Citation
Group velocity of lightning induced sferics

Material Information

Title:
Group velocity of lightning induced sferics a comparison between very low and extremely low frequencies
Uncontrolled:
Comparison between very low and extremely low frequencies
Creator:
Gillespie, Ryan J. ( author )
Language:
English
Physical Description:
1 electronic file (107 pages) : ;

Subjects

Subjects / Keywords:
Plasma (Ionized gases) ( lcsh )
Atmospherics ( lcsh )
Atmospherics ( fast )
Plasma (Ionized gases) ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Review:
Modeling and understanding of the plasma physics in the Earth's upper ionosphere has always been challenging for scientists. This is due mostly to the variability, complexity, and the inability to conduct direct measurements. The ionosphere is too far for weather balloons and too low for satellites to make direct measurements. Over the past 50 years, ground based stations have been used to obtain some information regarding the ionosphere.
Review:
The work done in this thesis adds onto previous work by placing two receivers side by side. One of the receivers records extremely low frequency (ELF: 3- 300 Hz) and the other records very low frequency (VLF: 3- 30 kHz). The receivers recorded data from July 19-21, 2016. The goal was to see if the group delay and time of arrival differed between the two receivers. This work also extended its analysis to compare differences between day and night with long and short distances.
Review:
The goal of this study was to use the time of arrival data to compute the group delay. These measurements could then be used to determine ionospheric height and conductivity.
Bibliography:
Includes bibliographical references.
System Details:
System requirements: Adobe Reader.
Statement of Responsibility:
by Ryan J. Gillespie.

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
on10131 ( NOTIS )
1013197142 ( OCLC )
on1013197142
Classification:
LD1193.E54 2017m G55 ( lcc )

Downloads

This item has the following downloads:


Full Text
GROUP VELOCITY OF LIGHTNING INDUCED SFERICS, A COMPARISON BETWEEN VERY LOW AND EXTREMELY LOW FREQUENCIES
by
RYAN J. GILLESPIE
B.S. University of Colorado Denver, 2015
A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Masters of Science Electrical Engineering Program
2017


This thesis for the Masters of Science degree by Ryan J. Gillespie has been approved for the
Department of Mathematical and Statistical Sciences
by
Mark Golkowski, Advisor Stephen Gedney, Chair Mark Golkowski Stephen Gedney Dan Connors
April 24, 2017
n


Gillespie, Ryan J. (M.S. Electrical Engineering)
Group Velocity of Lightning induced Sferics, A Comparison Between Very Low and Extremely Low Frequencies
Thesis directed by Assistant Professor Mark Golkowski
ABSTRACT
Modeling and understanding of the plasma physics in the Earths upper ionosphere has always been challenging for scientists. This is due mostly to the variability, complexity, and the inability to conduct direct measurements. The ionosphere is too far for weather balloons and too low for satellites to make direct measurements. Over the past 50 years, ground based stations have been used to obtain some information regarding the ionosphere.
The work done in this thesis adds onto previous work by placing two receivers side by side. One of the receivers records extremely low frequency (ELF: 3- 300 Hz) and the other records very low frequency (VLF: 3- 30 kHz). The receivers recorded data from July 19-21, 2016. The goal was to see if the group delay and time of arrival differed between the two receivers. This work also extended its analysis to compare differences between day and night with long and short distances.
The goal of this study was to use the time of arrival data to compute the group delay. These measurements could then be used to determine ionospheric height and conductivity.
m


The form and content of this abstract are approved. I recommend its publication.
Approved: Mark Golkowski
IV


DEDICATION
I dedicate this thesis to my friends and family who have helped me up through my education. I especially want to thank my loving wife who has helped me through long nights of studying for classes and tests. Without the support of her my education might have gone a different path. I would also like to specially thank my grandmother who pasted away March 28, 2017 and my parents who supported my decision to become an Electrical Engineer. Though the path was long and intensive, they were there every step of the process.


ACKNOWLEDGMENT
Id like to specially thank my adviser Mark Golkowski who got me involved in this research. This challenged me to think outside of the text book and really analyze real world problems which helped me become a better engineer.
vi


TABLE OF CONTENTS
Tables.................................................................... ix
Figures .................................................................. x
Chapter
1. Introduction............................................................... 1
1.1 Motivation.......................................................... 1
1.2 Scientific Background............................................... 1
1.2.1 Atmospheric Lightning ........................................ 1
1.2.2 Ionosphere ................................................... 3
1.2.3 Earth-Ionosphere Waveguide Model............................ 6
1.3 Comparison to Previous Work......................................... 8
1.4 Outline............................................................. 9
2. Slow Tail Propogation .................................................... 10
2.1 Sferics in Time Domain............................................. 10
2.2 Slow Tails ........................................................ 12
2.3 Earth-Ionpshpere As A PEC Waveguide............................... 15
2.4 Realistic Model Of Waveguide At ELF................................ 17
2.5 Chapter 2 Conclusion............................................... 19
3. Experimental Setup........................................................ 20
3.1 VLF Receivers...................................................... 20
3.1.1 VLF Hardware................................................. 24
3.2 ELF Receiver ...................................................... 31
3.2.1 ELF Hardware................................................. 31
3.3 Experimental Methodology........................................... 34
4. Data Results.............................................................. 38
4.1 Site Correction.................................................... 38
4.2 Recorded Data...................................................... 42
vii


5. Discussion
49
5.1 Analysis .......................................................... 49
5.2 Conclusion......................................................... 51
Appendix
A. Daytime Short Distances................................................. 52
B. Daytime Long Distances.................................................. 62
C. Nighttime Short Distances............................................... 72
D. Nighttime Long Distances................................................ 82
References............................................................... 92
viii


TABLES
Table
3.1 Possible antenna sizes and their properties [8]............ 27
3.2 ELF antenna parameters [9]................................................... 32
3.3 ELF receiver specifications for all six editions [9] 33
4.1 Table of site corrections based on distance, speed of light, and arrival time 41
4.2 Table of daytime short distances ............................................ 43
4.3 Statistics of group delay for daytime short distances for VLF corrected data 44
4.4 Statistics of group delay for daytime short distances for ELF corrected data 44
4.5 Table of daytime long distances.............................................. 45
4.6 Statistics of group delay for daytime long distances for VLF corrected data 45
4.7 Statistics of group delay for daytime long distances for ELF corrected data 45
4.8 Table of nighttime short distances........................................... 46
4.9 Statistics of group delay for nighttime short distances for VLF corrected
data......................................................................... 46
4.10 Statistics of group delay for nighttime short distances for ELF corrected
data......................................................................... 46
4.11 Table of nighttime long distances............................................ 47
4.12 Statistics of group delay for nighttime long distances for VLF corrected
data......................................................................... 47
4.13 Statistics of group delay for nighttime long distances for ELF corrected
data......................................................................... 47
4.14 Kolmogorov-Smirnov test for all four cases compared to one another . 48
IX


FIGURES
Figure
1.1 Fundamentals of lightning [3]............................................. 2
1.2 4th state of matter, plasma [4] 3
1.3 Ionospheric heights [5]................................................... 4
1.4 Dispersion relationship inside a plasma [6]............................... 6
1.5 Propogation modes in Earth ionosphere wave guide [1]...................... 7
2.1 Time domain of VLF sferic ............................................... 11
2.2 Time of arrival of VLF sferic ........................................... 12
2.3 Time domain of ELF sferic ............................................... 12
2.4 The upper plot shows an example sferic. The bottom is a low passed sferic
highlighting the ELF content and the slowtail [1] ..................... 13
2.5 Spectrogram of sferics highlighting group velocity near cutoff [2]....... 14
2.6 Group and phase velocity of a wave traveling through a medium [6] . 15
2.7 Wave speed for first mode in PEC waveguide .............................. 16
2.8 VLF data recorded on July 20, 2016 in Hugo. Red line indicates the arrival
time traveling at the speed of light................................... 17
2.9 Penetration heights of both electric and magentic fields [7]........ 18
3.1 VLF antenna located in Akhiok Alaska..................................... 21
3.2 VLF antenna at Paxson. The author and Brad Fox can be seen servicing
the system............................................................. 22
3.3 VLF antenna at Warsaw. CU Denver students Hamid Chorsi, Ashanthi
Maxworth, Ryan Jacobs are shown from left to right. Spring 2014 ... 23
3.4 All five of the UCD VLF receiver network................................. 23
3.5 Simple outline of Nemesis receiver ...................................... 24
3.6 Radiation pattern of small magnetic dipole............................... 25
3.7 Equivalent circuit model for small magnetic dipole in receiving mode [8] 26
x


3.8 Inside the pre-amp box of Nemesis system.............................. 27
3.9 Frequency and group delay of VLF receiver [8]......................... 28
3.10 Stanford receiver system. Antenna structure (upper left), pre-amplifier
(upper middle), receiver (upper right), and block diagram (bottom). . 29
3.11 VLF system used in this experiment calibration........................ 30
3.12 Map of ELF receivers [9]................................................ 31
3.13 Inside of ELF container................................................. 33
3.14 Antenna and pre-amp setup in Hugo on July 19th, 2016................... 35
3.15 Block Diagram of experiment setup....................................... 36
3.16 Computer, monitor, GPS module, GPS antenna configuration................ 36
4.1 Location of sferic in proximity to ELF station.......................... 39
4.2 Time domain of the ELF receiver looking at N/S and E/W channels . 40
4.3 Distribution of group delay through ELF receiver........................ 42
4.4 Time domain of the ELF and VLF data.................................. 43
4.5 Histogram of group velocities.......................................... 48
5.1 Time domain of two sferics at equal distances, one at night and during
the day [1]............................................................. 50
A.l ........................................................................ 52
A.2 ...................................................................... 52
A.3 ...................................................................... 53
A.4 ...................................................................... 53
A.5 ...................................................................... 54
A.6 ...................................................................... 54
A.7 ...................................................................... 55
A.8 ...................................................................... 55
A.9 ...................................................................... 56
A.10 ...................................................................... 56
xi


A.11 57
A.12 57
A.13 58
A.14 58
A.15 59
A.16 59
A.17 60
A.18 60
A.19 61
A. 20 61
B. l ..................................................................... 62
B.2 62
B.3 63
B.4 63
B.5 64
B.6 64
B.7 65
B.8 65
B.9 66
B.10 66
B.ll ...................................................................... 67
B.12 67
B.13 68
B.14 68
B.15 69
B.16 69
B.17 70
xii


B.18
70
B.19 71
B. 20 71
C. l ..................................................................... 72
C.2 72
C.3 73
C.4 73
C.5 74
C.6 74
C.7 75
C.8 75
C.9 76
C.10 76
C.ll ...................................................................... 77
C.12 77
C.13 78
C.14 78
C.15 79
C.16 79
C.17 80
C.18 80
C.19 81
C. 20 81
D. l ..................................................................... 82
D.2 82
D.3 83
D.4 83
xiii


D.5 84
D.6 84
D.7 85
D.8 85
D.9 86
D.10 86
D.ll ................................................................... 87
D.12 87
D.13 88
D.14 88
D.15 89
D.16 89
D.17 90
D.18 90
D.19 91
D.20 91
xiv


CHAPTER 1
INTRODUCTION
1.1 Motivation
This thesis explores how extremely low frequency (ELF: 3-300 Hz) and very low frequency (VLF: 3-30 kHz) electromagnetic waves propagate in the Earth-ionosphere wave guide. Two types of receivers measure the two different frequency bands. These signals are generated from lightning discharges. The arrival time of these lightning induced waves along with information of their source location from lightning detection networks allows for the estimation of group velocity in the Earth-ionosphere wave guide and its frequency dependence. This work involves a comparison of recorded data to theoretical plasma physics as well as assessment of the hardware used in the receivers.
1.2 Scientific Background
1.2.1 Atmospheric Lightning
Meaningful comparison of group delays between VLF and ELF waves generated by lightning requires understanding the source of both waves. Atmospheric lighting is a common meteorological event which is caused by an accumulation of electric charge that occurs between the ground and clouds. A discharge occurs when the electric potential reaches a point in which the electric breakdown of air is exceeded. This causes a path to develop for current to flow from the cloud to the ground. The result is often visible and can carry a significant amount of current on the order of tens to hundreds of kA. Figure 1.1 illustrates this phenomena.
1


How lightning develops
positive charges
-tp\
nt-^ + i
positive charges
2013 Encyclopaedia Britannica, Inc.
Figure 1.1: Fundamentals of lightning |3|
There are three main types of lightning discharges: cloud to cloud, cloud to ground, and ground to cloud. The discharges of interest consist of cloud to ground interactions since they radiate the most energy and thus produce the largest amplitude electromagnetic signals. Figure 1.1 depicts the more common cloud to ground discharge in which negative charge is transferred from the cloud to the ground. This type of discharge is called a negative cloud to ground (-CG) discharge and is more common than the opposite polarity (CG) since the cloud is typically polarized with negative charge closer to the ground and positive charge at higher altitude. Positive cloud to ground discharges occur less frequently, but can often have a larger peak current. Both -CG and CG events generate broadband electromagnetic waves with significant content in the ELF and VLF bands. Sometimes, CG events radiate more ELF content because the process is longer in time. Details on this are presented in Chapter 2.
Chapter 1.2.2 presents further discussion of what frequencies that are trapped in the Earth ionosphere waveguide and which frequencies propagate out into outer space. For now, it is sufficient to say that the ELF and VLF portion of the electromagnetic wave can travel great lengths along the surface of the Earth (sometimes around the
2


Earth). This is important in the studios of the ionosphere because how those wave propagate can provide information about the physic's of the ionospheric.1 plasma.
1.2.2 Ionosphere
The ionosphere forms part of the upper atmosphere and gets its name from the word ion. An ion is defined as "an electrically charged atom or group of atoms formed by the loss or gain of one or more electrons, as a cation (positive ion) which is created by electron loss and is attracted to the cathode in electrolysis, or as an anion (negative ion) which is created by an electron gain and is attracted to the anode" |4|. The ionosphere is made of electrons and ions, which together form what is known as a plasma.
Plasma can be thought of as the fourth state of matter. Figure 1.2 illustrates the fundamentals of what a plasma is and how it differs from the more common states of matter.
Figure 1.2: 4th state of matter, plasma |4|
As seen in Figure 1.2 the plasma state is achieved from the gas state after enough energy has been introduced so that electrons are no longer bound to the nucleus. This is because the electrons have enough kinetic: energy that they are no longer trapped in the potential energy created by the nucleus. To understand the source of this additional electron energy in the ionosphere, it is important to mention the larger context of the upper atmosphere as shown in Figure 1.3
3


Figure 1.3: Ionospheric heights |5|
The ionosphere is the region in between the gas rich environment that life resides in and the much emptier region of space around the planet. The ionosphere is the region where cosmic radiation from space and solar radiation from the sun interact with the gasses here on Earth. These two types of radiation are the source of the plasma that forms the ionosphere.
The main driver is the sun. Ultraviolet radiation from the sun is absorbed by the atmosphere whose density increases as one gets closer to the surface of the Earth. The increasing neutral gas density causes a peak in the density of free electrons (plasma state) to occur at around 350 km altitude in what is known as the F- region of the ionosphere. The photoionization process causes significant ionization all the way down to the D-region (60 90 km).
At night, the sun cannot excite any of the gas and therefore the amount of ionizing energy drops significantly. However, there are other sources from outer space that still have the potential of maintaining a plasma state. The main effect of nighttime radiation is that the D-region no longer resides around 60 km from the surface of the Earth. The D-region is restricted to higher elevations near 90 km.
In this work, the effective height of the ionosphere will be mentioned and calcu-
4


lated. This is in reference to the height of the D-region since it is the lowest region and the altitude at which ELF/VLF waves reflect as discussed in Chapter 1.2.3.
Plasma has a special property that allows electromagnetic waves to travel in the Earth-ionosphere wave guide. This is because plasma acts as a conductor or an insulator at different frequencies. To better understand, lets first explore what makes a plasma conductive. An important metric in plasma electrodynamic behavior is the plasma frequency which is defined as
COpe
Nee2
me0
(1.1)
Where Ne is defined as the electron density, e is charge of an electron, m is effective electron mass, and e0 is the permittivity of free space. If an electromagnetic wave has a lower angular frequency than the plasma frequency, the plasma can adapt quick enough to accommodate the changes in amplitude and thus acts like a conductor which can reflect an incident wave. At higher angular frequencies, the plasma cannot react fast enough to the changing fields and thus higher frequencies propagate through the plasma. To visualize this effect, Figure 1.4 which shows the relationship between ujp and k which is defined as the wave number.
5


(l)
Figure 1.4: Dispersion relationship inside a plasma |6|
In Chapter 2 it will be shown that the slope of the dispersion curve provides the group velocity of the wave. For this thesis, this will be a measurable quantity in the VLF and ELF data.
1.2.3 Earth-Ionosphere Waveguide Model
Xow that the ionosphere has been shown to act as a good conductor for ELF and VLF waves, lets examine what makes the Earth a good conductor. Refer to 1.2
7 = o-j/3 (1.2)
Where 7 is referred to as the propagation constant while a is defined as the attenuation constant, and /5 is defined as the phase constant. Xow lets define what Q' and /5 equal for a good conductor in equation 1.3 and E4
6


a ~
ufiocr
(1.3)
/5 ~
ujhqct
(1,4)
Where a is defined as the conductivity of the medium, uj is that the angular frequency, and q0 is the permeability of free space. For VLF and ELF electromagnetic waves the angular frequency is small. For wet soil, the conductivity is roughly 10-2. The result is the attenuation losses and phase constants are relatively small. For a perfect conductor, a = oo and j3 = oo because a = oo. Therefore, it is safe to say that the Earth at low frequencies acts as a good conductor.
We can simplify the Earth-ionosphere waveguide by modeling it as a parallel plate waveguide. In this model, a wave can travel in three different types of modes, TEM or TM0, TEm, and TMm. To explain what these modes mean its useful to visualize as in Figure 1.5.
z =
z =
Earth
Figure 1.5: Propogation modes in Earth ionosphere wave guide |1|
The T in the modes stands for transverse which means that certain field components will be fully perpendicular to the direction of propagation. The E and M refer to electric and magnetic field, respectively. Since lightning discharges, otherwise known as sferics, occur vertically between the so called "plate," the majority of
7


discharges propagate in the TM and TEM modes.
The effective height of the D-region determines the height of the wave guide. This height can be used to calculate in which modes the wave can travel in. This can be defined using the cutoff frequency which can be equated to,
77171 /i r \
OJ > 0JC = ----- (1.5)
Where we define a to be the height of the wave guide and m as the mode number. The higher the mode number the less the wave guide will support lower frequencies. For ELF and VLF waves, multimode propagation can be supported to about 10 modes.
1.3 Comparison to Previous Work
In previous works like that by Mackay [1] VLF and ELF observations of lightning induced waves were compared. The data used in Mackays analysis was taken from a single station in Antarctica. The location of this receiver will be further examined in Chapter 2, but for now its sufficient to say the data has very little noise. With the low noise environment, Mackay could low pass filter the data to isolate ELF content.
The motivation for this thesis came from conducting a different experiment than
was done by Mackay. Mackay was interested in using single station observations as
a method of global lightning geolocation. Here we investigate the inverse problem
in that we use lightning location data from the GLD360 network and compare the
observed propagation velocity to ionospheric conditions. In this experiment, two
different receivers will be used. As stated before, a VLF and an ELF station will be
deployed next to one another. This is done for a few reasons. First, the ELF receiver
is specifically designed to record ELF data. This is important because the traditional
wire loop antennas and hardware related configurations used in the VLF systems have
poor performance in the ELF range. Using the ferrite magnetic antennas, the quality
8


of the ELF data is increased. Secondly, the path of propagation will be the same for the two receivers. This allows a one to one comparison on the group delay since they will be traveling on the same path.
1.4 Outline
Chapter 2 will give some background on how the ionosphere affects sferic propagation. In Chapter 3, a discussion about the experimental work that recorded the data for both ELF and VLF receivers. This will include a brief summary of the equipment, location, and process of how the data was obtained. Chapter 4 is dedicated to presenting the recorded data. This includes 10 cases of daytime short distances, 10 cases for daytime long distances, 10 nighttime short distances and finally 10 nighttime long distances. In the last chapter, the recorded data will be compared to the theory presented in Chapters 1 and 2. Statistical tests are used to quantitatively compare and contrast all four cases.
9


