures and lookups on a global map.
2.5 Lightning Terminology
Before we embark on the task of understanding the theoretical details of calculations, it is
important to know some basics of lightning terminology. Figure 2. illustrates two quantifying factors associated with lightning - the current and the duration. Because the strength
of a lightning source is based on the amount of charge transfer, lines of constant charge
transfer have been drawn. In the first region of duration which is between 1lis to 10s, we
see that the lightning sources which are positive cloud-to-ground (+CG) have a typical
charge transfer of about 1 coulumb and sources which are negative cloud-to-ground (-CG)
have a charge transfer of .1 coulumb. These events are discrete strokes meaning that they
are short compared to Schumann Resonance time scales and good approximations to delta
impulse functions. Because of the short duration of these events and the limitation of the
Schumann Band , they have a flat spectral shape (i.e. white noise) characteristic similar to
that of a delta function. The majority of negative flashes to ground are composed of discrete strokes (Uman, 1987).
Figure 2.12: Lightning Diagram
Lightning
Diagram
Mesosphere Relaxation Time
I
10 MA
1 MA
100 KA
c· ~
S=j
d)
5-1
t·4
=3
10 KA
1 KA
100
10
1
0.1[us
10.0 s
1 ms
Duration
100 ms
In the second region of about Ims in duration, we see that the charge transfer of both
the +CG and -CG has increased . This is due to the longer duration of these lightning
events meaning that more charge can be transfered. Thus these events are so called 'fast'
continuing current lightning events because of their duration and the ability to transfer
charge. In the spectral domain, the appearance of a slow tail in the 200-500 Hz region is
probably associated with this fast continuing current.
For the third region, we have lightning events which last for a duration exceeding 40
milliseconds and as long as several hundred milliseconds. These events are the so called
long continuing currents and they have a higher charge transfer than any of the previous
discussed phenomena. The majority of positive CG's are characterized by continuing current in contrast to the situation for negative CG's discussed earlier (Uman, 1987). At ELF,
we have found that the source spectrum for positive CG's exhibits a declining power with
frequency. The spectral shape is thus said to be 'red' because of this enhanced low frequency energy. The +CG events in this region are so called Q-bursts which Ogawa first
named (Ogawa et al, 1966). These Q-burst events probably also exhibit the 'slow tail'
phenomenon because they are a continuation of these so called Ims events. The Q-bursts
are of special interest for they occur in large mesoscale convective complexes in which a
re-illumination of the laterally extensive 'spider' channel by the return stroke of these positive CG intensifies the electric field stress in the mesosphere which in turn causes ionization and optical emissions called sprites (Sentman et al, 1993; Lyons, 1994; Boccippio et
al, 1995; Pasko et al 1995).
The theoretical models which characterize these lightning events will provide important evidence to the details in the source spectra of lightning in these three regions. It will
allow us to classify further the special features which are associated with lightning in each
region. First we will look at the model developed by Wait (1962) and then implemented in
observations by Jones (1970). We will also look at Sentman's (1995) model and make
quantitative comparisons between the two.
Chapter 3
Theoretical Calculations for an Isotropic Cavity
3.1 The Models of Wait and Jones
The mathematical equations which determine the electromagnetic field components produced by a lightning source on the spherical earth with ionosphere varying only in the
radial direction are well established by Wait (1962). The radial electric field is given by
E Ids (o) - v (v + 1) P 0 (-cos 0)
E(o0) = i.
4a2 eohsin (ntv)
(3.1)
and the azimuthal magnetic field is
H (o) =
-Ids(co) -P (-cosO)
4ah sin (iv)
(3.2)
where Pv, and Pv1 are Legendre functions with complex subscripts and
v (v + 1) = k2a2S 2
(3.3)
a = radius of the earth
h = thickness of the cavity
0 = great circle distance between source and receiver
ids (c) = current moment of the source
This is essentially the mathematical model used for the treatment of transient observations later in this thesis. Here v is the complex eigenvalue and is a function of the angular
frequency co. S is the sine of the mode eigenangle (Jones 1970). These parameters are
related to the attentuation constant a (decibels per megameter, dB/Mm) and the phase
velocity V of the traveling waves in the homogeneous earth-ionospheric cavity by
S = ()-
i(5.49
(3.5)
where C is the speed of light, i is the imaginary unit, and fis the frequency
The propagational influence of the electromagnetic wave sits entirely in the eigenvalue
v. In computation, v is determined from the a and ratio of C/V both of which are experimental values. Jones (1970) derived the value of v as the mean value for the three ionosphere profiles of Jones, Pierce and Cole presented in Jones (1967). These three profiles
resulted in approximately the same eigenvalues and also predicted propagation parameters
that appear to agree with available experimental atmospherics and Schumann Resonance
data in the band 7Hz to 1 kHz (Chapman and Jones 1964). The values of a and C/V used
in the computation of v are obtained by this mean and can be summarized by the following empirical equations:
C
2
, = 1.64 - 0.17591ogf+ 0.01791 (logf)2
(3.6)
a = 0.06364dB/Mm
(3.7)
Jones (1970) argued that a and C/V are representative of the conditions achieved in the
actual earth-ionosphere waveguide meaning measurements agreed with predictions.
Therefore since the eigenvalues are associated with model parameters which agree with
measured data for the cavity resonances, they are the values appropriate for propagation
on a global scale.
Figure 3.1: Electric Field at 8, 14, 20, 26 Hz
1
10
x
-e
Electric Field at 8,
14, 20, 26 Hz
-
-
-
-
0
-
2
4i
2
4
1t4 ,
1ý9
1
20
12
(Mm)
14
16
18
20
10
12
14
1620
10
12
14
16
18
20
14
16
18
20
14
16
18
20
1i2
10
Distance in Megameters (Mm)
1
o.I
0.8I
0.4
0.2
O0
O x I o-
10
in Megameters
8
6
Distance
0.8a
0.6
0..4
0.2
0
S
2
4
O
2
4
6
8
i•;A
.
.
.
.
5.41 .
.
.
'
N4
in Megameters (Mm)
Distance
Figure 3.2: Magnetic Field at 8, 14, 20, 26 Hz
x
1u
-~1.5
1"1f
S0.5
I
S
x 10
2
4
6
-
8
Distance
12
10
12
in Megameters (Mm)
1.5
r o.s
S
2
4
6
8
,_
10
,._____,___
12,,._,
2
1.5
= 0.5
Distance in Megameters (Mm)
Figures 3.1 and 3.2 show plots of the radial electric field and the azimuthal magnetic
field respectively as a function of distance at four discrete frequencies of 8, 14, 20, 26 hz.
For each calculation, the Legendre functions Pvo and Pv 1 are represented by their respective zonal harmonic expansion as used by Jones (1989) and a total of 500 modal terms in
the expansions are used. The four frequencies above correspond to the lowest four modes
of the electromagnetic resonance of the earth-ionosphere cavity. It can be seen that for distances close to the source (< 1Mm), both fields blow up. This is due to singularities in the
zonal harmonic expressions of the two Legendre functions. Physically, the singularity
arises because power must flow from a point to be dissipated around the world. It is also
important to note the differences in the peaks and valleys in the two fields as one tranverses the great circle path. Specifically, at each mode far away from the singularities,
when one field reaches a local maximum, the other dips to a local minimum. This is the
structure of Schumann resonances for the radial electric and the azimuthal magnetic field.
Instead of computing the fields as function of distance at discrete frequencies, the
complete spectrum of radiating source at any distance on the great circle path can be generated as a function of frequency. These spectral shapes then become 'fingerprints' for the
source-receiver distance. Figures 3.3 and 3.4 show some of these spectra at selected distances from the receiver. Appendix A illustrates a set of spectra of the electric and the
magnetic field from 1 Mm to 20 Mm at intervals of 1 Mm. Interesting characteristics of
these spectra are evident as the distances increase from small source-receiver separation to
large source-receiver separation. One characteristic is the change of modal structure as the
distance between the source and receiver increases. At distances less than 10 Mm, the
structural changes between successive spectra are more gradual than that at distances
greater than 10 Mm. This feature in both the electric and magnetic field spectra is inportant in understanding the wave impedance.
x
10
-1
Figure 3.3: Electric Field Spectra Using the Wait/Jones Model
x 10 10
i• I -o
iz
6
1 -0
0
5
5
-
A:.AAA-A.A
i
42
1
45
3
2
1
O II.
0
50
Frequency
1O00
(Hz)
-j
0
!
0
.F
1
-
50
50
Frequency
100
100
(Hz)
50
Frequency
100
(Hz)
.
a
ME
i.
I
=E
x
x1O-'o
I
10
- 1
0
6
5
5
4
I
E2
12
v
4
\i••
vI v v
1
01
0 LC:T
50
100
Frequency (Hz)
01 LO
12
50
Frequency
100
(Hz)
50
Frequency
100
(Hz)
Figure 3.4: Magnetic Field Spectra Using the Wait/Jones Model
go
-O
o0
I ;:.:10
0.8
X
-
12
0.6
0.4
~0.2
"0
50
100
Frequency (Hz)
O.
:0.
10.,
0.ý
Frequency
(Hz)
Frequency (Hz)
Frequency (Hz)
3.2 Wave Impedance
Understanding these structural changes is the key to determining the match between an
experimental spectrum and many theoretical spectra, and this aspect is an essential step in
an algorithm which extracts a range from spectral characteristics. By taking the ratio of E
and H fields, we can eliminate the complication of the source spectrum Ids (o).
0
)
E(o)
Z(o) = E
H, (a)
v (v + 1) P, (-cos)
-=-i
ae,oPv1 (-cosO)
(3.8)
(3.8)
As Jones (1971) discovered, despite the irregular undulations of the contributing frequency spectra, the ratio of E and H has a relatively simple form. This ratio of E and H is
called the wave impedance and is a complex value for both E and H are complex values.
The advantage of the wave impedance over the radial electric and azimuthal magnetic
field expressions defined earlier is that the ratio of E and H is independent of the source
term Ids (o) . Each field expression can be thought of in the time domain as the convolution of a source term Ids (t) and a system function defined by the Earth-ionosphere cavity.
This implies the multiplication of the two in the frequency domain resulting in the previous two field expressions. Because both Ids (o) and the source-observer distance are
unknown quantities, it is advantageous to find an expression in terms of one variable. By
eliminating the Ids (o) variable defining the electromagnetic wave, the resulting expression becomes one-dimensional in 0 alone. Figures 3.5 and 3.6 depict the modulus and the
argument of the wave impedance at selected distances from the receiver. Here we have
normalized the modulus by the characteristic impedance of free space
0 which is
approximately 377 ohms. Therefore, the modulus is now dimensionless. Appendix II
shows a set of modulus and argument plots of the wave impedance from 1 Mm to 20 Mm
Figure 3.5: Modulus of the Wave Impedance Using the Wait/Jones Model
-- 4
2
0
50
100
Frequency (Hz)
25
20
E 15
5
Frequency (Hz)
Frequency (Hz)
Figure 3.6: Argument of the Wave Impedance Using the Wait/Jones Model
so0
100
Frequency (Hz)
FA
4
--
50
100
Frequency (Hz)
Frequency (Hz)
at intervals of 1 Mm. Here, the wave impedance spectra all show a decrease in magnitude of
the fluctuations towards higher frequencies as a result of the increase of the propagational
attentuation with frequency. What is more important to note is that the spectra all exhibit the
same shape. The only noticeable difference is the period of oscillations as the range
increases. Specifically, the period of oscillations increases as range between the source and
observer is increased on the great circle.
Interestingly, the relationship between the modulus and the argument of the wave
impedance reveals one distinct feature: both are unique functions of source-receiver distance. At a given source-receiver distance, the oscillations that pertain to a pair of modulus
and argument spectra all have the same period. And because this period is a function of the
source-receiver distance, it is possible to work the problem backwards. Essentially, if both
the modulus and the argument spectra of a given lightning excitation is known, then the two
spectra should exhibit the same period of oscillation. And thus from this period, it is then
possible to determine the source-receiver distance.
3.3 The Range-Frequency Curve
In theory, the wave impedance is described by its two parts: the modulus and the argument. The modulus as well as the argument has a characteristic period which is a function of
0, the geometric angle between the source and the receiver. The sequence of plots in Appendix B reveals this phenomenon. Specifically, as 0 increases from 1 Mm to 20 Mm, the periods of both the modulus and the argument functions increase. This period is called the peakto-peak frequency separation (PTPFS). In the previous section, it is suggested that once a
PTPFS is known, then it is possible to determine the range. Figure 3.7 illustrates the rangefrequency curve. The distance between the source and the observer is plotted as a function
of the peak-to-peak frequency separation. This curve allows an easy lookup to determine
the distance between the source and the observer given a PTPFS.
Figure 3.7: Range Frequency Curve
E
Me
."
"o
0
10
20~
o
40
peak-to-peak frequency separation in Hz
ou
3.4 The Lightning Source Term Ids(o)
The Ids(wo) is the current-dipole moment spectrum of the source lightning flash and is
an unknown quantity in both E and H field expressions. I is the lighning stroke current and
ds is the vertical length of the stroke. From lightning physics, the spectrum may reflect
either a discrete stroke (whitish spectrum) as stroke durations are very short compared to
Schumann Resonance time scales. Alternately a continuing current lightning event whose
time scale is comparable to the Schumann Resonance time scale has a spectrum whose
magnitude is decreasing with frequency (reddish spectrum). This value, however, cannot
be determined apriori. Only after the source-receiver range is known can the Ids(wo) be cal-
culated. Burke and Jones (1995) modeled this source term for the continuing current stroke
lightning as an exponential decay in the time domain as
1
Ids (t) = A e T
(3.9)
where A is the magnitude and T is the duration of the continuing current. The Fourier
Transform in the time domain solution becomes
Ids (co)
=
1
i (+ -
(3.10)
He computes the two parameters by a technique that produces an optimized curve fit to
each experimentally measured spectrum. However, this method is used only after one has
already determined that the spectrum is reddish and this is done post-apriori. A simpler
question to ask with an automated system is how an algorithm distinguishes between the
two different source spectra with only a source-receiver distance. This is the essential ingredient in solving for the two unknowns ( Ids(0o) and 0 ) in the E and H field expressions. We
shall examine this issue later in Chapter Six.
3.5 Source-Receiver Distance
The source-receiver distance is defined as the shortest distance which connects the lightning
source and the station from which measurements are taken. Therefore this path which connects the two points must be an arc on the great circle path. The electromagnetic waves radiated by the lightning source travel the great circle path and therefore reach the receiver in
minimum time. The radial electric E and the azimuthal magnetic H both express the sourcereceiver distance as 0. Because 0 is an arc angle in degrees, to convert to Mm, the following
expression is used.
distance (Mm) =
x circumference of the earth
(3.11)
The circumference of the earth is 40 Mm. Therefore, sources equidistant on either side
of the receiver will exhibit the same modulus and argument spectra because both will tranverse the same distance on the great circle arc to the receiver. In this sense, given a bearing
angle, only half of the great circle path which is 20 Mm is needed to define any source on
the globe.
3.6 Sentman Model
Sentman (1990) proposed a two-scale height ionosphere model with a different conductivity
profile in each height interval. The Wait-Jones model in contrast treats the effect of the ionosphere with a single complex eigenvalue v as discussed in Section 3.1. The two scale
height model was selected for Sentman's new approach because it treats the middle and
upper atmosphere as separate domains. In doing so, he derives a different set of expressions
for the radial electric and the azimuthal magnetic field.
E(w) = i-ds((o)o•.
2n+ 1
P O (-cos0)
2
4rta ohl n (0-0,) (0+0,n*)
(3.12)
H(o) =
(3.13)
Ids(c)
4na 3E hl , I
(-
2n+ 1
On) (n+
P (-cosO)
(C*)
where
(on =
27 x 5.8 1 + 2
,(n+
n
1)
(3.14)
Figure 3.8: Electric Field Spectra Using Sentman's Model
F
I
g
E
5
4
23
2
2
1
OV
50
Frequency
0
100
(Hz)
50
Frequency
50
Frequency
100
(Hz)
100
(Hz)
Figure 3.9: Magnetic Field Spectra Using Sentman's Model
-.--
1.4
-
12
.• .--
-
12
- 1
.-
.,
2
'
1.5
1.2
>1.5
51
!0.8
0.6
0.4
0.5
0.5
~-1.
0.2
0
50
so50
Frequency
C
K 10
-
100
100
(Hz)
13
x
10
50
Frequency
100
(Hz)
50
Frequency
100
(Hz)
-
4
--
3
I2
2
=1
31
'1
50
Frequency
100
(Hz)
10
1.4
-1.2
I
1
~0.6
S
0.4
C
0.5
0.2
0
0
Frequency
(Hz)
-
o
50
Frequency
-
2
Q-factors are specified by Qn = 5 for all resonant modes. Figures 3.8 and 3.9 show
selected E and H spectra at selected distances from the receiver using the Sentman model.
Appendix B contains the complete set of spectra from 1 Mm to 20 Mm at intervals of 1 Mm.
3.7 A Comparison of Models Used by Sentman and Jones
Sentman's model provides a cross-check of the model presented by Jones (1970). If Sentman's division of the two-scale ionosphere is a factor in the spectral shape of the radial electric and the azimuthal magnetic field, then serious consideration must be given to the fine
details in the height structure of the ionosphere. Figures 3.10 and 3.11 show spectra of Sentman's model (in dotted lines) superimposed on results for the Wait/Jones model (solid line).
At low frequencies (f < 35Hz), the two models are in agreement in terms of peak center frequency location. The magnitude of the two are slightly off but in general are in agreement
within 20%. At higher frequencies (f > 35Hz), the peak center frequency location of the two
models are not matched. We see the amplitude of Sentman's model drops down dramatically
as compared to Wait/Jones. We can no longer see definite modal structure in Sentman's model
beyond 60 Hz. This is due to the constant Q-value of 5 in Sentman's model. By assigning a
low Q at high frequencies, Sentman model predicts very little energy at those high frequencies. In the next section, we will see how changing this value will raise the high frequency
structure of Sentman's model. Figures 3.12 and 3.13 show the comparisons of the two models
in terms of the modulus and the argument of the wave impedance. Again the dotted line of
Sentman's model show agreement at low frequencies (f < 35 Hz). At high frequencies (f >35
Hz) Sentman's model displays some frequency drift of peak locations. Note that not all the
spectra generated by Sentman's
Figure 3.10: Comparison of Electric Field in Sentman and Wait/Jones
x 10"
x -o-"
1
0
100
50so
Frequency
(Hz)
S--1o
x
1 O0
50
8
100
64
2
100
50
LL.
