1dtu space, technical university of denmark 30140 geophysics part 2: solid earth physics lecture 8:...
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1 DTU Space, Technical University of Denmark
30140 GeophysicsPart 2: Solid Earth Physics
Lecture 8: Physics of Magnetism and Geomagnetism
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2 DTU Space, Technical University of Denmark
Topics of the second part of the course
# Date Topic Chapter in Lowrie Instructor
1 5/2 Earth System Jens Olaf Pepke Pedersen2 12/2 Earth System Jens Olaf Pepke Pedersen3 19/2 Earth System Jens Olaf Pepke Pedersen4 26/2 Earth System Jens Olaf Pepke Pedersen5 5/3 Solid Earth Overview 1 Chris Finlay6 12/3 Gravity 2 Nils Olsen7 19/3 Gravity 2 Nils Olsen8 26/3 Geomagnetism 5 Chris Finlay9 2/4 Geoelectricity 4 Nils Olsen10 9/4 Geomagnetism 5 Chris Finlay 16/4 Easter holidays
11 23/4 Seismology 3 Klaus Mosegaard12 30/4 Seismology 3 Klaus Mosegaard13 7/5 Seismology 3 Klaus Mosegaard
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3 DTU Space, Technical University of Denmark
4.0 A brief history of Geomagnetism
- 100 A.D. Magnetic compass invented
by the Chinese
- 1180 Compass described by Guyot de Provins
and Alexander Neckam in Europe
- 1600 William Gilbert's De Magnete (right):
`Earth itself is a great magnet’
- 1634 Henry Gellibrand realizes that
the geomagnetic field changes in time
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4 DTU Space, Technical University of Denmark
4.0 A brief history of Geomagnetism
- 1701 Edmund Halley publishes the
first geomagnetic field map (right)
- 1770 James Cook documents the
Earth’s magnetic field in the Pacific
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5 DTU Space, Technical University of Denmark
4.0 A brief history of Geomagnetism- 1820 Hans Christian Ørsted shows electric currents
produce magnetic fields
- 1832-1840 Carl Friedrich Gauss (right) measures
absolute magnetic intensity and makes first
global mathematic model of geomagnetic field
- 1906 Bernard Brunhes finds evidence of
geomagnetic reversals
- 1955 Invention of proton magnetometer allows
very accurate intensity determination
- 1980 MAGSAT satellite allows true global coverage of field measurements
- Post 1999: Era of continuous satellite observations
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6 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismWhat is a magnetic field?
- Observation: Nearby electric currents exert forces on each other
- Force on an element dl1 carrying current I1 due to another element dl2 carrying a current I2 is:
- Focusing on the force on dl1 and integrating over the elements dl2
we can write this as
where we have defined the magnetic flux density (or magnetic field) to be
B describes the force exerted on an
electrical current (moving charged particle)
by another electrical current.
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7 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismForces on currents and charged particles
Biot-Savart Law Lorenz force
Units of B : N A-1 m-1 = Tesla (T). 1nT= 10-9 T
(Credit: Lowrie, 2007)
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8 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismMagnetic field due to a long wire
(Credit: Lowrie, 2007)
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9 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismElementary sources of magnetic fields
Short bar magnet Small current loop Uniformly magnetized sphere
(Credit: Lowrie, 2007)
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10 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismMagnetic potential and field due to a dipole
Consider a pair of magnetic poles:
(Credit: Lowrie, 2007)
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11 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismMagnetized material
- Magnetization is the vector sum of all
magnetic moments in the material
- Each magnetic moment mi is associated with a current loop at an atomic scale
- The total magnetic field inside a magnetized material is
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12 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismMagnetized materials
(Credit: Lowrie, 2007)
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13 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismTypes of magnetization
k=C/T : Curie
LawParamagnetic
Paramagnetic
above T=θ:
Curie-Weiss Law
(Credit: Lowrie, 2007)
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14 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismTypes of magnetization
(Credit: Lowrie, 2007)
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15 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismThermo-remanent magnetization
(Credit: Lowrie, 2007)
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16 DTU Space, Technical University of Denmark
4.1 Physics of MagnetismDepositional remanent magnetization
(Credit: Lowrie, 2007)
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17 DTU Space, Technical University of Denmark
4.2 GeomagnetismMeasured Field Components
(Credit: Lowrie, 2007)
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18 DTU Space, Technical University of Denmark
4.2 GeomagnetismMagnetic field sources: Internal & External
Credit: ESA
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19 DTU Space, Technical University of Denmark
4.2 Geomagnetism External current systems: Magnetosphere
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20 DTU Space, Technical University of Denmark
4.2 Geomagnetism External current systems: Ionosphere
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21 DTU Space, Technical University of Denmark
4.2 GeomagnetismExample: Measured External Field Variations
- Regular daily variations due to solar quiet (Sq) current driven by solar heating of the ionosphere
- Irregular variations (e.g. geomagnetic storms) due to enhanced solar activity modulating magnetospheric currents (e.g. ring current amplitude and location)
(Credit: Lowrie, 2007)
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22 DTU Space, Technical University of Denmark
4.2 GeomagnetismSpherical Harmonic Description of Potential
n=m
m=0General case:
n ≠ m
(Credit: Lowrie, 2007)
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23 DTU Space, Technical University of Denmark
4.2 GeomagnetismSpherical harmonic spectra
(Credit: Lowrie, 2007)
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24 DTU Space, Technical University of Denmark
4.2 GeomagnetismSimplest model : An axial dipole
Br F
(Units = 103 nT)
Inclination and field intensity are simply
related to the site latitude:
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25 DTU Space, Technical University of Denmark
4.2 GeomagnetismTotal Intensity - F from IGRF (2010)
IGRF = International Geomagnetic Reference Field, up to SH degree n=13)
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26 DTU Space, Technical University of Denmark
4.2 GeomagnetismInclination - I from IGRF (2010)
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27 DTU Space, Technical University of Denmark
4.2 GeomagnetismEvolution of Declination - D
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28 DTU Space, Technical University of Denmark
4.2 GeomagnetismEvolution of Declination - D
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29 DTU Space, Technical University of Denmark
4.2 GeomagnetismEvolution of Declination - D
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30 DTU Space, Technical University of Denmark
4.2 GeomagnetismDeclination – D from IGRF (2010)
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31 DTU Space, Technical University of Denmark
4.2 GeomagnetismAxial Dipole Decay since 1840
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32 DTU Space, Technical University of Denmark
Next week: Geoelectricity
• Instructor: Prof. Nils Olsen
• Preparation: Read Chapter 4.3 [p.252-276], Lowrie (Geoelectricity)
• For 09.04.14, do Exercises 1-4 and 7-9 in Lowrie Chapter 5.10, pp360. We shall discuss in class.