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| | One of the best techniques inside that folks with diabetes can manage their mass is eating in a healthy way plus still lose mass is by growing their fiber ingestion. Vegetable and fruits are the greatest source of usual dietary fibers. So, persons with diabetes are often suggested to take inside ample of fresh greens. But, diabetics cannot take inside significant amounts of fruits considering fruits contain fructose, which gets changed into glucose inside the blood. So, diabetic individuals cannot receive their full supply of fiber from victuals alone.<br><br><br><br>It's certainly a big decision beginning about a new weight reduction program. Excitement, anticipation, a little of worry and apprehension. yet by following the standard steps one will reach one's goals and gain self esteem and self-confidence in the task.I hope these basic secrets can encourage you to start on a sensible fat loss system and assist we in making the right decisions before beginning a weight reduction plan.<br><br>To many women, BMI calculations may seem a fairly complicated and complex procedure which has no hope of understanding. But, which is completely untrue considering BMI calculation for ladies is not several scientific secret or magic. If you have ever chosen an online [http://safedietplans.com/calories-burned-walking calories burned walking] for girls online, you'd recognize at this point that if might require you to insert your height and weight before providing a amount because a final output.<br><br>We will say which obesity is a main condition which we are facing now days because persons are so busy inside their lifetime which they don't get time even to keep their body inside ideal shape. But, nearly all of we feel like putting extra fat from your body. Before we consider throwing mass from your body or putting up mass you really need to be aware of the exact calculation which we need to function on. BMI is a source that actually helps we to understand about the actual proportion of fat you ought to take out or place up.<br><br>Sara Fincher is a effective property agent plus, at five feet 3 and 125 pounds she looks plus feels good. But is wasn?t thus long ago which Sara tipped the scales at 200 pounds, and, like many people she couldn?t lose weight, in spite of struggling many diet and exercise programs.<br><br>Measuring a person's waist circumference puts most 'dislikers' of the BMI (see above)at ease considering it enables for a more accurate measuring of a person's body fat. If a muscular individual is rated as obese about the BMI, measuring their waist circumference will determine if that individual is indeed overweight.<br><br>By being aware of the importance of utilizing this type of calculator, you'll be able to spread the word that girls all over the world should utilize it irrespective of their age or nationality. You can do all of these and more once you recognize the value of utilizing a calories burned walking calculator for girls. |
| [[Image:Geodynamo Between Reversals.gif|thumb|Computer simulation of the [[Earth]]'s field in a period of [[normal polarity]] between reversals.<ref name=selfconsistent/> The lines represent magnetic field lines, blue when the field points towards the center and yellow when away. The rotation axis of the Earth is centered and vertical. The dense clusters of lines are within the Earth's core.<ref name=Glatzmaier>{{cite web |url=http://es.ucsc.edu/~glatz/geodynamo.html |title=The Geodynamo |last=Glatzmaier |first=Gary |publisher=University of California Santa Cruz |accessdate=20 October 2013}}</ref>]]
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| '''Earth's magnetic field''' (also known as the '''geomagnetic field''') is the [[magnetic field]] that extends from the [[Earth]]'s interior to where it meets the [[solar wind]], a stream of charged particles emanating from the [[Sun]]. Its magnitude at the Earth's surface ranges from 25 to 65 micro [[Tesla (unit)|Tesla]] (0.25 to 0.65 [[Gauss (unit)|Gauss]]). It is approximately the field of a [[magnetic dipole]] tilted at an angle of 10 degrees with respect to the rotational axis—as if there were a bar magnet placed at that angle at the center of the Earth. However, unlike the field of a bar magnet, Earth's field changes over time because it is generated by the motion of molten iron alloys in the Earth's [[outer core]] (the [[geodynamo]]).
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| The [[North Magnetic Pole]] wanders, but does so slowly enough that an ordinary [[compass]] remains useful for navigation. However, at random intervals, which average about several hundred thousand years, [[Geomagnetic reversal|the Earth's field reverses]], which causes the north and [[South Magnetic Pole]]s to change places with each other. These reversals of the [[geomagnetic pole]]s leave a record in rocks that allow [[paleomagnetism|paleomagnetists]] to calculate past motions of continents and ocean floors as a result of [[plate tectonics]].
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| The region above the [[ionosphere]] is called the [[magnetosphere]], and extends several tens of thousands of kilometers into [[outer space|space]]. This region protects the Earth from [[cosmic rays]] that would otherwise strip away the upper atmosphere, including the [[ozone layer]] that protects the earth from harmful ultraviolet radiation.
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| ==Importance==
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| The magnetic field of the Earth deflects most of the solar wind. The charged particles in the solar wind would strip away the ozone layer, which protects the Earth from harmful [[ultraviolet]] rays.<ref>{{cite journal |title=Solar wind hammers the ozone layer |first=Quirin |last=Shlermeler |date=3 March 2005 |doi=10.1038/news050228-12 |journal=News@nature |url=http://www.nature.com/news/2005/050228/full/news050228-12.html}}</ref> One stripping mechanism is for gas to be caught in bubbles of magnetic field, which are ripped off by solar winds.<ref>{{cite news |title=Solar wind ripping chunks off Mars |url=http://www.cosmosmagazine.com/news/2369/solar-wind-ripping-chunks-mars |work=Cosmos Online |date=25 November 2008 |accessdate=21 October 2013}}</ref> Calculations of the loss of carbon dioxide from the atmosphere of Mars, resulting from scavenging of ions by the solar wind, indicate that the dissipation of the magnetic field of Mars caused a near-total loss of its atmosphere.<ref>{{harvnb|Luhmann|Johnson|Zhang|1992}}</ref><ref>[http://scign.jpl.nasa.gov/learn/plate1.htm Structure of the Earth]. Scign.jpl.nasa.gov. Retrieved on 2012-01-27.</ref>
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| The study of past magnetic field of the Earth is known as [[paleomagnetism]].<ref name="McElhinny2000">{{cite book |last1=McElhinny |first1=Michael W. |last2=McFadden |first2=Phillip L. |title=Paleomagnetism: Continents and Oceans |publisher=Academic Press |year=2000 |isbn=0-12-483355-1 |ref=harv}}</ref> The polarity of the Earth's magnetic field is recorded in [[igneous rock]]s, and [[Geomagnetic reversals|reversals of the field]] are thus detectable as "stripes" centered on [[mid-ocean ridge]]s where the [[seafloor spreading|sea floor]] is spreading, while the stability of the [[geomagnetic pole]]s between reversals has allowed paleomagnetists to track the past motion of continents. Reversals also provide the basis for [[magnetostratigraphy]], a way of [[geochronology|dating]] rocks and sediments.<ref>{{cite book |last1=Opdyke |first1=Neil D. |last2=Channell |first2=James E. T. |title=Magnetic Stratigraphy |publisher=Academic Press |year=1996 |isbn=978-0-12-527470-8 |ref=harv}}</ref> The field also magnetizes the crust, and [[magnetic anomalies]] can be used to search for deposits of metal [[ores]].<ref>{{cite book |last1=Mussett |first1=Alan E. |last2=Khan |first2=M. Aftab |title=Looking into the Earth: An introduction to Geological Geophysics |year=2000 |publisher=Cambridge University Press |isbn=0-521-78085-3 |ref=harv}}</ref>
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| Humans have used [[compasses]] for direction finding since the 11th century A.D. and for navigation since the 12th century.<ref>{{cite book |last=Temple |first=Robert |title=The Genius of China |publisher=Andre Deutsch |year=2006 |isbn=0-671-62028-2 |ref=harv}}</ref> Although the [[North Magnetic Pole]] does shift with time, this wandering is slow enough that a simple [[compass]] remains useful for navigation.