0
o
x
so
,
50
Frequency
100
Frequency (Hz)
caý
10-10
1 0-10
V
ts
-5
100
(Hz)
4
3
DI
''
'
m
50
Frequency
100
(Hz)
Figure 3.11: Comparison of Magnetic Field in Sentman and Wait/Jones
x
10
-
1.4
1.2
E
0•.8
0.6
0.4
0.2
0
50
0
• 10
rK
100
Frequency (Hz)
-
Frequency (Hz)
3
r
-
x -10 1
8
'I^
2
0 O
'
50
Frequency
100
(Hz)
I.a2
2,
0
50
100
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Figure 3.12: Comparison of Modulus of Sentman and Wait/Jones
1
C
--
IA
25
20
E15
3
10
'V
5
50
100
Frequency (Hz)
O
4
1
0
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Figure 3.13: Comparison of Argument of Sentman and Wait/Jones
220
200
S180
S1 60
=E 140
120
100
cO
50
100
Frequency (Hz)
E
C"
220
200
180
160
-140
120
100
0
50
100
Frequency (Hz)
0
50
100
Frequency (Hz)
0
50
100
Frequency (Hz)
model exhibit the periodic shape of Wait/Jones. Instead, we see a slight deviation from the
regularly oscillatory shape which Wait/Jones predicted. Figure 3.14 illustrates a comparison of the range-frequency curve of the two models. Here we see Sentman's model results
in a slight upward shift in the range-frequency curve. This is due to the shift of frequency
peaks in the Sentman model. Thus the average peak-to-peak frequency separation in each
modulus and argument spectrum is lower than that of Wait/Jones. This is an important distinction in the two models because it results in two different range predictions. We also see
that the Sentman curve is jagged meaning that the structure of the modulus and argument
is not like the periodic functions as see in Wait/Jones' model. Therefore, the PTPFS is
unlikely going to be a smoothly varying function. The Sentman model departs from the
periodic nature in the wave impedance at high frequencies. In the next section, we will see
how changing the constant Q-value will change the structure of this curve.
Figure 3.14: Range Frequency Curve of Sentman and Wait/Jones
1
E
vs
0
5
10
15
20
25
30
35
peak-to-peak frequency separation in Hz
40
45
50
3.8 Q-values for the Earth-Ionosphere Cavity
The Quality Factor or Q-value is defined by Galejs (1965) as the ratio between the
energy stored in the cavity and the loss per cycle in the cavity. To compute this numerically, this is the height of the resonance curve divided by the width of the curve at half
maximum. There are however practical difficulties with this definition in the face of overlapping modes in the measured Schumann Spectra.
In the electric field spectrum, the Q-value is
Q
Re(S)
21m (S)
(3.15)
where S is given by (3.4) and in the magnetic field spectrum, the Q-value is
Q =
2Re (S) Im (S)
(3.16)
Because the stored electrical energy differs from the stored magnetic energy, an average of the two is
(Rs (S)) 2+ 1
4Re (S) Im (S)
(3.17)
This average is the so-called representative Q-value (Bliokh 1980). Figure 3.15 shows
the plot of these three sets of Q-values using values of S consistent with the numerical
complex eigenvalues of the Jones Model. In the figure, the representative Q-value is
approximately equal to 5 for frequencies near 32 Hz (fifth mode) but is monotonically
increasing with frequency. In Sentman's model, a fixed Q-value of 5 for n>1 is used (Sentman, 1995) where n is the number of modes in the summation. This assumption is in
Figure 3.15: Q-value of Electric and Magnetic Fields
4^
10U
Average Q-value
---- --- - -- - --I
Magnetic Field Q-value
Electric Field Q-value
I
I
40
60
Frequency (Hz)
I
reasonable agreement with the Wait/Jones model for frequencies less than 32 Hz (fifth
mode). However, if the summation is over 50 or 100 modes of the Schumann Resonance
as representated by the E and H field expressions in Sentman's model, then assigning a Qvalue of 5 for modes greater than 5 is not in accordance with Jones' model. Since Q-value
is defined as a function of frequency, it is appropriate to pick Q-values at the resonance
frequencies defined by Sentman's equation
f, = 5.8Jn (n+ 1)
(3.18)
Once we have obtained Q-values for each of the desired number of modes, then E and
H can be recalculated. Figures 3.16 and 3.17 illustrates the comparison of Jones' spectra
with the revised Sentman amplitdue spectra of the two fields using new Q-values as
Figure 3.16: Sentman's Electric Field Using Jones' Complex Eignenvalue v
dJX10-
X10-10
x10-
4
5
4~
~3
ii,
,/~iv
P,
i/OlA"Y
i3
2
"-1
0
50
Frequency
0
0
100
(Hz)
0
50
Frequency
100
(Hz)
0
Frequency
100
(Hz)
0-1o
xl
r-
8
100
(Hz)
o4
2
°
9
c
0a
50
Frequency
0-10o
xl
r-
_
1
x.av 1C
5k
I
50
Frequency
O
100
(Hz)
- -
12 3
01
(: 0L
0
VU v v~v
O
2
- 1
V
1 0
0
so50
Frequency
1 00
(Hz)
0
0
50
so50
Frequency
100
1 0
(Hz)
Figure 3.17: Sentman's Magnetic Field Using Jones' Complex Eignenvalue v
-
x10"
0.8
0.6
"
0.4
S0.2
)
0
c
)
50
100
x
' ~'
6
:4
E2
0
50
100
Frequency
(Hz)
Frequency (Hz)
1
S0.8
0.6
ME 0.4
0.2
0
Frequency
(Hz)
Frequency
(Hz)
Figure 3.18: Range Frequency Curve of Sentman and Wait/Jones
E
0
10
20
30
40
so50
Peak-to-Peak Frequency Separation in Hz
60
70
described above. Here, we see a better agreement with Jones at the low frequency (f <
30Hz). At higher frequencies (f > 30 Hz), we also see improvement. The modal structure
which had significantly decreased in this region is now visible due to the higher Q-values
assigned to the higher frequeny modes. However, there is still considerable difference in
the two models. Figure 3.18 shows the range-frequency curve for Jones and Sentman's
two calculations using two sets of Q-values. The calculation with adjusted Q-values is in
better agreement with Jones. This is expected because the approximation of Q=5 for
modes greater than n=5 is probably not accurate. However, there are considerable differences between Sentman and Jones. The descrepencies in the two models lie in the higher
frequencies ( f > 30 Hz). In order to really know which model more accurately describes
the Earth-ionosphere cavity and its effects on electromagnetic waves, we need to turn to
experimental data which are discussed in Chapter Six.
3.9 Eigenvalues and Eigenfrequencies
In the Wait/Jones model, the complex eigenvalue v was shown to be a function of frequency. Specifically,
v(v+l) = k2a2(C-i(5.49) ) 2
(3.19)
as discussed previously in Section 3.1. In Sentman's (1995) two scale height ionosphere
model, we have the complex eigenfrequency
defined as
, (5.8)(1 +
)n
(3.20)
(n+ 1)
Because the eigenvalue v is defined for all frequencies, we can express the complex
eigenvalue at discrete values of the complex eigenfrequency by merely extracting the
eigenvalue v at the real valued eigenfrequencies defined above. Nickolaenko's formulation in Bliokh et al (1980) offers another expression for these discrete complex eigenvalues v. It expresses the eigenvalues as a function of the eigenfrequencies.
v (f) (v (fn) + 1) = (7.5)2kan(n+1)(
+
(3.21)
The Q-value is determined by picking off the average Q-value of the electric and the
magnetic field defined at the modes specified by eigenfrequency in the expression above.
Figure 3.19 shows the comparison of Jones' and Nickolaenko's discrete eigenvalues at the
f
O1 ,
------
--
-------
·..
---
.
·. ·. ..
-
----
..
Z3 2
---
--
- ----
-
eigenfrequencies defined by the Schumann Resonance frequency modes. Here v is plotted
against the frequency. Figures 3.20 and 3.21 illustrates the imaginary and the real part of
v as a function of frequency. The complex eigenvalues in both formulations seem to agree
with each other to within five percent. The same can not be said of the imaginary part. We
see Nickolaenko's imaginary value for v is less than that of Jones. The existence of the
imaginary eigenvalue is a result of the dissipative system which does not have infinite resonance. This imaginary eigenvalue is increasing with frequency meaning that more attenuation is present at higher than at lower frequencies. In Nickolaenko's model for the
background resonance, there is less loss experienced by the electromagnetic wave than a
model presented by Jones. This fornulation for values of v was formulated based on the
observation of the background Schumann resonance level which do not show modes at
higher frequencies. Figure 3.22 shows the Q-value based on equation 3.21 and the equation
3.17.
Figure 3.22: Q-values of equation 3.21 and 3.17
9R.
25
/
20
......
15
,
......
".
..
.
...
10
Average Q-value, equ 3.17
.......... Magnetic Field ,equ 3.16
5
-
- -
- -
- -
-
-
ElectricField,equ3.15
Nickolaenko, equ. 3.21
A
U
0
100
200
300
frequency in Hz
400
500
600
We see in this case, Nickolaenko has predicted a much higher Q-value than the equations 3.15-3.17. We will see in the next section that Nickolaenko has an approximately
formulae for v and we will look at the effect on the Q-value of his formulae.
Jones' (1970) formulation of v is appropriate in modelling a damped system. These
eigenvalues are important determinants of the level of electric and magnetic spectra. The
imaginary component of the eigenvalue is important in this aspect. The comparison with
experimental data will show that the model presented by Jones for eigenvalues v is reasonably accurate.
Chapter 4
Asymptotic Approximations of the Theory for an Isotropic Cavity
4.1 Theory vs Approximation
In the last chapter, we examined the theoretical model for an isotropic cavity which
Wait (1962) had proposed. We took Wait's model and used the particular numerical eigenvalues v which Jones (1967) had derived. In addition, we saw how a two-scale height ionosphere model differed from Wait/Jones. In this chapter, we will look at the
approximations to the isotropic cavity model. We will compare the similarities and differences between the approximations and the theoretical model. By simplifying the complex
forms of the E and H field expressions, we hope to gain a better understanding of the physical system.
4.2 Nickolaenko's Approximation
While Wait/Jones model for the uniform ionosphere is a concise interpretation of electromagnetic wave propagation, summing hundreds of modes in the Legendre functions
Pvo and Pv' is essential in order to obtain convergent results for E and H. Thus, huge summations are required. Therefore, an efficient approximation to E and H becomes attractive.
Nickolaenko (1993) proposed an asymptotic formula to the Legendre functions Pvo and
P, 1 which are
0
P (-cos e) =
•
2
sCosn[(r-)v+
7CV+1sin8
(4.1)
P(-cos)
(4.2)
sinv(+-8)v
resulting in the wave impedance of
Zi
cot(
v(
-]
)+
(4.3)
cot[( -9))( V+
V+ CmaEo
0o
Here again 0 is the great circle displacement, a is the radious of the earth and o. is the
angular frequency of the electromagnetic wave. Nickolaenko further approximates the frequency dependence of eigenvalue v as
v(f) = (f-2) i- 10 2f
6
(4.4)
Figure 4.1 shows the Q-values of equation 3.17 associated with this approximation of
v together with the traditional Wait-Jones values from equations 3.15-3.17. We see that
Nickolaenko's approximation is similar to that of Sentman. The curve rises sharply near
Figure 4.1:
Average Q-value
,
- -i
nU
Magnetic Field Q-value
----..........
........
..
- -
- i -- 60
Frequency (Hz)
-
Electric Field Q-value
Nickolaenko Q-value
i
I
Figure 4.2: Nickolaenko's Electric Field Approximation vs Wait/Jones
xI
ýf I u5
-
w .'10-1o
4
--
4
y
·'
i1
::
-
-
t .v-
o-10X
'
I
4
3
22M
i
F
1
i
-O
so0
100
Frequency (Hz)
x
1
E
0
-•--
10
1
S0.5
o.s
0
5
P.-
x
5
10
100
so
Frequency (Hz)
l
o
-
6
5
4
E2
12
-"1
w
oI
Ir
OoL
--
---
50
100
Frequency (Hz)
n
0
-
-
--
50
100
Frequency (Hz)
---
0
-
Figure 4.3: Nickolaenko's Magnetic Field Approximation vs Wait/Jones
-xi -"'x10'
CS
I
I!20O
x 10
- 1
2
2.5
S21.5S
0.5
50
1 O0
Frequency (Hz)
2
S0.5
,,,-
--
50
100
Frequency (Hz)
Figure 4.4: Nickolaenko vs Wait/Jones-Modulus of Wave Impedance
2.5
2
5
1 .5
1
0.5
ccvo
50
Frequeno
y
1 00
(Hz)
Ui,
3
2.5
2
1.5
PMM AJii-
1
....
......
0.5
O\
0
50
100
Frequency (Hz)
2.5
2
1.5
IS
0.5
0 ~-~TI
50
100
Frequency (Hz)
Figure 4.5: Nickolaenko vs Wait/Jones-Argument of Wave Impedance
9
C..
-A
2-3 Hz and then levels out at Q=7 whereas Sentman assumes a constant Q=5.
Figures 4.2 and 4.3 show the comparisons of Nickolaenko's approximation to Wait/
Jones' theoretical approach in the E and H field spectra. It is obvious that Nickolaenko's
approach is only an asymptotic approximation meaning that precious details in the theoretical spectra will not be exhibited by the approximation. Overall, the maxima and minima in the theoretical E and H field are depicted in Nickolaenko's approximation. Figures
4.4 and 4.5 illustrate the comparison of the modulus and the argument of the wave impedance of Jones and Nickolaenko. Here, an important result shows that at close sourcereceiver distances ( < 5 Mm), the asymptotic approximation does not rise dramatically at
high frequencies whereas the theoretical calculations exhibit a monotonic rise as the frequency increases. This rise is due to the singularity of the zonal harmonic expansion of the
Legendre functions at small values of 0. Overall the modulus and argument do show slight
differences in the peak and valley locations. However, remember that in calculating Nickolaenko's approximation, we have used his approximate eigenvalue v expression previously described. Figures 4.6 and 4.7 show the comparison of Nickolaenko's
approximation to Wait/Jones E and H field spetra by using Jones eigenvalue v. Figures 4.
8 and 4.9 show the comparisons between the two in terms of the modulus and argument of
the wave impedance. Here we see better agreement in the argument of the wave impedance between the theoretical calculations although there remains a slight deviation of the
approximation from the Wait/Jones' model in terms of matching maxima and minima of
the mode structure.
However, a better judgement of the asymptotic approximation should be made with
the range-frequency curve. Figure 4.10 shows this comparison for the three calculations:
Nickolaenko using his v eigenvalues in equation 4.4, Nickolaenko using Jones' v eigenvalues, and Wait/Jones' theoretical model. Here we can see that the two calculations
Figure 4.6: Nickolaenko vs Wait/Jones Using Jones' Eigenvalue v for Electric Field
- 1
I .;;z
x
10
.w
o
5
5
- 10
x
-4
i
13
2
0
50
Frequency
K
-
10
r-M
8
-
`o
w
x I0
-
"
6.
RAAKmAl.
100
(Hz)
o
1
50
10
2
0
so50
Frequency
100
(Hz)
K SIo-"o
r-L
E
I2
1
0
·
%j-z
0
50
10
so50
1 O0
Frequency (Hz)
Frequency
Frequency (Hz)
(Hz)
Figure 4.7: Nickolaenko vs Wait/Jones Using Jones' Eigenvalue v for Magnetic Field
x 10
1
x 10
`
x 10
"
I
---- 1
- 2
-
'
I
1.2
1
0.
~0.8
8
0.6
.81
I
i.
0.8.
5
E 0.4
0.2
0
100
50
so50
100
Frequency (Hz)
50
S
100
Frequency (Hz)
X 10
-
<
11
10
-
12
a8
'
6O
0
50
100
Frequency (Hz)
50
100
Frequency (Hz)
0.8
0.6
S
0.4
0.2
0
Frequency (Hz)
Frequency
(Hz)
Figure 4.8: Nickola
4
3
2
1
0
50
100
Frequency (Hz)
25
20
O
50
100
Frequency (Hz)
Frequency (Hz)
Figure 4.9: Nickolaenko vs Wait/Jones Argument of Wave Impedance
C9
E
100
Frequency (Hz)
Frequency (Hz)
E
50
100
Frequency (Hz)
E
120
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
using Jones' v eigenvalues fall within five percent of each other in terms of the sourcereceiver distance at any given PTPFS. On the other hand, the calculation using Nickolaenko's approximation for v (equation 4.4) differs more than ten percent. Thus Nickolaenko's asymptotic approximation is valid as long as Jones' complete expression
(equation 3.19) for the eigenvalues v is employed.
Figure 4.10: Range Frequency Curve of Nickolaenko vs Wait/Jones
12
10
Wait/Jones Model
S- - - -.
Nickolaenko's Model (asymptotic v)
- - - - - Nickolaenko's Model (Jones' v)
5
.
..
111
...
!
I
20
30
40
so50
Peak-to-Peak Frequency Separation in Hz
60
70
4.3 Ishaq and Jones' Approximation
Ishaq and Jones (1977) proposed an asymptotic form similar to Nickolaenko's approximation. Their solution
coa - 1
2 4
is essentially identical to Nickolaenko except for the amplitude factor of v instead of
( +1
However,
).
Ishaq and Jones make the further approximation
Jv (v +
1
(4.6)
- i (5.49)
(4.7)
1) -v+
and because
Jv(v+
1) = ka
the wave impedance now becomes
Z= --
cot (-)
ka
(5.49)
-
= -t-
cot-
i (5.49)
(4.8)
where p'=a(rt-0) is the distance between the source and the antipode of the observer.
When we compare the results of this new approximation with Wait/Jones' theoretical
model, we draw similar conclusions as to the difference between the asymptotic approximation and the full theory. Figures 4.11 and 4.12 show the modulus and argument comparisons using the Ishaq and Jones' asymptotic approximation and the theoretical model.
Like the Nickolaenko approximation, we do not have the monotonic rise of the modulus
and the argument spectra with increasing frequency at small 0 values for Ishaq and Jones
because the approximation replaces the theoretical zonal harmonic expansion of the Legendre functions with a periodic cotangent function. Here, there is hardly any deviation in
the maxima and minima locations between the asymptotic and the theoretical spectra.
Looking at the range frequency curve in Figure 4.13 , we see that the approximation is
exactly superimposed on the theoretical model. There is no distinction between the two in
terms of the PTPFS. Therefore, the use of Ishaq and Jones's approximation is also valid.