CHAPTER 2
SLOW TAIL PROPOGATION
In this chapter, analysis of VLF and ELF waves in the Earth-ionosphere waveguide will be presented. This will include an in depth look at a sferic in the time domain in Chapter 2.1. In Chapter 2.2, the sferics will be broken down into their respective VLF and ELF content, and it will be shown how the time of arrival for ELF electromagnetic waves often lags that of the VLF portion. Lastly Chapter 2.3, will present equations derived from other works that can compute characteristics of the ionosphere using the time of arrival and group delay.
2.1 Sferics in Time Domain
There are often two ways to look at a signal: in the time domain and in the frequency domain. For the purposes of this thesis, the time domain will be used exclusively. This is because the purpose of this work is to determine the arrival time and group delay of the sferics. While spectrograms (frequency domain with time information) can be used as well, the sferics often can last up to a couple of milliseconds. Determining the time of arrival on a spectrogram, while not impossible, tends to be limited by the length of window in the short-term Fourier transform and is therefore inaccurate.
A typical sferic waveform is shown in Figure 2.1. The VLF receiver was designed to record up to 50 kHz signals. The data is sampled at 100 kHz. This gives rise to detailed waveforms and thus detecting time of arrival is considered to be more accurate than ELF signals which will be discussed later on in this section.
10


Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 2.623635e+03 kM
Figure 2.1: Time domain of VLF sferie
The figure presented in 2.1 plots an averaged amplitude over a period of time (in this ease 3 ms). The reason the amplitude is averaged is so that the positive and negative values can be represented. We can see that the sferie spans a time of about 0.5 ms. That being said, there is a lot of activity that can be seen at the beginning of the signal and then attenuates near the end.
The waveform of these signals depicts how these signals propagate. Each peak that represents different reflections off the Earth ionosphere wave guide. The first peak in this figure is the wave that has little or no reflections off the wave guide and is known as the ground wave. Hence, it is the fastest traveling part of the wave. The following peak is the part of the wave that may have bounced off the wave guide a couple of times and therefore arrives later. This continues until all of the wave has arrived at the recorded station. For such a complicated waveform it is important to define a time of arrival. Here it is defined by the first sharp peak. In figure 2.2 the time of arrival is defined at 9.53 ms. This will be the metric as to when all VLF signals time of arrival occurred.
11


Figure 2.2: Time of arrival of VLF sferie
Now lets look at what the ELF data looks like in the time domain. The recorded ELF data is coarser in nature due to its low sampling frequency which is about 800 Hz. Compared to the VLF sampling frequency, the time of arrival is harder to resolve. This will be explained further in Chapter 3. However, in Figure 2.3 the time of arrival can still be determined by picking the first peak of the waveform. Figure 2.2 and 2.3 are recordings of the same sferie. Time of arrival was calculated for 2.2 as being 9.53 ms, but in 2.3 this is found to be 14.64 ms. This is not compensating for any hardware corrections that will need to be done which will be discussed in Chapter 3 in detail.
2.2 Slow Tails
In this chapter, the waveform of a sferie will be characterized into its VLF and ELF content. The figures presented here come from the work by Maekay |1| and Mark Golkowskis course lecture notes |2| which highlight what portion of the waveform is characterized as the slow tail. This is best summarized in Figure 2.4, which shows a sferie VLF and ELF content.
12


Example Sferic
Time [ms]
Figure 2.4: The upper plot shows an example sferic. The bottom is a low passed sferic highlighting the ELF content and the slowtail |1|
The slowtail can be seen as the ELF content of the waveform that is delayed in time from the initial VLF content.
The bottom panel of Figure 2.4 was created by applying a low pass filter to the data in the top panel. In Chapter 1.2.3 the Earth ionosphere wave guide was defined, and it was stated that it can be approximated as a parallel plate waveguide. This can also be shown using a spectrogram which combines frequency and time domain as illustrated in 2.5
13


Seconds after 06:00:00 UT
Figure 2.5: Spectrogram of sferies highlighting group velocity near cutoff |2|
The red and yellow in 2.5 represent the magnitude of the sferies that are represented by the vertical lines. From 2.5 we can see that around 1.8 kHz the sferic is no longer vertical. This indicates that the waveform is being slowed down. For the lowest TE1 and TM1 modes this occurs around 1.8 kHz.
Up to this point, effects of the plasma on the sferic have been negated. It has been shown that in an ideal parallel wave guide that the group velocity decreases near the cutoff frequency. This assumes the boundaries are perfectly conducting materials and therefore the sferic sharply reflects off the ionosphere. In reality, this is not the ease. Rather at lower frequencies, the sferics waveform travels deeper into the plasma causing greater dispersion which in turn causes a decrease in group velocity. In Chapter 1.2.2 the dispersion relationship of a plasma was presented. This is shown in Figure 1.4. Here, it was shown that the slop of the line was related to the group velocity of the wave propagating through the plasma. At lower frequencies above the plasma frequency, the slope is shown to be less than that of higher frequencies. This
14


effect can also be seen in 2.6.
velocity
Figure 2.6: Group and phase velocity of a wave traveling through a medium |6|
2.3 Earth-Ionpshpere As A PEC Waveguide
For VLF waves, the bounds of the Earth-Ionosphere waveguide can be thought of as a perfectly electric conductor (PEC). Reviewing waveguide theory examine Equation 2.1 which defines what the cut off frequency is.
Fr
me
2h
(2,1)
Here, c is the speed of light, m is mode number, and h is the vertical height of the wave guide. For the daytime ionosphere height, we can assume the D-region resides at 70 km. The cut off frequency for the first mode using these values computes to
2.14 kHz.
The wave speed can then computed by using Equation 2.2. As the frequency increases, the wave speed increases until it reaches the speed of light. This is shown in Figure 2.3
(2,2)
15


x 106 Wave speed of first mode in waveguide
Figure 2.7: Wave speed for first mode in PEC waveguide
The way scientists have validated that the ionosphere acts like a PEC is through measurements of ground based stations. If the ionosphere was a PEC for VLF sferies, then the waves would be sharply reflected. This would then validate Equations 2.1 and 2.2 because those are the models for a PEC parallel plate waveguide. This can be seen in data recorded in this thesis on July 20th in Hugo.
16


10 15 20
Time ( mil seconds) after 19:47:03.061 UT
20 19 47 3 021 12.002901 -97.09781 -231 12 2.405807 1.37057.
Figure 2.8: VLF data recorded on July 20, 2016 in Hugo. Red line indicates the arrival time traveling at the speed of light
The beginning of the time plot indicates when the GLD network detected the sferic. The vertical red line takes the distance from the sferic and receiver and divides by the speed of light. This gives the time of arrival. What is shown is that the waveform lines up exactly with the theoretical time of arrival if it were traveling at the speed of light. Ultimately, this proves the Earth-Ionosphere wave guide can be thought of as a PEC parallel plate for VLF sferies.
2.4 Realistic Model Of Waveguide At ELF
ELF sferies propagate differently in the Earth-Ionosphere waveguide. This is because the interactions with the plasma cannot be represented with the PEC model. As stated in Chapter 2.2, there are plasma effects that alter the height of the wave guide. This is frequencydependent and can be seen in Figure 2.9. From this, it is notable that lower frequencies from the top plot, the magnetic held goes propagates deeper into the plasma. This in turn causes the bottom plot which shows how the group velocity slows down compared that of the higher frequencies.
17


120
. -hE
Vl

40 10 20 30 40 50
Figure 2.9: Penetration heights of both electric and magentic fields |7|
This is shown mathematically by defining the boundaries. There are the conduction boundary which acts on the electric held height he and the diffusion boundary which governs hm. These two boundaries are defined by the height dependent conductivity within the plasma. a(z) represents this quantity which can be explained by Equation 2.3.
a = t0uj (2.3)
U 4qoe (2.4)
1 da (2.5)
^ a dz
Let us now explore how this affects the arrival time of the sferic. In Maekay |1| the time of arrival is a function of propagation distance p. reflection height h, conductivity a which was defined in 2.3, and pulse width (in seconds) denoted as b. Together, these form Equation 2.6.
ts =
(2,6)
2
18


2.5 Chapter 2 Conclusion
In this chapter, the propagation of slowtails was examined. Chapter 2.1 highlighted time domain information which defined the arrival time for both VLF and ELF waves. This will be important in further chapters because the statistical modeling will investigate these arrival times. In Chapter 2.2, slowtails were isolated by their frequency content. VLF waves account for the portion of the sferic that arrives the quickest. The ELF content of the wave doesnt arrive until later in time. This was explained by looking at what happens near the cutoff frequency in the lower modes. It was found that this gives rise to what defines a slowtail. In Chapter 2.3, the Earth-ionosphere waveguide was modeled as a PEC parallel plate wavegiuide, which is a reasonable first order approximation for VLF wave propagation. Lastly, Chapter 2.4 examined how ELF sferics propagate in the Earth-ionosphere waveguide. It was shown that these waves travel further into the plasma. This results in using alternative equations to determine time of arrival as shown by Mackay [1].
19


CHAPTER 3
EXPERIMENTAL SETUP
This chapter highlights the authors contribution to the study of slowtails. In Chapter 3.1, the Electromagnetics and Plasma Physics Research Groups VLF receiver sites will be presented. Chapter 3.1.1 will explain the VLF receivers hardware. This will include calibrations, setup, and the network of receivers the University of Colorado Denver (UCD) Electromagnetics and Plasma Physics Research Group currently operates. Chapter 3.2 will discuss the ELF receiver used. This will include the design of the Krakow ELF group from Poland which is hosted by UCD. Chapter 3.3 will then cover how the experiment was designed and executed.
3.1 VLF Receivers
The Electromagnetics and Plasma Physics Research Group has five VLF receivers. One of the sites resides on a small island south of Kodiak Island named Akhiok in Alaska. Akhiok is a small village of Alaskan natives whose population is less than 100. The receiver is setup inside the school house which houses about 20 students ranging from kindergarten to high school. We were able to obtain this location by coordinating a series of outreach programs designed to get students interested in science and math. So far, these interactive programs have involved educating students on the fundamentals of static electrical charges using Van de Graff generators. Our efforts also lead students to learn basic programming and digital hardware implementations using Arduino micro-controllers. The VLF antenna at this site can be seen in Figure 3.1. This site was deployed in 2013 by the author and undergraduate research assistant Brad Fox.
20


Figure 3.1: VLF antenna located in Akhiok Alaska
North of that location in Alaska resides the groups Paxson site near the High Frequency Active Auroral Research Program (HAARP) facility in Gakona, Alaska. The Paxson site was originally operated and maintained by the Stanford VLF research group. In 2014, LXlDs Electromagnetics and Plasma Physics Research Group flew out there and brought the receiver back online and has maintained it since. This site can be seen in Figure 3.2
21


Figure 3.2: VLF antenna at Paxson. The author and Brad Fox can be seen servicing the system.
Moving to the Eastern United States, the group hosts a VLF receiver on the roof of the North Classroom building located on the Auraria campus home to the Electrical Engineering department. This site was established mainly for hardware testing of existing and future systems. While the data is often noisy due to the power consumption of the building itself and being in the heart of downtown Denver it still processes valuable information the group can use in their study of the ionosphere.
On the East coast, the group has a VLF receiver near Warsaw, Virginia. This was the groups second receiver to make up their VLF network. The site is located on a technical high school facility called Rappahannock Community College. Like Akhiok, outreach programs have been implemented to get students involved with science and math. Ashanthi Maxworth, one of the groups PhD students has worked with the students to record mosquito mating calls to generate spectrograms which help students locate and better understand biology. The school is heavily involved in biology studies so the programs are tailored to their curriculum. This site can be seen in Figure 3.3.
22


Figure 3.3: VLF antenna at Warsaw. CU Denver students Hamid Chorsi. Ashanthi
Maxworth, Ryan Jacobs are shown from left to right. Spring 2014
The groups first receiver was deployed in Ithaca, Xew York in a remote location on private property. This site provides valuable data because the site is not near major power lines and other electromagnetic sources of noise. Since this site is so remote, internet connection is slow and impossible to transfer data over the network. Because of this, the only way to transfer data between the site and the groups servers is hard drive exchanges via the postal service.
These five sites mark the Electromagnetics and Plasma Physics Research Group at UCD VLF network. A complete map of these locations can be found in Figure 3.12.
Wffi ... f
f 1
~ h.1 ..
Figure 3.4: All five of the UCD VLF receiver network
23


3.1.1 VLF Hardware
The receiver system is based on a legacy design out of Stanford University (.'ailed Atmospheric.' Weather Electromagnetic System for Observation, Modeling, and Education or AWESOME system |10|. The specific design used by the UCD group was obtained from the University of Florida and is referred to as the Nemesis. This system was designed to record frequencies 300 Hz-48 kHz. This system includes a desktop computer with a National Instruments DAQ PCI card. The computer is connected to the receiver and GPS module. The GPS sources the sampling frequency that is synched with a time synchronized lpps waveform. This allows all receivers to be synchronized in timing when recording data. The receiver is then attached to the pre-amp box which then in turn is connected to two wired loop antennas. A basic.' overview can be seen in Figure 3.5.
Antenna
GPS
Figure 3.5: Simple outline of Nemesis receiver
To begin, let us first look at the antennas. The receiver consists of two orthogonal
wired loop antennas. Since the wavelength of the frequencies recorded by this receiver
24


arc so largo compared to the size of the antennas, they can be considered as electrically small magnetic dipoles. FEKO software was used to show what the radiation pattern looks like for a small magnetic dipolo. This is shown in Figure 3.6. The antenna is sensitive to horizontal magnetic holds and has a directivity in the piano of the loop.
Figure 3.6: Radiation pattern of small magnetic dipolo
The simulated antenna was the smallest antenna size used for the Nemesis which is a 12 turn wired loop antenna. The antenna can be simplified into a circuit model in the receiving mode like in Figure 3.7
25


R* U
Figure 3.7: Equivalent circuit model for small magnetic dipole in receiving mode |8|
Mathematically the input impedance can be shown to be Zin = Ra + jXin = (Rr + Ri) + j(Xa + Xi) in which Rr is denoted as the radiation resistance, Rj is the ohmic resistance, Xa is the external inductance and finally Xi is the high frequency inductance.
It is important to note that the antennas can be constructed in different sizes. Larger antennas typically yield an improved signal to noise ratio so when possible, the larger sizes are used. A breakdown of the different sizes with their antenna characteristics can be shown in Table 3.2. The antenna used in this thesis was the right isosceles triangle with an area of 1.695 m2 in Table 3.2.
26


Table 3.1: Possible antenna sizes and their properties |8|
Shape Size, side or Ease Wire AWG N Ra Q La mHy fa Hz A m2 So V Hz^m"1 M kg
square 16.0 cm 20 47 1.002 0.998 159.8 0.02563 5.03x 10"3 0.132
56.7 cm 18 21 1.006 0.994 160.9 0.3219 8.96x10-* 0.331
1.70 m 16 11 0.987 1.013 155.0 2.892 1.89x10-* 0.831
4.90 m 14 6 0.972 1.029 150.5 24.05 4.13xl0-5 2.09
right 2.60 m 16 12 0.994 1.005 157.5 1.695 2.97x10-* 0.838
isosceles 8.39 m 14 6 1.004 0.996 160.3 17.59 5.74x10"* 2.15
triangle 27.3 m 12 3 1.035 0.967 170.3 187.0 1.10x10"* 5.56
60.7 m 10 2 0.959 1.043 146.3 920.9 3.22x10"* 13.1
202 m 8 1 1.005 0.995 160.9 10164 5.97 xl07 34.5
The antennas connect to the X/S and E/W channel of the pre-amp box. The preamp box design consists of the daughter board, line-matching transformers, and preamp cards. The inside of the pre-amp box is shown in Figure 3.14. Each channel has a pre-amp card to amplify the signal. The pre-amp cards have a gain of approximately 10 dB. The signal is sent in differential form in order to reduce noise coupling when the signal is sent to the receiver. The signal is sent through a 1000 foot 14 pin cable that is normally fed through a building to the receiver. The cable is often as long as possible in order to place the antennas as far away from noise sources.
Figure 3.8: Inside the pre-amp box of Nemesis system
27