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| Variations in the magnetic field strength have been correlated to rainfall variation within the [[tropics]].<ref>{{cite news |url=http://planetearth.nerc.ac.uk/news/story.aspx?id=296 |title=Link found between tropical rainfall and Earth's magnetic field |work=Planet Earth Online |date=20 January 2009 |publisher=National Environment Research Council |accessdate=19 April 2012}}</ref>
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| ==Main characteristics==
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| ===Description===
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| [[File:XYZ-DIS magnetic field coordinates.svg|thumb|Common coordinate systems used for representing the Earth's magnetic field.]]
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| At any location, the Earth's magnetic field can be represented by a three-dimensional vector (see figure). A typical procedure for measuring its direction is to use a compass to determine the direction of magnetic North. Its angle relative to true North is the ''declination'' ({{math|<var>D</var>}}) or ''variation''. Facing magnetic North, the angle the field makes with the horizontal is the ''inclination'' ({{math|<var>I</var>}}) or ''dip''. The ''intensity'' ({{math|<var>F</var>}}) of the field is proportional to the force it exerts on a magnet. Another common representation is in {{math|<var>X</var>}} (North), {{math|<var>Y</var>}} (East) and {{math|<var>Z</var>}} (Down) coordinates.<ref name=MMMch2/>
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| ====Intensity====
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| The intensity of the field is often measured in [[Gauss (unit)|gauss (G)]], but is generally reported in [[Tesla (unit)|nanotesla (nT)]], with 1 G = 100,000 nT. A nanotesla is also referred to as a gamma (γ).<ref name=NGDC>{{cite web |url=http://www.ngdc.noaa.gov/geomag/faqgeom.shtml |title=Geomagnetism Frequently Asked Questions |publisher=National Geophysical Data Center |accessdate=21 October 2013}}</ref> The [[Tesla]] is the [[SI]] unit of the [[Magnetic field]], '''B'''. The field ranges between approximately 25,000 and 65,000 nT (0.25–0.65 G). By comparison, a strong [[refrigerator magnet]] has a field of about {{convert|100|G|T}}.<ref>{{cite web |url=http://www.magnet.fsu.edu/education/tutorials/magnetminute/tesla-transcript.html |last1=Palm |first1=Eric |title=Tesla |publisher=National High Magnetic Field Laboratory |year=2011 |accessdate=20 October 2013}}</ref>
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| A map of intensity contours is called an ''isodynamic chart''. As the [[Earth's magnetic field#Geographical variation|2010 World Magnetic Model]] shows, the intensity tends to decrease from the poles to the equator. A minimum intensity occurs over South America while there are maxima over northern Canada, Siberia, and the coast of Antarctica south of Australia.<ref name="renamed_from_2010_on_20131022170733"/>
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| ====Inclination====
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| {{Main|Magnetic dip}}
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| The inclination is given by an angle that can assume values between -90° (up) to 90° (down). In the northern hemisphere, the field points downwards. It is straight down at the [[North Magnetic Pole]] and rotates upwards as the latitude decreases until it is horizontal (0°) at the magnetic equator. It continues to rotate upwards until it is straight up at the [[South Magnetic Pole]]. Inclination can be measured with a [[dip circle]].
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| An ''isoclinic chart'' (map of inclination contours) for the Earth's magnetic field is shown [[#Geographical variation|below]].
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| ====Declination====
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| {{Main|Magnetic declination}}
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| Declination is positive for an eastward deviation of the field relative to true north. It can be estimated by comparing the magnetic north/south heading on a compass with the direction of a [[celestial pole]]. Maps typically include information on the declination as an angle or a small diagram showing the relationship between magnetic north and true north. Information on declination for a region can be represented by a chart with isogonic lines (contour lines with each line representing a fixed declination).
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| ===Geographical variation===
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| <center>
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| Components of the Earth's magnetic field at the surface from the [[World Magnetic Model]] for 2010.<ref name="renamed_from_2010_on_20131022170733">{{Cite report |authors=Maus, S., S. Macmillan, S. McLean, B. Hamilton, A. Thomson, M. Nair, and C. Rollins |year=2010 |title=The US/UK World Magnetic Model for 2010-2015 |url=http://www.ngdc.noaa.gov/geomag/WMM/data/WMM2010/WMM2010_Report.pdf |publisher=National Geophysical Data Center |accessdate=18 October 2013}}</ref>
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| </center>
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| <gallery mode=packed align=center heights=155px>
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| File:WMM2010 F MERC.pdf|Intensity
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| File:World Magnetic Inclination 2010.pdf|Inclination
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| File:World Magnetic Declination 2010.pdf|Declination
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| </gallery>
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| ===Dipolar approximation===
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| [[Image:Geomagnetisme.svg|thumb|The variation between magnetic north (N<sub>m</sub>) and "true" north (N<sub>g</sub>).]]
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| {{See also|Dipole model of the Earth's magnetic field}}
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| Near the surface of the Earth, its magnetic field can be closely approximated by the field of a [[magnetic dipole]] positioned at the center of the Earth and tilted at an angle of about 10° with respect to the [[Earth's rotation|rotational axis]] of the Earth.<ref name=NGDC/> The dipole is roughly equivalent to a powerful bar [[magnet]], with its south pole pointing towards the [[Geomagnetic pole|geomagnetic North Pole]].<ref>{{cite news |first=Anne |last=Casselman |title=The Earth Has More Than One North Pole |newspaper=Scientific American |date=28 February 2008 |url=http://www.scientificamerican.com/article.cfm?id=the-earth-has-more-than-one-north-pole |accessdate=21 May 2013}}</ref> This may seem surprising, but the north pole of a magnet is so defined because, if allowed to rotate freely, it points roughly northward (in the geographic sense). Since the north pole of a magnet attracts the south poles of other magnets and repels the north poles, it must be attracted to the south pole of Earth's magnet. The dipolar field accounts for 80–90% of the field in most locations.<ref name=MMMch2/>
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| {{Clear}}
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| ===Magnetic poles===
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| [[File:Magnetic North Pole Positions.svg|thumb|The movement of Earth's North Magnetic Pole across the Canadian arctic, 1831–2007.]]
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| The positions of the magnetic poles can be defined in at least two ways: locally or globally.<ref>{{cite journal |first1=Wallace A. |last1=Campbell |url=http://onlinelibrary.wiley.com/doi/10.1029/96EO00237/abstract |title="Magnetic" pole locations on global charts are incorrect |journal=Eos, Transactions American Geophysical Union |volume=77 |issue=36 |page=345 |year=1996 |doi=10.1029/96EO00237 |bibcode=1996EOSTr..77..345C |ref=harv }}</ref>
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| One way to define a pole is as a point where the [[magnetic field]] is vertical.<ref>{{cite web |url=http://deeptow.whoi.edu/northpole.html |title=The Magnetic North Pole |publisher=Woods Hole Oceanographic Institution |accessdate=21 October 2013}}</ref> This can be determined by measuring the inclination, as described above. The inclination of the Earth's field is 90° (upwards) at the [[North Magnetic Pole]] and -90°(downwards) at the [[South Magnetic Pole]]. The two poles wander independently of each other and are not directly opposite each other on the globe. They can migrate rapidly: movements of up to {{convert|40|km}} per year have been observed for the North Magnetic Pole. Over the last 180 years, the North Magnetic Pole has been migrating northwestward, from Cape Adelaide in the [[Boothia Peninsula]] in 1831 to {{convert|600|km}} from [[Resolute Bay]] in 2001.<ref name="inconstant"/> The ''magnetic equator'' is the line where the inclination is zero (the magnetic field is horizontal).
