List of Tables ................................................ vii
List of Figures ................................................ ix
Abstract ..................................................... xiii
1. Introduction к Background .................................. 1
1.1 Introduction ............................................... 1
1.2 Background ................................................. 3
1.3 Historical Context ......................................... 4
1.4 Observing the Geomagnetic Field ............................ 6
1.5 Sources of the Geomagnetic Field .......................... 16
1.6 Mathematical Description of the Geomagnetic Field ......... 30
1.7 Geomagnetic Field Models .................................. 36
2. External Perturbations: As seen by the CHAMP satellite &
the TIE-GCM ............................................... 41
2.1 Introduction .............................................. 41
2.2 Dates Selected for Investigation .......................... 43
2.3 TIE-GCM Method ............................................ 47
2.4 A Quick Solar Quiet Verification .......................... 49
2.5 Calculation of Magnetic Perturbations ..................... 51
2.6 F10.7 Variation ............................................ 52
2.7 Kp Variation .............................................. 59
2.8 The TIE-GCM as a possibility for correcting magnetic
field data ................................................ 64
2.9 Conclusions ............................................... 75
3. Internal Variations: South Atlantic Anomaly from
the Earth's Surface to the Core-Mantle Boundary ........... 76
3.1 The South Atlantic Anomaly ................................ 76
3.2 Magnetic Observatories near the South Atlantic Anomaly .... 79
3.3 Field Models Utilized in this Study ....................... 80
3.4 Tracking the Center of the South Atlantic Anomaly ......... 81
3.5 Axial Dipole Moment - A Role in the SAA? .................. 87
3.6 Magnetic Radial Flux at the Core-Mantle Boundary .......... 96
3.7 Association of Total Unsigned Flux with Geomagnetic
Jerks .................................................... 104
4. Conclusions & Perspectives ............................... 113
4.1 ... for the External Field Perturbations ................. 113
4.2 ... for the Internal Field Variations .................... 114
APPENDICES .................................................... 116
A. Technical Aspects of Executing the TIE-GCM ................. 116
A.1 The Eclipse Machine .................................... 110
A.2 Procedure for Executing the TIE-GCM .................... 117
A.3 Comparison of the v1.6 and v1.8 TIE-GCM ................ 119
A.4 Altitude Variation in the Perturbation Calculation ..... 121
B. February 14, 2002 & August 4, 2004 Dayside Orbit Ranks ..... 123
С. Kp Dayside Orbit Ranks for the Quietest Day of Each Year
between 2001-2005 .......................................... 128
D. Plots of the Axial Moment Rate of Change ................... 139
REFERENCES .................................................... 146
BIOGRAPHICAL SKETCH ........................................... 156
LIST OF TABLES
2.1 The dates selected as the quietest day of each month
from 2001-2005 using International Q days ................. 43
2.2 The quietest day for each month in 2001 and its
associated model and magnetic activity parameters ......... 44
2.3 The quietest day for each month in 2002 and its
associated model and magnetic activity parameters ......... 44
2.4 The quietest day for each month in 2003 and its
associated model and magnetic activity parameters ......... 45
2.5 The quietest day for each month in 2004 and its
associated model and magnetic activity parameters ......... 45
2.6 The quietest day for each month in 2005 and its
associated model and magnetic activity parameters ......... 46
2.7 The constant values for POWER and CTPOTEN used in
the TIE-GCM as a way of varying the Kp .................... 60
2.8 Goodness of Fit Rankings of individual dayside orbit
tracks for runs of TIE-GCM using different values of Kp
for Feb 14, 2002 for the BF and Br components ............. 61
2.9 The quietest day of the year from 2001-2005 ............... 63
2.10 The overall most highly ranked Kp values for the
quietest day of the year in terms of component, year
and statistic ............................................. 63
2.11 Comparisons of the Lesur Model and the TIE-GCM for all
data on August 14, 2001 ................................... 66
2.12 Comparisons of the Lesur Model and the TIE-GCM for
mid-latitudes between ±50° on August 14, 2001 ............. 66
2.13 Gaussian fit parameters for the residual error
distributions of Models 1-5 ............................... 71
3.1 Some of the nearest ground magnetic observatories to
the South Atlantic Anomaly ................................ 79
3.2 Ranges for the rate of change of the axial dipole
moment at the CMB for every 10 years using gufm1 .......... 90
3.3 Ranges for the rate of change of the axial dipole
moment at the CMB for CM4, Magsat, OSVM, and CHAOS
models .................................................... 93
3.4 Linear fit parameters of trend segments in the total
unsigned flux shown in Fig. 3.19 ......................... 104
B.1 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Feb 14, 2002 for the BF and Br components ............. 124
B.2 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Feb 14, 2002 for the Bθ and Bφ components ............. 125
B.3 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Aug 4, 2004 for the BF and Br components .............. 126
B.4 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Aug 4, 2004 for the Bθ and Bφ components .............. 127
C.1 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Jun 28, 2001 for the BF and Br components ............. 129
C.2 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Jun 28, 2001 for the Bθ and Bφ components ............. 130
C.3 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different, values of Kp
on May 24, 2002 for the BF and Br components ............. 131
C.4 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on May 24, 2002 for the Bθ and Bφ components ............. 132
C.5 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Dec 19, 2003 for the BF and Br components ............. 133
C.6 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Dec 19, 2003 for the Bθ and Вφ components ............. 134
C.7 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Dec 4, 2004 for the BF and Br components .............. 135
C.8 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Dec 4, 2004 for the Bθ and Вφ components .............. 136