Once the signal enters the receiver, it then travels through the filter cards. This acts as an anti-aliasing filter restricting the bandwidth before the analog to digital converter so that the Xyquist theorem can be satisfied. The filter cards have a 12th order elliptical filter that has a -3 dB roll off at 47 kHz. The frequency response and group delay of the Nemesis can be shown in Figure 3.9.
Frequency (Hz)
Figure 3.9: Frequency and group delay of VLF receiver |8|
The receiver also takes in a series of timed pulses used for synchronizing of time and sampling. The signals are fed in from the programmable GPS module. The GPS module outputs a 1 pps and a 100 kHz pps. The 1 pps syncs the GPS time for accurate timing. The 100 kHz pps synchronizes the sampling frequency at the XI DAQ card. The receiver has a series of optional op-amps to provide an extra 30 dB gain to the signals.
Finally the signals are combined and sent to the computer via National Instruments cable that feeds into the DAQ card. A RS-232 serial cable also feeds into the computer from the GPS module to send in the UTC time which is used as a header within the .mat hies. The recording software from University of Florida allows configuration of the recordings. This includes narrowband configuration to tune into Navy transmitters and continuous/synoptic recording settings.
In 2015, the Stanford VLF Group officially disbanded their research. In the fall of 2016, the author had the opportunity to fly out to Stanford University and retrieve
28


old equipment. It was here that the group began implementing a hybrid system. The Stanford receivers were similar to the Nemesis system, but had several changes in order to get better performance in frequency response and noise reduction. The Stanford receivers are shown in Figure 3.10.
B-Field
Antenna
Preamplifier
Long Cable
Line Receiver
GPS
Antenna
Computer
Analog to Digital Conversion
Figure 3.10: Stanford receiver system. Antenna structure (upper left), pre-amplifier (upper middle), receiver (upper right), and block diagram (bottom).
The major system difference between the Nemesis and Stanford receiver was the use of an internal GPS module. In Stanfords receivers, a FPGA and crystal oscillator were used to generate the 1 pps and 100 kHz pps signals. While this made the receivers more compact and cheaper to produce, the leading issue was the timing synchronization with the GPS. Since the receiver used the crystal oscillator, it was susceptible to temperature variations. This would cause drifts in timing. Since the purpose of this work was to obtain very accurate timing data acquisition to determine time of arrival of the sferics, a hybrid system was devised.
The hybrid system would use the pre-amplifier of the Stanford system and the
29


receiver. GPS module, and software of the Nemesis system. This allowed for low noise response and precise timing of data. The hybrid system was used for the observations presented in this thesis.
Before the system could be used, a calibration needed to be done to ensure accurate data was being recorded in post-processing. To conduct the calibration, MAT-LAB was used to interface with a signal generator. The signal generator was fed into the pre-amp box via a BXC connected to a dummy loop. The dummy loop was designed to use a voltage divider to divide the signals amplitude down to levels normally seen by the receiver. The dummy loop also imitated the impedance of the antenna by using inductors and capacitors. The calibration code would then frequency and amplitude sweep signals that were being recorded by the software at the same time. This allowed the frequency response to be determined and therefore allow correction factors to be implemented. The calibration used in this experiment can be shown in Figure 3.11
,e Frequency spectrum N/S
Figure 3.11: VLF system used in this experiment calibration
30


3.2 ELF Receiver
The ELF receiver used in this experiment came from the Krakow ELF group in Poland 1111. The group is comprised of two institutions, Astronomical Observatory of the Jagiellonian University (JU) and Faculty of Electronics of the AGH University of Science and Technology (AGH). The group began their measurements back in 1992. So far, the group has won two awards for their work: 2010 Bronze medal on Geneva Inventions Salon and 2011 Congratulation Letter from Polish Ministry of Higher Education. Their work has also been important in the investigation of gravity waves that were detected in 2016 |12|.
Today, the group has a total of three ELF receivers. The first station deployed was in Poland in the groups home country. The group, with the help of Mark Golkowski, partnered up with the UCD Electromagnetics and Plasma Physics Group. The collaboration led to the second receiver deployment in Hugo, Colorado where the UCD Electromagnetics and Plasma Physics Group now services the station. The site started recording data in 2015. The newest station the Krakow group deployed was in Patagonia in Argentina, a map of their sites can be found in Figure 3.12.
Figure 3.12: Map of ELF receivers |9|
3.2.1 ELF Hardware
While the Krakow ELF group have has six different editions of their receiver, the
systems operate in a similar fashion. To start, the antennas used are made out of a
31


ferrite material that generates a constant magnetic.1 field with a DC voltage supply. The magnetic.1 held is disrupted when the magnetic.1 held of the sferic interacts with the constant magnetic.1 held. It is here that a signal can be generated. Since these antennas are very sensitive, the antennas are buried underground. This prevents any movement that might occur. Even moving the antennas slightly would induce noise as the Earths magnetic.1 held perturbs the constant magnetic.1 held generated by the antennas. From the antennas, the signal then travels down a cable and feeds into its respective channel, X/S and E/W. The antennas characteristics can be found in Table 3.2.
Table 3.2: ELF antenna parameters |9|
Characteristic AB1000 AB600 AA1000 AA1130 AA1500 AAS1130
year of design 1993 1997 2003 2009 2010 2012
number of units 1 2 2 6 2 0
bandwidth (-6dB) 50 Hz 60 Hz 150 Hz 150 Hz 75 Hz 400 Hz
length 1000 mm 600 mm 1000 mm 1130 mm 1500 mm 1130 mm
diameter 100x 100 mm 150 mm 60mm 90mm 90mm 90mm
weight 25 kg - 12 kg 13 kg 20 kg 13 kg
noise at 10 Hz - 0.2 pT/Hz1/2 0.05 pT/Hz1fl 0.05 pT/Hz1/2 0.01 pT/Hz1/2 0.015 pT/Hz1fl
power supply - - 10 V / 25 mW 10V/25 mW 10V/25 mW 10 V/120 mW
The Krakow receiver system is fully autonomous. The receiver runs off of three deep cycle marine batteries that are connected in parallel. The station can run on this battery bank for two months at a time. After those two months, a new set of fully charged batteries need to be installed. The data is stored on a SD card which is retrieved at the same time as the battery swap occurs. The specifications of the receiver can be found in Table 3.3. The version deployed in Hugo is the ELA10.
32


Table 3.3: ELF receiver specifications for all six editions |9|
Characteristic ELAl ELA2 ELA6 ELA7 ELA9 ELA10
year of design 1993 1997 2004 2006 2009 2012
period of operation 1994-2004 For test purpose only 2005 2007 Since Feb 6, 2007 expeditions Since Apr 27, 2013
purpose exp editions expeditions automatic recordings continuous recordings expeditions continuous recordings
antennas AB1000 AB600 AA1000 AA1000 AA1130 AAS1130
ADC 12 bit 12 bit 16 bit 16 bit 16 hit 16 bit
bandwidth 0.03-60 Hz 0.03-20/40/60HZ 0.03-60 Hz 0.03-60 Hz 0.03-60 Hz 0.03-300 Hz
sampling 180/240 Hz 50/100/180 Hz 175 Hz 175 Hz 175 Hz 900 Hz
data storage laptop laptop card CF/1GB card CF/4GB card CF/4GB card CF/32GB
interface RS232 RS232 RS232 RS232/RS485 RS485/USB RS485/USB
GPS time - - - + + +
time error minutes 30 s/ month 30 s/ month 500 M.S 500 p.s 200 p.s
battery 6 x R20 12 V/ 12Ah 12 V/ 260 Ah 12 V/ 260 Ah 12 V/ 260 Ah 12 V/ 260 Ah
power 80 mW 1400 mW 600 mW 600 mW 600 mW 800 mW
The inside of the military grade box where the receiver resides is shown in Figure 3.13.
Figure 3.13: Inside of ELF container
3.3 Experimental Methodology
33


The experiment conducted in this thesis involved setting up a VLF station next to the ELF station in Hugo, Colorado and recording for three days (July 19-21). As discussed in Chapter 3.2, Hugo is located about two hours east of Denver. The purpose of setting the receivers next to each other was to analyze the same paths of sferic propagation and observe how different frequencies arrive at different times.
The experiment first started by setting up a VLF hybrid receiver down in the UCD Electromagnetics and Plasma Physics Group laboratory. Here the receiver was calibrated before deployment. After that, a material list was made. This included the purchase of a small 750 watt 2-stroke gas generator and a solar panel kit. The generator served as a backup in case the solar panels were not able to power the VLF system. Unlike the ELF station, the VLF receiver consumed significantly more power because the system had to power a desktop computer, computer monitor, a GPS module, and of course, the receiver itself. It was measured that the VLF system drew 300 mA without the monitor and 430 mA with the monitor. This meant that a 45 Watt power system needed to be devised. The solar panel kit used was exactly 45 Watts which meant that during the day, the panels could power the system. This assumes clear skies and the panels be angled perfectly. Since these conditions could not be sustained all the time, the batteries were fully charged and thus the system would draw from the stored energy. To account for the night, an extra set of batteries were brought to sustain the system. If that failed, the generator would be used.
On July 19th at 4:00 am the author set out to Hugo to set up the VLF receiver. On arrival, the ELF station was examined and pronounced recording and working. After that, the setup began. First setup task was to unload the antennas and pre amp box 75 feet away from the ELF antennas as to prevent mutual coupling between the two systems. This is shown in Figure 3.14
34


Figure 3.14: Antenna and pre-amp setup in Hugo on July 19th. 2016
1000 feet to the north, the rest of the equipment was unloaded. The power system was then placed another 50 feet north. This was done to ensure minimal electromagnetic radiation sourced from the inverter. The power system consisted of the solar panels connected to the solar charging regulator. The regulator was connected to the battery bank in parallel to the solar panels on the input terminals and the output terminals connected to the 1500 watt inverter. The whole system setup can be shown in Figure 3.15.
35


Figure 3.15: Block Diagram of experiment setup
Using an extension cable, the inverter was connected to a power strip that housed the computer, monitor, and GPS module. This can be seen in Figure 3.16. It was a common practice to cover this segment of the system because it would over heat if it was in direct sun. It also protected the circuity from the rain that occurred on July 20.
Figure 3.16: Computer, monitor, GPS module, GPS antenna configuration
36


Subsequently, a 1000 foot cable connected the receiver and the pre-amp together. It was 1:00 pm once all the equipment was connected. The power supply was turned on and the initial data began recording to ensure everything was working properly. After verifying results, 1:20 pm marked the start time of recording data continuously.
On the hour, battery voltages were checked to ensure that the VLF system had sufficient power. For the most part, the solar system was able to supply the required power. On July 20 and 21 around 4:30 am the inverter alarm went off indicating that power was dropping both dates. A simple battery swap disabled the alarm. It was decided after the first time the power dropped to drive the spare batteries into the main town of Hugo and charge them at a rest area. This was beneficial because the gas generator and inverter would have added a significant amount of electromagnetic radiation near the antennas.
2:00 pm on July 21 marked the last recording. The power supply was turned off and cleanup of the camp site and the equipment began. Leaving the area, the ELF receiver was checked to verify it was recording data and did a battery check to evaluate the power levels of the batteries. It wouldnt be until August that the data could be retrieved and processed.
37


CHAPTER 4
DATA RESULTS
In this chapter, the data from both VLF and ELF receivers data will be examined. Data from the Global Lightning Detection network (GLD) was used to get the location and time of the causitive lightning of observed sferics [13]. This network is comprised of multiple VLF receivers stationed all around the world to triangulate sferics. Using MATLAB script created by Mark Golkowski, this data can be filtered to set geographical bounds and specify peak current limits. This is useful because it allows for the analysis of the four classifications set forth in this thesis. These include daytime short distances, daytime long distances, nighttime short distances, and nighttime long distances. In this work, long distances are characterized as being greater than 1500 km and short distances are anything less than that. Using the map package from MATLAB, distance is calculated by entering the longitude and latitude of the receiver and sferic location.
In Chapter 4.1, site corrections will be presented. This includes looking at the hardware group delay so that a more accurate depiction of the arrival time can be calculated. In Chapter 4.2, a few examples will be presented on how group delay and time of arrival was computed. Tables will then be presented to capture all 40 cases. All 40 figures and their respective maps can be found in the appendix section of this thesis.
4.1 Site Correction
To accurately determine the group velocity of the sferic, the delay of the signals through the receiver must be determined. For the VLF receiver it was determined that the group delay is on the order of 25 us for the VLF receiver. For the purpose of this work, this time is relativity small compared the group delay of the ELF system.
From the Krakow group, we were told that the group delay though the ELF system
38


was roughly 4.5 ms and included delay in the antenna as well as filtering hardware. However, there was difficulty in fully confirming this with experiment and because of this, an averaged measurable group delay was determined. The timing synchronization of the ELF receiver is also done in a way that the exact time of a sample may be off by a fraction of the sampling time. This is because while the sampling frequency is tuned via GPS time, the precise timing of the first sample in a file is not guaranteed to be on the rising edge of 1 pps GPS signal.
One way to experimentally determine the group delay in the ELF receiver is to look at observations sferies that originate very (dose to the receiver. Propagation of such waves will be minimally affected by the ionosphere and ground wave propagation will dominate, which should be traveling at the speed of light. Using time of arrival, distance, and the speed of light we can determine when this wave should have arrived and when it was actually recorded. The difference between these two determines the group delay through the hardware.
To begin this analysis, lets first look at a strike that occurred 109 km away from the ELF station. This can be found in the map in Figure 4.1.
109.3235kM Time Event:2016 7 21 1 38 27.881
Figure 4.1: Location of sferic in proximity to ELF station
39


Wo then look at the time domain of both channels and begin to determine the time of arrival by the first peak as explained in Chapter 2.1. This is found in Figure 4.2.
Figure 4.2: Time domain of the ELF receiver looking at X/S and E/W channels
A data point on the E/W channel indicates the first peak detected and its respective time. The vortical lino indicates the time when the GLD360 network detected the discharge. This GLD360 determined sfcric time will always mark the beginning of every subsequent plot. Next, the rod vortical lino takes the distance between the sfcric and station and divides it by the speed of light. This will indicate when the sferic should have arrived at the station if it was propagating at the maximum possible velocity. From Figure 4.2 the legend tells us that the arrival time for travel at the speed of light should be 0.367 ms after the GLD detected the sferic. Next, the blue vertical line indicates the arrival time if the wave were to travel at 99.3 %tho speed of light. Since the sferic occurred very close to the station this value, this number is very close to the speed of light at 0.364 ms after the GLD detection. Finally we look at the data point. Here, the arrival time was found to be 4.506 ms after the GLD detection.
40


This moans the group delay of the hardware is 4.506?bs 0.367ms = 4.139ms.
This process was done for 13 different cases. Each following the same methodology. The goal was to average all 13 cases to determine an averaged group delay through the hardware.
Table 4.1: Table of site corrections based on distance, speed of light, and arrival time
Distance (km) Speed of light propogation time (ms) Observed time of arrival (ms) Correction
109.325 0.36466 4.506 4.14134
121.7092 0.40598 4.506 4.10002
75.52509 0.25192 3.379 3.12708
83.38046 0.27183 4.506 4.23417
37.1913 0.12406 3.379 3.25494
146.4526 0.4851 4.506 4.0209
179.2191 0.59781 4.506 3.90819
178.4539 0.59526 4.506 3.91074
180.5611 0.60229 4.506 3.90371
192.9641 0.64366 3.3379 2.69424
182.9056 0.61011 4.506 3.89589
212.1667 0.70771 4.506 3.79829
219.531 0.73168 4.506 3.77432

Average 3.751063846
From the table it was computed that on average, 3.75 ms should bo subtracted from the ELF time of arrival in order to compensate for the group delay through the hardware. This can also bo highlighted by looking at the distribution using a histogram as shown in Figure 4.3.
41


Histogram of Site Correction Factors
2.6 2.8 3 3.2 3.4 3.6 3.6 4 4.2 4.4
Group Delay ms
Figure 4.3: Distribution of group delay through ELF receiver
4.2 Recorded Data
The observations in this experiment fall into one of four classifications. This chapter will highlight examples for each classification and then present tables that reflect all 40 eases. Figures from all the eases, as stated before, will be available in the appendix.
Beginning with daytime short distances we first present a side by side comparison of the recorded VLF and ELF data. Figure 4.4 plots both time domain signals and identifies their respective first peaks which is classified as the times of arrival.
42


2016 7 20 18 38 58.616 36.024754 -105.54019 -75 24 0.2 0.077801
Figure 4.4: Time domain of the ELF and VLF data
Just like in Chapter 4.1. data begins with the green vertical line indicating the time of the GLD detected CG discharge. The red and blue lines correspond with the arrival time at the speed of light and a fraction of the speed of light respectively. In Figure 4.4 we can see that the VLF (top plot) time of arrival was computed to be 1.36 ms after the GLD detection. Time of arrival for ELF (bottom plot) indicates a time of arrival at 4.506 ms. These times were recorded in Table 4.2. Within the table, time of arrivals are logged and site correction factor is added in. Lastly, the group delays are computed for corrected data for both ELF and VLF data.
Table 4.2: Table of daytime short distances
Event Index Distance km VLF time of arrival :LF time of arrival VLF site correction ELF site correction Group Delay VLF Group delay site correction VLF Group Delay ELF Group delay site correction ELF
UC16072018300038 2 370.3389 1.36 4.506 1.359975 0.754936154 0.908321765 0.908338463 0.27414949 1.636320627
UC16072018300055 9 216.7899 0.77 4.506 0.769975 0.754936154 0.939134115 0.939164607 0.160482305 0.95787341
UC16072019300031 14 322.4508 1.28 5.632 1.279975 1.880936154 0.840296948 0.84031336 0.190976579 0.571832325
UC16072019300032 16 321.1085 1.58 4.506 1.579975 0.754936154 0.677913078 0.677923804 0.237705873 1.418799003
UC16072019300035 19 269.8781 1.06 5.632 1.059975 1.880936154 0.849260795 0.849280825 0.159839567 0.478600212
UC16072019300035 20 317.7475 1.43 5.632 1.429975 1.880936154 0.741182918 0.741195876 0.188190975 0.563491521
UC16072019300051 27 362.2168 1.31 5.632 1.309975 1.880936154 0.922309307 0.922326908 0.214528621 0.642353112
UC16072101300044 48 112.4337 0.45 3.379 0.449975 -0.372063846 0.833418787 0.833465091 0.11099096 -1.007994886
UC16072101300047 50 113.3139 0.59 4.506 0.589975 0.754936154 0.640634721 0.640661867 0.083882487 0.500670796
UC16072101300057 54 110.4021 0.7 4.506 0.699975 0.754936154 0.526088237 0.526107027 0.081726979 0.487805179
Basie statistical analysis was tabulated in Table 4.3. Here we can compare the statistics for all four eases for corrected.
43


Table 4.3: Statistics of group delay for daytime short distances for VLF corrected data
VLF site correction

Mean 0.7S7S777S3
Standard Error 0.04327414
Median 0.83 6889 225
Standard Deviation 0.136844845
Sample Variance 0.018726512
Range 0.413057581
Minimum 0.526107027
Maximum 0.939164607
Count 10
Statistics for the ELF data were also generated in the same fashion as the VLF data. This is found in Table are 4.4.
Table 4.4: Statistics of group delay for daytime short distances for ELF corrected data
ELF site correction

Mean 0.62497513
Standard Error 0.223432504
Median 0.567661923
Standard Deviation 0.706555617
Sample Variance 0.49922084
Range 2.644315513
Minimum -1.007994886
Maximum 1.636320627
Sum 6.249751299
Count 10
The next set of tables presented are the remaining three classifications. Each classification will again have statistics for VLF and ELF data.
44