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| The global definition of the Earth's field is based on a mathematical model. If a line is drawn through the center of the Earth, parallel to the moment of the best-fitting magnetic dipole, the two positions where it intersects the Earth's surface are called the North and South [[geomagnetic pole]]s. If the Earth's magnetic field were perfectly dipolar, the geomagnetic poles and magnetic dip poles would coincide and compasses would point towards them. However, the Earth's field has a significant [[Multipole expansion|non-dipolar]] contribution, so the poles do not coincide and compasses do not generally point at either.
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| {{Clear}}
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| ==Magnetosphere==
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| [[File:Magnetosphere Levels.svg|thumb|An artist's rendering of the structure of a magnetosphere. 1) Bow shock. 2) Magnetosheath. 3) Magnetopause. 4) Magnetosphere. 5) Northern tail lobe. 6) Southern tail lobe. 7) Plasmasphere.]]
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| {{Main|Magnetosphere}}
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| Earth's magnetic field, predominantly dipolar at its surface, is distorted further out by the [[solar wind]]. This is a stream of charged particles leaving the Sun's [[corona]] and accelerating to a speed of 200 to 1000 kilometres per second. They carry with them a magnetic field, the [[interplanetary magnetic field]] (IMF).<ref name=MerrillMagnetosphere>{{cite book |last=Merrill |first=Ronald T. |title=Our Magnetic Earth: The Science of Geomagnetism |year=2010 |publisher=The University of Chicago Press |location=Chicago |isbn=9780226520506 |pages=126–141}}</ref>
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| The solar wind exerts a pressure, and if it could reach Earth's atmosphere it would erode it. However, it is kept away by the pressure of the Earth's magnetic field. The [[magnetopause]], the area where the pressures balance, is the boundary of the [[magnetosphere]]. Despite its name, the magnetosphere is asymmetric, with the sunward side being about 10 [[Earth radius|Earth radii]] out but the other side stretching out in a [[magnetotail]] that extends beyond 200 Earth radii.<ref name=ParksIntro>{{cite book|last=Parks|first=George K.|title=Physics of space plasmas : an introduction|year=1991|publisher=Addison-Wesley|location=Redwood City, Calif.|isbn=0201508214|location=Chapter 1}}</ref> Sunward of the magnetopause is the [[bow shock]], the area where the solar wind slows abruptly.<ref name=MerrillMagnetosphere/>
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| Inside the magnetosphere is the [[plasmasphere]], a donut-shaped region containing low-energy charged particles, or [[Plasma (physics)|plasma]]. This region begins at a height of 60 km, extends up to 3 or 4 Earth radii, and includes the [[ionosphere]]. This region rotates with the Earth.<ref name=ParksIntro/> There are also two concentric tire-shaped regions, called the [[Van Allen radiation belt]]s, with high-energy ions (energies from 0.1 to 10 million [[Electronvolt|electron volts]] (MeV)). The inner belt is 1–2 Earth radii out while the outer belt is at 4–7 Earth radii. The plasmasphere and Van Allen belts have partial overlap, with the extent of overlap varying greatly with solar activity.<ref>{{cite press release|title=Cluster shows plasmasphere interacting with Van Allen belts |date=10 September 2013 |url=http://sci.esa.int/cluster/52802-cluster-shows-plasmasphere-interacting-with-van-allen-belts/ |authors=Fabien Darrouzet, Johan De Keyser and C. Philippe Escoubet |publisher=European Space Agency |accessdate=22 October 2013}}</ref>
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| As well as deflecting the solar wind, the Earth's magnetic field deflects [[cosmic ray]]s, high-energy charged particles that are mostly from outside the [[Solar system]]. (Many cosmic rays are kept out of the Solar system by the Sun's magnetosphere, or [[heliosphere]].<ref>{{cite news|title=Shields Up! A breeze of interstellar helium atoms is blowing through the solar system |author=<!-- Author not provided --> |date=27 September 2004 |newspaper=Science@NASA |accessdate=23 October 2013}}</ref>) By contrast, astronauts on the Moon risk exposure to radiation. Anyone who had been on the Moon's surface during a particularly violent solar eruption in 2005 would have received a lethal dose.<ref name=MerrillMagnetosphere/>
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| Some of the charged particles do get into the magnetosphere. These spiral around field lines, bouncing back and forth between the poles several times per second. In addition, positive ions slowly drift westward and negative ions drift eastward, giving rise to a [[ring current]]. This current reduces the magnetic field at the Earth's surface.<ref name=MerrillMagnetosphere/> Particles that penetrate the ionosphere and collide with the atoms there give rise to the lights of the [[aurora (astronomy)|aurora]]e and also emit [[X-rays]].<ref name=ParksIntro/>
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| The varying conditions in the magnetosphere, known as [[space weather]], are largely driven by solar activity. If the solar wind is weak, the magnetosphere expands; while if it is strong, it compresses the magnetosphere and more of it gets in. Periods of particularly intense activity, called [[geomagnetic storm]]s, can occur when a [[coronal mass ejection]] erupts above the Sun and sends a shock wave through the Solar System. Such a wave can take just two days to reach the Earth. Geomagnetic storms can cause a lot of disruption; the "Halloween" storm of 2003 damaged more than a third of NASA's satellites. The largest documented storm occurred in 1859. It induced currents strong enough to short out telegraph lines, and aurorae were reported as far south as Hawaii.<ref name=MerrillMagnetosphere/><ref>{{cite journal|first=Sten |last=Odenwald |title=The great solar superstorm of 1859 |journal=Technology through time |publisher=NASA |volume=70 |year=2010 |url=http://sunearthday.gsfc.nasa.gov/2010/TTT/70.php |accessdate=24 October 2013}}</ref>
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| ==Time dependence==
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| ===Short-term variations===
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| [[Image:Magnetic Storm Oct 2003.jpg|thumb|'''Background''': a set of traces from magnetic observatories showing a [[magnetic storm]] in 2000.<br /> '''Globe''': map showing locations of observatories and contour lines giving horizontal magnetic intensity in [[Micro-|μ]] [[Tesla (unit)|T]].]]
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| The geomagnetic field changes on time scales from milliseconds to millions of years. Shorter time scales mostly arise from currents in the [[ionosphere]] ([[ionospheric dynamo region]]) and [[magnetosphere]], and some changes can be traced to [[geomagnetic storm]]s or daily variations in currents. Changes over time scales of a year or more mostly reflect changes in the [[Earth's interior]], particularly the iron-rich [[Inner core|core]].<ref name=MMMch2/>
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| Frequently, the Earth's [[magnetosphere]] is hit by [[solar flare]]s causing [[geomagnetic storm]]s, provoking displays of [[Aurora (astronomy)|aurorae]]. The short-term instability of the magnetic field is measured with the [[K-index]].<ref>{{cite web |url=http://www.swpc.noaa.gov/info/Kindex.html |title=The K-index |publisher=Space Weather Prediction Center |accessdate=20 October 2013}}</ref>
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| Data from [[THEMIS]] show that the magnetic field, which interacts with the [[solar wind]], is reduced when the magnetic orientation is aligned between Sun and Earth - opposite to the previous hypothesis. During forthcoming [[Coronal mass ejection|solar storms]], this could result in [[Power outage|blackouts]] and disruptions in [[artificial satellite]]s.<ref>{{cite web |first=Bill |last=Steigerwald |url=http://www.nasa.gov/mission_pages/themis/news/themis_leaky_shield.html |title=Sun Often "Tears Out A Wall" In Earth's Solar Storm Shield |work=THEMIS: Understanding space weather |publisher=NASA |date=16 December 2008 |accessdate=20 August 2011}}</ref>
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| ===Secular variation===
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| {{Main|Geomagnetic secular variation}}
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| [[Image:Earth Magnetic Field Declination from 1590 to 1990.gif|thumb|Estimated declination contours by year, 1590 to 1990 (click to see variation).]]