Figure 4.11: Modulus of the Wave Impedance in Ishaq and Jones' Approximation
2.5
2
0.5
0
50
100
Frequency (Hz)
0
2
:· ·
2
0.5
0
50
100
Frequency (Hz)
E1
21
I=
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Figure 4.12: Argument of the Wave Impedance in Ishaq and Jones' Approximation
240
rVI
220
S200
1 80
: :
160
·'
1 40
I
0
50
100
Frequency (Hz)
0
50
100
Frequency (Hz)
140
100
0
so0
Frequency
0
50
100
Frequency (Hz)
I
Figure 4.13: Range Frequency Curve of Ishaq and Jones Approximation
1
1
1
1
E
01
C)
0,
0O
0
10
20
30
40
50
Peak-to-Peak Frequency Separation in Hz
60
70
4.4 Ishaq and Jones vs Nickolaenko
If both approximations are considered valid asymptotic representations of the theoretical model, which one is more accurate? Figure 4.14 shows the range frequency curve of
the two asymptotic approximation against the theoretical model. It is clear that the differences between the two approximations are slight. However, Ishaq and Jones' model seems
to come closer to the theoretical model which Jones had previously developed.
4.5 Sentman's model
Sentman's model does not presently have an asymptotic representation, so comparisons with the other asymptotic approximations have not been made.
Figure 4.14: Range Frequency Curve of Two Approximations against Wait/Jones
E
C.,
(U
Peak-to-Peak Frequency Separation in Hz
D
Chapter 5
Automation of Analysis on Global Location of Lightning
Transients
5.1 Digital Time Series Sequences of ELF Transients
The digital time series of the three components (EW Magnetic, NS Magnetic, and Vertical Electric) are produced by sampling the respective analog signal at 350 Hz with a 12bit Data Translation 2801-A Analog-to-Digital Board. The samples are interleaved, meaning that each EW Magnetic sample always precedes the NS Magnetic sample by 1/
(3x350) seconds. Likewise, each NS Magnetic sample precedes the Vertical Electric sample by 1/(3x350) seconds and therefore, each Vertical Electric sample lags the EW Magnetic sample by 2/(3x350) seconds. This interleaved sampling introduces phase
differences which are crucial in our analysis. Consider the three analog channels of 8 Hz
sine waves shown in Figure 5.1. Figure 5.2 shows the interleaved samples of all three
channel values plotted on one graph. If the channels are interleaved sampled at 350 Hz, we
see that the nominal value of the three channels do not differ appreciably. Now consider a
signal at 60Hz shown in figure 5.3. Figure 5.4 shows the interleaved samples of the channels at 350 Hz. We now see that the three channels appear phase shifted with respect to
each other.
This is the result of interleaved sampling. Figures 5.5 and 5.6 show the X-Y plot of the
synthetic 8 and 60Hz magnetic channels. It is clear that at 8 Hz, we have a nearly linearly
polarized signal whereas at 60Hz, the ellipse is more circular indicating a shift in phase of
the two signals. Therefore the use of interleaved sampling introduced a phase error in the
digital time series. Specifically, the phase error is c/I where co is the angular frequency
Figure 5.1:
I
-I
seconds
1
0.5
-0.5
-1
0.02
0
0.04
0.06
0.08
0.1
0.12
seconds
ELI
seconds
Figure 5.2:
Interleaved Sampling at 350 Hz of the Three 8 Hz Channels
1.5
"EW Magnetic
1
mL
o NS Magnetic
x Vertical Electric
-
0.5
xO
0
x
to
0
0
o
x
ox
0x
x 0
0S
X0
C
x )
S
X
x
-0.5
x
-1
-10
I
I
0.02
0.04
I
0.06
seconds
I
0.08
I
0.1
-
0.12
Figure 5.3:
Three 60 Hz analog channels
oz
0.5-
0
0.002
0.004
0.006
0.008
seconds
0.01
0.012
0. 014
0.016
Figure 5.4:
Interleaved Sampling at 350 Hz of the Three 60 Hz Channels
·
F.
·
·
·
·
·
·
EW Magnetic
o NS Magnetic
x Vertical Electric
0
0.5
F
x
00
x
0
0-0.5
0
x
-1
-1
o
I
51
.
0
0
0.002
0.004
I
0.006
I
0.008
seconds
0I.I0
I
0.01
0, I,1
0.012
I
0.014
0
I
0.016
Figure 5.5:
X-Y Plot of 8 Hz Analog Interleaved Sampled at 350 Hz
Figure 5.6:
X-Y Plot of 60 Hz Analog Interleaved Sampled at 350 Hz
-0.5
0
EW Magnetic
0.5
1I
and I is the interleaved frequency between successive samples. In the case of 350 Hz sampling on three channels, the interleaved frequency is (nx350) Hz, where n, the number of
channels, equals 3. Because of this phase error, we later used 2000 Hz sampling with an
associated interleave frequency of 6000 Hz. Figures 5.7 and 5.8 show the X-Y plot of the
8 and 60 Hz magnetic channels. Here, we see that both plots are polarized meaning that
the phase differences between the two magnetic channels have dramatically decreased. Of
course the tradeoff for a more frequently sampled analog sequence is less storage space.
Figure 5.7:
X-Y Plot of 8 Hz Analog Interleaved Sampled at 2000 Hz
Figure 5.8:
X-Y Plot of 60 Hz Analog Interleaved Sampled at 2000 Hz
EW Magnetic
5.2 Windowing the Time Series of the ELF Transient
As the digital time series sequence is examined by the automated process, signals
which exceed a certain threshold relative to the background Schumann level on the vertical electric field channel are analysed. Before the analysis, it is important for the automation process to capture enough time series sequence of the transient so that an analysis is
possible. This means that at least one entire period of every resonant modes is present. The
lowest frequency Schumann mode is 8 Hz. This translates to 125 milliseconds after the
initial onset of the ELF transient. In addition, the plane wave generated by the lightning
transients can travel around the globe several times before the signal is damped significantly into the background. Because this wave has a phase velocity approximately 2/3 of
the speed of light (Ishaq and Jones, 1977), a maximum time of approximately 190 milliseconds is needed to traverse the circumference in the great circle path. Figure 5.9 shows
this around-the-world time series phenomenon. We want to include this phenomenon in
the analysis because it gives one complete cycle in the propagation of the electromagnetic
waves.
Figure 5.9: Around-the-World Phenomenon in the Vertical Electric
.5
time (seconds)
35
It is also important not to capture another transient of comparable amplitude in the
same time window. Having two transients will introduce superposition of modal structure
from each transient and therefore, an analysis will not reveal the correct range and bearing
estimates. Implementing this aspect into the process comes from experience of looking at
the time series transients. By looking at the intervals between large transient events, we
can estimate the maximum time at the start of an event before the arrival of the next.
Empirically, this value is about 250 milliseconds after the trigger marker of an ELF transient.
Figure 5.10: Windowing a Triggered ELF Event on the Vertical Electric
Windowing a Triggered ELF Event on the Vertical Electric Channel
0.02
The Box-Car Analysis Window
--
0.02
i
Ar'-'-
Trigger Marker
-0-03
O
0.05
0.1
0.15
seconds
0.2
0.25
i
As shown in Figure 5.10, the digital time series is triggered on the third channel which
is the vertical electric. When a value of the Vertical Electric exceeds a threshold voltage,
then 50 milliseconds of samples prior to and 250 milliseconds of samples following the
trigger value are recorded. 50 milliseconds prior to the trigger gives us sufficient time to
capture the initial rise of the event itself from the background level. 250 milliseconds is
often the maximum time between one event and the next. Therefore, this 300 milliseconds
window of the digital time series has one large transient ready for analysis. The Schumann
Resonance level is a running mean of the time series signals. Because this level varies
annually and diurnally, constant adjustment of the trigger value is necessary. Thus to
examine ELF transients which have a small SNR of 3, the trigger value is set to three
times the Schumann Background level. This will allow us to capture events at least three
times above the Schumann background.
5.3 Linearly Least Squares Fit to Magnetic Lissajous Plot
Once we have obtained the 300 millisecond window (50 milliseconds before and 250
milliseconds after the trigger marker) of an ELF transient shown in Figure 5.10, we are on
the way to find the bearing and range of the event. The first step in the process is finding
the line of least squares fit in the two magnetic field measurements (NS and EW Magnetic). The plot of the NS Magnetic versus the EW Magnetic tells us the direction of the
electromagnetic wave. In addition it will give us the Azimuthal Magnetic Field Ho.which
is needed for the wave impedance calculation of the source range. For a vertical lightning
channel and without any distortion in the waveguide of the Earth-ionosphere cavity, a plot
of the NS versus the EW would reveal a straight line going through the origin with a slope
m. From this slope we can determine the direction of the travelling wave. Figures 5.11 and
5.12 show the lissajous plots of NS versus EW Magnetic field for a typical event sampled
at 350 Hz and at 2000 Hz, respectively. It is clear that the two plots are different because
of the interleaved sampling discussed in Section 5.1 which has the effect of phase shifting
the NS Magnetic of the 350 Hz wave. Thus the 350 Hz plot reveals considerable irregularities from the straight line. The 2000 Hz wave is less affected by the interleaved sampling
than the 350 Hz wave because of a higher sampling rate which in turn has a higher inter-
leave frequency. Nonetheless both of these waves probably experience some distortion in
the wave
Figure 5.11:
350 Hz Lissajous Plot
-
x 10
8
6
.
. .
...
e
Linear Least Squares Line
-6
-8
-
-
-8
-6
4
-4
-2
0
2
4
-2
0
2
4
,
EW Magnetic (Amperes/Meter)
6
6
8
x 10
Figure 5.12:
-s
2000 Hz Lissajous Plot
x 10
6-
4-
Linear Least Squares Line
2-2
-4
-6
-6
-4
-2
0
2
4
EW Magnetic (Amperes/Meter)
6
x 10,
guide due to the non-uniformity of the earth-ionosphere cavity. Therefore, we must fit a
linear least squares line to the set of data in order to find the best direction of the travelling
wave. Curvefitting a line through the sample points is done by finding the major axis of a
best fitting ellipse. When selecting the pairs of points to calculate a confidence ellipse, it is
important to use those points which have high SNR with respect to the Schumann background level. Specifically, this is the period immediately following the initial onset of the
ELF transient. Figure 5.13 shows a typical time series of the three fields. For about 50 milliseconds following the initial onset of the signal, we see a high SNR. The 50 millisecond
sample points allow us to fit a linear least squares line through all the sample points.
Figure 5.13: Typical Three Channel Time Series
x 10,
0.05
•
-8
0.03 :
0.02
w
0.1
0.15
time series magnetic (EW) vs seconds
0.2
0.25
•
initial onset
_ __
I
0.05
0.1
0.15
I
I
0.25
time series magnetic (NS) vs seconds
~ ---
-1
I
50 ms
CD0.01
0
> -0.01
-0.02-0.03 0
0.05
0.1
0.15
time series electric vs seconds
0.2
0.25
To calculate the slope of the major axis in figures 5.11 and 5.12, we start off with the
EW and NS Magnetic time sequence.
EW Magnetic (Intial rise to 50 ms after) = [X1, X2, X3, ...
,Xn]
(5.1)
NS Magnetic (Initial rise to 50 ms after) = [Y 1 122,Y3,-...
(5.2)
Yn]
We now calculate the sum of each channel, each channel squared and the product of
the two respective values.
sumx = (X 1+ X2 + X3 + ... + Xn)
sumy = ( Y
sumxx=
+
Y2
+
Y3 +"'
X +X2
sumyy=
+
Yn)
(5.3)
(5.4)
+X3
n
(5.5)
...
+ n
(5.6)
I+Y2)23+
sumxy= (X1 Y +X2 Y2 +X 3 Y3 +...+Xn Yn)
(5.7)
The average of the two channels is
sumx
n
(5.8)
sumy
avey =n
(5.9)
avex =
-
The variance and co-variance are defined as
devx =
sumxx
-
sumx
n
devy =
sumyy - S n
devxy= (sumxy- sumx n sumy J
(5.10)
(5.11)
(5.12)
and the standard deviations are defined as
s2x =
s2y -
sxy
devx
(n - 1)
(5.13)
devy
(5.14)
devxy
(n - 1)
(5.15)
(n - )
and the root is defined as
root
s2x + s2y + J(s2x + s2y) 2 -
4
(s2x - s2y-sxy2)]
(5.16)
where the slope and the y-intercept of the line of least squares fit are
slope (major-axis) =
sxy
(root - s2(,
y-intercept = avey - slope -avex
(5.17)
(5.18)
where the angle of the slope is
y = 90 - atan (slope)
(5.19)
where atan is the arctangent function. Figure 5.14 shows that the angle Xyis defined
from the north in a clockwise manner meaning that due north is 0 degrees, due east is 90
degrees, due south is 180 degrees, and due west is 270 degrees.
Figure 5.14: Angle of the Best Fit Line
N
slope
'V
5.4 Finding the Azimuthal Magnetic Field HQ
Once we have the slope of the major axis of the best fitting ellipse, the Azimuthal
Magnetic Field Ho can be calculated. Ho is essentially the projection of the pairs of points
defined by (EW magnetic, NS magnetic) onto the best fitting line. The projection of a
point (EW magnetic, NS magnetic) onto the best fit line is simply the dot product of two
vectors:
vector, = (EW magnetic) - i+ (NS magnetic )
vector2 =
1
I1+ slope2
.
•-+
]
slope
spe
(5.20)
(5.21)
J + slope2
where vector1 is defined from origin to the point defined by the pair (EW Magnetic,
NS Magnetic) and vector 2 is the unit vector on the best fit line translated to the origin.
Therefore,
H = vector, * vector 2
(5.22)
(EW magnetic)
+(NS magnetic ) 2slope
2
/1+ slope
i + slope
Ho is the combined expression for the EW and NS Magnetic field. Without any distortions in the wave guide, Ho is simply the arctangent of each pair of points defined by the
two magnetic fields. However, as seen in figures 5.11 and 5.12, the deviations from a
straight line can cause significant changes to the actual Azimuthal Magnetic field by simply taking the arctangent of each point. The calculation of the least squares line gives us a
better estimate of Hý. Ultimately, HO is used along with Vertical Electric field to calculate
the wave impedance which in essence tells us the range from the source to the receiver.
Thus having a polarized lissajous plot of the EW and NS magnetic is important because it
allows a well defined linear line to fit all the points onto the line.
Figure 5.15:
Lissajous Plot of an Ill-Defined Polarization
x 10-6
8
T int r I poct Rm1Cc T
Lim C/
6
a)
E
c0
_-4
-6
-8 -8
-8
-6
-4
-2
0
2
4
6
-6
-4
-2
0
2
4
6
EW Magnetic (Amperes/Meter)
8
8
x10~
Figure 5.16:
x 10-5
Lissajous Plot of an Ill-Defined Polarization
10.80.60.4
2
0.2
0.
-
.2
" -0.2
n -0.4
-0.6
-0.8
-1
-1
-0.5 _
0_0.5
-0.5
0
_
0.5
EW Magnetic (Amperes/Meter)
1
1
x 10-
Figures 5.15 and 5.16 show some lissajous plots which do not show well defined
polarizations. Therefore a best fit line in each case is not a good approximation to the
points defined by the lissajous and Ho will not be a well defined azimuthal field of an ELF
transient. The reason for such a non-linearly polarized lissajous is often the superposition
of more than one event of comparable magnitude in the time series as discussed earlier in
Section 5.2. The superposition of these event will thus represent the combined electromagnetic field of two discrete sources. In this case, it is not possible to obtain a well
defined HO for the ELF transient in question. Additional possible explanations for a departure from linear polarization are the vaguaries in the waveguide and the irregularities of
the lightning source. It is difficult to assesss quantitatively the contributions from these
various effects in any one event.
5.5 Computing the Bearing from Receiver to Source
The flow of electromagnetic energy in a wave field is governed by the equation
S = Ex H
(5.24)
which defines the direction of the power flux density where S is the Poynting vector,
E is the vertical electric field vector and H, is the azimuthal magnetic field vector whose
absolute value we have calculated in section 5.4. The power flux density shows the direction of power flow and therefore, the bearing of the source is 180 degrees (opposite direction) from S. Figure 5.17 shows all the vectors that are associated with computing the
bearing.
North
East
Figure 5.17:
S is determined by finding the cross product of E and H- at every sample point of the
ELF event. S will be a vector perpendicular to both the vertical Electric field vector and
the H, vector defined by the origin to a point on the best fit line. In addition, s will be
.-.
coplanar to H,. However, remember that we have already calculated the best fit line which
defines Hn. This line has an angle xv from due north given by equation 5.19. Therefore,
since S is both perpendicular and coplanar to H , the bearing is either +90 degrees or -90
degrees from the angle y based on the positive or negative relative values for E and Ho.
Table 5.1 summarizes the values of Ez and Ho and the effect on the bearing based on these
values.We see that when E and Ho are both positive or negative, the bearing is -90 degrees
from the angle V of the best fit line. Otherwise, the bearing is +90 degrees from
. When
determining the bearing, we will use only those values of Ez and Ho which have the largest
SNR.As mentioned in section 5.3, these are the sample points from the initial onset of the
event to 50 milliseconds after the onset. The initial rise or onset of E and H4 is the initial
positive or negative excursion above the background level. To keep track of the background level, we average the 35 milliseconds of points from the beginning of our 300 mil-
Ids (m) =
E(co) -4na2eohsin (xv)
(5.51)
i - v (v + 1) Pv (-cos0)
Ids (o) =H H(o) 14ahsin (tv)
(552)
PV (-cos0)
Therefore, we need to generate theoretical values at the frequency values specified by
the experiment. Once the theoretical values are obtained, a complex division of the experimental spectrum by the theoretical spectrum at each frequency specified by E(o) and
Ho(o) will generate two Ids(o) source terms. Theoretically, these two terms should be
equal in magnitude.
x 10
7
Figure 5.23: Source Spectrum of a Positive Ground Flash
lda(w) of a Positive
Ground Flash
_iM
Figure 5.24: Source Spectrum of a Negative Ground Flash
Automation of Analysis
Figure 5.25: Flowchart for Automated Analysis of ELF Transients. Sections of the text
with details are indicated parenthetically
After calculating HO, the bearing of the source with respect to the receiver is computed. Next, we find the DFT of the E and HO which give us frequency representations of
the time series sequence. At this point we calculate the wave impedance and extract the
modulus and the argument from the wave impedance. We now take the DFT of the modu-
100
lus and the argument to find the quefrency representations which will tell us the PTPFS of
the modulus and the argument.
If there is a match between the modulus and the argument, then we find the average
distance based on the two PTPFS on the Range Frequency Curve. We also calculate the
standard deviation of the two values from the mean. Finally, we solve for the latitude and
longitude of the source using spherical geometry. After all the relevant information is
stored in a data file, the automated procedure returns to the digital time series to search for
another ELF transient suitable for processing.