Table 4.5: Table of daytime long distances
Event Index Distance km VLF time of arrival ELF time of arrival VLF site correction ELF site correction Group Delay VLF Group delay site correction VLF Group Delay ELF Group delay site correction ELF
UC20160720221010 329 1671.159 5.83 11.26 5.829975 7.508936154 0.956155471 0.956159571 0.495060959 0.742366999
UC16072017300032 98 2627.209 9.08 13.52 9.079975 9.768936154 0.965135014 0.965137672 0.648182391 0.897070652
UC16072017300045 104 2732.017 9.53 14.64 9.529975 10.88893615 0.956246357 0.956248866 0.622474576 0.836907082
UC16072019300047 217 3036.129 10.29 14.64 10.289975 10.88893615 0.984201771 0.984204163 0.69176477 0.930066637
UC16072019300047 218 2026.82 7.03 11.26 7.029975 7.508936154 0.961698975 0.961702395 0.600421296 0.900359739
UC16072019300047 219 2622.19 9.03 13.52 9.029975 9.768936154 0.968625066 0.968627748 0.646944109 0.895356896
UC16072019300053 223 1831.448 6.65 11.26 6.649975 7.508936154 0.918654579 0.918658033 0.542544667 0.813571034
UC16072019300053 224 3029.462 10.62 13.52 10.619975 9.768936154 0.951525189 0.951527429 0.747425851 1.034421492
UC16072019300054 225 2028.041 7.03 10.14 7.029975 6.388936154 0.962278323 0.962281745 0.667141678 1.058833028
UC16072021000025 301 1958.672 6.64 11.26 6.639975 7.508936154 0.983949779 0.983953484 0.580233262 0.870086841
Table 4.6: Statistics of group delay for daytime long distances for VLF corrected data
VLF site correction

Mean 0.960850111
Standard Error 0.005841504
Median 0.96199207
Standard Deviation 0.018472456
Sample Variance 0.000341232
Range 0.06554613
Minimum 0.918658033
Maximum 0.984204163
Sum 9.608501106
Count 10
Table 4.7: Statistics of group delay for daytime long distances for ELF corrected data
ELF site correction

Mean 0.89790404
Standard Error 0.030070482
Median 0.896213774
Standard Deviation 0.095091215
Sample Variance 0.009042339
Range 0.316466029
Minimum 0.742366999
Maximum 1.058833028
Count 10
45


Table 4.8: Table of nighttime short distances
Event Index Distance km VLF time of arrival ELF time of arrival VLF site correctio ELF site correction Group Delay VLF Group delay site correction VLF Group Delay ELF Group delay site correction ELF
UC16072004000012 36 156.4039 0.71 4.506 0.709975 0.754936154 0.734798949 0.734824823 0.115780571 0.691061424
UC16072004000015 42 465.5825 1.56 4.506 1.559975 0.754936154 0.995523111 0.995539065 0.344655138 2.057148867
UC16072005000013 96 222.5837 0.83 3.379 0.829975 -0.372063846 0.894529283 0.894556228 0.219727524 -1.995515858
UC16072005000014 97 304.2701 1.75 5.632 1.749975 1.880936154 0.579963318 0.579971603 0.180208772 0.53959078
UC16072005000015 98 586.4009 2.34 5.632 2.339975 1.880936154 0.835907204 0.835916134 0.347305195 1.039919857
UC16072005000026 100 439.0157 2.4 5.632 2.399975 1.880936154 0.610166145 0.610172501 0.260013982 0.778547823
UC16072005000028 101 410.1689 1.93 4.506 1.929975 0.754936154 0.708899575 0.708908758 0.303634305 1.812307137
UC16072005000028 102 409.9416 1.52 5.632 1.519975 1.880936154 0.899617098 0.899631895 0.242794387 0.726987987
UC16072006000012 109 231.5153 1.77 4.506 1.769975 0.754936154 0.436300517 0.43630668 0.171383026 1.022936723
UC16072006000018 110 230.7183 1.58 4.506 1.579975 0.754936154 0.487084437 0.487092144 0.170793034 1.019415226
Table 4.9: Statistics of group delay for nighttime short distances for VLF corrected data
VLF site correction
Mean 0.718291983
Standard Error 0.059517265
Median 0.721866791
Standard Deviation 0.188210119
Sample Variance 0.035423049
Range 0.559232386
Minimum 0.43630668
Maximum 0.995539065
Count 10
Table 4.10: Statistics of group delay for nighttime short distances for ELF corrected data
ELF site correction

Mean 0.769239997
Standard Error 0.344020559
Median O.S9S9S1524
Standard Deviation 1.087888528
Sample Variance 1.183501448
Range 4.052664725
Minimum -1.995515858
Maximum 2.057148867
Count 10
46


Table 4.11: Table of nighttime long distances
Event Index Distance km VLF time of arrival ELF time of arrival VLF site correctio ELF site correction Group Delay VLF Group delay site correction VLF Group Delay ELF Group delay site correction ELF
UC16072005000011 70 3071.261 10.9 14.64 10.899975 10.88893615 0.939873758 0.939875914 0.699769397 0.940828729
UC16072005000020 71 2196.811 7.45 10.14 7.449975 6.388936154 0.983593656 0.983596956 0.722660033 1.146947247
UC16072005000022 72 2896.398 9.82 13.52 9.819975 9.768936154 0.983843562 0.983846067 0.714596434 0.988986275
UC16072005000028 78 2192.167 7.83 14.64 7.829975 10.88893615 0.933880207 0.933883188 0.499472815 0.671533189
UC16072005000028 79 3057.121 10.78 13.52 10.779975 9.768936154 0.945960854 0.945963047 0.754249852 1.043865764
UC16072006000011 108 3147.418 10.68 13.52 10.679975 9.768936154 0.98302026 0.983022561 0.776527838 1.074698023
UC16072006000018 110 1848.859 6.64 11.26 6.639975 7.508936154 0.928784608 0.928788105 0.547702468 0.821305398
UC16072006000025 117 3123.689 10.86 13.52 10.859975 9.768936154 0.959438761 0.95944097 0.770673443 1.066595665
UC16072006000026 118 3643.571 12.96 16.9 12.959975 13.14893615 0.937781222 0.937783031 0.71915057 0.924306309
UC16072006000026 119 3002.889 10.38 14.64 10.379975 10.88893615 0.964986467 0.964988791 0.684191224 0.919884127
Table 4.12: Statistics of group delay for nighttime long distances for VLF corrected data
VLF site correction

Mean 0.956118863
Standard Error 0.006897614
Median 0.952702009
Standard Deviation 0.02181217
Sample Variance 0.000475771
Range 0.055057962
Minimum 0.928788105
Maximum 0.983846067
Count 10
Table 4.13: Statistics of group delay for nighttime long distances for ELF corrected data
ELF site correction
Mean 0.959895073
Standard Error 0.043848383
Median 0.964907502
Standard Deviation 0.138660761
Sample Variance 0.019226807
Range 0.475414058
Minimum 0.671533189
Maximum 1.146947247
Count 10
Histograms were generated for both daytime and nighttime. This highlights distributions of the classifications as well as determine out liars. Daytime histrogram
47


can bo found in figure
group delay _____________________________group delay
Figure 4.5: Histogram of group velocities
A powerful statistical tool that employed hero is the two-sample Kolmogorov-Smirnov tost, which provides a probability if two sample sots are from the same distribution. In this tost a null hypothesis is proposed that the two sample sots come from the same distribution. A p-valuo is then ealeualtod. A p-valuo below 0.05 is taken to moan that the two sample sots are from different distributions and the null hypothesis should bo rejected. For the four classifications presented in this work, the two-sample Kolmogorov-Smirnov tost was conducted between each sot to determine how related one sot is to another. This is presented in Table 4.14.
Table 4.14: Kolmogorov-Smirnov tost for all four eases compared to one another
Test cases Mean Rejected p k
Daytime short VLF vs. Nighttime short VLF 0.7878, 0.7182 0 0.6751 0.3
Daytime long VLF vs. Nighttime long VLF 0.9608, 0.9561 0 3.13E-01 0.4

Daytime short ELF vs. Nighttime short ELF 0.6249, 0.7692 0 3.13E-01 0.4
Daytime long ELF vs. Nighttime long ELF 0.8979, 0.9599 1 0.031 0.6
48


CHAPTER 5
DISCUSSION
In Chapter four, data was presented in the form of tables. These tables included statistics of group delay of daytime short distances, daytime long distances, nighttime short distances, and nighttime long distances. The Kolmogorov-Smirnov test was then presented to quantify the relationship of the data sets compared to each other. In this chapter, an in depth analysis will be conducted to see how Chapter 3.3 methodology compares to theoretical results presented in Chapter 2. In Chapter 5.1, results from Chapter 4.1 will be examined. In Chapter 5.2, a brief conclusion will be presented to highlight how the experiment presented in this thesis contributes to knowledge of the plasma physics in the ionosphere.
5.1 Analysis
Referencing Table 4.2 or any of the ELF columns it can be observed that the group delays can at times be inaccurate. For example, in the first column of 4.2, the ELF group delay was calculated to be 160 % faster than the speed of light. Physically this is impossible. However, the sampling frequency of the ELF receiver as mentioned in Chapter 3.2.1 is 888 Hz. This means the resolution is significantly lower than that of the VLF receiver. This is why all the ELF data looks courser. The arrival time (indicated by the first peak) might be off by a sample. This means the arrival time could be off by as much as 1 ms. For short distances, this was clearly an issue since the arrival time of the sferic traveling at the speed of light was a fraction of a ms. This is why some of the data, especially subtracting the site correction indicates that the wave is traveling faster than the speed of light. However, this was consistently calculated so the distributions of the data sets were to some degree accurate and therefore tests such as Kolmogorov-Smirnov were valid.
In Mackays work [1], it was proposed that during the day, slowtails are very
weak and sometimes non existent. This meant that the ELF content was significantly
49


reduced compared to nighttime. This was due to the ionospheric.1 height as discussed in Chapter 1.2.2. To see this effect, refer to Figure 5.1
Figure 5.1: Time domain of two sferics at the day |1|
equal distances, one at night and during
The Kolmogorov-Smirnov test can support these results simply by looking at Daytime long ELF vs. Nighttime long ELF in Table 4.14. It was shown that the null hypothesis was rejected, thus meaning that there is a significant difference between ELF propagation velocity day vs. night for a significance level of 5 percent.
For the VLF data sets, it was shown that the null hypothesis was supported for Daytime long VLF vs. Nighttime long VLF. This could only mean that VLF signals generated from sferics are supported during both at night and day. ELF signals however, act differently due to the rising ionospheric height given the cutoff frequency and modes presented in chapter 1.
Furthermore, these results can be further proven by looking at the statistical analysis in Chapter 4.2. The averaged group delay for ELF daytime long was computed to be 89.7 % that of the speed of light as shown in table 4.7. Compared to nighttime long distances the average group delay was computed to be 95.9 % of the speed of light in Table 4.13. This validates that at nighttime, ELF signals act like VLF signals as shown in Table 4.12 which computes the averaged group delay to be 95.6 % of speed of light.
50


5.2 Conclusion
In this work an experiment was carried out to observe the difference in sferic group velocity between the ELF and VLF bands for nighttime and daytime ionospheric conditions. The experiment involved two co-located receivers recording over a 24 hour period. A power supply using a solar panel and battery bank was deployed to allow the VLF system to operate off the power grid. Global Lightning Detection Network (GLD360) lightning location data was used to make time of arrival observations of sferics on both systems. For both systems the time of the first peak was used as the arrival time. The group delay through the ELF receiver was estimated using nearby sferics and assuming direct path propagation to the receiver. A Kolmogorov-Smirnoff statistical test was used to evaluate differences in observations over day vs night conditions. Results show agreement with theory that ELF propagation velocity is strongly affected by the ionospheric height that changes for day vs. night. The results show that is possible to use ELF sferic arrival time as a potential ionospheric diagnostics. Noise and uncertainty in the results was caused by the lack of precision sampling synchronization in the ELF system and the low sampling rate of 888 HZ, which could yield errors on the order of a N 0.5 ms. Suggestions for future work include averaging over a larger number of events and using a more sophisticated method of determining arrival time than the first peak observation used here. In this context we note that the GLD360 network utilized a canonical waveform bank to get precision time of arrival for sferic from VLF observations. Such a wavebank for ELF sferic observations could also be developed.
51


APPENDIX A. Daytime Short Distances
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 3.703379e+02 kM
Dclay^Disfcncc/0.99S'C 1.244 I I Delav=QielaacG/C = 1.23&3 I
J|X 116
1
0 2 4 6 8 10 12 Time (mil seconds) after 18:38:58.616 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 3,703379e+02 kM 14 16
1 X: 4.506 1 1 1 1 Y: 20.03 NLDDetecton |

2 4 6 8 10 12 14 16
Time (mil seconds) after 18:43:58.616 UT
Figure A.l:
370.3379kM Time Event:2016 7 20 18 38 58.616
Figure A.2


Amplitude Amplitude
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 2.167899e+02 kM
-300 -------------------------------------1------------------------------------1------------------------------------1-----------------
0 2 4 6 8 10 12 14
Time (mil seconds) after 18:55:54.383 UT
Figure A.3:
Figure A.4:


Amplitude
-2 0 2 4 6 8 10 12 14 16
Time (mil seconds) after 19:31:35.528 UT
Figure A.5:
322.4508kM Time Evcnt:2016 7 20 19 31 35.528
Figure A.6


Amplitude
10'
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 3.211085e+02 kM
----Delaj^Dstanc&O.SSa'C -1.0737
----DelayDstercfrC 1.1711
0 5 10 15
100 50 0 -50 -100 -150
0 5 10 15
Time (mil seconds) after 19:32:45.936 UT
Hugo ELF 20-Ju|.MWSMUK kM
I
Figure A.7:
Figure A.8


10'
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 2.698781e+02 kM
200 r 100 -
Time (mil seconds) after 19:35:25.939 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 2.698781e+02 kM
Time (mil seconds) after 19:35:25.939 UT
Figure A.9:
269.8781 kM Time Evcnt:2016 7 20 19 35 25.939
Figure A. 10


10
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 3.177475e+02 kM
CD
:v:
E
<
0 2 4 6 8 10 12 14 16
Time (mil seconds) after 19:35:54.512 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 3.177475e+02 kM
100
50
0
-50
-100
Time (mil seconds) after 19:35:54.512 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 3.177475e+02 kM
0
2
4 6 8 10 12
Time (mil seconds) after 19:35:54.512 UT
14
Figure A.ll:
317.7475kM Time Evcnt:2016 7 20 19 35 54.512
Figure A. 12


0 5 10 15
Time (mil seconds) after 19:51:12.786 UT
Figure A. 13:
Figure A. 14


Amplitude
3 x104 Hugo VLF 21-Jul-2016 UT N/S Antenna Distance 1.124337e+02 kM

Jx0.45 yV:-1.799e+04
2 4 6 8 10 12 14 Time (mil seconds) after 01:44:31.275 UT Hugo ELF 21-Jul-2016 UT E/W Antenna Distance 1.124337e+02 kM
IIIIII X: 3.379 Y:fl594x -
| 0 377631
- i i i i i i
0 2 4 6 8 10 12 14
Time ( mil seconds) after 01:49:31.275 UT
Figure A. 15:
Figure A. 16


10
Hugo VLF 21-Jul-2016 UT N/S Antenna Distance 1.133139e+02 kM
Time (mil seconds) after 01:47:23.035 UT
Figure A. 17:
Figure A. 18


11
E 0
Hugo VLF 21-Jul-2016 UT N/S Antenna Distance 1.104021e+02 kM
a;
§ 200
E 0
<
-200
-400
0
Time (mil seconds) after 01:57:33.429 UT Hugo ELF 21-Jul-2016 UT E/W Antenna Distance 1.104021 e+02 kM
Time (mil seconds) after 01:57:33.429 UT
Figure A. 19:
110.4021kM Time Evcnt:2016 7 21 1 57 33.429
Figure A.20:


APPENDIX B. Daytime Long Distances
0 5 10 15 20 25
Time (mil seconds) after 17:32:09.166 UT
Figure B.l:
Figure B.2


5000
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 2.732017e+03 kM
60
Time (mil seconds) after 17:45:22.432 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 2.732017e+03 kM
40 - 1.20r
E
<
0
-20 -
Time (mil seconds) after 17:45:22.432 UT
Figure B.3:
2732.0173KM Time Evont:2016 7 20 17 45 22.432
Figure B.4


Amplitude Amplitude
Hugo VLF 20-Jul-2016 UT E/W Antenna Distance 3.036129e+03 kM
0 5 10 15 20 25
Time ( mil seconds) after 19:47:03.061 UT
Figure B.5:
3036.1286kM Time Event:2016 7 20 19 47 3.061
Figure B.6:


Amplitude Amplitude
0 2 4 6 8 10 12 14 16
Time (mil seconds) after 19:47:11.629 UT
Figure B.7:

Figure B.8


0 5 10 15 20 25
Time ( mil seconds) after 19:47:19.359 UT
Figure B.9:
Figure B.10


AmP"tude Amplitude
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 1.831448e+03 kM
0 5 J X: 5.65 r
v6 i
| MppSssro'BMc*66211
10 15
I IITie (11 Delay=Dstar,0.993-C =61521 'id.Z t.U 1 Hugo ELF 20-Jul-2016=,^Lc=B,O9, istance 1.831448e+03 kM
\, // \ *1126 \ Y: 4.524
Time (mil seconds) after 19:58:27.396 UT
Figure B.ll:
Figure B.12


6000
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 3.029462e+03 kM
4000 -2000 -
-2000 -4000 L

Time (mil seconds) after 19:53:46.555 UT Hugo ELF 20-Jul-2016 UT E/W Antenna Distance 3.029462e+03 kM
I I
^4 / I D ay-Zishncc/lSH-C 10.17641
N. / | Deay=DislancefC = IQ 1G&2 |
z
\ X: 13 52
Y: 15.84
i i I
Time ( mil seconds) after 19:58:46.555 UT
Figure B.13:
Figure B.14


-5 0 5 10 15 20 25
Time ( mil seconds) after 19:59:33.484 UT
Figure B.15:
Figure B.16


Amplitude Amplitude
Hugo VLF 20-Jul-2016 UT E/W Antenna Distance 1.958672e+03 kM
Wnf f! iffr f P1 f j |f 'If _ I De ay-Diatance/C S.53S4 I |IhNhnh#^ 1 _
5 10 15 20 25 Time ( mil seconds) after 21:25:21.227 UT Hugo ELF 20-Jul-2016 UT E/W Antenna Distance 1.958672e+03 kM
\ / \ / \ X 11,25 I DelaY"Distaice/0.993'C 6.57951 \ /Y,-133.B NLD De.eciion | I DelavDistaice/C 6.5334 I
0
5
10 15 20
Time ( mil seconds) after 21:25:21.227 UT
25
Figure B.17:
1958.672kNI Time Evcnt:2016 7 20 21 25 21.227
B.18:
Figure


Figure B.19:
Figure B.20:
71


Amplitude Amplitude
APPENDIX C. Nighttime Short Distances
Figure C.l:
Figure C.2:


2000
Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 4.655825e+02 kM
1000
O a ik, 1
E -1000 -2000
-3000
0


n4> Time (mil seconds) after 04:15:21.044 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 4.655825e+02 kM
400 200 -
r^lay=r)islHiiiyJC 1 f
Time (mil seconds) after 04:15:21.044 UT
Figure C.3:
465.5825KM Time Evcnt:2016 7 20 4 15 21.044
Figure C.4:


Amplitude Amplitude
0 2 4 6 8 10 12 14
Time ( mil seconds) after 05:18:37.996 UT
Figure C.5:
Figure C.6:


Amplitude Amplitude
0 2 4 6 8 10 12 14 16
Time (mil seconds) after 05:19:10.781 UT
Figure C.7:
Figure C.8


600
400 - § 200 -
e o -
< ________
-200 -
-400 0
Time (mil seconds) after 05:15:22.868 UT Hugo ELF 20-Jul-2016 UT N/S Antenna Distance 5.864009e+02 kM
Time (mil seconds) after 05:15:22.868 UT
Figure C.9:
Figure C.10:
76


:10'
Hugo VLF 20-Jul-2016 UT E/W Antenna Distance 4.390157e+02 kM
0 2 4 6 8 10 12 14 16
Time ( mil seconds) after 05:26:15.487 UT Hugo ELF 20-Jul-2016 UT E/W Antenna Distance 4.390157e+02 kM
0 2 4 6 8 10 12 14 16
Time ( mil seconds) after 05:26:15.487 UT
Figure C.ll:
439.0157kM Time Evcnt:2016 7 20 5 26 15.487
Figure C.12


Amplitude
Time (mil seconds) after 05:28:11.639 UT
Figure C.13:
Figure C.14:


Amplitude Amplitude
x104 Hugo VLF 20-Jul-2016 UT E/W Antenna Distance 4.099416e+02 kM
- I 1.52 : 1899
5 10 15 Time (mil seconds) after 05:28:11.663 UT Hugo ELF 20-Jul-2016 UT E/W Antenna Distance 4.099416e+02 kM
- x: 5.o32 ym 1 1
0 5 10 15
Time ( mil seconds) after 05:33:11.663 UT
Figure C.15:
409.9416kM Time Evcnt:2016 7 20 5 28 11.663
Figure C.16:


, x104 Hugo VLF 20-Jul-2016 UT E/W Antenna Distance 2.315153e+02 kM
4 | | | |
-
X: 1.77 Y: -2.56et04
0 2 4 6 8 10 12 14 16
2000
1000
u
V
f 0
E
<
-1000
-2000
0 2 4 6 8 10 12 14 16
Time ( mil seconds) after 06:12:52.618 UT Hugo ELF 20-Jul-2016 UT E/W Antenna Distance 2.315153e+02 kM
X: <1.506 Y: -1566
Time (mil seconds) after 06:12:52.618 UT
Figure C.17:
Figure C.18:
80


E
<
- 1Q4_______________________________Hugo VLF 20-Jul-2016 LIT E/W Antenna Distance 2.307183e+02 kM

X: 1.58 Y: -1.162e*04 I Delay-Distance/!) 933-0-0 775021 I Deiay-iMalance/C 0.73S59 I
0 5 10 15
Time ( mil seconds) after 06:18:24.548 UT
g
E
<
Hugo ELF 20-Jul-2016 UT E/W Antenna Distance 2.307183e+02 kM
Time (mil seconds) after 06:23:24.548 UT
15
Figure C.19:
Figure C.20:
81


APPENDIX D. Nighttime Long Distances
0 5 10 15 20 25
Time (mil seconds) after 05:11:40.823 UT
Figure D.l:
Figure D.2:


Amplitude i Amplitude
0 2 4 6 8 10 12 14 16 18 20
Time (mil seconds) after 05:20:47.828 UT
Figure D.3:
2196.8111kM Time Event:2016 7 20 5 20 47.828
Figure D.4:


Amplitude Amplitude
0
5 10 15
Time (mil seconds) after 05:22:02.290 UT
20
25
Figure D.5:

Figure D.6


x104 Hugo VLF 20-Jul-2016 UT N/S Antenna Distance 2.192167e+03 kM
1 X: 7.03 Y: 2576
[CT^
0 5 10 15 20 25
Time (mil seconds) after 05:28:24.673 UT
Figure D.8


Amplitude Amplitude
0 5 10 15 20 25
Time (mil seconds) after 05:33:45.364 UT
20 5 28 -16.364 12.338878 -95.158038 -193 15 2.217791 276638
Figure D.9:
3057.1207kM Time Event:2016 7 20 5 28 45.364
Figure D.10


Full Text

PAGE 1

GROUPVELOCITYOFLIGHTNINGINDUCEDSFERICS,ACOMPARISON BETWEENVERYLOWANDEXTREMELYLOWFREQUENCIES by RYANJ.GILLESPIE B.S.UniversityofColoradoDenver,2015 Athesissubmittedtothe FacultyoftheGraduateSchoolofthe UniversityofColoradoinpartialfulllment oftherequirementsforthedegreeof MastersofScience ElectricalEngineeringProgram 2017

PAGE 2

ThisthesisfortheMastersofSciencedegreeby RyanJ.Gillespie hasbeenapprovedforthe DepartmentofMathematicalandStatisticalSciences by MarkGolkowski,Advisor StephenGedney,Chair MarkGolkowski StephenGedney DanConnors April24,2017 ii

PAGE 3

Gillespie,RyanJ.M.S.ElectricalEngineering GroupVelocityofLightninginducedSferics,AComparisonBetweenVeryLowand ExtremelyLowFrequencies ThesisdirectedbyAssistantProfessorMarkGolkowski ABSTRACT ModelingandunderstandingoftheplasmaphysicsintheEarth'supperionospherehasalwaysbeenchallengingforscientists.Thisisduemostlytothevariability, complexity,andtheinabilitytoconductdirectmeasurements.Theionosphereistoo farforweatherballoonsandtoolowforsatellitestomakedirectmeasurements.Over thepast50years,groundbasedstationshavebeenusedtoobtainsomeinformation regardingtheionosphere. Theworkdoneinthisthesisaddsontopreviousworkbyplacingtworeceivers sidebyside.OneofthereceiversrecordsextremelylowfrequencyELF:3-300Hz andtheotherrecordsverylowfrequencyVLF:3-30kHz.Thereceiversrecorded datafromJuly19-21,2016.Thegoalwastoseeifthegroupdelayandtimeofarrival dieredbetweenthetworeceivers.Thisworkalsoextendeditsanalysistocompare dierencesbetweendayandnightwithlongandshortdistances. Thegoalofthisstudywastousethetimeofarrivaldatatocomputethegroup delay.Thesemeasurementscouldthenbeusedtodetermineionosphericheightand conductivity. iii

PAGE 4

Theformandcontentofthisabstractareapproved.Irecommenditspublication. Approved:MarkGolkowski iv

PAGE 5

DEDICATION Idedicatethisthesistomyfriendsandfamilywhohavehelpedmeupthroughmy education.Iespeciallywanttothankmylovingwifewhohashelpedmethroughlong nightsofstudyingforclassesandtests.Withoutthesupportofhermyeducation mighthavegoneadierentpath.Iwouldalsoliketospeciallythankmygrandmother whopastedawayMarch28,2017andmyparentswhosupportedmydecisionto becomeanElectricalEngineer.Thoughthepathwaslongandintensive,theywere thereeverystepoftheprocess. v

PAGE 6

ACKNOWLEDGMENT I'dliketospeciallythankmyadviserMarkGolkowskiwhogotmeinvolvedinthis research.Thischallengedmetothinkoutsideofthetextbookandreallyanalyzereal worldproblemswhichhelpedmebecomeabetterengineer. vi

PAGE 7

TABLEOFCONTENTS Tables........................................ix Figures.......................................x Chapter 1.Introduction...................................1 1.1Motivation................................1 1.2ScienticBackground..........................1 1.2.1AtmosphericLightning.....................1 1.2.2Ionosphere............................3 1.2.3Earth-IonosphereWaveguideModel...............6 1.3ComparisontoPreviousWork.....................8 1.4Outline..................................9 2.SlowTailPropogation.............................10 2.1SfericsinTimeDomain.........................10 2.2SlowTails................................12 2.3Earth-IonpshpereAsAPECWaveguide................15 2.4RealisticModelOfWaveguideAtELF.................17 2.5Chapter2Conclusion..........................19 3.ExperimentalSetup...............................20 3.1VLFReceivers..............................20 3.1.1VLFHardware..........................24 3.2ELFReceiver..............................31 3.2.1ELFHardware..........................31 3.3ExperimentalMethodology.......................34 4.DataResults...................................38 4.1SiteCorrection..............................38 4.2RecordedData..............................42 vii

PAGE 8

5.Discussion....................................49 5.1Analysis.................................49 5.2Conclusion................................51 Appendix A.DaytimeShortDistances............................52 B.DaytimeLongDistances............................62 C.NighttimeShortDistances...........................72 D.NighttimeLongDistances...........................82 References ......................................92 viii

PAGE 9

TABLES Table 3.1Possibleantennasizesandtheirproperties[8]...............27 3.2ELFantennaparameters[9].........................32 3.3ELFreceiverspecicationsforallsixeditions[9].............33 4.1Tableofsitecorrectionsbasedondistance,speedoflight,andarrivaltime41 4.2Tableofdaytimeshortdistances......................43 4.3StatisticsofgroupdelayfordaytimeshortdistancesforVLFcorrecteddata44 4.4StatisticsofgroupdelayfordaytimeshortdistancesforELFcorrecteddata44 4.5Tableofdaytimelongdistances.......................45 4.6StatisticsofgroupdelayfordaytimelongdistancesforVLFcorrecteddata45 4.7StatisticsofgroupdelayfordaytimelongdistancesforELFcorrecteddata45 4.8Tableofnighttimeshortdistances......................46 4.9StatisticsofgroupdelayfornighttimeshortdistancesforVLFcorrected data......................................46 4.10StatisticsofgroupdelayfornighttimeshortdistancesforELFcorrected data......................................46 4.11Tableofnighttimelongdistances......................47 4.12StatisticsofgroupdelayfornighttimelongdistancesforVLFcorrected data......................................47 4.13StatisticsofgroupdelayfornighttimelongdistancesforELFcorrected data......................................47 4.14Kolmogorov-Smirnovtestforallfourcasescomparedtooneanother..48 ix

PAGE 10

FIGURES Figure 1.1Fundamentalsoflightning[3]........................2 1.24thstateofmatter,plasma[4].......................3 1.3Ionosphericheights[5]............................4 1.4Dispersionrelationshipinsideaplasma[6].................6 1.5PropogationmodesinEarthionospherewaveguide[1]..........7 2.1TimedomainofVLFsferic.........................11 2.2TimeofarrivalofVLFsferic........................12 2.3TimedomainofELFsferic.........................12 2.4Theupperplotshowsanexamplesferic.Thebottomisalowpassedsferic highlightingtheELFcontentandtheslowtail[1].............13 2.5Spectrogramofsfericshighlightinggroupvelocitynearcuto[2].....14 2.6Groupandphasevelocityofawavetravelingthroughamedium[6]...15 2.7WavespeedforrstmodeinPECwaveguide...............16 2.8VLFdatarecordedonJuly20,2016inHugo.Redlineindicatesthearrival timetravelingatthespeedoflight.....................17 2.9Penetrationheightsofbothelectricandmagenticelds[7]........18 3.1VLFantennalocatedinAkhiokAlaska...................21 3.2VLFantennaatPaxson.TheauthorandBradFoxcanbeseenservicing thesystem...................................22 3.3VLFantennaatWarsaw.CUDenverstudentsHamidChorsi,Ashanthi Maxworth,RyanJacobsareshownfromlefttoright.Spring2014...23 3.4AllveoftheUCDVLFreceivernetwork.................23 3.5SimpleoutlineofNemesisreceiver.....................24 3.6Radiationpatternofsmallmagneticdipole.................25 3.7Equivalentcircuitmodelforsmallmagneticdipoleinreceivingmode[8]26 x

PAGE 11

3.8Insidethepre-ampboxofNemesissystem.................27 3.9FrequencyandgroupdelayofVLFreceiver[8]...............28 3.10Stanfordreceiversystem.Antennastructureupperleft,pre-amplier uppermiddle,receiverupperright,andblockdiagrambottom...29 3.11VLFsystemusedinthisexperimentcalibration..............30 3.12MapofELFreceivers[9]...........................31 3.13InsideofELFcontainer...........................33 3.14Antennaandpre-ampsetupinHugoonJuly19th,2016.........35 3.15BlockDiagramofexperimentsetup.....................36 3.16Computer,monitor,GPSmodule,GPSantennaconguration......36 4.1LocationofsfericinproximitytoELFstation...............39 4.2TimedomainoftheELFreceiverlookingatN/SandE/Wchannels..40 4.3DistributionofgroupdelaythroughELFreceiver.............42 4.4TimedomainoftheELFandVLFdata..................43 4.5Histogramofgroupvelocities........................48 5.1Timedomainoftwosfericsatequaldistances,oneatnightandduring theday[1]...................................50 A.1........................................52 A.2........................................52 A.3........................................53 A.4........................................53 A.5........................................54 A.6........................................54 A.7........................................55 A.8........................................55 A.9........................................56 A.10........................................56 xi

PAGE 12

A.11........................................57 A.12........................................57 A.13........................................58 A.14........................................58 A.15........................................59 A.16........................................59 A.17........................................60 A.18........................................60 A.19........................................61 A.20........................................61 B.1........................................62 B.2........................................62 B.3........................................63 B.4........................................63 B.5........................................64 B.6........................................64 B.7........................................65 B.8........................................65 B.9........................................66 B.10........................................66 B.11........................................67 B.12........................................67 B.13........................................68 B.14........................................68 B.15........................................69 B.16........................................69 B.17........................................70 xii

PAGE 13

B.18........................................70 B.19........................................71 B.20........................................71 C.1........................................72 C.2........................................72 C.3........................................73 C.4........................................73 C.5........................................74 C.6........................................74 C.7........................................75 C.8........................................75 C.9........................................76 C.10........................................76 C.11........................................77 C.12........................................77 C.13........................................78 C.14........................................78 C.15........................................79 C.16........................................79 C.17........................................80 C.18........................................80 C.19........................................81 C.20........................................81 D.1........................................82 D.2........................................82 D.3........................................83 D.4........................................83 xiii

PAGE 14

D.5........................................84 D.6........................................84 D.7........................................85 D.8........................................85 D.9........................................86 D.10........................................86 D.11........................................87 D.12........................................87 D.13........................................88 D.14........................................88 D.15........................................89 D.16........................................89 D.17........................................90 D.18........................................90 D.19........................................91 D.20........................................91 xiv

PAGE 15

CHAPTER1 INTRODUCTION 1.1Motivation ThisthesisexploreshowextremelylowfrequencyELF:3-300Hzandverylow frequencyVLF:3-30kHzelectromagneticwavespropagateintheEarth-ionosphere waveguide.Twotypesofreceiversmeasurethetwodierentfrequencybands.These signalsaregeneratedfromlightningdischarges.Thearrivaltimeoftheselightning inducedwavesalongwithinformationoftheirsourcelocationfromlightningdetection networksallowsfortheestimationofgroupvelocityintheEarth-ionospherewave guideanditsfrequencydependence.Thisworkinvolvesacomparisonofrecorded datatotheoreticalplasmaphysicsaswellasassessmentofthehardwareusedinthe receivers. 1.2ScienticBackground 1.2.1AtmosphericLightning MeaningfulcomparisonofgroupdelaysbetweenVLFandELFwavesgenerated bylightningrequiresunderstandingthesourceofbothwaves.Atmosphericlightingis acommonmeteorologicaleventwhichiscausedbyanaccumulationofelectriccharge thatoccursbetweenthegroundandclouds.Adischargeoccurswhentheelectric potentialreachesapointinwhichtheelectricbreakdownofairisexceeded.This causesapathtodevelopforcurrenttoowfromthecloudtotheground.Theresult isoftenvisibleandcancarryasignicantamountofcurrentontheorderoftensto hundredsofkA.Figure1.1illustratesthisphenomena. 1

PAGE 16

Figure1.1:Fundamentalsoflightning[3] Therearethreemaintypesoflightningdischarges:cloudtocloud,cloudto ground,andgroundtocloud.Thedischargesofinterestconsistofcloudtoground interactionssincetheyradiatethemostenergyandthusproducethelargestamplitudeelectromagneticsignals.Figure1.1depictsthemorecommoncloudtoground dischargeinwhichnegativechargeistransferredfromthecloudtotheground.This typeofdischargeiscalledanegativecloudtoground-CGdischargeandismore commonthantheoppositepolarity+CGsincethecloudistypicallypolarizedwith negativechargeclosertothegroundandpositivechargeathigheraltitude.Positive cloudtogrounddischargesoccurlessfrequently,butcanoftenhavealargerpeak current.Both-CGand+CGeventsgeneratebroadbandelectromagneticwaveswith signicantcontentintheELFandVLFbands.Sometimes,+CGeventsradiatemore ELFcontentbecausetheprocessislongerintime.Detailsonthisarepresentedin Chapter2. Chapter1.2.2presentsfurtherdiscussionofwhatfrequenciesthataretrappedin theEarthionospherewaveguideandwhichfrequenciespropagateoutintoouterspace. Fornow,itissucienttosaythattheELFandVLFportionoftheelectromagnetic wavecantravelgreatlengthsalongthesurfaceoftheEarthsometimesaroundthe 2

PAGE 17

Earth.Thisisimportantinthestudiesoftheionospherebecausehowthesewave propagatecanprovideinformationaboutthephysicsoftheionosphericplasma. 1.2.2Ionosphere Theionosphereformspartoftheupperatmosphereandgetsitsnamefromthe wordion.Anionisdenedas"anelectricallychargedatomorgroupofatoms formedbythelossorgainofoneormoreelectrons,asacationpositiveionwhichis createdbyelectronlossandisattractedtothecathodeinelectrolysis,orasananion negativeionwhichiscreatedbyanelectrongainandisattractedtotheanode"[4]. Theionosphereismadeofelectronsandions,whichtogetherformwhatisknownas aplasma. Plasmacanbethoughtofasthefourthstateofmatter.Figure1.2illustratesthe fundamentalsofwhataplasmaisandhowitdiersfromthemorecommonstatesof matter. Figure1.2:4thstateofmatter,plasma[4] AsseeninFigure1.2theplasmastateisachievedfromthegasstateafterenough energyhasbeenintroducedsothatelectronsarenolongerboundtothenucleus.This isbecausetheelectronshaveenoughkineticenergythattheyarenolongertrapped inthepotentialenergycreatedbythenucleus.Tounderstandthesourceofthis additionalelectronenergyintheionosphere,itisimportanttomentionthelarger contextoftheupperatmosphereasshowninFigure1.3 3