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| Changes in Earth's magnetic field on a time scale of a year or more are referred to as ''secular variation''. Over hundreds of years, [[magnetic declination]] is observed to vary over tens of degrees.<ref name=MMMch2/> A movie on the right shows how global declinations have changed over the last few centuries.<ref name=declination>{{cite journal |last=Jackson |first=Andrew |last2=Jonkers |first2=Art R. T. |last3=Walker |first3=Matthew R. |title=Four centuries of Geomagnetic Secular Variation from Historical Records |journal=Philosophical Transactions of the Royal Society A |volume=358 |pages=957–990 |year=2000 |jstor=2666741 |ref=harv |issue=1768 |bibcode=2000RSPTA.358..957J |doi=10.1098/rsta.2000.0569}}</ref>
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| The direction and intensity of the dipole change over time. Over the last two centuries the dipole strength has been decreasing at a rate of about 6.3% per century.<ref name=MMMch2/> At this rate of decrease, the field would reach zero in about 1600 years.<ref name=GSC>{{cite web |url=http://nrhp.focus.nps.gov |title=Secular variation |work=Geomagnetism |publisher=Canadian Geological Survey |year=2011 |accessdate=18 July 2011}}</ref> However, this strength is about average for the last 7 thousand years, and the current rate of change is not unusual.<ref name=Constable_dipole>{{Cite book |last=Constable |first=Catherine |chapter=Dipole Moment Variation |pages=159–161 |year=2007 |editor-last=Gubbins |editor-first=David |editor2-last=Herrero-Bervera |editor2-first=Emilio |title=Encyclopedia of Geomagnetism and Paleomagnetism |publisher=Springer-Verlag |doi=10.1007/978-1-4020-4423-6_67 |ref=harv |isbn=978-1-4020-3992-8}}</ref>
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| A prominent feature in the non-dipolar part of the secular variation is a ''westward drift'' at a rate of about 0.2 degrees per year.<ref name=GSC/> This drift is not the same everywhere and has varied over time. The globally averaged drift has been westward since about 1400 AD but eastward between about 1000 AD and 1400 AD.<ref name=Dumberry>{{cite journal |last=Dumberry |first=Mathieu |last2=Finlay |first2=Christopher C. |title=Eastward and westward drift of the Earth's magnetic field for the last three millennia |journal=Earth and Planetary Science Letters |volume=254 |pages=146–157 |year=2007 |doi=10.1016/j.epsl.2006.11.026 |ref=harv |bibcode = 2007E&PSL.254..146D |url=http://www.epm.geophys.ethz.ch/~cfinlay/publications/dumberry_finlay_epsl07.pdf}}</ref>
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| Changes that predate magnetic observatories are recorded in archaeological and geological materials. Such changes are referred to as ''paleomagnetic secular variation'' or ''paleosecular variation (PSV)''. The records typically include long periods of small change with occasional large changes reflecting [[geomagnetic excursion]]s and reversals.<ref name=TauxeCh1>{{harvnb|Tauxe|1998|loc=Chapter 1}}</ref>
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| ===Magnetic field reversals===
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| [[Image:Geomagnetic polarity late Cenozoic.svg|right|thumb|180px|Geomagnetic polarity during the late [[Cenozoic Era]]. Dark areas denote periods where the polarity matches today's polarity, light areas denote periods where that polarity is reversed.]]
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| {{main|Geomagnetic reversal}}
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| Although the Earth's field is generally well approximated by a magnetic dipole with its axis near the rotational axis, there are occasional dramatic events where the North and South [[geomagnetic poles]] trade places. Evidence for these ''geomagnetic reversals'' can be found worldwide in [[basalt]]s, sediment cores taken from the ocean floors, and seafloor magnetic anomalies.<ref>{{cite book |last=Vacquier |first=Victor |title=Geomagnetism in marine geology |year=1972 |publisher=Elsevier Science |location=Amsterdam |isbn=9780080870427 |page=38 |edition=2nd}}</ref> Reversals occur at apparently random intervals ranging from less than 0.1 million years to as much as 50 million years. The most recent geomagnetic reversal, called the [[Brunhes–Matuyama reversal]], occurred about 780,000 years ago.<ref name="inconstant">{{cite news |url=http://science.nasa.gov/science-news/science-at-nasa/2003/29dec_magneticfield/ |title=Earth's Inconstant Magnetic Field |work=Science@Nasa |last=Phillips |first=Tony |date=29 December 2003 |accessdate=27 December 2009}}</ref><ref name=MMMch5>{{harvnb|Merrill|McElhinny|McFadden|1996|loc=Chapter 5}}</ref> Another global reversal of the Earth's field, called the Laschamp event, occurred during the last ice age (41,000 years ago). However, because of its brief duration it is labelled an ''excursion''.<ref>{{cite news |url=http://www.sciencedaily.com/releases/2012/10/121016084936.htm |title=Ice Age Polarity Reversal Was Global Event: Extremely Brief Reversal of Geomagnetic Field, Climate Variability, and Super Volcano |doi=10.1016/j.epsl.2012.06.050 |publisher=ScienceDaily |date=16 October 2012 |accessdate=21 March 2013}}</ref><ref name=MMMexcursion>{{harvnb|Merrill|McElhinny|McFadden|1996|pp=148–155}}</ref>
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| The past magnetic field is recorded mostly by [[iron oxides]], such as [[magnetite]], that have some form of [[ferrimagnetism]] or other magnetic ordering that allows the Earth's field to magnetize them. This [[remanent magnetization]], or ''remanence'', can be acquired in more than one way. In lava flows, the direction of the field is "frozen" in small magnetic particles as they cool, giving rise to a [[thermoremanent magnetization]]. In sediments, the orientation of magnetic particles acquires a slight bias towards the magnetic field as they are deposited on an ocean floor or lake bottom. This is called ''detrital remanent magnetization''.<ref name=McElhinny2000/>
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| Thermoremanent magnetization is the form of remanence that gives rise to the magnetic anomalies around [[Mid-ocean ridge|ocean ridges]]. As the seafloor spreads, [[magma]] wells up from the [[Mantle (geology)|mantle]] and cools to form new basaltic crust. During the cooling, the basalt records the direction of the Earth's field. This new basalt forms on both sides of the ridge and moves away from it. When the Earth's field reverses, new basalt records the reversed direction. The result is a series of stripes that are symmetric about the ridge. A ship towing a magnetometer on the surface of the ocean can detect these stripes and infer the age of the ocean floor below. This provides information on the rate at which seafloor has spread in the past.<ref name=McElhinny2000/>
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| [[Radiometric dating]] of lava flows has been used to establish a ''geomagnetic polarity time scale'', part of which is shown in the image. This forms the basis of [[magnetostratigraphy]], a geophysical correlation technique that can be used to date both sedimentary and volcanic sequences as well as the seafloor magnetic anomalies.<ref name=McElhinny2000/>
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| Studies of lava flows on [[Steens Mountain]], Oregon, indicate that the magnetic field could have shifted at a rate of up to 6 degrees per day at some time in Earth's history, which significantly challenges the popular understanding of how the Earth's magnetic field works.<ref name="nature.com">{{cite journal |title=New evidence for extraordinarily rapid change of the geomagnetic field during a reversal |url=http://www.nature.com/nature/journal/v374/n6524/abs/374687a0.html |journal=Nature |date=20 April 1995 |doi=10.1038/374687a0 |last1=Coe|first1=R. S. |last2=Prévot |first2=M. |last3=Camps |first3=P. |volume=374 |issue=6524 |page=687 |bibcode=1995Natur.374..687C |ref=harv |url=http://www.es.ucsc.edu/~rcoe/eart110c/Coeetal_Steens_Nature95.pdf}}</ref>
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| Temporary dipole tilt variations that take the dipole axis across the equator and then back to the original polarity are known as ''excursions''.<ref name=MMMexcursion/>