However, if there is no match between the periodicity based on the modulus and the
argument, then we must decide whether the signal has reached the end of the 250 millisecond window after the trigger marker. If the last point has not been reached , the procedure
adds one more data point to the three time series sequence and returns to the Linear Least
Squares Fit procedure. If the signal has reached the end of the 250 milliseconds of sample
points after the trigger marker, then it is concluded that no match is achievable and therefore the event is discarded. The procedure then returns to the digital time series sequence
to wait for another event which exceeds the threshold value
The automated procedure will add up to 50 milliseconds more data points to the 250
milliseconds (50 milliseconds and 200 milliseconds before and after the trigger marker) of
points with which it had originally started off. As a reminder, the procedure always zeropads up to 2048 points when taking the Discrete Fourier Transfrom regardless of the window size being examined. In the event of no match between periodicity based on the modulus and argument, the procedure adds one more data points to the sequence and returns to
the Linear Least Squares Fit Line function and tries to find a match in the modulus and the
argument with the newly added point. In the end, either no match is found for periodicity
between the modulus and the argument after 50 iterations of data points and the event is
discarded, or the event has a match and the relevant information is stored.
This automated procedure is realized by a computer program using the C programming language. The code is included in the Appendix. Another program written in Matlab
was also used to generate the pictures in the automated procedure and is also included in
the Appendix. The Matlab program is the earlier version of the two and has graphics capabilities. It was used to verify in graphics form all the details of the automated procedure
first before commiting to a C-coded program.
In the next section, we will look at the results of the procedure. Specifically, we will
relate physical insights to the ELF events which have been processed by the automated
procedure.
102
Chapter 6
Application to Observed Transients
6.1 Introduction
In this chapter, we will show results based on the automation procedure which we have r
implemented. Specifically, because Schumann Resonances is a global phenomenon, we
:
want to find examples of events on the globe which other lightning detection systems also
detect. This will provide validity to Schumann Resonances. We will compare results •fr•
, .
the three data sets. First, we compare data collected during the Sprites '95 Campaign and
..
look at ELF events accompanying Sprites, a luminous phenomenon in the mesosphere,,
over large thunderstorms. Then we provide comparisons with the Optical Transient Detec: :Ar.:T
tor in space and show how our data obtained from Schumann Resonances matches events
detected over the globe. Finally, we will look at a special set of large amplitudes events,
which will provide additional understanding of lightning transients.
6.2 The Sprites '95 Campaign
The Sprites '95 Campaign was a research effort funded by NASA's Kenned•y Space 1
Center to help uncover a new class of lightning related luminous phenomenon in the lower
ionosphere. These light producing events are believed to be generated by large mesdscale
convective systems (MCS) in which re-illumination of the 'spider' lightning channel bye
the return stroke of positive cloud-to-ground lightning intensifies the electric field stiress in"'
the ionosphere and thus causes ionization and light emission. During the summer of 1995,
we collected Schumann Resonance data simultaneous with the occurrence of large mesoscale convective storms in the Midwestern United States. The campaign director, Dr.
103
:ei
the Midwest, we would expect a lag between the time which NLDN locates an event and
when we see it in the SR data.
Camera Time
NLDN Time
NLDN
Signal
Strength
Camera Time
NLDN Time
(UT)
(UT)
NLDN
Signal
Strength
04:32:19.620
04:32:19:632
+640.4
07:03:59.674
07:03:59.656
+718.8
04:35:01.115
04:35:01.125
+412.2
07:04:00:107
07:04:00:101
+480..3
04:37:02:836
04:37:02.821
+240.2
07:05:46.180
07:05:46.180
+999.7
04:40:21.401
04:40:21.399
+377.6
07:07:07.061
07:07:07.055
+205.5
04:43:26.386
04:43:26:367
+423.8
07:07:33.220
07:07:33.188
+142.9
04:46:10:750
04:46:10.739
+225.2
07:09:42.516
07:09:42.577
+369.2
04:48:53.213
04:48:53.198
+157.9
07:16:32.992
07:16:32.982
+176.1
04:56:48.420
04:56:48.405
+339.4
07:24:09.381
07:24:09:383
+475.0
05:35:05.548
05:35:05.557
+249.0
07:35:44.742
07:35:44.736
+184.5
05:52:11.672
05:52:11.660
+578.7
07:48:29.639
07:48:29.640
+206.5
05:55:18.993
05:55:19.000
+271.9
08:00:34.696
08:00:34.681
+113.1
06:02:36.429
06:02:36.420
+442.0
08:01:18.474
08:01:18.470
+286.3
06:19:37.816
06:19:37.810
+335.3
08:18:45.085
08:18:45.084
+544.0
06:25:56.260
06:25:56.267
+332.6
08:23:55.595
08:23:55.593
+464.9
06:28:19.737
06:28:19.731
+139.3
08:33:34.373
08:33:34.380
+318.3
06:31:15:646
06:31:15.634
+247.6
08:36:48:000
08:36:47.982
+370.9
06:38:49.032
06:38:49.074
+101.9
08:41:11.997
08:41:12.005
+362.5
06:40:40.771
06:40:40.758
+182.1
08:44:08.306
08:44:08.288
+531.9
06:48:01.150
06:48:01.141
+366.9
08:44:08.740
08:44:08.748
+536.7
06:49:59:001
06:49:59:005
+610.0
08:49:08.039
08:49:08.034
+882.1
06:51:39.034
06:51:39.979
+133.3
08:49:08.773
08:49:08.765
+517.8
06:57:53.942
06:57:53.923
+804.0
08:51:52.269
08:51:52.262
+368.1
06:57:54.042
06:57:54.053
+370.2
08:55:11.702
08:55:11.686
+395.6
Table 6.1: Sprites Events with NLDN Timing and Strength Information on 07/24/95
105
Figure 6.1: Positive Ground Flash with Accompanying Sprite at 04:43:26.366
NLDN Bearing=267.7degrees
Bearing = 282.1 degrees
z
z
CJ
E
o
0..
E
0-
0
100
200
time(Milliseconds)
-100
300
-50
0
50
100
EW (Micro-Amp/meter)
Cr
a)
CD,
CL.
E
I 20
^
--
80
Frequency (Hz)
40
60
0
100
20
40
So
au
l
oo
Frequency(Hz)
Figure 6.1 shows a typical Sprite-associated ELF event which had a corresponding
NLDN and Schumann Resonance match where the occurrence of the NLDN event is indicated by a stem with a circle superimposed on the Schumann Resonance data. We see that
the NLDN event precedes the Schumann Resonance transient by approximately 5-10 milliseconds. The bearing of the event from our site according to NLDN is 268 degrees. From
our bearing plot of the two magnetic channels, we have a bearing of 278 degrees. This
descrepency is due to the 350 Hz interleaved sampling of our system which is discussed in
Section 5.1. In the DFT of the Schumann data, we plot the theoretical Wait/Jones spectrum
106
in dotted lines. The actual distance used in calculating the theoretical spectrum is obtained
by NLDN and we see that the experimental and theoretical spectrum match well in the
peaks of the modes at frequencies below 60 Hz. Notice the huge 8 Hz component in the
magnetic spectrum which is not in the theoretical calculations, the latter based on equations 2.1 and 2.2 and an impulsive ( white noise) source. This is typical of the 40 Sprite
events detected on this day. We see the source term spectrum shows an amplitude declining with frequency (red) which is associated with positive cloud-to-ground events. The
null around 60 Hz in the source term and the magnetic spectra is the 60 Hz notch filter
Figure 6.2: Positive Ground Flash with an Accompanying Sprite at 06:48:01.141
NLDN Bearing=262.9degrees
120
Bearing = 272.1degrees
lat=35.42, iong=-99.21
-100
z
80
z•L 80.
60
peak=73.38kA, mult=l
40
JK"
5aLt.'4otvrSM
r
r
20
41
E
-I
r
0o
o
S2(
F
E
N7-IK7
v 1
-20
V
-21
-40
-46
i
r
-60
-6(
I
0
100
200
time(Milliseconds)
·
300
-50
1.
·
0
50
EW (Micro-Amp/meter)
15
1.
3:
E
= 10
E 10.
0.
O
0
Frequency (Hz)
107
20
40
60
80
Frequency(Hz)
100
implemented in our system. Figure 6.2 shows another Sprite-associated ELF event which
also corresponded with an NLDN positive CG. Again we see the NLDN event preceding
the SR transient by 5-10 milliseconds which is consistent with a wave travelling from
Oklahoma to Greenwich, Rhode Island. The huge 8 Hz component in the magnetic spectrum is also present. This is more evident in the source term spectrum where we see a large
declining amplitude with frequency which would suggest a long continuing current discussed in Section 2.4. In addition to that, we see that the modes in the theoretical spectrum
match that of the magnetic field spectrum indicating again that this single event excite
the Earth-ionosphere cavity.
Figure 6.3: Negative Ground Flash with no accompanying Sprite at 04:38:05.898
Bearing = 259.3degrees
NLDN Bearing=249.9degrees
25
20
15
E0
0
10
0,
c -10
-15
E
I
-
-20
0
-25
time(Milliseconds)
EW (Micro-Amp/meter)
current moment
-
x 10 6
DFT of Hphi
x 106
Ids(w)
4
5
3.5
=
CO 1
3
.•
2.5
M
2
S1.5
E
E
0.5
n
O
20
40
60
80
Frequency (Hz)
100
O0
108
20
40
60
80
Frequency(Hz)
100
Figure 6.3 shows another NLDN event which appears as a Schumann Resonance
transient. Here we do not see the long continuing current component at 8 Hz. We see that
this event is a negative cloud-to-ground lightning and by looking at the spectrum of the
source term, we discover a relatively flat amplitude response with frequency. This is characteristic of the an impulse delta function which would suggest that this event is a discrete
negative stroke lightning. It is also well established that the majority of single stroke negative ground flashes do no exhibit continuing current (Rakov and Uman, 1991). When
comparing the theoretical spectrum to the experimental spectrum, we find good agreement
Figure 6.4: Positive Ground Flash with no accompanying Sprite 04:38:36.453
NLDN Bearing=262.7degrees
Bearing = 276.2degrees
60
60
-
40
40
20
E20
Z
2
-20
lat=35.34, Ilong=-99.17
S-20
peak=70.28kA, mult=l
-40
dist=2.48Mm
-60
•-_40
E
20
0o
2 -60
-80
0D
100
200
time(Milliseconds)
-50
0
50
EW (Micro-Amp/meter)
300
current moment
N
0
(D
=
CI
E
-cc
Frequency (Hz)
Frequency(Hz)
109
between the two for frequencies below 60 Hz. (The strongly rising component near 0 Hz
is an artifact of our bandpass filter.) The higher mode frequencies in the Wait/Jones model
(Appendix A) attentuate significantly above 60 Hz whereas in the experimental model, we
do see SR modes beyond 60 Hz.
In Figure 6.4, we have an event which is detected by NLDN to be a +CG located near
the area where Lyons located the Sprites but this event was not seen by the camera. We see
that this event exhibits a strong 8 Hz component as seen in the sprite events. We also see
an enhancement in the higher frequencies beyond 60 Hz. The overall comparison between
Figure 6.5: Positive CG with no accompanying Sprite at 04:48:00.000
Bearing = 274.8degrees
NLDN Bearing=266.5degrees
- 80
60
40
°
40
0
E 20
Q.
E
-20
0
100
200
time(Milliseconds)
-20 -10
0
10
20
EW (Micro-Amp/meter)
300
5
cD
4
cn
$9
A3
0.
E
n
0
20
40
60
80
Frequency (Hz)
100
Frequency(Hz)
110
Wait/Jones theoretical spectrum and the experimental data reveal well matched mode
peaks. Figure 6.5 shows yet another +CG without an accompanying Sprite. Here, we do
not see the huge component at 8 Hz as previously seen in 6.1, 6.2, and 6.4. However, we
still have a source term spectrum that is declining with frequency suggesting that this
event is a continuing current.
In Figure 6.6, we show a non-sprite event which is a ground flash of negative polarity
and has a large 8 component in the magnetic spectrum. This event has a peak current of
120.3 kA which places it above the normal negative cloud-to-ground lightning event. In
Figure 6.6: Negative Ground Flash, no Sprite , NLDN Time 05:17:09.200
NLDN Bearing=205.4degrees
Bearing = 195.5degrees
50
z
40
E
30
20
-2
E
- 10
U' -20
I
-1
-30
-40
-12
-50
-50
0
time(Milliseconds)
50
EW (Micro-Amp/meter)
Ids(w)
x 106
2
5
a)
U,
a)
a)
a-
0.5
€a,
Frequency (Hz)
O
20
40
60
80
Frequency(Hz)
100
the source term spectrum, we do not see an amplitude slowly declining with frequency.
The higher mode frequency appear to be strong all the way up to 120 Hz which is the high
frequency limit of our instrument. We have a good match in the frequencies of the resonant modes between the theoretical spectrum and the experiment. This event is atypical of
many negative cloud-to-ground lightnings which tend to exhibit white noise spectra similar to the one presented in Figure 6.3.
Overall, all 40 ELF events associated with Sprites exhibited the large 8 Hz component
and their respective source term spectra are all quite 'red'. However, the same cannot be
attributed to ordinary +CG lightning. While some have the long 8 Hz oscillation suggestive of a long continuing current nature of these event, this is not a characterisitic of all the
+CG. We have also shown an event which is negative in polarity and its source term spectrum resembles that of an impulse function which has a flat frequency response. Lastly, we
found a -CG event which has a large 8 Hz component in the magnetic spectrum. However,
the source spectrum shows very little attentuation in the higher frequencies above 60 Hz.
We have said this event is atypical because of the large peak current.
Notice that in this Section, we have selected events which have considerable Signalto-noise ratio (SNR). Because of the high SNR, we are able to analyse them without much
difficulty. In the next section we will compare our Schumann Resonance data with events
obtained by the Optical Transient Detectorin space. In this comparison, we will show low
SNR events as well as high SNR events around the globe. By doing so, we can make an
estimate about the necessary SNR which will allow the automated procedure to calculate a
correct range and bearing.
112
6.3 Optical Transients Detector (OTD)
The Optical Transient Detector was launched in April, 1995 into a nearly polar orbit
(Christian, 1995). It has a field of view of 1300x 1300 kilometers and provides global daytime and nighttime lightning coverage. It detects optical energy at the cloud top produced
by lightning and has information such as flash location, total cloud-top optical energy, and
duration. On the average, the satellite observes approximately 0l lighning flashes per
month. These flashes can be either positive or negative cloud-to-ground lightning events,
or intracloud events. In order to generate instances of simultaneous SR time series data
with OTD, we set the recording system on our instruments in continuous time series mode
which collects data points from the three channels at 350 Hz. Because SR signals are a
superposition of all the lightning activity on the globe, we must determine which criterion
will most likely excite the SR above the background level. We must select the Schumann
Resonance data which has a relatively quiet background level. Transient Event in a quiet
background will process whereas if the SNR is too low, the superposition of other events
will cause significant mode distortion in the field spectra. Based on the assumption that a
long-continuing current is the exciter of SR and that +CG's are more likely to exhibit this
feature, we want to also select good candidates from the OTD. A necessary step in selecting candidate OTD events to compare with SR data is the optical energy. OTD flashes
which have a large optical energy in a specified area are most likely to be theoe events
which rise above the background level. the Based on these criteria a set of 40 OTD events
were chosen which had respective SR signals in the time series with a relatively low background level. (D.Boccippio, personal communication)
Table 6.2 listsl the 40 OTD events which matched a signal in the SR data. We have
listed the actual range and bearing of the OTD events along with the estimations of range
113
Table 6.2: OTD Events as seen from space and their location based on the ELF Automated Procedure
Time
(UT)
Arg Success
Bearing Mod
Est.
Latitude Longitude Bearing Range
(deg)
(deg)
(deg) (Mm) Bearing Error Range Range Process
225
04:49:03.344
42.8
-65.2
74
0.56
82.08
1.55
0.94
0.94
n
228
230
228
230
225
230
236
236
232
227
232
227
266
236
233
235
233
232
226
239
239
233
236
227
230
225
235
233
225
229
235
230
230
238
227
225
227
000
000
04:20:09.508
17:25:20.128
06:03:22.064
17:19:48.064
06:36:06.876
17:21:25.352
16:07:41.276
03:29:09.632
04:50:21.782
17:53:15.348
17:27:35.608
06:54:30.756
07:38:03.298
05:06:46.590
04:05:08.144
20:19:25.064
05:45:21.678
19:21:29.592
18:35:59.484
04:34:13.172
02:58:48.324
04:09:04.558
03:33:32.856
01:58:31.899
07:30:44.200
03:43:22.454
14:05:43.848
05:09:36.938
03:42:31.540
16:57:31.699
15:50:59.208
07:20:43.136
05:38:09.634
22:38:36.128
04:17:23.442
05:47:52.166
04:16:57.398
00:00:00.000
00:00:00.000
47.3
39.9
43.3
29.1
45.1
27.4
19.2
18.5
18.1
18.3
14.1
20.8
21.5
25.3
13.3
40.3
16.6
11.4
10.1
16.6
5.6
6.5
5.7
14.8
50.0
-39.5
39.2
36.7
-41.3
28.1
22.9
16.6
10.8
-41.5
-44.3
-44.0
-42.3
16.5
14.9 I
-70.1
-61.0
-88.3
-65.6
-91.0
-65.4
-69.8
-66.9
-75.4
-66.6
-71.5
-93.8
-95.1
-99.8
-70.7
-111.2
-91.1
-77.5
-75.1
-94.9
-74.4
-61.8
-63.3
-14.2
102.8
-9.8
115.6
111.7
-5.1
106.0
104.1
82.2
103.3
161.4
118.3
109.2
110.2
-93.8
-94.1
10
97
285
156
292
157
175
168
189
167
189
229
231
243
178
281
220
191
186
226
184
163
165
100
4
136
354
357
134
2
4
28
6
252
245
194
230
224
222
0.66
0.92
1.37
1.48
1.61
1.67
2.48
2.59
2.61
2.62
3.04
3.09
3.12
3.14
3.14
3.29
3.32
3.39
3.50
3.54
3.99
4.01
4.07
6.23
9.83
10.96
11.02
11.32
11.38
12.27
12.84
13.02
14.18
15.66
19.14
19.72
19.82
3.49
3.66m
5.60
113.24
300.80
161.93
300.80
159.00
172.79
175.70
185.25
170.50
175.30
232.97
242.20
249.35
174.46
237.41
213.79
218.09
173.13
228.64
194.31
166.08
166.80
115.19
3.16
143.10
349.50
356.63
139.76
0.27
3.63
29.27
7.31
243.44
203.40
188.32
265.71
226.30
226.02
2.92
3.70
3.11
1.04
2.06
4.89
3.87
5.18
6.18
6.98
2.30
6.26
8.16
2.80
1.84
9.90
4.24
6.78
6.29
10.04
5.38
3.85
37.79
4.93
6.13
3.54
8.44
4.40
3.17
5.92
5.10
5.52
8.51
9.88
14.47
10.73
24.40
4.85
19.14
0.07
0.95
1.29
1.97
1.63
10.11
3.19
2.31
0.07
10.11
4.40
16.41
5.81
16.77
3.01
4.75
3.35
13.32
11.19
3.35
2.66
3.01
0.07
6.17
9.75
10.83
11.55
13.32
10.11
17.13
12.97
14.02
15.73
16.07
17.13
4.05
15.73
4.05
4.05
4.05
0.95
1.29
1.29
1.29
14.02
6.88
16.77
16.77
16.41
3.01
17.13
6.17
2.31
3.01
15.05
17.13
8.31
10.47
3.35
6.52
3.35
17.13
17.13
9.39
10.83
11.91
12.26
10.47
16.67
11.91
16.41
16.77
16.77
16.41
17.13
17.13
5.10
3.70-
n
y
y
y
y
n
n
y
y
n
y
y
n
y
y
n
y
y
n
y
n
y
n
y
n
y
y
y
y
n
n
n
n
n
n
n
n
n
n
I
I
114
Figure 6.7: Range Estimation Error From Modulus of the Wave Impedance
16
E14S12
W10-
x
E
42
o
.CD
C-
W
x
X
x
X
2
0
4
6
X
8
10
12
14
Actual Location of Events in Mm
16
18
20
and bearing from the automated procedures. The events are indexed by range in increasing
order. There are two range estunates based on the modulus and the argument of the wave
impedance, respectively which are discussed in Section 5.7.