PAGE 18

Figure1.3:Ionosphericheights[5] Theionosphereistheregioninbetweenthegasrichenvironmentthatliferesides inandthemuchemptierregionofspacearoundtheplanet.Theionosphereisthe regionwherecosmicradiationfromspaceandsolarradiationfromthesuninteract withthegasseshereonEarth.Thesetwotypesofradiationarethesourceofthe plasmathatformstheionosphere. Themaindriveristhesun.Ultravioletradiationfromthesunisabsorbedbythe atmospherewhosedensityincreasesasonegetsclosertothesurfaceoftheEarth.The increasingneutralgasdensitycausesapeakinthedensityoffreeelectronsplasma statetooccurataround350kmaltitudeinwhatisknownastheF-regionof theionosphere.Thephotoionizationprocesscausessignicantionizationalltheway downtotheD-region )]TJ/F16 11.9552 Tf 13.2 0 Td [(90km. Atnight,thesuncannotexciteanyofthegasandthereforetheamountofionizing energydropssignicantly.However,thereareothersourcesfromouterspacethat stillhavethepotentialofmaintainingaplasmastate.Themaineectofnighttime radiationisthattheD-regionnolongerresidesaround60kmfromthesurfaceofthe Earth.TheD-regionisrestrictedtohigherelevationsnear90km. Inthiswork,theeectiveheightoftheionospherewillbementionedandcalcu4

PAGE 19

lated.ThisisinreferencetotheheightoftheD-regionsinceitisthelowestregion andthealtitudeatwhichELF/VLFwavesreectasdiscussedinChapter1.2.3. Plasmahasaspecialpropertythatallowselectromagneticwavestotravelin theEarth-ionospherewaveguide.Thisisbecauseplasmaactsasaconductororan insulatoratdierentfrequencies.Tobetterunderstand,letsrstexplorewhatmakes aplasmaconductive.Animportantmetricinplasmaelectrodynamicbehavioristhe plasmafrequencywhichisdenedas pe = s N e e 2 m 0 .1 Where N e isdenedastheelectrondensity, e ischargeofanelectron, m is eectiveelectronmass,and 0 isthepermittivityoffreespace.Ifanelectromagnetic wavehasalowerangularfrequencythantheplasmafrequency,theplasmacanadapt quickenoughtoaccommodatethechangesinamplitudeandthusactslikeaconductor whichcanreectanincidentwave.Athigherangularfrequencies,theplasmacannot reactfastenoughtothechangingeldsandthushigherfrequenciespropagatethrough theplasma.Tovisualizethiseect,Figure1.4whichshowstherelationshipbetween p and k whichisdenedasthewavenumber. 5

PAGE 20

Figure1.4:Dispersionrelationshipinsideaplasma[6] InChapter2itwillbeshownthattheslopeofthedispersioncurveprovidesthe groupvelocityofthewave.Forthisthesis,thiswillbeameasurablequantityinthe VLFandELFdata. 1.2.3Earth-IonosphereWaveguideModel NowthattheionospherehasbeenshowntoactasagoodconductorforELFand VLFwaves,let'sexaminewhatmakestheEarthagoodconductor.Referto1.2 = )]TJ/F20 11.9552 Tf 11.955 0 Td [(j .2 Where isreferredtoasthepropagationconstantwhile isdenedasthe attenuationconstant,and isdenedasthephaseconstant.Nowlet'sdenewhat and equalforagoodconductorinequation1.3and1.4 6

PAGE 21

' r 0 2 .3 r 0 2 .4 Where isdenedastheconductivityofthemedium, isthattheangular frequency,and 0 isthepermeabilityoffreespace.ForVLFandELFelectromagnetic wavestheangularfrequencyissmall.Forwetsoil,theconductivityisroughly 10 )]TJ/F18 7.9701 Tf 6.587 0 Td [(2 Theresultistheattenuationlossesandphaseconstantsarerelativelysmall.Fora perfectconductor, = 1 and = 1 because = 1 .Therefore,itissafetosay thattheEarthatlowfrequenciesactsasagoodconductor. WecansimplifytheEarth-ionospherewaveguidebymodelingitasaparallelplate waveguide.Inthismodel,awavecantravelinthreedierenttypesofmodes, TEM or TM 0 TE m ,and TM m .Toexplainwhatthesemodesmeanit'susefultovisualize asinFigure1.5. Figure1.5:PropogationmodesinEarthionospherewaveguide[1] The T inthemodesstandsfortransversewhichmeansthatcertaineldcomponentswillbefullyperpendiculartothedirectionofpropagation.The E and M refertoelectricandmagneticeld,respectively.Sincelightningdischarges,otherwiseknownassferics,occurverticallybetweenthesocalled"plate,"themajorityof 7

PAGE 22

dischargespropagateinthe TM and TEM modes. TheeectiveheightoftheD-regiondeterminestheheightofthewaveguide.This heightcanbeusedtocalculateinwhichmodesthewavecantravelin.Thiscanbe denedusingthecutofrequencywhichcanbeequatedto, !>! c = m a p .5 Wherewedene a tobetheheightofthewaveguideand m asthemodenumber. Thehigherthemodenumberthelessthewaveguidewillsupportlowerfrequencies. ForELFandVLFwaves,multimodepropagationcanbesupportedtoabout10 modes. 1.3ComparisontoPreviousWork InpreviousworkslikethatbyMackay[1]VLFandELFobservationsoflightning inducedwaveswerecompared.ThedatausedinMackay'sanalysiswastakenfroma singlestationinAntarctica.Thelocationofthisreceiverwillbefurtherexaminedin Chapter2,butfornowit'ssucienttosaythedatahasverylittlenoise.Withthe lownoiseenvironment,MackaycouldlowpasslterthedatatoisolateELFcontent. Themotivationforthisthesiscamefromconductingadierentexperimentthan wasdonebyMackay.Mackaywasinterestedinusingsinglestationobservationsas amethodofgloballightninggeolocation.Hereweinvestigatetheinverseproblem inthatweuselightninglocationdatafromtheGLD360networkandcomparethe observedpropagationvelocitytoionosphericconditions.Inthisexperiment,two dierentreceiverswillbeused.Asstatedbefore,aVLFandanELFstationwillbe deployednexttooneanother.Thisisdoneforafewreasons.First,theELFreceiver isspecicallydesignedtorecordELFdata.Thisisimportantbecausethetraditional wireloopantennasandhardwarerelatedcongurationsusedintheVLFsystemshave poorperformanceintheELFrange.Usingtheferritemagneticantennas,thequality 8

PAGE 23

oftheELFdataisincreased.Secondly,thepathofpropagationwillbethesamefor thetworeceivers.Thisallowsaonetoonecomparisononthegroupdelaysincethey willbetravelingonthesamepath. 1.4Outline Chapter2willgivesomebackgroundonhowtheionosphereaectssfericpropagation.InChapter3,adiscussionabouttheexperimentalworkthatrecordedthe dataforbothELFandVLFreceivers.Thiswillincludeabriefsummaryoftheequipment,location,andprocessofhowthedatawasobtained.Chapter4isdedicatedto presentingtherecordeddata.Thisincludes10casesofdaytimeshortdistances,10 casesfordaytimelongdistances,10nighttimeshortdistancesandnally10nighttime longdistances.Inthelastchapter,therecordeddatawillbecomparedtothetheory presentedinChapters1and2.Statisticaltestsareusedtoquantitativelycompare andcontrastallfourcases. 9

PAGE 24

CHAPTER2 SLOWTAILPROPOGATION Inthischapter,analysisofVLFandELFwavesintheEarth-ionospherewaveguidewillbepresented.Thiswillincludeanindepthlookatasfericinthetime domaininChapter2.1.InChapter2.2,thesfericswillbebrokendownintotheir respectiveVLFandELFcontent,anditwillbeshownhowthetimeofarrivalfor ELFelectromagneticwavesoftenlagsthatoftheVLFportion.LastlyChapter2.3, willpresentequationsderivedfromotherworksthatcancomputecharacteristicsof theionosphereusingthetimeofarrivalandgroupdelay. 2.1SfericsinTimeDomain Thereareoftentwowaystolookatasignal:inthetimedomainandinthe frequencydomain.Forthepurposesofthisthesis,thetimedomainwillbeused exclusively.Thisisbecausethepurposeofthisworkistodeterminethearrival timeandgroupdelayofthesferics.Whilespectrogramsfrequencydomainwith timeinformationcanbeusedaswell,thesfericsoftencanlastuptoacoupleof milliseconds.Determiningthetimeofarrivalonaspectrogram,whilenotimpossible, tendstobelimitedbythelengthofwindowintheshort-termFouriertransformand isthereforeinaccurate. AtypicalsfericwaveformisshowninFigure2.1.TheVLFreceiverwasdesigned torecordupto50kHzsignals.Thedataissampledat100kHz.Thisgivesrise todetailedwaveformsandthusdetectingtimeofarrivalisconsideredtobemore accuratethanELFsignalswhichwillbediscussedlateroninthissection. 10

PAGE 25

Figure2.1:TimedomainofVLFsferic Thegurepresentedin2.1plotsanaveragedamplitudeoveraperiodoftimein thiscase3ms.Thereasontheamplitudeisaveragedissothatthepositiveand negativevaluescanberepresented.Wecanseethatthesfericspansatimeofabout 0.5ms.Thatbeingsaid,thereisalotofactivitythatcanbeseenatthebeginning ofthesignalandthenattenuatesneartheend. Thewaveformofthesesignalsdepictshowthesesignalspropagate.Eachpeak thatrepresentsdierentreectionsotheEarthionospherewaveguide.Therst peakinthisgureisthewavethathaslittleornoreectionsothewaveguideand isknownasthegroundwave.Hence,itisthefastesttravelingpartofthewave.The followingpeakisthepartofthewavethatmayhavebouncedothewaveguidea coupleoftimesandthereforearriveslater.Thiscontinuesuntilallofthewavehas arrivedattherecordedstation.Forsuchacomplicatedwaveformitisimportantto deneatimeofarrival.Hereitisdenedbytherstsharppeak.Ingure2.2the timeofarrivalisdenedat9.53ms.ThiswillbethemetricastowhenallVLF signalstimeofarrivaloccurred. 11

PAGE 26

Figure2.2:TimeofarrivalofVLFsferic Nowlet'slookatwhattheELFdatalookslikeinthetimedomain.Therecorded ELFdataiscoarserinnatureduetoitslowsamplingfrequencywhichisabout800 Hz.ComparedtotheVLFsamplingfrequency,thetimeofarrivalishardertoresolve. ThiswillbeexplainedfurtherinChapter3.However,inFigure2.3thetimeofarrival canstillbedeterminedbypickingtherstpeakofthewaveform.Figure2.2and2.3 arerecordingsofthesamesferic.Timeofarrivalwascalculatedfor2.2asbeing 9.53ms,butin2.3thisisfoundtobe14.64ms.Thisisnotcompensatingforany hardwarecorrectionsthatwillneedtobedonewhichwillbediscussedinChapter3 indetail. Figure2.3:TimedomainofELFsferic 2.2SlowTails Inthischapter,thewaveformofasfericwillbecharacterizedintoitsVLFand ELFcontent.ThegurespresentedherecomefromtheworkbyMackay[1]andMark Golkowski'scourselecturenotes[2]whichhighlightwhatportionofthewaveformis characterizedastheslowtail.ThisisbestsummarizedinFigure2.4,whichshowsa sfericVLFandELFcontent. 12

PAGE 27

Figure2.4:Theupperplotshowsanexamplesferic.Thebottomisalowpassed sferichighlightingtheELFcontentandtheslowtail[1] TheslowtailcanbeseenastheELFcontentofthewaveformthatisdelayedin timefromtheinitialVLFcontent. ThebottompanelofFigure2.4wascreatedbyapplyingalowpassltertothe datainthetoppanel.InChapter1.2.3theEarthionospherewaveguidewasdened, anditwasstatedthatitcanbeapproximatedasaparallelplatewaveguide.This canalsobeshownusingaspectrogramwhichcombinesfrequencyandtimedomain asillustratedin2.5 13

PAGE 28

Figure2.5:Spectrogramofsfericshighlightinggroupvelocitynearcuto[2] Theredandyellowin2.5representthemagnitudeofthesfericsthatarerepresentedbytheverticallines.From2.5wecanseethataround1.8kHzthesfericis nolongervertical.Thisindicatesthatthewaveformisbeingsloweddown.Forthe lowest TE 1 and TM 1 modesthisoccursaround1.8kHz. Uptothispoint,eectsoftheplasmaonthesferichavebeennegated.Ithas beenshownthatinanidealparallelwaveguidethatthegroupvelocitydecreasesnear thecutofrequency.Thisassumestheboundariesareperfectlyconductingmaterials andthereforethesfericsharplyreectsotheionosphere.Inreality,thisisnot thecase.Ratheratlowerfrequencies,thesferic'swaveformtravelsdeeperintothe plasmacausinggreaterdispersionwhichinturncausesadecreaseingroupvelocity. InChapter1.2.2thedispersionrelationshipofaplasmawaspresented.Thisisshown inFigure1.4.Here,itwasshownthattheslopofthelinewasrelatedtothegroup velocityofthewavepropagatingthroughtheplasma.Atlowerfrequenciesabovethe plasmafrequency,theslopeisshowntobelessthanthatofhigherfrequencies.This 14

PAGE 29

eectcanalsobeseenin2.6. Figure2.6:Groupandphasevelocityofawavetravelingthroughamedium[6] 2.3Earth-IonpshpereAsAPECWaveguide ForVLFwaves,theboundsoftheEarth-Ionospherewaveguidecanbethought ofasaperfectlyelectricconductorPEC.Reviewingwaveguidetheoryexamine Equation2.1whichdeneswhatthecutofrequencyis. F c = mc 2 h .1 Here, c isthespeedoflight, m ismodenumber,and h istheverticalheightofthe waveguide.Forthedaytimeionosphereheight,wecanassumetheD-regionresides at70km.Thecutofrequencyfortherstmodeusingthesevaluescomputesto 2.14kHz. ThewavespeedcanthencomputedbyusingEquation2.2.Asthefrequency increases,thewavespeedincreasesuntilitreachesthespeedoflight.Thisisshown inFigure2.3 v g = c s 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( F c f 2 .2 15

PAGE 30

Figure2.7:WavespeedforrstmodeinPECwaveguide ThewayscientistshavevalidatedthattheionosphereactslikeaPECisthrough measurementsofgroundbasedstations.IftheionospherewasaPECforVLFsferics, thenthewaveswouldbesharplyreected.ThiswouldthenvalidateEquations2.1 and2.2becausethosearethemodelsforaPECparallelplatewaveguide.Thiscan beseenindatarecordedinthisthesisonJuly20thinHugo. 16

PAGE 31

Figure2.8:VLFdatarecordedonJuly20,2016inHugo.Redlineindicatesthe arrivaltimetravelingatthespeedoflight ThebeginningofthetimeplotindicateswhentheGLDnetworkdetectedthe sferic.Theverticalredlinetakesthedistancefromthesfericandreceiveranddivides bythespeedoflight.Thisgivesthetimeofarrival.Whatisshownisthatthe waveformlinesupexactlywiththetheoreticaltimeofarrivalifitweretravelingat thespeedoflight.Ultimately,thisprovestheEarth-Ionospherewaveguidecanbe thoughtofasaPECparallelplateforVLFsferics. 2.4RealisticModelOfWaveguideAtELF ELFsfericspropagatedierentlyintheEarth-Ionospherewaveguide.Thisis becausetheinteractionswiththeplasmacannotberepresentedwiththePECmodel. AsstatedinChapter2.2,thereareplasmaeectsthataltertheheightofthewave guide.Thisisfrequency )]TJ/F16 11.9552 Tf 9.298 0 Td [(dependentandcanbeseeninFigure2.9.Fromthis,itis notablethatlowerfrequenciesfromthetopplot,themagneticeldgoespropagates deeperintotheplasma.Thisinturncausesthebottomplotwhichshowshowthe groupvelocityslowsdowncomparedthatofthehigherfrequencies. 17

PAGE 32

Figure2.9:Penetrationheightsofbothelectricandmagenticelds[7] Thisisshownmathematicallybydeningtheboundaries.Therearetheconductionboundarywhichactsontheelectriceldheight h e andthediusionboundary whichgoverns h m .Thesetwoboundariesaredenedbytheheightdependentconductivitywithintheplasma. z representsthisquantitywhichcanbeexplainedby Equation2.3. = o .3 = 1 4 o 2 .4 = 1 d dz .5 Letusnowexplorehowthisaectsthearrivaltimeofthesferic.InMackay [1]thetimeofarrivalisafunctionofpropagationdistance ,reectionheight h conductivity whichwasdenedin2.3,andpulsewidthinsecondsdenotedas Together,theseformEquation2.6. t s =0 : 09 2 h r o + p 2 .6 18

PAGE 33

2.5Chapter2Conclusion Inthischapter,thepropagationofslowtailswasexamined.Chapter2.1highlightedtimedomaininformationwhichdenedthearrivaltimeforbothVLFand ELFwaves.Thiswillbeimportantinfurtherchaptersbecausethestatisticalmodelingwillinvestigatethesearrivaltimes.InChapter2.2,slowtailswereisolatedby theirfrequencycontent.VLFwavesaccountfortheportionofthesfericthatarrives thequickest.TheELFcontentofthewavedoesn'tarriveuntillaterintime.This wasexplainedbylookingatwhathappensnearthecutofrequencyinthelower modes.Itwasfoundthatthisgivesrisetowhatdenesaslowtail.InChapter2.3, theEarth-ionospherewaveguidewasmodeledasaPECparallelplatewavegiuide, whichisareasonablerstorderapproximationforVLFwavepropagation.Lastly, Chapter2.4examinedhowELFsfericspropagateintheEarth-ionospherewaveguide. Itwasshownthatthesewavestravelfurtherintotheplasma.Thisresultsinusing alternativeequationstodeterminetimeofarrivalasshownbyMackay[1]. 19

PAGE 34

CHAPTER3 EXPERIMENTALSETUP Thischapterhighlightstheauthorscontributiontothestudyofslowtails.In Chapter3.1,theElectromagneticsandPlasmaPhysicsResearchGroupsVLFreceiversiteswillbepresented.Chapter3.1.1willexplaintheVLFreceivershardware. Thiswillincludecalibrations,setup,andthenetworkofreceiverstheUniversityof ColoradoDenverUCDElectromagneticsandPlasmaPhysicsResearchGroupcurrentlyoperates.Chapter3.2willdiscusstheELFreceiverused.Thiswillincludethe designoftheKrakowELFgroupfromPolandwhichishostedbyUCD.Chapter3.3 willthencoverhowtheexperimentwasdesignedandexecuted. 3.1VLFReceivers TheElectromagneticsandPlasmaPhysicsResearchGrouphasveVLFreceivers. OneofthesitesresidesonasmallislandsouthofKodiakIslandnamedAkhiokin Alaska.AkhiokisasmallvillageofAlaskannativeswhosepopulationislessthan 100.Thereceiverissetupinsidetheschoolhousewhichhousesabout20students rangingfromkindergartentohighschool.Wewereabletoobtainthislocationby coordinatingaseriesofoutreachprogramsdesignedtogetstudentsinterestedinscienceandmath.Sofar,theseinteractiveprogramshaveinvolvededucatingstudents onthefundamentalsofstaticelectricalchargesusingVandeGragenerators.Our eortsalsoleadstudentstolearnbasicprogramminganddigitalhardwareimplementationsusingArduinomicro-controllers.TheVLFantennaatthissitecanbeseenin Figure3.1.Thissitewasdeployedin2013bytheauthorandundergraduateresearch assistantBradFox. 20