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| ===Earliest appearance===
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| A paleomagnetic study of Australian red dacite and [[pillow basalt]] has estimated the magnetic field to have been present since at least {{Ma|3450}}.<ref>{{cite journal |url=http://onlinelibrary.wiley.com/doi/10.1029/JB085iB07p03523/abstract |first1=T. N. W. |last1=McElhinney |first2=W. E. |last2=Senanayake |title=Paleomagnetic Evidence for the Existence of the Geomagnetic Field 3.5 Ga Ago |journal=Journal of Geophysical Research |volume=85 |page=3523 |year=1980 |bibcode = 1980JGR....85.3523M |doi=10.1029/JB085iB07p03523 |ref=harv}}</ref><ref name=Tarduno2009>{{cite journal |last=Usui |first=Yoichi |coauthors=Tarduno, John A., Watkeys, Michael, Hofmann, Axel, Cottrell, Rory D. |title=Evidence for a 3.45-billion-year-old magnetic remanence: Hints of an ancient geodynamo from conglomerates of South Africa |journal=Geochemistry Geophysics Geosystems |year=2009 |volume=10 |issue=9 |doi=10.1029/2009GC002496 |bibcode=2009GGG....1009Z07U |ref=harv}}</ref><ref>{{cite journal |last=Tarduno |first=J. A. |coauthors=Cottrell, R. D., Watkeys, M. K., Hofmann, A., Doubrovine, P. V., Mamajek, E. E., Liu, D., Sibeck, D. G., Neukirch, L. P., Usui, Y. |title=Geodynamo, Solar Wind, and Magnetopause 3.4 to 3.45 Billion Years Ago |journal=Science |date=4 March 2010 |volume=327 |issue=5970 |pages=1238–1240 |doi=10.1126/science.1183445 |bibcode=010Sci...327.1238T |pmid=20203044 |ref=harv}}</ref>
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| ===Future===
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| [[Image:Brunhes geomagnetism western US.png|thumb|Variations in virtual axial dipole moment since the last reversal.]]
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| At present, the overall geomagnetic field is becoming weaker; the present strong deterioration corresponds to a 10–15% decline over the last 150 years and has accelerated in the past several years; geomagnetic intensity has declined almost continuously from a maximum 35% above the modern value achieved approximately 2,000 years ago. The rate of decrease and the current strength are within the normal range of variation, as shown by the record of past magnetic fields recorded in rocks (figure on right).
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| The nature of Earth's magnetic field is one of [[heteroscedastic]] fluctuation. An instantaneous measurement of it, or several measurements of it across the span of decades or centuries, are not sufficient to extrapolate an overall trend in the field strength. It has gone up and down in the past for no apparent reason. Also, noting the local intensity of the dipole field (or its fluctuation) is insufficient to characterize Earth's magnetic field as a whole, as it is not strictly a dipole field. The dipole component of Earth's field can diminish even while the total magnetic field remains the same or increases.
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| The Earth's [[North Magnetic Pole|magnetic north pole]] is drifting from northern [[Canada]] towards [[Siberia]] with a presently accelerating rate—{{convert|10|km}} per year at the beginning of the 20th century, up to {{convert|40|km}} per year in 2003,<ref name="inconstant"/> and since then has only accelerated.<ref>{{cite web |url=http://news.nationalgeographic.com/news/2009/12/091224-north-pole-magnetic-russia-earth-core.html |title=North Magnetic Pole Moving Due to Core Flux |last=Lovett |first=Richard A. |date=December 24, 2009}}</ref>
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| ==Physical origin==
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| {{main|Dynamo theory}}
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| The Earth's magnetic field is believed to be generated by electric currents in the conductive material of its core, created by [[convection current]]s due to heat escaping from the core. However the process is complex, and computer models that reproduce some of its features have only been developed in the last few decades.
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| ===Earth's core and the geodynamo===
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| [[Image:Outer core convection rolls.jpg|thumb|A schematic illustrating the relationship between motion of conducting fluid, organized into rolls by the Coriolis force, and the magnetic field the motion generates.<ref>{{cite web |title=How does the Earth's core generate a magnetic field? |work=USGS FAQs |publisher=United States Geological Survey |url=http://www.usgs.gov/faq/?q=categories/9782/2738 |accessdate=21 October 2013}}</ref>]]
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| The Earth, many other planets in the Solar System, the Sun and other stars all generate magnetic fields through the motion of highly [[conductive]] fluids.<ref name=Weiss>{{cite journal |last=Weiss |first=Nigel |title=Dynamos in planets, stars and galaxies |journal=Astronomy and Geophysics |year=2002 |volume=43 |issue=3 |pages=3.09–3.15 |doi=10.1046/j.1468-4004.2002.43309.x|bibcode = 2002A&G....43c...9W }}</ref> The Earth's field originates in its core. This is a region of iron alloys extending to about 3400 km (the radius of the Earth is 6370 km). It is divided into a solid [[inner core]], with a radius of 1220 km, and a liquid [[outer core]].<ref>{{cite journal |last=Jordan |first=T. H. |title=Structural Geology of the Earth's Interior |journal=Proceedings of the National Academy of Sciences |year=1979 |volume=76 |issue=9 |pages=4192–4200 |doi=10.1073/pnas.76.9.4192|bibcode = 1979PNAS...76.4192J }}</ref> The motion of the liquid in the outer core is driven by heat flow from the inner core, which is about {{convert|6000|K}}, to the core-mantle boundary, which is about {{convert|3800|K}}.<ref>{{cite news |title=Earth's Center Is 1,000 Degrees Hotter Than Previously Thought, Synchrotron X-Ray Experiment Shows |date=25 April 2013 |newspaper=ScienceDaily |author=European Synchrotron Radiation Facility |url=http://www.sciencedaily.com/releases/2013/04/130425142355.htm |accessdate=21 October 2013}}</ref> The pattern of flow is organized by the rotation of the Earth and the presence of the solid inner core.<ref name=Buffett2000>{{cite journal |first1=B. A. |last1=Buffett |title=Earth's Core and the Geodynamo |journal=Science |volume=288 |issue=5473 |year=2000 |pages=2007–2012 |doi=10.1126/science.288.5473.2007 |bibcode = 2000Sci...288.2007B |ref=harv}}</ref>
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| The mechanism by which the Earth generates a magnetic field is known as a [[Dynamo theory|dynamo]].<ref name=Weiss/> A magnetic field is generated by a feedback loop: current loops generate magnetic fields ([[Ampère's circuital law]]); a changing magnetic field generates an electric field ([[Faraday's law of induction|Faraday's law]]); and the electric and magnetic fields exert a force on the charges that are flowing in currents (the [[Lorentz force]]).<ref>{{cite book |last=Feynman |first=Richard P. |authorlink=Richard Feynman |title=The Feynman lectures on physics |year=2010 |publisher=BasicBooks |location=New York |isbn=9780465024940 |pages=13-3,15-14,17-2 |edition=New millennium}}</ref> These effects can be combined in a [[partial differential equation]] for the magnetic field called the ''magnetic induction equation'':
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| :<math>\frac{\partial \mathbf{B}}{\partial t} = \eta \nabla^2 \mathbf{B} + \nabla \times (\mathbf{u} \times \mathbf{B}) </math>
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| where {{math|'''u'''}} is the velocity of the fluid; {{math|'''B'''}} is the [[Magnetic field|magnetic B-field]]; and {{math|η{{=}}1/σμ}} is the [[magnetic diffusivity]], a product of the electrical conductivity {{math|σ}} and the [[Permeability (electromagnetism)|permeability]] {{math|μ}} .<ref name=MMMch8>{{harvnb|Merrill|McElhinny|McFadden|1996|loc=Chapter 8}}</ref> The term {{math|∂'''B'''/∂''t''}} is the time derivative of the field; {{math|∇<sup>2</sup>}} is the [[Laplace operator]] and {{math|∇×}} is the [[curl (mathematics)|curl operator]].