Before we examine some of the events in detail, a cursory study of the 40 events can
tell us the quality of the automated procedure which we have used to estimate the range
and the bearing. Figure 6.7 shows the error in the range estimation from the modulus of
Figure 6.8: Range Estimation Error From Argument of the Wave Impedance
I0
X
E
.2
x
E
'tC0.
.o
E
Co
a
W0
x xx
x
x
51
ccC
U)
x
x
w
u)
XX
0
xx
xxx
,,
x
Xy
0
.
.
2
.
•XX
i3~~
4
x
x
6
t
i
X
~
xx
I
,,
I,
10
12
8
14
Actual Location of Events in Mm
115
I
16
18
20
Figure 6.9: Bearing Estimation Error
--
A-
x
-
40
30
o20
10
x
E
U
x
xx
0
xx
X•X
X
XX
xx
m -10
x
x
x
xx
-20
-30
I
-An
-A+
0
50
!
100
x
,||
i
I
150
200
250
300
Actual Bearing of Events in Degrees
350
400
the wave impedance. We have plotted the actual range of the 40 OTD events to see if there
is any preference to the estimation process with range.
We can see that overall, the estimation predicts most of the OTD events to within 2
Mm of the actual range which is a 10% error. At longer distances, the error is less than at
shorter distances of the actual event. Figure 6.8 shows the range estimation error from the
Figure 6.10: Difference of the Two Range Estimates as a Function of the Actual Range
18
16
.
xx
E 14
x
cc
x
X
E
'< 8
64-
•
2
x
x
x
x
xx
x
x
x
X
2
4
x
X
6 A0
8
10
12
14
Actual Range of Events in Mrn
116
16
18
20
argument of the wave impedance. Here we see a similar graph to that of 6.7. The majority
of the events have an error less than 2 Mm. However, we do see a slight increase in
therange error. Overall, the two graphs show similar behavior in two different regions.In
Figure 6.9, we plot the bearing estimation error as a function of the actual bearing of these
40 in degrees. Overall, the majority of events has an error less than 10 degrees which is a
3% error. In Figure 6.10, we have the difference of the two range estimations at plotted as
function of the actual range. Here again we have a graph similar to that in figures 6.7 and
6.8. We see the majority of the events have a difference between the two ranges less than
2 Mm. Like Figure 6.7 and 6.8 we see a huge descrepency around the events at 4 Mm. We
will take a look at these events. In addition, we will provide examples of a short range and
a long range event.
Figure 6.11 shows an event which matched the SR data with good accuracy. First, the
bearing comparison reveals a difference of 4 degrees. Notice the polarized lissajous and its
linear least squares fit. We see that the spectra of E and H match reasonably well with the
theoretical dashed curve, at least for low frequencies. The modulus and argument of the
wave impedance both exhibit the periodic nature discussed in Section 5.7. The average
PTPFS of the two waveforms is 7.126 Hz. We see that this corresponds to a distance of
2.57 Mm on the Range Frequency Curve. This differs slightly from the 3.3 Mm range
detected by the OTD. The source term ids (co) exhibits a large 8 Hz component in the electric field spectrum.
We now compare this set of graphs to an event which has large error in boththe modulus and the argument estimation. Figure 6.12 shows an event which returned poor estimates of range in both the modulus and the argument. We see that the time series signal is
barely above the Schumann background. In addition, we can observe that during this
period , there exist other transients of comparable size in the same window. This is evident
117
Figure 6.11: OTD Event well located with Schumann Resonance data
05:45:21.678 UTC, day =233
Bear =220.Odeg, Dist =3.3Mm
bearing = 216 degrees
a)
a)
E
E
-10
0
-15
0
0.1
0.2
H(phi) vs seconds
-40 -20 0 20 40
microAmp/meter
0.1
0.2
electric vs seconds
x 106
x 10-5
1
N
N 1.5
r-a)
Cr
E
1
a)
a)
a)
E
S0.5
aQ
00
E
2
E
0
0
DFT of Hvs frequency (Hz)
20
40
60
Source Term vs Hz
freq(Hz); dist = 2.7Mm
x 10- 3
x 106
t
a)
a)
E
a)
a)
a)
E
I
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
freq(Hz); dist = 2.4Mm
118
60
0
20
40
Source Term vs Hz
Figure 6.12: OTD Event which did not match well with Schumann Resonance Data
03:33:32.856 UTC, day =236
Bear =165.0deg, Dist =4.1Mm
bearing = 144 degrees
I-·
wt
CL
F
.o -5
0
0.1
0.2
H(phi) vs seconds
0
-5
0
5
microAmp/meter
0.1
0.2
electric vs seconds
x 10- 6
3
-,4
N
x 106
-2.5
0
U,..
0
C')
1.5
E
0
.1
5
E
I
0
0
0.5
.
VV
V\IkAI\.]k
S
V V vv\v
-
0
0
20
40
60
DFT of Hvs frequency (Hz)
K
A&A
r\1/-
20
40
60
freq(Hz); dist = 3Mm
x 10-3
n,
V
0
20
40
Source Term vs Hz
x 106
N
tý
a,
E
C',
01
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 10.6Mm
119
0
20
40
Source Term vs Hz
in the lissajous plot which shows a poorly defined polarization. We see that the theoretical
spectra are nowhere close to the experiment and that the wave impedance model thus
returns two estimates which are not related to each in any way.
The above signal is typical of other events which do not process well. Specifically,
these are the events which have a low SNR and are interrupted by another event of comparable size before the wave can make a whole trip around the world. A SNR of at least 4-5
above a relatively stable background is usually a good indicator of a processable event.
However, this includes the criterion that the ELF event is uninterrupted during this period
by other transients of comparable size.
We now look at a long range event in Figure 6.13. First we notice that the lissajous
plot is non-polarized meaning that there contains maybe one or more other events during
the onset of this event. We see this from the deviations from the linearized polarization
and also from the time series wave forms. Next when we look at the spectra of the magnetic and the electric field, we find the theoretical calculations of the two fields do indeed
have some resemblence to the observations. Specifically, for frequencies less than 30 Hz,
the modes are rather well matched in both fields. For modes above 30 Hz, we notice a
strong attentuation with frequency. When we look at the modulus and the argument of the
wave impedance, we see very little periodic structure of the theory. This is due to the
superposition of another event of comparable size which occurred within the window of
analysis. In the source term, however, we do a curve declining with frequency which is
characteristic of a positive event. Overall, we can say the SNR is about 3-4 above a noisy
background. As said in previous statements, these events are not going to be processable
because the SNR is below the necessary threshold for good estimation of range and bearing. In the Appendix, we show all the 40 events with the same type of analysis as here.
The dashed curves on all of these plots represent the theoretical predictions for the OTD
120
Figure 6.13: A Long Distance OTD Event
22:38:36.128 UTC, day =238 Bear =252.0deg, Dist =15.7Mm
bearing = 64.78 degrees
E
I--
C-
E
0
I..
E -1
0
0.1
0.2
H(phi) vs seconds
0
-10
0
10
microAmp/meter
0.1
0.2
electric vs seconds
x 10- s
x10 7
25
N
N
20
CT
t
15
U.
CL
(I,
b-0
E
10
C.
0
E 0.5
5
u
I-
0
20
40
60
0)FT of H vs frequency (Hz)
l
0h
v
s-~~n~i
ýt
20
40
60
(0
freq(Hz); dist = 7.1Mm
x 10-'
A
U-
0
5
40
20
Source Term vs Hz
x 107
N
-5
N
tý
C)
64
cr
t
cr
0)1
C')
2~
-E2
0)
>1
E
0
a-
I
0
20
40
60
DFT of E vs frequency (Hz)
A
0
20
40
freq(Hz); dist = 12Mm
60
0
20
40
Source Term vs Hz
measured ranges from Rhode Island. Table 6.2 lists the processing status of all the events.
The right-most column indicates whether the event was processed or the event could not
be processed. Nearly half (19) of the forty OTD events were successfully processed, in the
sense that the two range estimates agreed within 1 Mm with the OTD range. . The success
rate is lower than the Sprite events of Section 6.3 where all forty of those events seemed to
be located by the automated system. The reason for this difference is that the OTD events
are global lightning events which means that they have travelled far distances through the
wave guide to get to the receiver. There are a number of factors which might affect this
wave. There are the distortions caused by the wave guide and the attentuation factor v
which is a function of frequency. In addition, during this day, the background level was
relatively high and therefore any signals with a low SNR will be affected by this noise
level.
6.4 Large Amplitude ELF Events Sampled at 2k Hz
Now that we have established some ground truth in the location of SR transient events, we
are ready to look at a set of events which will tell us certain aspects of the lightning phenomenon. The final set of ELF event we will look examine comes from the 2 kHz sampled
SR data. Before November of 1995, the Rhode Island system was recording data by interleaved sampling at350 Hz. Because of the possible problems in direction finding due to
the interleaved sampling, we increased the sampling rate on the three analog signals to
2kHz. From this we recorded events in trigger mode. This means that any signal above a
certain threshold value (±200mV on the Ez channel) is stored in the computer for later
analysis. We collected events from November 27, 1995 through January 2, 1996 . Then we
ran the automated procedure on these events and produced 5414 candidates which were
cleanly processed. By this, we mean that the modulus and argument estimation of range
fall within 1 Mm of each other. We have plotted all of these points in Figure 6.14. In this
map we see three different regions of major lightning concentration - South America,
Africa, and the Pacific Islands. The greatest concentration is in South America. This is to
be expected. The Wait/Jones model predicts that near the receiver, the source is strongly
enhanced. This is seen in the E and H field expressions as discussed in Section 3.1. The
model states that because of a singularity near the source, we would expect events in this
region to be strong. Therefore long distance are not as affected by this factor. Figures 6.15
-6.18 show the distribution of lightning when we divide the day into four 6 hour segments
. We see that in the time interval from 0 to 6:00 UTC, the world is the most quiet with a
total lightning count of 1161. We also do not see event in the Asia Pacific. Going from
6:00 to 12:00 UTC, we see more of Asia getting filled with lightning events. There are
however some events located over the Sahara Desert which is inconsistent with the nature
of thunderstorms in that region. As we move from 12:00 to 18:00 UTC, we see the evidence of the African Continent as a major region of lightning activity. In addition, there
are a lot of coastal events which appear off of the left comer tip of Africa. Finally, during
18:00 to 24:00 UTCwe see an enhancement of the South American lightning production.
In all the four time graphs, we did see the presence of South America. This is to be
expected because we are dominated by the region closest to us based on the Wait/Jones
model. However, we do notice an increase in the amount of South American lightning
events during this period.
123
Figure 6.14:
Latitude
,b
100
60
41J
-
000000
t
u,
0000
s
00
0
ft
0
o
O
0rt-a
N)
t
b)
0
0
0
L,
U'
H
0
t3
O
0
0,
0
N
°°
¢gl
..
Kl)
K)
0
0o
00
i°
0
0
(D
0°°
0
n,
O
Kt
I
00
0
124
Figure 6.15:
Latitude
O
I-I
0
ou,t
u'
H
r-a
'I
03
4
t"
O
3
09
a
eD
C
C
t-
0-"
O
125
Figure 6.16:
Latitude
0
'N
Y
O
O
01
-- j
tO
3
0
N.)
K)
a
Cp
rt
z
U'
CT2
Ct
It
O
-.3
126
Figure 6.17:
Latitude
0
tQo
co
--1
bi
C0
c3
0
bi
OC
C
Ln
A.
0
d0
L'it.
Ln
N)
0
U'
cpr
C
0
H
Ho
H
(D
U,
N
r-1
0
H
O
0l
0o
0
H3
-.
00
O
127
Figure 6.18:
Latitude
0
H
\D
L,
b0
-,
oo
Ln
-'
0
C
C
C
C
Figure 6.19: Diurnal Variation of Transient Coujnts
03
Eu
E
0
5
10
UTC Time
15
20
In Figure 6.19 we plot the number of transients as a function of time. We do see the characteristics which have been described above. There is a diurnal cycle to the number of
transient occurrences. In generating these 5414 events, we used a relatively high SNR.
Here, we have selected 26 large amplitude transients examples to show in the Appendix.
We will examine some of these events and see why we can have confidence in the automated procedure. Figure 6.20 shows a typical event sampled at 2kHz. Here, we see that
the SNR is at least 10 on both the magnetic and electric field. The bearing plot is tight giving us an accurate bearing. In the magnitude spectra of the magnetic and electric field, we
have an almost perfect match between the theoretical and the experimental data. The wave
impedance is like the theoretical periodic sequence in the Wait/Jones model. We see that
this event is a negative cloud-to-ground lightning and the source term derived from the
magnetic spectrum is relatively flat with frequency. Most of the 5414 signals which the
automated procedure has chosen are of this form. Figure 6.21 shows another event which
is a more distant event. Here we see that the SNR is about the same as that in Figure 6.20.
In the spectra of the two field, we see peaks closely matched with the theoretical calculations. We see in the wave impedance that the peaks are now more widely spaced indicating a long distance event. (see plots in the Appendix for various ranges)
129
Figure 6.20: A large amplitude transient event sampled at 2kHz with negative polarity
2kHz sampling -004
2kHz sampling -004
0 0.05 0.1 0.15 0.2
seconds
x10 H(phi) vs
0 0.05 0.1 0.15
electric vs seconds
frequency (Hz)
bearing =154.6 degrees
0.2
-50
x10
freq(Hz); dist =5.3Mm
Source Term vs Hz
x
40
20
frequency (Hz)
60
0
60
20
40
freq(Hz); dist= 5.4Mm
130
0
50
microAmp/meter
7 SO
Source Term vs Hz
It is interesting that this event is relatively large in amplitude considering that it travelled
10 Mm from the source to receiver. It has a bigger amplitude than the event in Figure 6.20
which travelled only 5 Mm. By looking at the source term of this 10 Mm, we see a graph
declining with frequency which would suggest that this negative cloud-to-ground lightning event had a long continuing current. In addition, it would explain the high amplitude
despite the distance between the source and the receiver.
Because we are saturated by events from South America, we do not see a real distribution of lightning activity every day. Asia oftentimes does not come through in the expected
window 6:00 - 12:00 UTC. Africa, however, can be seen with good accuracy. In addition,
the appreciable number of events over the Atlantic Ocean which first glance may seem a
little puzzling. However, a comparison of the data with expected winter lightning distribution, suggests that these ocean events are probable.
In essence global maps can be generated every day for what we interpret to be positive
and negative cloud-to-ground lightning events. By using the automated procedure to process raw time signals, we can essential obtain and monitor the global distribution of lightning.
Figure 6.21: Long Distant 2k Hz Event
2kHz sampling -012
2kHz sampling - 012
bearing =102.1 degrees
E
>o11.
U)
0 0.05 0.1
-5H(phi) vs
x10
0,15 0.2
seconds
0 0.05 0.1 0.15 0.2
electric vs seconds
-50
0
50
microAmp/meter
xlO
frequency (Hz)
freq(Hz); dist =10.1Mm
Source Term
vs Hz
xlO7
20
40
frequency (Hz)
60
0
60
20
40
freq(Hz); dist= 10Mm
132
20
40
60
Source Term vs Hz
Chapter 7
Conclusions
7.1 Review of Analysis
An automated procedure has been developed for the global location of large amplitude
lightning transients in the Schumann resonance band. We have seen how the automated
procedure processes a lightning event in Chapter 5. In Chapter 6, we compared our results
with two simultaneous measurements and found well matched results supporting the
ground truth procedure from space for Schumann Resonances. We have also seen how the
different models discussed in Chapter 3 relate to each other and furthermore, how the
parameters which govern the electromagnetic waves are examined and fitted to the experimental data. Overall, the results indicate that Schumann Resonance methods provide a
sound tool for analysing the global transient population.
We have also studied asymptotic models which showed good agreement with the theoretical calculations. This provided us with a much simplified expression in which the complicated Legendre Polynomials are reduced to sines and cosines.
7.2 Improvements
The automated procedure does have its limitations. For instance, its bandwidth for
locating a lightning event currently extends from 4 to 60 Hz because of the 60 Hz notch
filter. By eliminating the 60 Hz notch filter, we can extend the wave impedance to higher
frequencies. This would mean that longer range events would be detectable. Under the
current system, a maximum range of 15 Mm is possible based on the PTPFS of about 25
Hz. Another aspect deserving consideration is the SNR. We have said that analysing
events which have a low SNR will show superposition of modes with other comparable
events in the same window. We would like to further examine these events which are dominated by the background Schumann level. This will allow us to classify the positive and
negative cloud-to-ground lightning events more readily and see if intra-cloud lightning
events are included in the Schumann background. Another research topic is to compare
simultaneous recording of the background Schumann resonance and compare with the
transient events on a global basis. We also need to generate more detailed global maps of
the transients.This will give us insight into the relationship between thunderstorms on the
convective scale and the mesoscale systems occur later in the diurnal cycle.