PAGE 35

Figure3.1:VLFantennalocatedinAkhiokAlaska NorthofthatlocationinAlaskaresidesthegroup'sPaxsonsiteneartheHigh FrequencyActiveAuroralResearchProgramHAARPfacilityinGakona,Alaska. ThePaxsonsitewasoriginallyoperatedandmaintainedbytheStanfordVLFresearch group.In2014,UCD'sElectromagneticsandPlasmaPhysicsResearchGroupew outthereandbroughtthereceiverbackonlineandhasmaintaineditsince.Thissite canbeseeninFigure3.2 21

PAGE 36

Figure3.2:VLFantennaatPaxson.TheauthorandBradFoxcanbeseenservicing thesystem. MovingtotheEasternUnitedStates,thegrouphostsaVLFreceiveronthe roofoftheNorthClassroombuildinglocatedontheAurariacampushometothe ElectricalEngineeringdepartment.Thissitewasestablishedmainlyforhardware testingofexistingandfuturesystems.Whilethedataisoftennoisyduetothepower consumptionofthebuildingitselfandbeingintheheartofdowntownDenveritstill processesvaluableinformationthegroupcanuseintheirstudyoftheionosphere. OntheEastcoast,thegrouphasaVLFreceivernearWarsaw,Virginia.This wasthegroup'ssecondreceivertomakeuptheirVLFnetwork.Thesiteislocated onatechnicalhighschoolfacilitycalledRappahannockCommunityCollege.Like Akhiok,outreachprogramshavebeenimplementedtogetstudentsinvolvedwith scienceandmath.AshanthiMaxworth,oneofthegroupsPhDstudentshasworked withthestudentstorecordmosquitomatingcallstogeneratespectrogramswhich helpstudentslocateandbetterunderstandbiology.Theschoolisheavilyinvolved inbiologystudiessotheprogramsaretailoredtotheircurriculum.Thissitecanbe seeninFigure3.3. 22

PAGE 37

Figure3.3:VLFantennaatWarsaw.CUDenverstudentsHamidChorsi,Ashanthi Maxworth,RyanJacobsareshownfromlefttoright.Spring2014 Thegroup'srstreceiverwasdeployedinIthaca,NewYorkinaremotelocation onprivateproperty.Thissiteprovidesvaluabledatabecausethesiteisnotnear majorpowerlinesandotherelectromagneticsourcesofnoise.Sincethissiteisso remote,internetconnectionisslowandimpossibletotransferdataoverthenetwork. Becauseofthis,theonlywaytotransferdatabetweenthesiteandthegroupsservers isharddriveexchangesviathepostalservice. ThesevesitesmarktheElectromagneticsandPlasmaPhysicsResearchGroup atUCDVLFnetwork.AcompletemapoftheselocationscanbefoundinFigure 3.12. Figure3.4:AllveoftheUCDVLFreceivernetwork 23

PAGE 38

3.1.1VLFHardware ThereceiversystemisbasedonalegacydesignoutofStanfordUniversitycalled AtmosphericWeatherElectromagneticSystemforObservation,Modeling,andEducationorAWESOMEsystem[10].ThespecicdesignusedbytheUCDgroupwas obtainedfromtheUniversityofFloridaandisreferredtoastheNemesis.Thissystem wasdesignedtorecordfrequencies300Hz-48kHz.Thissystemincludesadesktop computerwithaNationalInstrumentsDAQPCIcard.Thecomputerisconnected tothereceiverandGPSmodule.TheGPSsourcesthesamplingfrequencythatis synchedwithatimesynchronized1ppswaveform.Thisallowsallreceiverstobe synchronizedintimingwhenrecordingdata.Thereceiveristhenattachedtothe pre-ampboxwhichtheninturnisconnectedtotwowiredloopantennas.Abasic overviewcanbeseeninFigure3.5. Figure3.5:SimpleoutlineofNemesisreceiver Tobegin,letusrstlookattheantennas.Thereceiverconsistsoftwoorthogonal wiredloopantennas.Sincethewavelengthofthefrequenciesrecordedbythisreceiver 24

PAGE 39

aresolargecomparedtothesizeoftheantennas,theycanbeconsideredaselectrically smallmagneticdipoles.FEKOsoftwarewasusedtoshowwhattheradiationpattern lookslikeforasmallmagneticdipole.ThisisshowninFigure3.6.Theantennais sensitivetohorizontalmagneticeldsandhasadirectivityintheplaneoftheloop. Figure3.6:Radiationpatternofsmallmagneticdipole ThesimulatedantennawasthesmallestantennasizeusedfortheNemesiswhich isa12turnwiredloopantenna.Theantennacanbesimpliedintoacircuitmodel inthereceivingmodelikeinFigure3.7 25

PAGE 40

Figure3.7:Equivalentcircuitmodelforsmallmagneticdipoleinreceivingmode[8] Mathematicallytheinputimpedancecanbeshowntobe Z in = R a + jX in = R r + R l + j X a + X i inwhich R r isdenotedastheradiationresistance, R l isthe ohmicresistance, X a istheexternalinductanceandnally X i isthehighfrequency inductance. Itisimportanttonotethattheantennascanbeconstructedindierentsizes. Largerantennastypicallyyieldanimprovedsignaltonoiseratiosowhenpossible, thelargersizesareused.Abreakdownofthedierentsizeswiththeirantenna characteristicscanbeshowninTable3.2.Theantennausedinthisthesiswasthe rightisoscelestrianglewithanareaof1.695 m 2 inTable3.2. 26

PAGE 41

Table3.1:Possibleantennasizesandtheirproperties[8] TheantennasconnecttotheN/SandE/Wchannelofthepre-ampbox.Thepreampboxdesignconsistsofthedaughterboard,line-matchingtransformers,andpreampcards.Theinsideofthepre-ampboxisshowninFigure3.14.Eachchannelhasa pre-ampcardtoamplifythesignal.Thepre-ampcardshaveagainofapproximately 10dB.Thesignalissentindierentialforminordertoreducenoisecouplingwhen thesignalissenttothereceiver.Thesignalissentthrougha1000foot14pincable thatisnormallyfedthroughabuildingtothereceiver.Thecableisoftenaslongas possibleinordertoplacetheantennasasfarawayfromnoisesources. Figure3.8:Insidethepre-ampboxofNemesissystem 27

PAGE 42

Oncethesignalentersthereceiver,itthentravelsthroughtheltercards.This actsasananti-aliasinglterrestrictingthebandwidthbeforetheanalogtodigital convertersothattheNyquisttheoremcanbesatised.Theltercardshavea12th orderellipticallterthathasa-3dBrolloat47kHz.Thefrequencyresponseand groupdelayoftheNemesiscanbeshowninFigure3.9. Figure3.9:FrequencyandgroupdelayofVLFreceiver[8] Thereceiveralsotakesinaseriesoftimedpulsesusedforsynchronizingoftime andsampling.ThesignalsarefedinfromtheprogrammableGPSmodule.The GPSmoduleoutputsa1ppsanda100kHzpps.The1ppssyncstheGPStime foraccuratetiming.The100kHzppssynchronizesthesamplingfrequencyattheNI DAQcard.Thereceiverhasaseriesofoptionalop-ampstoprovideanextra30dB gaintothesignals. FinallythesignalsarecombinedandsenttothecomputerviaNationalInstrumentscablethatfeedsintotheDAQcard.ARS-232serialcablealsofeedsintothe computerfromtheGPSmoduletosendintheUTCtimewhichisusedasaheader withinthe.matles.TherecordingsoftwarefromUniversityofFloridaallowscongurationoftherecordings.ThisincludesnarrowbandcongurationtotuneintoNavy transmittersandcontinuous/synopticrecordingsettings. In2015,theStanfordVLFGroupociallydisbandedtheirresearch.Inthefall of2016,theauthorhadtheopportunitytoyouttoStanfordUniversityandretrieve 28

PAGE 43

oldequipment.Itwasherethatthegroupbeganimplementingahybridsystem. TheStanfordreceiversweresimilartotheNemesissystem,buthadseveralchanges inordertogetbetterperformanceinfrequencyresponseandnoisereduction.The StanfordreceiversareshowninFigure3.10. Figure3.10:Stanfordreceiversystem.Antennastructureupperleft,pre-amplier uppermiddle,receiverupperright,andblockdiagrambottom. ThemajorsystemdierencebetweentheNemesisandStanfordreceiverwas theuseofaninternalGPSmodule.InStanford'sreceivers,aFPGAandcrystal oscillatorwereusedtogeneratethe1ppsand100kHzppssignals.Whilethismade thereceiversmorecompactandcheapertoproduce,theleadingissuewasthetiming synchronizationwiththeGPS.Sincethereceiverusedthecrystaloscillator,itwas susceptibletotemperaturevariations.Thiswouldcausedriftsintiming.Sincethe purposeofthisworkwastoobtainveryaccuratetimingdataacquisitiontodetermine timeofarrivalofthesferics,ahybridsystemwasdevised. Thehybridsystemwouldusethepre-amplieroftheStanfordsystemandthe 29

PAGE 44

receiver,GPSmodule,andsoftwareoftheNemesissystem.Thisallowedforlownoise responseandprecisetimingofdata.Thehybridsystemwasusedfortheobservations presentedinthisthesis. Beforethesystemcouldbeused,acalibrationneededtobedonetoensureaccuratedatawasbeingrecordedinpost-processing.Toconductthecalibration,MATLABwasusedtointerfacewithasignalgenerator.Thesignalgeneratorwasfedinto thepre-ampboxviaaBNCconnectedtoadummyloop.Thedummyloopwasdesignedtouseavoltagedividertodividethesignalsamplitudedowntolevelsnormally seenbythereceiver.Thedummyloopalsoimitatedtheimpedanceoftheantenna byusinginductorsandcapacitors.Thecalibrationcodewouldthenfrequencyand amplitudesweepsignalsthatwerebeingrecordedbythesoftwareatthesametime. Thisallowedthefrequencyresponsetobedeterminedandthereforeallowcorrection factorstobeimplemented.Thecalibrationusedinthisexperimentcanbeshownin Figure3.11 Figure3.11:VLFsystemusedinthisexperimentcalibration 30

PAGE 45

3.2ELFReceiver TheELFreceiverusedinthisexperimentcamefromtheKrakowELFgroupin Poland[11].Thegroupiscomprisedoftwoinstitutions,AstronomicalObservatoryof theJagiellonianUniversityJUandFacultyofElectronicsoftheAGHUniversityof ScienceandTechnologyAGH.Thegroupbegantheirmeasurementsbackin1992. Sofar,thegrouphaswontwoawardsfortheirwork:2010-BronzemedalonGeneva InventionsSalonand2011-CongratulationLetterfromPolishMinistryofHigher Education.Theirworkhasalsobeenimportantintheinvestigationofgravitywaves thatweredetectedin2016[12]. Today,thegrouphasatotalofthreeELFreceivers.Therststationdeployedwas inPolandinthegroupshomecountry.Thegroup,withthehelpofMarkGolkowski, partneredupwiththeUCDElectromagneticsandPlasmaPhysicsGroup.ThecollaborationledtothesecondreceiverdeploymentinHugo,ColoradowheretheUCDElectromagneticsandPlasmaPhysicsGroupnowservicesthestation.Thesitestarted recordingdatain2015.TheneweststationtheKrakowgroupdeployedwasinPatagoniainArgentina.amapoftheirsitescanbefoundinFigure3.12. Figure3.12:MapofELFreceivers[9] 3.2.1ELFHardware WhiletheKrakowELFgrouphavehassixdierenteditionsoftheirreceiver,the systemsoperateinasimilarfashion.Tostart,theantennasusedaremadeoutofa 31

PAGE 46

ferritematerialthatgeneratesaconstantmagneticeldwithaDCvoltagesupply. Themagneticeldisdisruptedwhenthemagneticeldofthesfericinteractswith theconstantmagneticeld.Itisherethatasignalcanbegenerated.Sincethese antennasareverysensitive,theantennasareburiedunderground.Thispreventsany movementthatmightoccur.Evenmovingtheantennasslightlywouldinducenoise astheEarth'smagneticeldperturbstheconstantmagneticeldgeneratedbythe antennas.Fromtheantennas,thesignalthentravelsdownacableandfeedsinto itsrespectivechannel,N/SandE/W.Theantenna'scharacteristicscanbefoundin Table3.2. Table3.2:ELFantennaparameters[9] TheKrakowreceiversystemisfullyautonomous.Thereceiverrunsoofthree deepcyclemarinebatteriesthatareconnectedinparallel.Thestationcanrunon thisbatterybankfortwomonthsatatime.Afterthosetwomonths,anewsetof fullychargedbatteriesneedtobeinstalled.ThedataisstoredonaSDcardwhich isretrievedatthesametimeasthebatteryswapoccurs.Thespecicationsofthe receivercanbefoundinTable3.3.TheversiondeployedinHugoistheELA10. 32

PAGE 47

Table3.3:ELFreceiverspecicationsforallsixeditions[9] TheinsideofthemilitarygradeboxwherethereceiverresidesisshowninFigure 3.13. Figure3.13:InsideofELFcontainer 3.3ExperimentalMethodology 33

PAGE 48

TheexperimentconductedinthisthesisinvolvedsettingupaVLFstationnext totheELFstationinHugo,ColoradoandrecordingforthreedaysJuly19-21. AsdiscussedinChapter3.2,HugoislocatedabouttwohourseastofDenver.The purposeofsettingthereceiversnexttoeachotherwastoanalyzethesamepathsof sfericpropagationandobservehowdierentfrequenciesarriveatdierenttimes. TheexperimentrststartedbysettingupaVLFhybridreceiverdowninthe UCDElectromagneticsandPlasmaPhysicsGrouplaboratory.Herethereceiverwas calibratedbeforedeployment.Afterthat,amateriallistwasmade.Thisincluded thepurchaseofasmall750watt2-strokegasgeneratorandasolarpanelkit.The generatorservedasabackupincasethesolarpanelswerenotabletopowerthe VLFsystem.UnliketheELFstation,theVLFreceiverconsumedsignicantlymore powerbecausethesystemhadtopoweradesktopcomputer,computermonitor,a GPSmodule,andofcourse,thereceiveritself.ItwasmeasuredthattheVLFsystem drew300mAwithoutthemonitorand430mAwiththemonitor.Thismeantthat a45Wattpowersystemneededtobedevised.Thesolarpanelkitusedwasexactly 45Wattswhichmeantthatduringtheday,thepanelscouldpowerthesystem.This assumesclearskiesandthepanelsbeangledperfectly.Sincetheseconditionscould notbesustainedallthetime,thebatterieswerefullychargedandthusthesystem woulddrawfromthestoredenergy.Toaccountforthenight,anextrasetofbatteries werebroughttosustainthesystem.Ifthatfailed,thegeneratorwouldbeused. OnJuly19that4:00amtheauthorsetouttoHugotosetuptheVLFreceiver. Onarrival,theELFstationwasexaminedandpronouncedrecordingandworking. Afterthat,thesetupbegan.Firstsetuptaskwastounloadtheantennasandpre ampbox75feetawayfromtheELFantennasastopreventmutualcouplingbetween thetwosystems.ThisisshowninFigure3.14 34

PAGE 49

Figure3.14:Antennaandpre-ampsetupinHugoonJuly19th,2016 1000feettothenorth,therestoftheequipmentwasunloaded.Thepower systemwasthenplacedanother50feetnorth.Thiswasdonetoensureminimal electromagneticradiationsourcedfromtheinverter.Thepowersystemconsisted ofthesolarpanelsconnectedtothesolarchargingregulator.Theregulatorwas connectedtothebatterybankinparalleltothesolarpanelsontheinputterminals andtheoutputterminalsconnectedtothe1500wattinverter.Thewholesystem setupcanbeshowninFigure3.15. 35

PAGE 50

Figure3.15:BlockDiagramofexperimentsetup Usinganextensioncable,theinverterwasconnectedtoapowerstripthathoused thecomputer,monitor,andGPSmodule.ThiscanbeseeninFigure3.16.Itwasa commonpracticetocoverthissegmentofthesystembecauseitwouldoverheatifit wasindirectsun.ItalsoprotectedthecircuityfromtherainthatoccurredonJuly 20. Figure3.16:Computer,monitor,GPSmodule,GPSantennaconguration 36

PAGE 51

Subsequently,a1000footcableconnectedthereceiverandthepre-amptogether. Itwas1:00pmoncealltheequipmentwasconnected.Thepowersupplywasturned onandtheinitialdatabeganrecordingtoensureeverythingwasworkingproperly. Afterverifyingresults,1:20pmmarkedthestarttimeofrecordingdatacontinuously. Onthehour,batteryvoltageswerecheckedtoensurethattheVLFsystemhad sucientpower.Forthemostpart,thesolarsystemwasabletosupplytherequired power.OnJuly20and21around4:30amtheinverteralarmwentoindicatingthat powerwasdroppingbothdates.Asimplebatteryswapdisabledthealarm.Itwas decidedafterthersttimethepowerdroppedtodrivethesparebatteriesintothe maintownofHugoandchargethematarestarea.Thiswasbenecialbecausethe gasgeneratorandinverterwouldhaveaddedasignicantamountofelectromagnetic radiationneartheantennas. 2:00pmonJuly21markedthelastrecording.Thepowersupplywasturned oandcleanupofthecampsiteandtheequipmentbegan.Leavingthearea,the ELFreceiverwascheckedtoverifyitwasrecordingdataanddidabatterycheckto evaluatethepowerlevelsofthebatteries.Itwouldn'tbeuntilAugustthatthedata couldberetrievedandprocessed. 37