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| The first term on the right hand side of the induction equation is a [[diffusion]] term. In a stationary fluid, the magnetic field declines and any concentrations of field spread out. If the Earth's dynamo shut off, the dipole part would disappear in a few tens of thousands of years.<ref name=MMMch8/>
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| In a perfect conductor ({{math|σ{{=}}∞}}), there would be no diffusion. By [[Lenz's law]], any change in the magnetic field would be immediately opposed by currents, so the flux through a given volume of fluid could not change. As the fluid moved, the magnetic field would go with it. The theorem describing this effect is called the ''frozen-in-field theorem''. Even in a fluid with a finite conductivity, new field is generated by stretching field lines as the fluid moves in ways that deform it. This process could go on generating new field indefinitely, were it not that as the magnetic field increases in strength, it resists fluid motion.<ref name=MMMch8/>
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| The motion of the fluid is sustained by [[convection]], motion driven by buoyancy. The temperature increases towards the center of the Earth, and the higher temperature of the fluid lower down makes it buoyant. This buoyancy is enhanced by chemical separation: As the core cools, some of the molten iron solidifies and is plated to the [[inner core]]. In the process, lighter elements are left behind in the fluid, making it lighter. This is called ''compositional convection''. A [[Coriolis effect]], caused by the overall planetary rotation, tends to organize the flow into rolls aligned along the north-south polar axis.<ref name=Buffett2000/><ref name=MMMch8/>
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| The average magnetic field in the Earth's outer core was calculated to be 25 G, 50 times stronger than the field at the surface.<ref>{{cite journal|first1=Bruce A. |last1=Buffett |url=http://www.nature.com/nature/journal/v468/n7326/full/nature09643.html |title=Tidal dissipation and the strength of the Earth's internal magnetic field |journal=[[Nature (journal)|Nature]] |volume=468 |pages=952–954 |year=2010|bibcode = 2010Natur.468..952B |doi = 10.1038/nature09643 |issue=7326 |pmid=21164483|laysummary=http://www.science20.com/news_articles/first_measurement_magnetic_field_inside_earths_core | laysource=Science 20|ref=harv}}</ref>
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| ====Numerical models====
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| The equations for the geodynamo are enormously difficult to solve, and the realism of the solutions is limited mainly by computer power. For decades, theorists were confined to creating ''kinematic dynamos'' in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. Kinematic dynamo theory was mainly a matter of trying different flow geometries and seeing whether they could sustain a dynamo.<ref name=Kono2002>{{cite journal|last=Kono|first=Masaru|coauthors=Paul H. Roberts|title=Recent geodynamo simulations and observations of the geomagnetic field|journal=[[Reviews of Geophysics]]|year=2002|volume=40|issue=4|pages=1–53|doi=10.1029/2000RG000102|bibcode = 2002RvGeo..40.1013K|ref=harv }}</ref>
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| The first ''self-consistent'' dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan<ref>{{cite journal|last=Kageyama|first=Akira|coauthors=Sato, Tetsuya, the Complexity Simulation Group,|title=Computer simulation of a magnetohydrodynamic dynamo. II|journal=Physics of Plasmas|date=1 January 1995|volume=2|issue=5|pages=1421–1431|doi=10.1063/1.871485|bibcode = 1995PhPl....2.1421K|ref=harv }}</ref> and one in the United States.<ref name=selfconsistent>{{cite journal|last=Glatzmaier|first=Gary A.|coauthors=Roberts, Paul H.|title=A three-dimensional self-consistent computer simulation of a geomagnetic field reversal|journal=Nature|year=1995|volume=377|issue=6546|pages=203–209|doi=10.1038/377203a0|bibcode = 1995Natur.377..203G|ref=harv }}</ref><ref>{{cite journal|last=Glatzmaier|first=G|coauthors=Paul H. Roberts|title=A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle|journal=Physics of the Earth and Planetary Interiors|year=1995|volume=91|issue=1–3|pages=63–75|doi=10.1016/0031-9201(95)03049-3|ref=harv|bibcode = 1995PEPI...91...63G }}</ref> The latter received a lot of attention because it successfully reproduced some of the characteristics of the Earth's field, including geomagnetic reversals.<ref name=Kono2002/>
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| ===Currents in the ionosphere and magnetosphere===
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| Electric currents induced in the [[ionosphere]] generate magnetic fields ([[ionospheric dynamo region]]). Such a field is always generated near where the atmosphere is closest to the Sun, causing daily alterations that can deflect surface magnetic fields by as much as one degree. Typical daily variations of field strength are about 25 nanoteslas (nT) (one part in 2000), with variations over a few seconds of typically around 1 nT (one part in 50,000).<ref>{{cite journal |first1=Janez |last1=Stepišnik |title=Spectroscopy: NMR down to Earth |journal=[[Nature (journal)|Nature]] |volume= 439 |pages=799–801 |year=2006|bibcode = 2006Natur.439..799S |doi = 10.1038/439799a |issue=7078 |ref=harv }}</ref>
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| ==Measurement and analysis==
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| ===Detection===
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| The Earth's magnetic field strength was measured by [[Carl Friedrich Gauss]] in 1835 and has been repeatedly measured since then, showing a relative decay of about 10% over the last 150 years.<ref>{{cite journal |journal=[[Annual Review of Earth and Planetary Sciences]] |volume=1988 |issue=16 |page=435 |title=Time Variations of the Earth's Magnetic Field: From Daily to Secular |first1=Vincent |last1=Courtillot |author1-link=Vincent Courtillot |first2=Jean Louis |last2=Le Mouel |doi=10.1146/annurev.ea.16.050188.002133|bibcode = 1988AREPS..16..389C |year=1988 |ref=harv }}</ref> The [[Magsat]] satellite and later satellites have used 3-axis vector magnetometers to probe the 3-D structure of the Earth's magnetic field. The later [[Ørsted (satellite)|Ørsted satellite]] allowed a comparison indicating a dynamic geodynamo in action that appears to be giving rise to an alternate pole under the Atlantic Ocean west of S. Africa.<ref name="pmid11948347">{{cite journal |last1=Hulot |first1=G. |last2=Eymin |first2=C. |last3=Langlais |first3=B. |last4=Mandea |first4=M. |last5=Olsen |first5=N. |title=Small-scale structure of the geodynamo inferred from Oersted and Magsat satellite data |journal=[[Nature (journal)|Nature]] |volume=416 |issue=6881 |pages=620–623 |date=April 2002 |pmid=11948347 |doi=10.1038/416620a |url= |ref=harv|bibcode = 2002Natur.416..620H }}</ref>
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| Governments sometimes operate units that specialize in measurement of the Earth's magnetic field. These are [[geomagnetic observatories]], typically part of a national [[Geological survey]], for example the [[British Geological Survey]]'s [[Eskdalemuir Observatory]]. Such observatories can measure and forecast magnetic conditions such as magnetic storms that sometimes affect communications, electric power, and other human activities.
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| The [[Intermagnet|International Real-time Magnetic Observatory Network]], with over 100 interlinked geomagnetic observatories around the world has been recording the earths magnetic field since 1991.