Lastly, we can make the final step of looking at the time series behaviour of the source
term Ids(co). This will tell about the charge transfer aspect of an ELF event. By having the
charge transfer of a lightning event we can better understand the optical emission from
Sprites and the tendency for positive ground flashes to be so closely associated with them.
134
References
Balser, M. and Wagner, C.A. (1960). Observations of earth-ionosphere cavity resonances,
Nature (London), 188, 638.
Balser, M. and Wagner, C.A. (1962). Diurnal power variations in the Earth-ionosphere cavity
modes and their relationship to world-wide thunderstorm activity, J. Geophys. Res., 67, 619.
Bliokh, P.V., Nikolaenko, A.P., and Filippov, Yu. F. (1980). Schumann Resonances in the
Earth-Ionosphere Cavity, Peter Peregrinus, London.
Boccippio D, Williams E, Heckman S, Lyons W, Baker I and Boldi B. (1995). Sprites,
Extreme-Low-Frequency Transients, and Positive Ground Strokes, Science,269,1088-1091.
Burke C.P. and Jones D.L.I. (1994 in press) On the Polarity and Continuing Currents in
Unusually Large Lightning Flashes Deduced From ELF Events.
Burke C.P. and Jones D.L.I. (1994 in press) Radiolocation in the Lower ELF Frequency Band.
Chapman, F.W. and Jones, D.L.I. (1964). Earth-ionosphere cavity resonances and the propagation of extremely low frequency radio waves, Nature (London), 202, 654.
Christian H, Goodman S, Bakeslee R J, Driscoll K, and Mach D. (1995) The Optical Transient
Detector. EOS, Vol. 76, No. 46 , F129.
Clayton, M.D., and Polk, C. (1974). Diurnal Variation and Absolute Intensity of World-Wide
Lightning Activity, September 1970 to May 1971, in Proc. conf. Electrical Processes in atmospheres, Garmisch-Partenkirchen,Germany.
Erdelyi A, Magnus W, Oberhettinger F and Tricomi F. G. (1953) Higher Transcendental Functions vol 1 (New York): McGraw-Hill)
Galejs, Janis. (1965). Schumann resonances. Radio Sci.,69:1043-2728.
Ishaq M. and Jones, D.L.I. (1977). Method of obtaining radiowave propagation parameters for
the Earth-ionosphere duct at ELF, Electronic Letters, Voll13. No.9 p2 5 3 -2 5 4 .
Jones, D.L.I. (1967). Schumann resonances and ELF propagation for inhomogeneous isotropic ionospheric profiles, J. Atmos. Terr. Phys., 29, 1037.
Jones, D.L.I. (1970). Numerical computations of terrestrial ELF electromagnetic wave fields
in the frequency domain, Radio Sci., 5, 803.
Jones, D.L.I. and Burke, C.P. (1990). Zonal harmonic series expansions of Legendre functions
and associated Legendre functions, J. Phys. A: Math. Gen., 23,3159.
Jones, D.L.I. and Joyce, G.S. (1989). The computation of ELF radio wave fields in the earthionosphere duct, J. Atmos. Terr. Phys., 51, 233.
Jones, D.L.I. and Kemp, D.T. (1970). Experimental and theoretical observations of Schumann
resonances, J. Atmos. Terr. Phys., 32 1095.
Jones, D.L.I. and Kemp, D.T. (1971). The nature and average magnitude of the sources of
transient excitation of the Schumann resonances, J. Atmos. Terr. Phys., 33, 557.
Lyons, W.A. (1994). Low-light video observations of frequent luminous structures in the
stratosphere above thunderstorms, Mon Wea. Rev., 122, 1940-1946,.
Madden, T. and Thompson, W. (1965). Low-frequency electromagnetic oscillations of the
Earth-ionosphere cavity, Rev. Geophys., 3, 211.
Nelson, P.H., (1967). Ionospheric Perturbations and Schumann Resonance Data, Ph.D. Thesis,
Massachusetts Institute of Technology, Cambridge, MA.
Nickolaenko A.P. and Kudiniseva I. G (1994). A modified technique to locate the sources of
ELF transient events. J. Atmos. Terr. Phys., vol 56, no. 11, pp 1 4 9 3 - 14 9 8 .
Ogawa, T., Miura, T., Owaki, M., and Tanaka, Y. (1966). Observations of natural ELF and
VLF electromagnetic noises by using ball antennas, J. Geomage. Geoelctr., 18, 443.
Ogawa, T., Fraser-Smith, A.C., Gendrin, R., Tanaka, Y., and Yasuhara, M. (1967). Worldwide
simultaneity of occurrence of a Q-type ELF burst in the Schumann resonance frequency range, J.
Geomag. Geoelectr., 19, 377.
Oppenheim, Alan and Shafer, D. (1989). Discrete Signal Processing. New York: PrenticeHall.
Pasko, V.P., U.S. Inan, Y.N. Taranenko and T.F. Bell. (1995). Upward dischages in the mesosphere due to intense quasi-electrostatic thundercloud fields. Geophysics, Res. lett 22, 365-368.
Polk, C. and Fitchen, F. (1962). Schumann resonances of the earth-ionosphere cavity:
extremely low frequency reception at Kingston,R.I. J. Res. NBS Radio Sci., 66D, 313.
Rycroft, M.J. (1965). Resonances of the earth-ionosphere cavity observed at Cambridge,
England, Radio Sci. J. Res. NBS, 69D, 1071.
Schumann, W.O. (1952). Uber die strahlungslosen eigenschwingungen einer leitenden kugel,
die von einer luftschicht und einer ionospharenhull umgeben ist. Z. naturforsch, 7a: 149.
Schumann, W.O. (1957). Uber elektrische Eigenschiwingungen des Hohlraumes Erde-Luftlonosphare, erregt durch Blitzentladungen, A. Agnew. Phys., 9, 373..
Sentman, D.D. (1987). Magnetic elliptical polarization of Schumann resonances, Radio Sci.,
22, 595.
Sentman, D.D. (1990). Approximate Schumann resonance parameters for a two scale height
ionosphere, J. Atmos. Terr. Phys., 52, 35.
Sentman, D.D. (1995). Schumann Resonances, Handbook of Atmospheric Electrodynamics.Volume I , Volland H editor, CRC Press Inc.
Sentman, D. D.and E.M. Westcott (1993). Observations of upper atmosphere optical flashes
recorded from an aircraft, Geophs. Res. Lett, 20, 2857-2860, 1993.
Uman, M.A. (1987). The Lightning Discharge, International Geophysical Series, Vol. 39,
Academic Press, Orlando, FL.
Wait, J.R. (1962). On the propagation of VLF and ELF radio waves when the ionophere is not
sharply bounded. J. Res. Nat. Bur. Stand., Sect. D., 66, 53.
Williams, E.R., (1992). The Schumann resonance: a global tropical thermometer, Science,
256, 1184.
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13 Mm
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Appendix C
(July 24, 1995 Sprite Events)
NLDN Bearing=267.7degrees
Bearing = 282.1 degrees
lat=37.31, long=-99.37
pe
4,I u*\
IVV
=82.44kA, mult=l
100
,dit :2.41 Mm
50
50
0
0
-50
-50
-100
-100
100
200
time(Milliseconds)
x 10- 5
300
-100
DFT of Hphi
-50
0
50
100
EW (Micro-Amp/meter)
x 107
Ids(w)
2.5
2
N2
N
a)
I
Cr
S1.5
C,,
T 1.5
aC
C-
a,
E
E
0.5
0.5
n
0
20
40
60
80
Frequency (Hz)
100
0
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=268.7degrees
Bearing = 279.6degrees
40
120
0
30
100
Z
9n
E
E80
4-,
a,
E
0
60
,m•
E
<0o
0
40
o
S-10
E
E 20
Lo
-20
20
-30
-20
-40
100
200
time(Milliseconds)
x 10- 5
300
-40
DFT of Hphi
-20
0
20
EW (Micro-Amp/meter)
x 106
Ids(w)
1.2
N
-1
"CT0.8
S0.6
C)
2
0.2
ft
0
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
40
NLDN Bearing=267.8degrees
Bearing = 278.2degrees
4 t".
I UU
80
L
a)
a)
r=
60
C.
E
<,
0
40
S-20
20
z -40
0
-60
-80
-20
100
200
time(Milliseconds)
x 10- 6
300
-50
0
50
EW (Micro-Amp/meter)
DFT of Hphi
x 106
Ids(w)
3.5
-2.5
N 3
N
I
,2.5
a)
2
2
21.5
a)
1.5
a)
E
<
-
E
1
0.5
0.5
n
0
20
40
60
80
Frequency (Hz)
100
0
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=267.9degrees
Bearing = 278.0degrees
120
40
-J 100
30
Z
z
20
E
0r
zk:
°!
IL
E
L.
I-
0
0
L..
,I
0
E
I--
LL
C
Cl
z -20
0o0
-30
.°
-20
-40
300
100
200
time(Milliseconds)
x 10- 5
1.2
•
DFT of Hphi
-40
-20
0
20
EW (Micro-Amp/meter)
x 106
A
Ids(w)
I 0.8
Cl
00.6
e 0.4
E
0.2
0
0
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
Bearing = 280.4degrees
NLDN Bearing=267.7degrees
80
100
lat=37.33, long=-99.28
60
80
peak=51.04kA, mult=2
40
60
E
-&
rFiet--'3 AKAm
JIlJEL·.AATIAIA
II
E
40
20
o
0
2 -20
20
Cn
0
-20
z
L
-40
-YT
-60
100
200
time(Milliseconds)
1.5
x
10 - 5
300
-80
DFT of Hphi
-50
0
50
EW (Micro-Amp/meter)
x 106
Ids(w)
8
N
f=:
I
N7
i
6
C,
C/)
5u
C3
)0.5
a
E,
E
2
1
20
40
60
80
Frequency (Hz)
100
0
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=267.3degrees
Bearing = 276.6degrees
40
30
20
L.
E
E
<0
Z -10
-20
-10
-30
-20
100
200
time(Milliseconds)
x 10 - 6
300
-40
-40
DFT of Hphi
-20
0
20
EW (Micro-Amp/meter)
x 106
Ids(w)
7
N
6
I3
U,
I6
t4
)5
23
a3
E
E
<2
2
1
1
0
0
20
40
60
80
Frequency (Hz)
100
20
60
40
80
Frequency(Hz)
100
NLDN Bearing=262.8degrees
Bearing = 272.3degrees
60
100
40
1;Z
0>
50
E
<I-
0
O
-20
0
C4
z
-40
-60
-50
100
200
time(Milliseconds)
x 10- 5
-50
300
DFT of Hphi
0
50
EW (Micro-Amp/meter)
x 106
Ids(w)
1.4
12
1.2
N
N0)
1=
W
w 8
n 0.8
(D
S6
Z 0.6
CL
4.
E4
E 0.4
2
0.2
20
40
60
80
Frequency (Hz)
100
0
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=267.8degrees
Bearing = 280.0degrees
lat=37.41, long=-99.12
100
100 - peak=82.18kA, mult=l
I st=2.39Mm
80
60
-j
40
50 I-
20
k
LVAAA~A
~i\)
i~vvt
0
AA ý
AA
-20
-40
-50
-60
IJ
II
-100 I~
C0
x 10-5
-80
100
200
time(Milliseconds)
300
-100
-100
DFT of Hphi
-50
0
50
EW (Micro-Amp/meter)
x 107
Ids(w)
2.5
2
N
N
0.5
C
0)
E=
CL
03
1
E
0.5
0.5
c
A'
•
0
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
100
NLDN Bearing=263.5degrees
Bearing = 278.1 degrees
60
lat=36.41, long=-97.06
150
peak=1 15.7kA, mult=l
; #-
SUI•L---..-.IVII
OaKA
40
II
100
E
c- 20
E
E
<
c0
50
o
E
.
.,U
S-20
-40
-50
I
I
I
100
200
time(Milliseconds)
x
10 -5
-60
300
DFT of Hphi
-50
0
EW (Micro-Amp/meter)
x 106
Ids(w)
1
N5
S0.8
Cr4
v,
~0.6
CO,
~ 0.4
E
E2
0.2
0
0
20
40
60
80
Frequency (Hz)
100
0
0
20
40
80
60
Frequency(Hz)
100
50
NLDN Bearing=265.2degrees
Bearing = 265.3degrees
50
100
40
30
S) 20
50
n
E
< o
S-10
0
Uo
z -20
-30
-40
-50
-50
100
200
time(Milliseconds)
x 10- 5
1.4
300
DFT of Hphi
-50
0
EW (Micro-Amp/meter)
x 106
Ids(w)
1.2
I
Ca
U0.8
0.6
aO
aD
E 0.4
0.2
20
40
60
80
Frequency (Hz)
100
20
40
60
80
Frequency(Hz)
100
50
NLDN Bearing=263.1 degrees
Bearing = 274.8degrees
50
100
40
80
z
30
-J
z
0
E 60
20
(
r-
E
0
0
" 20
-10
E
E
<
z -20
0
-30
S-20
-40
-40
100
200
time(Milliseconds)
x 10-5
300
-50
-50
EW (Micro-Amp/meter)
DFT of Hphi
x 106
Ids(w)
1
0.9
7
0.8
( 0.7
6
I(D'
Cr 5
Cr0.6
U,
S0.5
~ 0.4
a)
e4
E 0.3
E
<2
0.2
1
0.1
0
0
20 40
60
80 100
Frequency (Hz)
20
40
60
080
100
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=264.3degrees
Bearing = 276.1 degrees
140
40
-120
30
-J
z 100
20
E
< 80
E
0
E
< 0
40
0
E
z<c
20
o 20
E
0
-30
-40
-40
-40
100
200
time(Milliseconds)
x 10-5
300
-40
DFT of Hphi
-20
0
20
EW (Micro-Amp/meter)
x 106
Ids(w)
18
16
N
N
,- 1.5
14
12
cr10
C)
8
E
E
0.5
6
4
2
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
40
NLDN Bearing=262.9degrees
Bearing = 272.1 degrees
120
60
. 100
Z
40
j80
dJ~
E 60
0)
0
E
<0 o
D 20
20
E
E
r -20
-40
-40
-60
-60
5 -40
100
200
time(Milliseconds)
•
x 10-5
A
300
-50
DFT of Hphi
0
EW (Micro-Amp/meter)
x 106
1.8
Ids(w)
i.E
1.6
1
A
N
a)
03
-rl
a)
1.2
S10
1
C5
a)
aC
C')
a)
2 0.8
00.6
E
vr
E
0.4
0.2
0
0
20
40
60
80
Frequency (Hz)
100
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=262.6degrees
Bearing = 273.9degrees
lat=36.07, long=-97.13
150
peak=122kA, mult=2
E
Z
zZ0
60
c
IUIIL---...UIVII
t
di
228M
40
II
a 100
E
01
E
I-
< o
50
0
a>
03
E
E
n
A
n
0
U)
-20
z
0
Or
-40
-50
-60
100
200
time(Milliseconds)
x 10-5
-50
300
DFT of Hphi
0
EW (Micro-Amp/meter)
x 106
v
Ids(w)
1.8
12
1.6
=
1.4
= 10
I
I
co
0.6
E 4
0.4
2
0.2
0r
•
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=262.1 degrees
Bearing = 272.7degrees
200
100
150
100
50
50
0
0
-50
-50
-100
-100
100
200
-100
300
time(Milliseconds)
x 10- 5
-50
0
50
100
EW (Micro-Amp/meter)
DFT of Hphi
x 107
Ids(w)
3.5
2.5
3
2
.2.5
1.
1.5
1.5
E
E
0.5
0.5
0
0'
0
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=262.6degrees
Bearing = 270.3degrees
lat=36.05, long=-97.16
60
peak=143.8kA, mult=l
z 150
;,+r)
rO A A..
),UI3zL~.LOIVII II
-J
40
z
E
<I 100
a)
|
o
a)
E
S50
0
-20
E
I--
E
<
I-
st
0
B
z
.,_.
W"~
-40
-60
-50
100
200
time(Milliseconds)
0
x 10-
-50
300
DFT of Hphi
14
0
50
EW (Micro-Amp/meter)
x 106
Ids(w)
1.8
12
1.6
1.4
S10
E 1.2
0
cr
a 8
c 0.8
6
E-0.6
E4
0.4
2
0.2
20
40
60
80
Frequency (Hz)
100
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=262.2degrees
Bearing = 271.6degrees
30
Zc
L.JI
20
zI.-
rcl
P
a_
a)
S20
E
< o0
0
a)
E -20
E
< -40
-10
z
-20
S-60
-30
-80
100
200
time(Milliseconds)
x 10- 5
300
-20
0
20
EW (Micro-Amp/meter)
DFT of Hphi
x 107
Ids(w)
2.5
1.8
N 1.6
I 1.4
S1.2
1.5
( 0.8
E 0.6
0.4
0.5
0.2
20
40
60
80
Frequency (Hz)
100
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=262.1 degrees
Bearing = 263.7degrees
lat=35.26, Iong=-98.78
20
peak=199.9kA, mult=l
200
I
,,
,,
A"
,Ul~jL=L.L)31VIIII
15
A.A
10
150
5
0
100
-5
-10
50
-15
V
x 10- 5
~L"
100
200
time(Milliseconds)
-20
~
300
-20
DFT of Hphi
-10
0
10
EW (Micro-Amp/meter)
x 106
Ids(w)
1.8
1.6
iz'1.4
1.2
10
cr
-0.8
-5
80.6
E
0.4
E
0.2
n
0
20
40
60
80
Frequency (Hz)
100
n
0
20
40
60
80
Frequency(Hz)
100
20
NLDN Bearing=262degrees
Bearing = 272.8degrees
80
80
z
a
Z
60
-...
E 40
!~
40
E 20
w
0
4-'
0
E
C.-20
E
o -40
-60
~zE -20
-40
-60
0
-60
-80
100
200
time(Milliseconds)
x 10-5
300
-50
0
50
EW (Micro-Amp/meter)
DFT of Hphi
x 106
Ids(w)
16
1.8
14
1.6
N
N
a1.4
12
I
1:10
ci)
S1.2
-" 8
( 0.8
6
E 0.6
E
< 4
0.4
2
0.2
0
0
20
40
60
80
Frequency (Hz)
100
0'
0
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=262.6degrees
Bearing = 355.2degrees
70
lat=35.91, long=-97.57
60
-
50
10
peak=23kA, mult=l
40
i-
30
K
5
0
-,dit=•3.9Mm
•4
g
=
i
I,•.llll
!