C.9 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different values of Kp
on Dec 23, 2005 for the BF and Br components ............. 137
C.10 Goodness of Fit Rankings of individual dayside orbit
tracks for TIE-GCM runs using different, values of Kp
on Dec 23, 2005 for the Bθ and Bφ components ............. 138
LIST OF FIGURES
1.1 The geomagnetic field at the Earth's surface ............... 4
1.2 A sketch of the Earth's geomagnetic field lines ............ 5
1.3 Geomagnetic field components at the Sitka (SIT) Magnetic
Observatory ................................................ 8
1.4 The global distribution of INTERMAGNET observatories ....... 9
1.5 Diagram of the CHAMP satellite with locations for
the main instrument packages .............................. 11
1.6 CHAMP satellite orbit decay ............................... 15
1.7 The main sources of the Earth's magnetic field ............ 17
1.8 Global secular variation .................................. 18
1.9 An example of secular variation from the Niemegk
Magnetic Observatory ...................................... 19
1.10 An example of some geomagnetic jerks in Europe ............ 20
1.11 Association of Geomagnetic Jerks with Length of Day
variations ................................................ 21
1.12 The MF5 Lithospheric Field ................................ 22
1.13 Diagram of the magnetosphere .............................. 23
1.14 Ionospheric election density profiles ..................... 25
1.15 Diagram of the ionosphere ................................. 26
1.16 The Kp index for July October 2003 ........................ 28
1.17 The Dst index for October 2003 ............................ 30
1.18 Magnetic Field Components ................................. 31
1.19 Geocentric North, East, Center coordinate system .......... 32
1.20 The power spectrums of various magnetic field models ...... 37
1.21 Martian magnetic field .................................... 38
2.1 Activity indices including the Kp range (red) and
F10.7 (blue) for the selected rank 1 Q-days of each
month ..................................................... 47
2.2 The eastward and northward components of
the height-integrated horizontal current density,
in A/m, predicted by the TIE-GCM for February 14, 2002
using GPI inputs .......................................... 48
2.3 The Sq current system for equinox conditions in units of
kA ........................................................ 50
2.4 The northward and eastward components of the magnetic
perturbation, in nT, predicted by the TIE GCM for
February 14, 2002 using GPI inputs ........................ 53
2.5 The total field and downward component of the magnetic
perturbation, in nT, predicted by the TIE-GCM for
February 14, 2002 using GPI inputs ........................ 54
2.6 The CHAMP residual and TIE-GCM perturbation prediction
data along the satellite orbit track for one orbit pass
on February 14. 2002 between ±50° latitude ................ 55
2.7 Dayside orbit passes for February 14, 2002 showing
TIE-GCM predictions using different F10.7 and CHAMP/CHAOS
an CHAMP/CHAOS/TIE-GCM residuals .......................... 57
2.8 Time-series of the average orbit pass statistics MDEV
and Mean for each of the selected days spanning
the years 2001-2003 for the Bθ component .................. 58
2.9 A comparison of the effects of varying Kp on the TIE-GCM
prediction for a dayside orbit pass on February 14,
2002, using a constant F10.7 of 190 ........................ 62
2.10 A sample dayside orbit comparing the Lesur Model with
the TIE-GCM ............................................... 65
2.11 The data distribution for the Magfit Models ............... 68
2.12 A Sample orbit showing the TIE-GCM correction for
Model 3 ................................................... 69
2.13 Global maps of the TIE-GCM correction ..................... 70
2.14 The error distributions for Magfit Model 1 ................ 71
2.15 The error distributions for Magfit Model 2 ................ 72
2.16 The error distributions for Magfit Model 3 ................ 73
2.17 Difference plots for Models 1, 2 and 3 .................... 74
3.1 The 30-80 keV proton flux count for August 2005 ........... 77
3.2 Proton flux in a slice through the Earth .................. 78
3.3 The SAA ground track from 1590-2005 and the total field
from CHAOS in 2005 ........................................ 82
3.4 SAA ground track and strength from 1590-2005 .............. 83
3.5 The velocity of the SAA computed using the gufm1 .......... 84