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| The military determines local geomagnetic field characteristics, in order to detect ''anomalies'' in the natural background that might be caused by a significant metallic object such as a submerged submarine. Typically, these [[magnetic anomaly detector]]s are flown in aircraft like the UK's [[Hawker Siddeley Nimrod|Nimrod]] or towed as an instrument or an array of instruments from surface ships.
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| Commercially, [[geophysical]] [[prospecting]] companies also use magnetic detectors to identify naturally occurring anomalies from [[ore]] bodies, such as the [[Kursk Magnetic Anomaly]].
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| ===Crustal magnetic anomalies===
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| [[Image:Magnetic Field Earth.png|thumb|A model of short-wavelength features of Earth's magnetic field, attributed to lithospheric anomalies.<ref>{{cite web|last=Frey|first=Herbert|title=Satellite Magnetic Models|url=http://core2.gsfc.nasa.gov/terr_mag/sat_models.html|work=Comprehensive Modeling of the Geomagnetic Field|publisher=[[NASA]]|accessdate=13 October 2011}}</ref>]]
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| [[Magnetometer]]s detect minute deviations in the Earth's magnetic field caused by iron [[Artifact (archaeology)|artifacts]], kilns, some types of stone structures, and even ditches and [[midden]]s in [[archaeological geophysics]]. Using magnetic instruments adapted from airborne [[magnetic anomaly detector]]s developed during World War II to detect submarines, the magnetic variations across the ocean floor have been mapped. [[Basalt]] — the iron-rich, volcanic rock making up the ocean floor — contains a strongly magnetic mineral ([[magnetite]]) and can locally distort compass readings. The distortion was recognized by Icelandic mariners as early as the late 18th century. More important, because the presence of magnetite gives the basalt measurable magnetic properties, these magnetic variations have provided another means to study the deep ocean floor. When newly formed rock cools, such magnetic materials record the Earth's magnetic field.
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| ===Statistical models===
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| Each measurement of the magnetic field is at a particular place and time. If an accurate estimate of the field at some other place and time is needed, the measurements must be converted to a model and the model used to make predictions.
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| ====Spherical harmonics====
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| {{See also|Multipole expansion}}
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| [[Image:harmoniques spheriques positif negatif.png|thumb|Schematic representation of spherical harmonics on a sphere and their nodal lines. {{math|<var>P</var><sub>ℓ <var>m</var></sub>}} is equal to 0 along {{math|<var>m</var>}} [[great circle]]s passing through the poles, and along {{math|ℓ-<var>m</var>}} circles of equal latitude. The function changes sign each ℓtime it crosses one of these lines.]]
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| [[Image:VFPt four charges.svg|thumb|Example of a quadrupole field. This could also be constructed by moving two dipoles together. If this arrangement were placed at the center of the Earth, then a magnetic survey at the surface would find two magnetic north poles (at the geographic poles) and two south poles at the equator.]]
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| The most common way of analyzing the global variations in the Earth's magnetic field is to fit the measurements to a set of [[spherical harmonics]]. This was first done by [[Carl Friedrich Gauss]].<ref name=Wallace2003>{{cite book|last=Campbell|first=Wallace H.|title=Introduction to geomagnetic fields|year=2003|publisher=[[Cambridge University Press]]|location=New York|isbn=978-0-521-52953-2|edition=2nd|ref=harv}}, p.1</ref> Spherical harmonics are functions that oscillate over the surface of a sphere. They are the product of two functions, one that depends on latitude and one on longitude. The function of longitude is zero along zero or more great circles passing through the North and South Poles; the number of such ''[[nodal line]]s'' is the absolute value of the ''order'' {{math|<var>m</var>}}. The function of latitude is zero along zero or more latitude circles; this plus the order is equal to the ''degree'' ℓ. Each harmonic is equivalent to a particular arrangement of magnetic charges at the center of the Earth. A ''[[Magnetic monopole|monopole]]'' is an isolated magnetic charge, which has never been observed. A ''[[Magnetic dipole|dipole]]'' is equivalent to two opposing charges brought close together and a ''[[quadrupole]]'' to two dipoles brought together. A quadrupole field is shown in the lower figure on the right.<ref name=MMMch2>{{harvnb|Merrill|McElhinny|McFadden|1996|loc=Chapter 2}}</ref>
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| Spherical harmonics can represent any [[scalar field]] (function of position) that satisfies certain properties. A magnetic field is a [[vector field]], but if it is expressed in Cartesian components {{math|<var>X, Y, Z</var>}}, each component is the derivative of the same scalar function called the ''[[magnetic potential]]''. Analyses of the Earth's magnetic field use a modified version of the usual spherical harmonics that differ by a multiplicative factor. A least-squares fit to the magnetic field measurements gives the Earth's field as the sum of spherical harmonics, each multiplied by the best-fitting ''Gauss coefficient'' {{math|<var>g<sub>m</sub></var><sup>ℓ</sup>}} or {{math|<var>h<sub>m</sub></var><sup>ℓ</sup>}}.<ref name=MMMch2/>
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| The lowest-degree Gauss coefficient, {{math|<var>g</var><sub>0</sub><sup>0</sup>}}, gives the contribution of an isolated magnetic charge, so it is zero. The next three coefficients – {{math|<var>g</var><sub>1</sub><sup>0</sup>}}, {{math|<var>g</var><sub>1</sub><sup>1</sup>}}, and {{math|<var>h</var><sub>1</sub><sup>1</sup>}} – determine the direction and magnitude of the dipole contribution. The best fitting dipole is tilted at an angle of about 10° with respect to the rotational axis, as described earlier.<ref name=MMMch2/>
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| =====Radial dependence=====
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| Spherical harmonic analysis can be used to distinguish internal from external sources if measurements are available at more than one height (for example, ground observatories and satellites). In that case, each term with coefficient {{math|<var>g<sub>m</sub></var><sup>ℓ</sup>}} or {{math|<var>h<sub>m</sub></var><sup>ℓ</sup>}} can be split into two terms: one that decreases with radius as {{math|1/<var>r</var><sup>ℓ+1</sup>}} and one that ''increases'' with radius as {{math|<var>r</var><sup>ℓ</sup>}}. The increasing terms fit the external sources (currents in the ionosphere and magnetosphere). However, averaged over a few years the external contributions average to zero.<ref name=MMMch2/>
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| The remaining terms predict that the potential of a dipole source ({{math|ℓ{{=}}1}}) drops off as {{math|1/<var>r</var><sup>2</sup>}}. The magnetic field, being a derivative of the potential, drops off as {{math|1/<var>r</var><sup>3</sup>}}. Quadrupole terms drop off as {{math|1/<var>r</var><sup>4</sup>}}, and higher order terms drop off increasingly rapidly with the radius. The radius of the [[outer core]] is about half of the radius of the Earth. If the field at the core-mantle boundary is fit to spherical harmonics, the dipole part is smaller by a factor of about 8 at the surface, the quadrupole part by a factor of 16, and so on. Thus, only the components with large wavelengths can be noticeable at the surface. From a variety of arguments, it is usually assumed that only terms up to degree {{math|14}} or less have their origin in the core. These have wavelengths of about {{convert|2000|km}} or less. Smaller features are attributed to crustal anomalies.<ref name=MMMch2/>
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| ====Global models====