I
-5
20 t-
-10
ýIkvr,,ý
,h\lk·
100
time(Milliseconds)
x 10 - 6
-20
-25
Y~vi
200
-10
-15
300
-20
DFT of Hphi
-10
0
10
20
EW (Micro-Amp/meter)
x 106
Ids(w)
4.5
4
5
N
)3.5
C
3
2.5
CD3
g
02
2
a)
E
E 1.5
1
0.5
20
40
80
60
Frequency (Hz)
100
20
40
60
80
Frequency(Hz)
100
NLDN Bearing=260.5degrees
Bearing = 268.6degrees
30
100
20
a)
50
a)
E
1.
E
0
0
-10
-50
-20
-30
-100
100
200
time(Milliseconds)
x 10- 5
300
-20
0
20
EW (Micro-Amp/meter)
DFT of Hphi
x 107
Ids(w)
1.8
2.5
N-1.6
N
N
I
1.4
1.2
1
S1.5
U)
r)
2 0.8
a)
cn
E
E 0.6
0.4
0.5
0.2
0
0
20
40
60
80
Frequency (Hz)
100
0
20
40
60
80
Frequency(Hz)
100
Appendix D
(40 Optical Transient Detector Events)
17:19:48.064 UTC, day =230
Bear =156.0deg, Dist =1.5Mm
20
bearing = 158.3 degrees
IIT···-·---C-··-__~-·--1
15
10
50
5
·I
0
-5
-50
-5
-10
·
-50
0
50
microAmp/meter
-15
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10- 5
·
x 106
2.5
N
t-
2
01.5
C,
C,
1.5
1
C,
E
0.5
0
0
20
40
60
DFT of H vs frequency (Hz)
x 10-3
17 4
20
40
60
freq(Hz); dist = 2.1 Mm
20
40
Source Term vs Hz
x 106
40
30
--
20
10
f3
a,
0)2
0
E
-10
0
-ZU
>1
-30
0
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 2.3Mm
0
20
40
60
Source Term vs Hz
Bear =178.0deg, Dist =3.1Mm
04:05: 8.144 UTC, day =233
bearing = 173.1 degrees
· __
50
5
0
0
-5
-50
·
·
-50
-10
microAmp/meter
0.1
0.2
electric vs seconds
0.1
0.2
H(phi) vs seconds
x 10- 6
x 106
5
1.2
N
N
S4
1
t8
c60.8
6
&3
Ur)
-•
C-
L.
U-0.6
E(n
0-2
E
2,
ci
S0.4
L..
0
0.2
n
20
40
60
DFT of H vs frequency (Hz)
0
0
20
40
60
freq(Hz); dist = 2.1Mm
20
40
60
Source Term vs Hz
x 10- 3
X 106
20
---2
I
V-
I--
N
0
r3
S1.5
40
U.
E2
< -60
Ec
E
-E 1
00.5
0
0
20
40
60
DFT of E vs frequency (Hz)
-80
0
20
40
60
freq(Hz); dist = 2.4Mm
0
20
40
Source Term vs Hz
60
02:58:48.324 UTC, day =239
Bear =184.0deg, Dist =4.0Mm
bearing = 198.3 degrees
·
10
U)
'
'
a.0
E
: :·
:'.:·?J:
'
-10 !
E
-10
0
0.1
0.2
H(phi) vs seconds
0
0
10
microAmp/meter
0.1
0.2
electric vs seconds
x 10- 6
x 106
5
1.5
N
N
1=2.5
cr
CD
104
0r
z
U-
2
CD
ICL
-2-3
CD
E
E
81.5
E
-o
0.5
o
CL
a-
<E
Al
U.5
l.1
0
20
40
60
DFT of H vs frequency (Hz)
0
2
0
60
40
freq(Hz); dist = 2.1Mm
x 10-3
40
60
Source Term vs Hz
20
x10 s
N
S2
1.5
ca
E
34D
-a
L.
0
> 0.5
E
At
%,#
20
40
60
DFT of E vs frequency (Hz)
0
0
20
40
freq(Hz); dist = 6.1Mm
60
20
40
60
Source Term vs Hz
Bear = 4.0deg, Dist =12.8Mm
15:50:59.208 UTC, day =235
6
bearing = 6.154 degrees
4
a0
- o
x
-5
E -2
-10
·
-4
-10
-10
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10- 6
_·
0
microAmp/meter
x 106
3.5
-4
- 2.5
2
03
S1.5
<EL
2a
E
I.'I-
0.5
0
0
60
40
20
20
40
60
DFT of H vs frequency (Hz)
v
00
freq(Hz); dist = 1.7Mm
x 10- 3
NZ
r-
20
40
60
Source Term vs Hz
x 106
4
2
a1)
63
C/)
L.
a 1.5
-C
E
CO
cE
L..
>0.5
E
I.
0
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
freq(Hz); dist = 12Mm
60
0
20
40
Source Term vs Hz
Bear =186.0deg, Dist =3.5Mm
18:35:59.484 UTC, day =226
15
bearing = 175.7 degrees
10
20
5
10
E
i-----
"-5
0
E
-10
£ -10
-E
15
i·
-20
-20
-20
0
0.1
0.2
H(phi) vs seconds
0
microAmp/meter
0.1
0.2
electric vs seconds
x 10- 6
X 106
3.5
"Ni 5
C2
~·--r"c~-T-
2
N3
4
3
- 2.5
.1.5
I1
uU- 2
09
C.
S1.5
E
02
E1
0A
0
20
40
60
DFT of H vs frequency (Hz)
0
E
1
E05
E
0.5
0.5
0
0
20
40
60
20
40
Source Term vs Hz
freq(Hz); dist = 1.2Mm
x 10-3
x 106
2.5
50
N
0
0)
-c
-50
3
0)
E
> 0.5
-100
0
A
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 11.2Mm
20
40
60
Source Term vs Hz
Bear =10.0deg, Dist =0.7Mm
04:20: 9.508 UTC, day =228
bearing = 6.359 degrees
20
10
50
0
0
-10
-50
E
-50
0
50
microAmp/meter
-20
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10-5
x 107
2.5
0.8
-1.2
N
N
CD
2
-C
- 0.8
0,
E
U)
1.5
U- 0.6
-.
0.4
II
E 0.6
0
0 0.4
0-
E
<0.5
S0.2
ES0.2
1/3
60
0
20
40
DFT of H vs frequency (Hz)
0
40
60
20
freq(Hz); dist = 4.7Mm
20
40
Source Term vs Hz
x 10- 3
X 106
3.5b
12
220
3
0510
N
N
-2.5
200
8
S2
1.
180
u-
e 6
E
P 160
CO
S4
9 140
0.5
nV
0
20
40
60
DFT of E vs frequency (Hz)
E2
120
<
0\
0
20
40
60
freq(Hz); dist = 3Mm
0
20
40
Source Term vs Hz
Bear =191.0deg, Dist =3.4Mm
19:21:29.592 UTC, day =232
20
bearing = 220.7 degrees
15
CD
10
5
E
0
E
0
-5
0
E -10
-10
-10
0
10
microAmp/meter
-15
0
0.1
0.2
H(phi) vs seconds
0
x 10-6
·~I~--r
·--
8
·----
X 106
~----
6
5
N
N
a)
N
I
cJ4
6
E
0.1
0.2
electric vs seconds
=5
4
cJ
L.3
4
0.
cL2
E2
V~
le
I
.03
I
E
E2
nA
i
f
0
I
0
20
40
60
DFT of H vs frequency (Hz)
\I
C
A
.·
AA
·-
E
.I
-4
A'V
20
40
60
freq(Hz); dist = 2.6Mm
20
40
Source Term vs Hz
x 10- 3
X 106
7
2
N
1.5
a
1
0.5
0
0
20
40
60
DFT of E vs frequency (Hz)
Co
5
a)
-50
E3
a)
0L
<EI
-100
0
20
40
60
freq(Hz); dist = 2.4Mm
20
40
60
Source Term vs Hz
03:29: 9.632 UTC, day =236
Bear =168.0deg, Dist =2.6Mm
20
bearing = 174.9 degrees
15
20
k
a)
10 L
EO
L~c~--~rx.
-5
0
10 i
E -10
-20n
-15
L_
-20
0
0.1
0.2
H(phi) vs seconds
0
20
microAmp/meter
0.1
0.2
electric vs seconds
x 10-6
4
5
4
3
x 106
Nc
a)
C,)
2
E
a)
aEl
El
0.
0
20
40
60
0
DFT of H vs frequency (Hz)
20
40
Source Term vs Hz
freq(Hz); dist = 2.4Mm
x 10-3
2.5
2t
Ct 1.5
x 106
-200
,3.5
-300
a
Er 2.5
-400
-2,
a)
-500
C)
E
11.5
1
C,
-600
> 0.5
n
0
20
40
60
DFT of E vs frequency (Hz)
3
a)
-700
< 0.5
-8A0n
"""
0
20
60
40
ffreq(Hz); dist = 14.3Mm
0
0
20
40
60
Source Term vs Hz
05:38: 9.634 UTC, day =230
Bear = 6.0deg, Dist =14.2Mm
bearing = 11.09 degrees
·I
i<
·· .
·i
-5
-5
0
5
microAmp/meter
-2
0
0.2
0.1
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10- 6
x 106
A
N
2
S
5
a,
1.5
4
,2
E
E 0.5
E
E
€3
n
0
20
40
60
DFT of H vs frequency (Hz)
0
freq(Hz); dist = 1.2Mm
x 10- 3
20
40
Source Term vs Hz
x 106
3.5
N
2
S1.5
N
200
a,3
100
r 2.5
2
1 1.5
0.5
-100
(D 1
-200
< 0.5
> 0.5
C'
0
20
40
60
DFT of E vs frequency (Hz)
n
0
20
40
60
freq(Hz); dist = 1.2Mm
0
20
40
60
Source Term vs Hz
Bear =97.0deg, Dist =0.9Mm
17:25:20.128 UTC, day =230
bearing = 109.5 degrees
20
50
100
wr
50
E
*
0
0
0
0
-10
-50
-20
-100
-50
-100
-100
-100
-30
0.1
0.2
H(phi) vs seconds
0.1
0.2
electric vs seconds
x 10- 5
100
microAmp/meter
x 106
2.5
6
N
N -4
N
X5
LO
2
t-
C?
C)
03
II 4
1.5
Uo
U03
E
02
E
--
"•2
O
C-
<I1
E 0.5
0
20
40
60
DFT of H vs frequency (Hz)
0
--
40
60
20
freq(Hz); dist = 0.5Mm
x 10- 3
tr
20
20
40
60
Source Term vs Hz
x 106
7
N6
0
0
450
N
": 400
I(
a)
U5
U-
E
-2
350
1
300
"3
0
0
20
40
60
DFT of E vs frequency (Hz)
300
0
20
40
60
freq(Hz); dist = 0.8Mm
0
20
40
60
Term
vs
Hz
Source
Bear =229.0deg, Dist =3.1 Mm
06:54:30.756 UTC, day =227
bearing = 236.1 degrees
5
0
-5
-2
-10
-10
-10
0
0.1
0.2
H(phi) vs seconds
0.1
0.2
electric vs seconds
0
x 10- 5
0
10
microAmp/meter
x 106
1
'4
N
a)
z0.8
en 5
C1
3
I4
0.6
U-
3)
03
C0.4
.L
-02
<l
0
E 0.2
<0
n
0
20
40
60
DFT of H vs frequency (Hz)
'
n'
0
20
40
60
0
freq(Hz); dist = 2.7Mm
x 10- 3
20
40
60
Source Term vs Hz
x 106
N
N
•3
a)
.E
Co
1.5
a)
a)
L.
a)
E
I
Co
00.5
0
0
20
40
60
DFT of E vs frequency (Hz)
E
0
20
40
60
freq(Hz); dist = 13.3Mm
20
40
Source Term vs Hz
Bear =175.0deg, Dist =2.5Mm
16:07:41.276 UTC, day =236
20
6
10
4
bearing = 171.8 degrees
20
L
10
E -2
0
·· ·· ··· ... ···
:·
10 r
-10
-20
-4
-20
-20
-_
0
0.2
0.1
inds
H(phi) vs secc
0
0.1
0.2
electric vs seconds
x 10- 6
2.5
6
N
V-5
3
N
a)
I
-,
(o
U1)
1-5 3
E
22
E
a)
0
0
20
40
60
DFT of H vs frequency (Hz)
x 106
N2
o 2.5
')
LL
1.5
2
a)
0-1.5
0-~
0
0
E
1
< 0.5
0.5
0
•|
0
--
20
40
--
60
0
freq(Hz); dist = 1.4Mm
x 10- 3
2.5
0
20
microAmp/meter
20
40
60
Source Term vs Hz
x 106
50
,3.5
N
U)
0
2.5
S1.5
E
1
a)
-50
S1.5
-100
< 0.5
> 0.5
n
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 1.4Mm
0
20
40
Source Term vs Hz
Bear =220.0deg, Dist =3.3Mm
05:45:21.678 UTC, day =233
bearing = 216 degrees
50
40
t 20
E
E
O
. -20
-40
-40 -20
0 20 40
microAmp/meter
-50
0
0.1
0.2
electric vs seconds
0.1
0.2
H(phi) vs seconds
x 10-
x 106
I
N
1.5
N
S1.5
Q)
-C
CL
a)
a)
4-'
E
'a
0r
o 0.5
0.5
E
E
A
0
20
40
60
DFT of -I vs frequency (Hz)
40
60
20
freq(Hz); dist = 2.7Mm
Source Term vs Hz
X 10- 3
X 106
5
20
-10
t4
0
08
a3
-20
Co
6
-40
E2
o
>1
E
-60
C4
-80
E2
-100
0
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 2.4Mm
0
20
40
Source Term vs Hz
16:57:31.699 UTC, day =229
Bear = 2.0deg, Dist =12.3Mm
bearing = 1.144 degrees
6
_ 1
4
.
0)
it..
E2
0
·. ~::'·.~C.
r·..·.... · .·;
4.'
00
:
-5
-10
-4
-10
_Ri
0
0.1
0.2
H(phi) vs seconds
I
.··;
-5
-2
-10
· '·
microAmp/meter
0.1
0.2
0 electric vs seconds
0-
x 106
x 10-6
N)3
C
t:
N 40
64
cr
3
E
w2
Co
CO)
`2 2
So120
l10
ii 30
a1
E
0· ·
20
40
60
DFT of H vs frequency (Hz)
0
20
40
60
Source Term vs Hz
freq(Hz); dist = 3.2Mm
x 10800
x 106
N
I 700
II
D 600
I-
Ep500
400
0D
20
40
60
0
20
40
60
DFT of E vs frequency (IHz)
freq(Hz); dist = 12.7Mm
v
--
0
20
40
60
Source Term vs Hz
Bear =189.0deg, Dist =2.6Mm
04:50:21.782 UTC, day =232
bearing = 184.6 degrees
·
5
0
x.
-5
-5
-10
-1C)
0
-10
0.1
0.2
H(phi) vs seconds
0
x 10- 6
3
microAmp/meter
0.1
0.2
electric vs seconds
x 106
3
2
N2.5
,2.5
N
t1.5
2
C,)
u- 1.5
EI
I0O .
0
E
< 0.5
1
<E 0.5
0.5
A
-
0
20
40
60
DFT of H vs frequency (Hz)
0
--
20
40
--
60
0
freq(Hz); dist = 1.7Mm
x 10- 3
20
40
60
Source Term vs Hz
x 106
-300
2
a)
-c
1.5
N2
-340
-360
C,
a)
-320
1
-380
-400
S0.5
-420
-440
0
0
20
40
60
40
60
0
20
DFT of E vs frequency (Hz)
freq(Hz); dist = 2.4Mm
C,
a)
E 10.5
E
1
a0.5
E
<Q
0
20
40
60
Source Term vs Hz
01:58:31.899 UTC, day =227
Bear =100.0deg, Dist =6.2Mm
bearing = 112.2 degrees
20
a)
E
_
0
-10
-10
-ZU
A,,
E
-20
0
0.1
0.2
H(phi) vs seconds
0
-20
0
20
microAmp/meter
0.1
0.2
electric vs seconds
x 10-6
x 106
12
N
a6
8
E
(n 4
2
5E
U,
a)
E4.
"-2
<
0
E
E
<2
n
0
0
20
40
60
DFT of H vs frequency (Hz)
x 10
N
2
0
freq(Hz); dist = 6.1 Mm
3
12
2.5
20
40
60
Source Term vs Hz
x 106
- 10
a8
-C
C,
-E1
(6)
E
g4
0.5
E2
> 0.5
01
0
20
60
40
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 7.1Mm
20
40
Source Term vs Hz
06:03:22.064 UTC, day =228
Bear =285.0deg, Dist =1.4Mm
bearing = 295.7 degrees
40
'lii..........
S20
E
E
-5
... .
0
.. ..
0
0.1
0.2
H(phi) vs seconds
-20
4A0
-40
-40 -20
-10
- tv
O
0
0
20
microAmp/meter
0.1
0.2
electric vs seconds
40
X 106
x 10 - 6
4
N8
tý
C)
N
1
I-
g6
&3
(6
u)
CI)
a.
a
a2
00
U) 4E
-o
oO
E02
E 2
0
0
20
40
60
DFT of H vs frequency (Hz)
0
freq(Hz); dist = 1.2Mm
0
20
40
60
Source Term vs Hz
x 106
x 10- 3
220
2.5
200
2
U)
1.5
L 180
a
0160
o
>0.5
140
n
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 1.5Mm
20
40
60
Source Term vs Hz
05:47:52.166 UTC, day =225 Bear =194.0deg, Dist =19.7Mm
bearing = 170.6 degrees
·
5
EO
E -5
-5
0
5
microAmp/meter
-3
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10 - 6
x 106
8
-4
N
3
N
N
r( 2.5
I2
(I)
a,
C-
33
a)
al
E 20n
N
6
t:cr
-Cl
I-I
CL
u_4
2 1
E
02
E
1.5
03
0.