PAGE 52

CHAPTER4 DATARESULTS Inthischapter,thedatafrombothVLFandELFreceiversdatawillbeexamined.DatafromtheGlobalLightningDetectionnetworkGLDwasusedtogetthe locationandtimeofthecausitivelightningofobservedsferics[13].Thisnetwork iscomprisedofmultipleVLFreceiversstationedallaroundtheworldtotriangulate sferics.UsingMATLABscriptcreatedbyMarkGolkowski,thisdatacanbeltered tosetgeographicalboundsandspecifypeakcurrentlimits.Thisisusefulbecause itallowsfortheanalysisofthefourclassicationssetforthinthisthesis.These includedaytimeshortdistances,daytimelongdistances,nighttimeshortdistances, andnighttimelongdistances.Inthiswork,longdistancesarecharacterizedasbeing greaterthan1500kmandshortdistancesareanythinglessthanthat.Usingthemap packagefromMATLAB,distanceiscalculatedbyenteringthelongitudeandlatitude ofthereceiverandsfericlocation. InChapter4.1,sitecorrectionswillbepresented.Thisincludeslookingatthe hardwaregroupdelaysothatamoreaccuratedepictionofthearrivaltimecanbe calculated.InChapter4.2,afewexampleswillbepresentedonhowgroupdelayand timeofarrivalwascomputed.Tableswillthenbepresentedtocaptureall40cases. All40guresandtheirrespectivemapscanbefoundintheappendixsectionofthis thesis. 4.1SiteCorrection Toaccuratelydeterminethegroupvelocityofthesferic,thedelayofthesignals throughthereceivermustbedetermined.FortheVLFreceiveritwasdetermined thatthegroupdelayisontheorderof25 u sfortheVLFreceiver.Forthepurposeof thiswork,thistimeisrelativitysmallcomparedthegroupdelayoftheELFsystem. FromtheKrakowgroup,weweretoldthatthegroupdelaythoughtheELFsystem 38

PAGE 53

wasroughly4.5msandincludeddelayintheantennaaswellaslteringhardware. However,therewasdicultyinfullyconrmingthiswithexperimentandbecause ofthis,anaveragedmeasurablegroupdelaywasdetermined.ThetimingsynchronizationoftheELFreceiverisalsodoneinawaythattheexacttimeofasample maybeobyafractionofthesamplingtime.Thisisbecausewhilethesampling frequencyistunedviaGPStime,theprecisetimingoftherstsampleinaleisnot guaranteedtobeontherisingedgeof1ppsGPSsignal. OnewaytoexperimentallydeterminethegroupdelayintheELFreceiveristo lookatobservationssfericsthatoriginateveryclosetothereceiver.Propagationof suchwaveswillbeminimallyaectedbytheionosphereandgroundwavepropagation willdominate,whichshouldbetravelingatthespeedoflight.Usingtimeofarrival, distance,andthespeedoflightwecandeterminewhenthiswaveshouldhavearrived andwhenitwasactuallyrecorded.Thedierencebetweenthesetwodeterminesthe groupdelaythroughthehardware. Tobeginthisanalysis,let'srstlookatastrikethatoccurred109kmawayfrom theELFstation.ThiscanbefoundinthemapinFigure4.1. Figure4.1:LocationofsfericinproximitytoELFstation 39

PAGE 54

Wethenlookatthetimedomainofbothchannelsandbegintodeterminethe timeofarrivalbytherstpeakasexplainedinChapter2.1.ThisisfoundinFigure 4.2. Figure4.2:TimedomainoftheELFreceiverlookingatN/SandE/Wchannels AdatapointontheE/Wchannelindicatestherstpeakdetectedanditsrespectivetime.TheverticallineindicatesthetimewhentheGLD360networkdetected thedischarge.ThisGLD360determinedsferictimewillalwaysmarkthebeginning ofeverysubsequentplot.Next,theredverticallinetakesthedistancebetweenthe sfericandstationanddividesitbythespeedoflight.Thiswillindicatewhenthe sfericshouldhavearrivedatthestationifitwaspropagatingatthemaximumpossiblevelocity.FromFigure4.2thelegendtellsusthatthearrivaltimefortravelatthe speedoflightshouldbe0.367msaftertheGLDdetectedthesferic.Next,theblue verticallineindicatesthearrivaltimeifthewaveweretotravelat99.3 % thespeedof light.Sincethesfericoccurredveryclosetothestationthisvalue,thisnumberisvery closetothespeedoflightat0.364msaftertheGLDdetection.Finallywelookatthe datapoint.Here,thearrivaltimewasfoundtobe4.506msaftertheGLDdetection. 40

PAGE 55

Thismeansthegroupdelayofthehardwareis 4 : 506 ms )]TJ/F15 11.9552 Tf 11.955 0 Td [(0 : 367 ms =4 : 139 ms Thisprocesswasdonefor13dierentcases.Eachfollowingthesamemethodology.Thegoalwastoaverageall13casestodetermineanaveragedgroupdelay throughthehardware. Table4.1:Tableofsitecorrectionsbasedondistance,speedoflight,andarrivaltime Fromthetableitwascomputedthatonaverage,3.75msshouldbesubtracted fromtheELFtimeofarrivalinordertocompensateforthegroupdelaythrough thehardware.Thiscanalsobehighlightedbylookingatthedistributionusinga histogramasshowninFigure4.3. 41

PAGE 56

Figure4.3:DistributionofgroupdelaythroughELFreceiver 4.2RecordedData Theobservationsinthisexperimentfallintooneoffourclassications.This chapterwillhighlightexamplesforeachclassicationandthenpresenttablesthat reectall40cases.Figuresfromallthecases,asstatedbefore,willbeavailablein theappendix. Beginningwithdaytimeshortdistanceswerstpresentasidebysidecomparison oftherecordedVLFandELFdata.Figure4.4plotsbothtimedomainsignalsand identiestheirrespectiverstpeakswhichisclassiedasthetimesofarrival. 42

PAGE 57

Figure4.4:TimedomainoftheELFandVLFdata JustlikeinChapter4.1,databeginswiththegreenverticallineindicatingthe timeoftheGLDdetectedCGdischarge.Theredandbluelinescorrespondwiththe arrivaltimeatthespeedoflightandafractionofthespeedoflightrespectively.In Figure4.4wecanseethattheVLFtopplottimeofarrivalwascomputedtobe 1.36msaftertheGLDdetection.TimeofarrivalforELFbottomplotindicates atimeofarrivalat4.506ms.ThesetimeswererecordedinTable4.2.Withinthe table,timeofarrivalsareloggedandsitecorrectionfactorisaddedin.Lastly,the groupdelaysarecomputedforcorrecteddataforbothELFandVLFdata. Table4.2:Tableofdaytimeshortdistances BasicstatisticalanalysiswastabulatedinTable4.3.Herewecancomparethe statisticsforallfourcasesforcorrected. 43

PAGE 58

Table4.3:StatisticsofgroupdelayfordaytimeshortdistancesforVLFcorrected data StatisticsfortheELFdatawerealsogeneratedinthesamefashionastheVLF data.ThisisfoundinTableare4.4. Table4.4:StatisticsofgroupdelayfordaytimeshortdistancesforELFcorrected data Thenextsetoftablespresentedaretheremainingthreeclassications.Each classicationwillagainhavestatisticsforVLFandELFdata. 44

PAGE 59

Table4.5:Tableofdaytimelongdistances Table4.6:StatisticsofgroupdelayfordaytimelongdistancesforVLFcorrecteddata Table4.7:StatisticsofgroupdelayfordaytimelongdistancesforELFcorrecteddata 45

PAGE 60

Table4.8:Tableofnighttimeshortdistances Table4.9:StatisticsofgroupdelayfornighttimeshortdistancesforVLFcorrected data Table4.10:StatisticsofgroupdelayfornighttimeshortdistancesforELFcorrected data 46

PAGE 61

Table4.11:Tableofnighttimelongdistances Table4.12:StatisticsofgroupdelayfornighttimelongdistancesforVLFcorrected data Table4.13:StatisticsofgroupdelayfornighttimelongdistancesforELFcorrected data Histogramsweregeneratedforbothdaytimeandnighttime.Thishighlightsdistributionsoftheclassicationsaswellasdetermineoutliars.Daytimehistrogram 47

PAGE 62

canbefoundingure Figure4.5:Histogramofgroupvelocities Apowerfulstatisticaltoolthatemployedhereisthetwo-sampleKolmogorovSmirnovtest,whichprovidesaprobabilityiftwosamplesetsarefromthesame distribution.Inthistestanullhypothesisisproposedthatthetwosamplesetscome fromthesamedistribution.Ap-valueisthencalcualted.Ap-valuebelow0.05is takentomeanthatthetwosamplesetsarefromdierentdistributionsandthenull hypothesisshouldberejected.Forthefourclassicationspresentedinthiswork,the two-sampleKolmogorov-Smirnovtestwasconductedbetweeneachsettodetermine howrelatedonesetistoanother.ThisispresentedinTable4.14. Table4.14:Kolmogorov-Smirnovtestforallfourcasescomparedtooneanother 48

PAGE 63

CHAPTER5 DISCUSSION InChapterfour,datawaspresentedintheformoftables.Thesetablesincluded statisticsofgroupdelayofdaytimeshortdistances,daytimelongdistances,nighttime shortdistances,andnighttimelongdistances.TheKolmogorov-Smirnovtestwasthen presentedtoquantifytherelationshipofthedatasetscomparedtoeachother.Inthis chapter,anindepthanalysiswillbeconductedtoseehowChapter3.3methodology comparestotheoreticalresultspresentedinChapter2.InChapter5.1,resultsfrom Chapter4.1willbeexamined.InChapter5.2,abriefconclusionwillbepresented tohighlighthowtheexperimentpresentedinthisthesiscontributestoknowledgeof theplasmaphysicsintheionosphere. 5.1Analysis ReferencingTable4.2oranyoftheELFcolumnsitcanbeobservedthatthe groupdelayscanattimesbeinaccurate.Forexample,intherstcolumnof4.2,the ELFgroupdelaywascalculatedtobe160 % fasterthanthespeedoflight.Physically thisisimpossible.However,thesamplingfrequencyoftheELFreceiverasmentioned inChapter3.2.1is888Hz.Thismeanstheresolutionissignicantlylowerthanthat oftheVLFreceiver.ThisiswhyalltheELFdatalookscourser.Thearrivaltime indicatedbytherstpeakmightbeobyasample.Thismeansthearrivaltime couldbeobyasmuchas1ms.Forshortdistances,thiswasclearlyanissuesince thearrivaltimeofthesferictravelingatthespeedoflightwasafractionofams. Thisiswhysomeofthedata,especiallysubtractingthesitecorrectionindicatesthat thewaveistravelingfasterthanthespeedoflight.However,thiswasconsistently calculatedsothedistributionsofthedatasetsweretosomedegreeaccurateand thereforetestssuchasKolmogorov-Smirnovwerevalid. InMackay'swork[1],itwasproposedthatduringtheday,slowtailsarevery weakandsometimesnonexistent.ThismeantthattheELFcontentwassignicantly 49

PAGE 64

reducedcomparedtonighttime.Thiswasduetotheionosphericheightasdiscussed inChapter1.2.2.Toseethiseect,refertoFigure5.1 Figure5.1:Timedomainoftwosfericsatequaldistances,oneatnightandduring theday[1] TheKolmogorov-Smirnovtestcansupporttheseresultssimplybylookingat DaytimelongELFvs.NighttimelongELFinTable4.14.Itwasshownthatthenull hypothesiswasrejected,thusmeaningthatthereisasignicantdierencebetween ELFpropagationvelocitydayvs.nightforasignicancelevelof5percent. FortheVLFdatasets,itwasshownthatthenullhypothesiswassupported forDaytimelongVLFvs.NighttimelongVLF.ThiscouldonlymeanthatVLF signalsgeneratedfromsfericsaresupportedduringbothatnightandday.ELF signalshowever,actdierentlyduetotherisingionosphericheightgiventhecuto frequencyandmodespresentedinchapter1. Furthermore,theseresultscanbefurtherprovenbylookingatthestatistical analysisinChapter4.2.TheaveragedgroupdelayforELFdaytimelongwascomputedtobe89.7 % thatofthespeedoflightasshownintable4.7.Comparedto nighttimelongdistancestheaveragegroupdelaywascomputedtobe95.9 % ofthe speedoflightinTable4.13.Thisvalidatesthatatnighttime,ELFsignalsactlike VLFsignalsasshowninTable4.12whichcomputestheaveragedgroupdelaytobe 95.6 % ofspeedoflight. 50

PAGE 65

5.2Conclusion Inthisworkanexperimentwascarriedouttoobservethedierenceinsfericgroup velocitybetweentheELFandVLFbandsfornighttimeanddaytimeionospheric conditions.Theexperimentinvolvedtwoco-locatedreceiversrecordingovera24hour period.Apowersupplyusingasolarpanelandbatterybankwasdeployedtoallow theVLFsystemtooperateothepowergrid.GlobalLightningDetectionNetwork GLD360lightninglocationdatawasusedtomaketimeofarrivalobservationsof sfericsonbothsystems.Forbothsystemsthetimeoftherstpeakwasusedasthe arrivaltime.ThegroupdelaythroughtheELFreceiverwasestimatedusingnearby sfericsandassumingdirectpathpropagationtothereceiver.AKolmogorov-Smirno statisticaltestwasusedtoevaluatedierencesinobservationsoverdayvsnight conditions.ResultsshowagreementwiththeorythatELFpropagationvelocityis stronglyaectedbytheionosphericheightthatchangesfordayvs.night.The resultsshowthatispossibletouseELFsfericarrivaltimeasapotentialionospheric diagnostics.Noiseanduncertaintyintheresultswascausedbythelackofprecision samplingsynchronizationintheELFsystemandthelowsamplingrateof888HZ, whichcouldyielderrorsontheorderofaN0.5ms.Suggestionsforfuturework includeaveragingoveralargernumberofeventsandusingamoresophisticated methodofdeterminingarrivaltimethantherstpeakobservationusedhere.Inthis contextwenotethattheGLD360networkutilizedacanonicalwaveformbanktoget precisiontimeofarrivalforsfericfromVLFobservations.SuchawavebankforELF sfericobservationscouldalsobedeveloped. 51

PAGE 66

APPENDIXA.DaytimeShortDistances FigureA.1: FigureA.2: 52

PAGE 67

FigureA.3: FigureA.4: 53

PAGE 68

FigureA.5: FigureA.6: 54

PAGE 69

FigureA.7: FigureA.8: 55

PAGE 70

FigureA.9: FigureA.10: 56

PAGE 71

FigureA.11: FigureA.12: 57

PAGE 72

FigureA.13: FigureA.14: 58

PAGE 73

FigureA.15: FigureA.16: 59

PAGE 74

FigureA.17: FigureA.18: 60

PAGE 75

FigureA.19: FigureA.20: 61

PAGE 76

APPENDIXB.DaytimeLongDistances FigureB.1: FigureB.2: 62

PAGE 77

FigureB.3: FigureB.4: 63

PAGE 78

FigureB.5: FigureB.6: 64

PAGE 79

FigureB.7: FigureB.8: 65

PAGE 80

FigureB.9: FigureB.10: 66

PAGE 81

FigureB.11: FigureB.12: 67

PAGE 82

FigureB.13: FigureB.14: 68

PAGE 83

FigureB.15: FigureB.16: 69

PAGE 84

FigureB.17: FigureB.18: 70

PAGE 85

FigureB.19: FigureB.20: 71

PAGE 86

APPENDIXC.NighttimeShortDistances FigureC.1: FigureC.2: 72

PAGE 87

FigureC.3: FigureC.4: 73

PAGE 88

FigureC.5: FigureC.6: 74

PAGE 89

FigureC.7: FigureC.8: 75

PAGE 90

FigureC.9: FigureC.10: 76

PAGE 91

FigureC.11: FigureC.12: 77

PAGE 92

FigureC.13: FigureC.14: 78

PAGE 93

FigureC.15: FigureC.16: 79

PAGE 94

FigureC.17: FigureC.18: 80

PAGE 95

FigureC.19: FigureC.20: 81

PAGE 96

APPENDIXD.NighttimeLongDistances FigureD.1: FigureD.2: 82

PAGE 97

FigureD.3: FigureD.4: 83

PAGE 98

FigureD.5: FigureD.6: 84

PAGE 99

FigureD.7: FigureD.8: 85

PAGE 100

FigureD.9: FigureD.10: 86

PAGE 101

FigureD.11: FigureD.12: 87

PAGE 102

FigureD.13: FigureD.14: 88

PAGE 103

FigureD.15: FigureD.16: 89

PAGE 104

FigureD.17: FigureD.18: 90

PAGE 105

FigureD.19: FigureD.20: 91

PAGE 106

REFERENCES [1] C.Mackay Lightninglocationusingtheslowtailsofsferics ,RadioSci.,45, RS5010 [2] M.Golkowski CourseLecture ,Golkowski,M.,April1.Waveguides GroupVelocity.LecturepresentedatCourseLectureinColorado,Denver. [3] kidsbritannica HowLightningdevelops[Showstheformationoflightning]. ,.RetrievedMarch10,2017,from http://kids.britannica.com/elementary/art-183837/Cloud-to-ground-lightningforms-when-negative-electrical-charges-build [4] teleconnections WhatisPlasma[Describes4thstateofmatter.] ,. RetrievedMarch20,2017,fromhttp://tetronics.com/our-technology/what-isplasma/ [5] Luxorion AlIonosphericPerturbations[Ionosphereheights]. ,.Retrieved March20,2017,fromhttp://www.astrosurf.com/luxorion/qsl-perturbation.htm [6] MPQ InducedTransparency[Dispersionrelationplasma]. ,.Retrieved March20,2017,fromhttp://www2.mpq.mpg.de/lpg/research/RelLasPlas/RelLas-Plas.html [7] Greifinger,C.,Greifinger,P. ApproximatemethodfordeterminingELF eigenvaluesintheearth-ionospherewaveguide. ,RadioScience,13,831837.doi:10.1029/rs013i005p00831 [8] Paschal,E.W. TheDesignofBroad-BandVLFReceiverswithAir-CoreLoop Antennas. ,SpaceTelecommunicationsandRadioscienceLaboratory.Retrieved March23,2017. [9] KrakowELFGroup WelcomeonKrakowELFGroupsite.n.d. ,Retrieved March23,2017,fromhttp://www.oa.uj.edu.pl/elf/index.html [10] Cohen,M.,Inan,U.,Paschal,E. SensitiveBroadbandELFVLFRadio ReceptionWiththeAWESOMEInstrument. ,IEEETransactionsonGeoscience andRemoteSensing,48,3-17.doi:10.1109/tgrs.2009.2028334 [11] A.Kuak,J.Kubisz,S.Kucjasz,A.Michalec,J.Mynarczyk, Z.Nieckarz,M.Ostrowski,S.Ziba ExtremelylowfrequencyelectromagneticeldmeasurementsattheHylatystationandmethodologyofsignal analysis ,RadioScience,49,doi:10.1002/2014RS005400,2014 92

PAGE 107

[12] Kowalska-Leszczynska,I.,Bizouard,M.,Bulik,T.,Christensen,N., Coughlin,M.,Gokowski,M.,Rohde,M. Globallycoherentshortdurationmagneticeldtransientsandtheireectongroundbasedgravitational-wave detectors. ,ClassicalandQuantumGravity,34,074002.doi:10.1088/13616382/aa60eb [13] Said,R.K.,M.B.Cohen,andU.S.Inan. Highlyintenselightningoverthe oceans:EstimatedpeakcurrentsfromglobalGLD360observations. ,Journalof GeophysicalResearch:Atmospheres,118,6905-6915.doi:10.1002/jgrd.50508 93