3.6 SAA track for CM4 and IGRF ................................ 85
3.7 SAA ground track and strength from 5000B.C.-2005A.D.
calculated using various models ........................... 87
3.8 The gufm1 rate of change of the axial moment for every
50 years between 1600 and 1950 at the CMB for spherical
harmonic degree n=10 in units of mT/century ............... 89
3.9 CM4 rate of change of the axial dipole moment for 1960
1990 at the CMB calculated for n=10 and n=13 in units of
mT/century ................................................ 91
3.10 CHAOS, CM4 & OSVM rate of the change of axial moment in
2000 and 2005 at the CMB for n=10 and n=13 in units of
mT/century ................................................ 92
3.11 CHAOS rate of change of the axial moment for 2000 & 2005
and the difference at the CMB, n=10 in units of
mT/century ................................................ 94
3.12 Magsat & CHAOS rate of the change of axial moment in
1980, 2000 & 2005 at the CMB for either n=10 or n=18 in
units of mT/century ....................................... 95
3.13 The radial magnetic field for 2002.5 at the core-mantle
boundary using the CHAOS model ............................ 96
3.14 The secular variation of the radial field at
the core-mantle boundary computed using the CHAOS model
for 2002.5 ................................................ 97
3.15 Maps of the global flux calculated from the CM4 for
years 1960, 1980, and 2000 labeled with the locations
of two reversed-flux patches .............................. 99
3.16 A series of plots of flux polarity calculated using
the gufm1 for spherical harmonic degree 10 ............... 101
3.17 Comparison of the total unsigned flux and normal
polarity flux computed using the gufm1 ................... 102
3.18 Evolution of magnetic flux associated with
reversed-flux patches, computed using the gufm1 at
degree n=10 from 1590-1990 ............................... 103
3.19 The total unsigned magnetic flux computed from various
geomagnetic models from 1960-2005 ........................ 105
3.20 The east component of the secular variation at
a selection of SAA area, magnetic observatories .......... 106
3.21 The total unsigned flux, its first time-derivative and
its second time-derivative calculated using the gufm1
and compared with the sign-changed declination
component of secular variation from CLF .................. 108
3.22 Maps of both the radial fluх polarity at the CMB and
total field at the surface for 1600, 1650, 1700, 1750,
and 1800 ................................................. 110
3.23 Maps of both the radial flux polarity at the CMB and
total field at the surface for 1850, 1900, 1950, and
1990 ..................................................... 111
3.24 Maps of both the radial flux polarity at the CMB and
total field at the surface for 1790 and 1870 ............. 112
4.1 SWARM Mission satellites ................................. 114
A.1 A comparison of the v1.6 and v1.8 TIE-GCM for a dayside
orbit pass on February 14, 2002, using a constant
F10.7=190 and constant Kp=0 ............................... 120
A.2 A comparison of the v1.6 and v1.8 TIE GCM for
a nightside orbit pass on February 14, 2002, using
a constant F10.7=190 and a constant Kp=0 .................. 120
A.3 Difference of maximum altitude range in computation of
magnetic perturbation .................................... 122
D.1 The gufm1 rate of change of the axial moment for every
10 years between 1600 and 1740 at the CMB for spherical
harmonic degree n=10 in units of mT/century .............. 140
D.2 The gufm1 rate of change of the axial moment for every
10 years between 1750 and 1890 at the CMB for spherical
harmonic degree n=10 in units of mT/century .............. 141
D.3 The gufm1 rate of change of the axial dipole nionicmt
for every 10 years between 1900 and 1990 at the CMB for
spherical harmonic degree n=10 in units of mT/century .... 142
D.4 Rate of change of the axial dipole moment for the CM4,
CHAOS, OSVM and Magsat at the CMB for spherical
harmonic degree n=10 in units of mT/century .............. 143
D.5 Rate of change of the axial dipole moment for the CM4,
CHAOS, OSVM and Magsat at the CMB for spherical
harmonic degree n=13 in units of mT/century .............. 144
D.6 The rate of change of the axial dipole moment for CHAOS
and CM4 models and the difference at the CMB for
spherical harmonic degree n=10 in units of mT/century .... 145
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