0
20
40
60
DFT of H vs frequency (Hz)
0
<0.5
0
20
40
60
freq(Hz); dist = 3.5Mrr 1
0
x 10-3
2.5
20
40
60
Source Term vs Hz
X 106
1000
S1 0
Cn
1.5
t
800
8
600
6
400
E
-4
S2
200
Cl
> 0.5
(1)
:1
0
20
60
40
DFT of EEvs frequency (Hz)
I
0
20
40
60
freq(Hz); dist = 5.5Mm
0
40
20
Source Term vs Hz
03:43:22.454 UTC, day =225
Bear =136.0deg, Dist =11.0Mm
1
I
bearing = 139.9 degrees
5
5
0
0
-5
-2
-5
-10
-10
-10
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10- s
10
x 107
1
4
N
N
S0.8
Z:
I
cr
c6
-2-0.6
4a>
U)
3
cr
0,
U)
U-
S04
U)
"-L2
U)
0.4
E
*0
0 1
E0.5
E0.2
0
A
0A
20
40
60
DFT of H vs frequency (Hz)
0
0OU
20
40
60
0
freq(Hz); dist = 10.8Mm
x 10- 3
20
40
Source Term vs Hz
x 10
750
2
I
-
0
microAmp/meter
N 700
650
1.5
a0
S600
E
a.
00.5
~500
550
450
n
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
freq(Hz); dist =9.4Mm
60
tjA I
0
40
20
60
Source Term vs Hz
Bear =165.0deg, Dist =4.1 Mm
03:33:32.856 UTC, day =236
bearing = 144 degrees
5
EO
So5
-5
-3
-5
0
5
microAmp/meter
-10
0
0.1
0.2
0
H(phi) vs seconds
0.1
0.2
electric vs seconds
x 106
• A
x 10
j
.- I
N
I)
3
C2
-2.5
N
a)
20
15
t
U-
a)
110
0,
E1
0
CE
2
E
E1;=1.5
E
5
<0.5
0
n
2
20
40
60
0
DFT of H vs frequency (Hz)
n
0
20
40
60
freq(Hz); dist = 3Mm
0
X10-3
20
40
Source Term vs Hz
X 106
1100
2
1000
V-C
1.5
1
o0.5
0
0
20
40
60
DFT of E vs frequency (Hz)
900
800
700
Ann
0l
0
20
40
60
freq(Hz); dist = 10.6Mm
0
20
40
60
Source Term vs Hz
07:20:43. 136 UTC, day =230
Bear =28.0deg, Dist =13.0Mm
8
bearing = 208.8 degrees
6
CD
. -2
CL
-b
cI
U-
-2
-6
0
0.1
0.2
H(phi) vs seconds
-5
0
5
microAmp/meter
0.1
0.2
electric vs seconds
0
x 10- 6
x 106
8
N16
t
U)
t
a
CD
a)4
E3
E
S2
C)
E
<1
0
0
20
40
60
DFT of H vs frequency (Hz)
0
freq(Hz); dist = 13.3Mm
20
40
60
Source Term vs Hz
x 106
0%A
x 10
2.5
C)
C
2
1.5
o
> 0.5
A
20
40
60
DFT of E vs frequency (Hz)
0
0
20
40
freq(Hz); dist = 1.8Mm
60
0
20
40
60
Source Term vs Hz
Bear =226.0deg, Dist =3.5Mm
04:34:13.172 UTC, day =239
bearing = 232.1 degrees
10
L-
aC
0
o
E -2
'
.4
-IU
-10
-10
-4
-15
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10- 6
0
10
microAmp/meter
x 106
4
N
-=4
N
M
4
3
U.L
E12
0)
EU
L.
0
2
E
E.
El
<z
O
<1
0
20
40
60
DFT of H vs frequency (Hz)
0
0
20
40
60
Xl0
20
40
60
Source Term vs Hz
x 106
x 10
N
0
freq(Hz); dist = 2.6Mm
2
-c
5U) 1.5
a,1
> 0.5
0
0
20
40
60
DFT of E vs frequency (Hz)
-50
0
20
40
freq(Hz); dist = 3.8Mm
60
0
20
40
Source Term vs Hz
60
Bear =231.0deg, Dist =3.1Mm
07:38: 3.298 UTC, day =266
bearing = 238.2 degrees
10
5
5
0
0
-5
-5
-10
-10
-10
0
0.2
0.1
H(phi) vs seconds
0
0.2
0.1
electric vs seconds
x 10-6
0
10
microAmp/meter
x 106
5
2
c4
-2-3
8
N
N
I:
;- 6
S1.5
Ii
CO
cn
Uo
-,
C)
e4
1
E
S0.5
0
E2
:ýE0.5
E
0
0
20
40
20
40
60
freq(Hz); dist = 5.6Mm
60
D)FT of H vs frequency (Hz)
x 10- 3
20
40
60
Source Term vs Hz
x 106
820
2.5
1
800
N
N
-
0
2
M 780
E6
0r
or 760
1.5
1
> 0.5
U,
740
4-
a 720
II
E
E
0)
< 700
680
0
60
0
20
40
DFT of E vs frequency (IHz)
'3
0
20
40
60
freq(Hz); dist = 5.3Mm
0
20
40
60
Source Term vs Hz
04:59: 3.344 UTC, day =225
Bear =74.0deg, Dist =0.6Mm
bearing = 82.46 degrees
20
-10
-20
-10
0
0
0.1
0.2
H(phi) vs seconds
-20
0.1
0.2
electric vs seconds
x 10- 5
0
20
microAmp/meter
x 107
5
N4
a)
V-
54
r 3
3
E2
E2
KWI
a)
C0
I
.
0
20
40
60
DFT of H vs frequency (Hz)
E
v
20
40
60
freq(Hz); dist = 6.8Mm
0
x 107
• A
x 10
0
3.5
20
40
60
Source Term vs Hz
5
S3
-50
- 2.5
c2
a)
4
-100
4--a
I
S1.5
Co
-150
0
0.5
-200
0
0
20
0
20
40
60
40
60
DFT of E vs frequency (Hz)
freq(Hz); dist = 6.5Mm
2
E
0
20
40
Source Term vs Hz
60
14:05:43.848 UTC, day =235 Bear =354.0deg, Dist =11.0Mm
bearing = 166.7 degrees
_I
_
_
·
20
0
E
x
E
0
~..
. -10
E
-10
°..
-20
-5
-20
-20
0
0
0.1
0.2
H(phi) vs seconds
x 10- 6
20
microAmp/meter
0.1
0.2
electric vs seconds
x 106
3
A-
N
N2.5
6
cI1 2
r 5
0)
tC
U4
U)
0)
1
L..
E
I
a)
0.5
a-
E
0.5
E
<1
0
0
20
40
60
DFT of H vs frequency (Hz)
__
3
40
60
0
20
freq(Hz); dist = 11.1Mm
Source Term vs Hz
x 106
dlf'•
x IU
650
N
( 10
N
I 600
C')
II
-1.5
cU
-- 550
(D
E 6
4
500
0
E2
>0.5
0
0
20
40
60
DFT of E vs frequency (Hz)
450
20
40
60
freq(Hz); dist = 11.1Mm
0
0
20
40
60
Source Term vs Hz
07:30:44.200 UTC, day =230
Bear = 4.0deg, Dist =9.8Mm
3
I
bearing = 186.3 degrees
8
6
E2
0
-5
E -2
-4
-2
0
0.1
0.2
H(phi) vs seconds
-5
0
5
microAmp/meter
0.1
0.2
electric vs seconds
x 105
x 10- 6
N
3.5
3
3
6=2.5
••2.5
U8
a,
E 1.5
E 1.5
C)
E
< 0.5
0.5
0
0
20
40
60
DFT of H vs frequency (Hz)
x 10- 3
0
freq(Hz); dist = 0.3Mm
-400
12
60
20
40
Source Term vs Hz
x 105
N
t10
N
-450
==8
Cl
L--
1.5
a, 1
E0.5
o60.5
-500
a,6
E
D4
-550
E2
-Ann
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 0.6Mm
20
40
60
Source Term vs Hz
04:09: 4.558 UTC , day =233
Bear =163.0deg, Dist =4.0Mm
bearing = 346 degrees
.- I
La>
EO
·· ,
,· r..·.
·..
x
E -10
-10
-10
0
0
0.1
0.2
H(phi) vs seconds
0
10
microAmp/meter
0.1
0.2
electric vs seconds
x 10- 6
x 10
1.5
6
N
I
a5
co
cr)
0crC:4
Q)3
a)
E
02
E
1
LL
aCL
- 0.5
0
<1
60
0
20
40
DFT of H vs frequency (Hz)
0O
20
40
Source Term vs Hz
20
40
60
freq(Hz); dist = 3.6Mm
x 10- 3
x
106
N
t8
N
-c
(1.5
E4
E
co
00.5
C-
n
20
40
60
DFT of E vs frequency (Hz)
0
E
2
tA
0
20
40
60
freq(Hz); dist = 3.3Mm
0
20
40
60
Source Term vs Hz
Bear =222.0deg, Dist =3.7Mm
00:00: 0.000 UTC, day =0
bearing = 229 degrees
5
0
-5
-10
-2
0
-10
0.2
0.1
H(phi) vs seconds
0.1
0.2
electric vs seconds
10
0
microAmp/meter
X 106
x 10- 6
3.5
3
'R4
N3
a)
2.5
2
9 2.5
-3
(0
it
cn
2
1..2
1.5
E
2
a.
1.5
E
I i
-0:0~ 1
CL
a
E
<0.5
0.5
A
20
40
60
DFT of H vs frequency (Hz)
0
20
40
0
60
freq(Hz); dist = 2Mm
x 10-3
20
40
60
Source Term vs Hz
x 106
400
L •
t
N380
N
at
1.5
9 360
04
a)
to
/ 340
0.5
E3
a)
0L 320
o 0.5
0A
0
20
40
60
DFT of E vs frequency (Hz)
02
300
280
0
20
40
60
freq(Hz); dist = 2.1Mm
20
40
Source Term vs Hz
Bear =281.0deg, Dist =3.3Mm
20:19:25.064 UTC, day =235
bearing = 238.7 degrees
10
10
5
5
0
0
-5
-5
-10
-10
-10
0
0.1
0.2
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
• A
0
10
microAmp/meter
x 106
x 10
7
N
N
I
C,)
6C,
II
2 4
Oq
CO
U- 2
0-
32
E
<1
0.'
0
20
40
60
DFT of H vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 4.2Mm
Source Term vs Hz
x 10- 3
x 106
6
N
t
N
. 2
0"
15
1.5
4
0)
o
0.5
E(1
0.
Ci
0
20
40
60
DFT of E vs frequency (Hz)
0
20
40
60
freq(Hz); dist = 6.1Mm
0
20
40
Source Term vs Hz
Bear =167.0deg, Dist =2.6Mm
17:53:15.348 UTC, day =227
bearing = 167.4 degrees
10
5
'
0
0
.*
·~····
-5
-in
-1Iu
-10
10
0
microAmp/meter
-4
-15
0
0.2
0.1
H(phi) vs seconds
0
0.1
0.2
electric vs seconds
x 10- 6
x 105
2
I--
N
t4
N
I
E32
h
a)
S1.5
a,
-
10
i,
3
a,
E2
a)
0-
E
cL4
E
20.5
0.
0
w
0
20
40
60
DFT of H vs frequency (Hz)
0
8
6
20
40
60
0
freq(Hz); dist = 0.8Mm
x 10-3
x 106
2.5
N
-z
20
40
60
Source Term vs Hz
-200
2
2
-300
-C
a)
CT
-400
E
D
>
a) 1.5
-500
a
U,
C0
0
n0.5
-600
> 0.5
1
-7nn
20
40
60
DFT of E vs frequency (Hz)
0
20
40
freq(Hz); dist = 7.1Mm
60
0
20
40
60
Source Term vs Hz
Bear =157.0deg, Dist =1.7Mm
6
17:21:25.352 UTC, day =230
4
10
bearing = 154.6 degrees
20
5
0
0
>0
-5
-10
-10
E -2
-15
-9n
-4
-20
0
-20
0
0.1
0.2
H(phi) vs seconds
20
microAmp/meter
0.1
0.2
electric vs seconds
• A
x 106
x 10
N5
N
a 1.5
a2
4
II
3
cn 1
go
CL
"0
60
2o 0.5
+0
El
E
40
60
0
20
freq(Hz); dist = 11.2Mm
20
40
60
0
DFT of H vs frequency (Hz)
Source Term vs Hz
x 10- 3
x 106
440
2.5
N
a 2
E-C
Cr
w 1.5
L..
N8
N420
b 400
g6
( 380
E4
a)
1
. 360
> 0.5
< 340
(0
0
0
20
40
60
DFT of E vs frequency (Hz)
E2
320
0
20
40
60
freq(Hz); dist = 1.7Mm
0
20
40
Source Term vs Hz
Bear =189.0deg, Dist =3.0Mm
17:27:35.608 UTC, day =232
bearing = 175 degrees
50
0
X
-50
-10
-50
0
0.1
0.2
H(phi) vs seconds
0
microAmp/meter
0.1
0.2
electric vs seconds
x 10- 5
8
1
N
x 106
2.5
N
2
10.8
-C
Co
Co
U)
1.5
S0.6
0•
"~0.4
E 0.2
4
E
1
Z0.5
20
40
60
DFT of H vs frequency (Hz)
0
20
40
60
0
freq(Hz); dist = 2.7Mm
x 10- 3
X 106
-8
20
N
t:
N
M
2.5
CD
o0 o
2
6
0)
4-,
L -10
E44
$2
E
0)
f-2
CL -20
0-)
0
<...
0.5
C0
0
20
40
60
Source Term vs Hz
--U
-4A
IIv
20
40
60
DFT of E vs frequency (Hz)
0
20
40
freq(Hz); dist = 2.1Mm
60
A
0
20
40
60
Source Term vs Hz
22:38:36.128 UTC, day =238 Bear =252.0deg, Dist =15.7Mm
bearing = 64.78 degrees
-2
-4
-%
0
0.1
0.2
H(phi) vs seconds
-10
0
0
10
microAmp/meter
0.1
0.2
electric vs seconds
x 10-5
x 107
,°
25
2
20
15
N
I
1.5
C',
L.
1
E
10 · · · ·
E 0.5
--
20
0
40
60
DFT of H vs frequency (Hz)
....
0
zc~ _
|
20
40
60
0
freq(Hz); dist = 7.1Mm
x 10-3
m
20
40
60
Source Term vs Hz
x107
5
N
C,
5
N
cD4
0
4
.0)
(,
0)
0
CD
0)
12
E
n
E
0-
20
40
60
DFT of E vs frequency (Hz)
0
•I
0
20
40
60
freq(Hz); dist = 12Mm I
0
20
40
60
Source Term vs Hz
Bear =243.0deg, Dist =3.1 Mm
8
05:06:46.590 UTC, day =236
20
bearing = 250.4 degrees
6
20
34
CD
CD
0,
a)
E
C,
E
E 0
0
0
20
-2
F -10
.o-10
-4
-20
-6
-20
0
-20
0.1
0.2
H(phi) vs seconds
0
20
microAmp/meter
0.1
0.2
electric vs seconds
x 106
x IU
3.5
S3
-C
S0.8
I--,
d6
Cr5
4
2.5
0"
a 0.6
N
U2
0.
3
1.5
01
CL
E 0.4
<a.
"2
E:
0.5
u0
I..
0
20
40
60
DFT of H vs frequency (Hz)
2.5
20
40
60
freq(Hz); dist = 2.4Mm
x 10- 3
X 106
400
N
2
V-
C 1.5
N
N
390
0
380
.C,
2
n 370
C,
04
360
E
0
L
> 0.5
0
20
40
Source Term vs Hz
0
20
40
60
DFT of E vs frequency (Hz)
6
350
ECU3
340
E
330
0
20
40
60
freq(Hz); dist = 2.3Mm
20
40
Source Term vs Hz
Bear =292.0deg, Dist =1.6Mm
06:36: 6.876 UTC, day =225
bearing = 297.7 degrees
10
50
5
0
0
-5
-10
-J
=50
-15
0
0
0.2
0.1
H(phi) vs seconds
-50
0
50
microAmp/meter
0.1
0.2
electric vs seconds
x 106
x 10- 5
0.8
N-2.5
N
-c
g 2
1.5
- 15
c.0.6
LL
C,
, 10
0. 4
E
0.
aE-
20.2
E 0.5
n
0
20
40
60
DFT of -Hvs frequency (Hz)
-
0
--
20
40
-x
60
--
0
20
40
Source Term vs Hz
freq(Hz); dist = 1.8Mm
x 10- 3
15
6
x 106
N
4
03
o3
E
co 2
E5
E
V)
loll
0
0
20
40
60
DFT of E vs frequency (Hz)
0
U
0
20
40
freq(Hz); dist = 2.4Mm
60
0
20
40
Source Term vs Hz
Bear =357.0deg, Dist =11.3Mm
05:09:36.938 UTC, day =233
bearing = 176 degrees
....
-5
E
-5
-10
-10
0
0.1
0.2
H(phi) vs seconds
0
microAmp/meter
0.1
0.2
electric vs seconds
x 10- 6
x 106
5
4
4
I
3g
ua-2
03
(0.2
1.5
(0
i 1i
Cn
a_0
E
L.
2
N
E
E 0.5
0
0
0>
0
20
40
20
40
60
freq(Hz); dist = 1.4Mm
60
DFT of H vs frequency (Hz)
0
x 106
x 10-3
2.5
2
20
40
60
Source Term vs Hz
800
N
co
3
750
a-
2.5
'1700
1.5
0
(I,
II
2
c) 650
U-
E1
- 600
0.
0
2 550
>0.5
f)
0
20
40
60
DFT of E vs frequency (Hz)
E 1.5
C'
0
E 0.5
500
450A
C
20
40
60
freq(H z): dist = 12.1Mm
-/I
C''-
0
20
40
60
Source Term vs Hz
Appendix E
(2000 Hz Sampled Events)
0
II
o
0
cn
N
CD
-4.
0
o
0
Arg PTPFS =9.13Hz
X
L
-- ,. · · ·
.i
r·
..
~-c··
;-·
~II
co
I
N
0
in 4•
C-r
N)
-o
o ",4
x
C,,
0(
0C.)
Cr,
cn
Co
N-0
Amp-meter/sqrt(hertz)
0
3
r
r
·-- ·
3
0
N)
r
r
)
oC
0
,·
·-
'
(D
C(
O0
f•
0
N)
C
O
~
'-
Mod PTPFS =8.9Hz
I'-
Amperes/meter/sqrt(hertz)
c
L.;
0
o
0
o
o
( .
'I....
-. C.•.
•
rV
o
N)
0
0
0
0
0
Volts/meter/sqrt(hertz)
N)
0
O01
0
0
0
microAmp/meter
10
0
milli-Volts/meter
-;r -----
0
micro-Amps/meter
---
N
I
C/
CD
--q
CD
'
r
':
r;
-
C::
~ i:
· · · ·h
ii
i.
''i·
4
'h
;cC'
·· .·
G
0
0
0
-
-
C0
-r..
00
0
----
Arg PTPFS =8.11Hz
.,·
.
0
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