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| The [[International Association of Geomagnetism and Aeronomy]] maintains a standard global field model called the [[International Geomagnetic Reference Field]]. It is updated every 5 years. The 11th-generation model, IGRF11, was developed using data from satellites ([[Ørsted (satellite)|Ørsted]], [[CHAMP (satellite)|CHAMP]] and [[SAC-C]]) and a world network of geomagnetic observatories.<ref>{{cite journal |doi=10.5047/eps.2010.11.005 |title=Evaluation of candidate geomagnetic field models for IGRF-11 |year=2010 |authors=C. C. Finlay, S. Maus, C. D. Beggan, M. Hamoudi, F. J. Lowes, N. Olsen, E. Thébault |journal=Earth, Planets and Space |volume=62 |issue=10 |pages=787 |url=http://www.geomag.us/info/Smaus/Doc/Finlay_etal_IGRF11eval_sub.pdf |bibcode = 2010EP&S...62..787F |ref=harv}}</ref> The spherical harmonic expansion was truncated at degree 10, with 120 coefficients, until 2000. Subsequent models are truncated at degree 13 (195 coefficients).<ref>{{cite web |url=http://www.ngdc.noaa.gov/IAGA/vmod/igrfhw.html |title=The International Geomagnetic Reference Field: A "Health" Warning |date=January 2010 |publisher=National Geophysical Data Center |accessdate=13 October 2011}}</ref>
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| Another global field model, called [[World Magnetic Model]], is produced jointly by the National Geophysical Data Center and the [[British Geological Survey]]. This model truncates at degree 12 (168 coefficients). It is the model used by the [[United States Department of Defense]], the [[Ministry of Defence (United Kingdom)]], the [[North Atlantic Treaty Organization]], and the [[International Hydrographic Office]] as well as in many civilian navigation systems.<ref>{{cite web |title=The World Magnetic Model |url=http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml |publisher=National Geophysical Data Center |accessdate=14 October 2011}}</ref>
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| A third model, produced by the [[Goddard Space Flight Center]] ([[NASA]] and [[GSFC]]) and the [[Danish Space Research Institute]], uses a "comprehensive modeling" approach that attempts to reconcile data with greatly varying temporal and spatial resolution from ground and satellite sources.<ref>{{cite web |last=Herbert |first=Frey |title=Comprehensive Modeling of the Geomagnetic Field |url=http://core2.gsfc.nasa.gov/CM/ |publisher=NASA}}</ref>
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| ==Biomagnetism==
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| {{Main|Magnetoception}}
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| Animals including birds and turtles can detect the Earth's magnetic field, and use the field to navigate during [[bird migration|migration]].<ref>{{cite journal |last1=Deutschlander |first1=M. |last2=Phillips |first2=J. |last3=Borland |first3=S. |year=1999 |title=The case for light-dependent magnetic orientation in animals |journal=Journal of Experimental Biology |volume=202 |issue=8 |pages=891–908 |pmid= 10085262 |ref=harv}}</ref> Cows and wild deer tend to align their bodies north-south while relaxing, but not when the animals are under high voltage power lines, leading researchers to believe magnetism is responsible.<ref name='Burda2009'>{{cite journal |doi=10.1073/pnas.0811194106 |title=Extremely low-frequency electromagnetic fields disrupt magnetic alignment of ruminants |year=2009 |last1=Burda |first1=H. |last2=Begall |first2=S. |last3=Cerveny |first3=J. |last4=Neef |first4=J. |last5=Nemec |first5=P. |journal=Proceedings of the National Academy of Sciences |volume=106 |issue=14 |pages=5708|bibcode = 2009PNAS..106.5708B }}</ref><ref name='Nature summary'>{{cite journal |doi=10.1038/458389a |title=Biology: Electric cows |year=2009 |journal=Nature |volume=458 |page=389 |pmid=19325587 |last1=Dyson |first1=P. J. |issue=7237 |bibcode=2009Natur.458Q.389. |ref=harv}}</ref> In 2011 a group of [[Czechs|Czech]] researchers reported their failed attempt to replicate the finding using different [[Google Earth]] images.<ref>{{cite journal |last1=Hert |first1=J |last2=Jelinek |first2=L |last3=Pekarek |first3=L |last4=Pavlicek |first4=A |year=2011 |title=No alignment of cattle along geomagnetic field lines found |journal=Journal of Comparative Physiology |volume=197 |issue=6 |pages=677–682 |pmid= |ref=harv}} [http://link.springer.com/article/10.1007%2Fs00359-011-0628-7]</ref>
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| ==See also==
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| {{Portal|Earth sciences|Physics}}
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| {{Wikipedia books|Geomagnetism}}
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| {{Commons|Earth's magnetic field}}
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| * [[Geomagnetic jerk]]
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| * [[Geomagnetic latitude]]
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| * [[History of geomagnetism]]
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| * [[Magnetic field of the Moon]]
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| * [[Magnetosphere of Jupiter]]
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| * [[Magnetotellurics]]
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| * [[Carnegie (ship)]]
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| * [[Galilee (ship)]]
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| ==References==
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| {{reflist|2}}
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| == Further reading ==
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| {{Refbegin}}
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| * {{cite book|last=Campbell|first=Wallace H.|title=Introduction to geomagnetic fields|year=2003|publisher=[[Cambridge University Press]]|location=New York|isbn=978-0-521-52953-2|edition=2nd|ref=harv}}
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| * {{cite book|first1=Neil F. |last1=Comins |year=2008 |title=Discovering the Essential Universe |publisher=[[W. H. Freeman]] |edition=Fourth |isbn=978-1-4292-1797-2|ref=harv}}
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| * {{cite journal |doi=10.1073/pnas.93.2.646 |last1=Herndon |first1=J. M. |title=Substructure of the inner core of the Earth |journal=[[PNAS]] |volume=93 |issue=2 |pages=646–648 |date=1996-01-23 |pmid=11607625 |pmc=40105|bibcode = 1996PNAS...93..646H |ref=harv }}
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| * {{cite journal |last1=Hollenbach |first1=D. F. |title=Deep-Earth reactor: Nuclear fission, helium, and the geomagnetic field |journal=[[PNAS]] |volume=98 |issue=20 |date=2001-09-25 |doi=10.1073/pnas.201393998 |pmid=11562483 |pmc=58687|bibcode = 2001PNAS...9811085H |last2=Herndon |first2=J. M. |pages=11085–90 |ref=harv }}
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| * {{cite journal |first1=Jeffrey J. |last1=Love |title=Magnetic monitoring of Earth and space |url=http://geomag.usgs.gov/downloads/publications/pt_love0208.pdf |journal=[[Physics Today]] |volume=61 |issue=2 |pages=31–37 |year=2008 |doi=10.1063/1.2883907|bibcode = 2008PhT....61b..31H |ref=harv}}
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| * {{cite journal |last1=Luhmann |first1=J. G. |last2=Johnson |first2=R. E. |last3=Zhang |first3=M. H. G. |title=Evolutionary impact of sputtering of the Martian atmosphere by O<sup>+</sup> pickup ions |journal=[[Geophysical Research Letters]] |volume=19 | issue=21 |pages=2151–2154 |year=1992|ref=harv|bibcode = 1992GeoRL..19.2151L |doi = 10.1029/92GL02485 }}
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| * {{cite book|first=Ronald T. |last=Merrill |year=2010 |title=Our Magnetic Earth: The Science of Geomagnetism|publisher=[[University of Chicago Press]]|isbn=0-226-52050-1|ref=harv}}
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| * {{cite book|last=Merrill|first= Ronald T.|last2=McElhinny|first2=Michael W.|last3=McFadden|first3=Phillip L.|title=The magnetic field of the earth: paleomagnetism, the core, and the deep mantle|publisher=[[Academic Press]]|year=1996|isbn=978-0-12-491246-5|ref=harv}}
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| * {{cite web |url=http://www.newton.dep.anl.gov/askasci/gen99/gen99256.htm |title=Temperature of the Earth's core |work=NEWTON Ask a Scientist |year=1999 |accessdate=September 2011|ref=harv}}
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| * {{cite book |last=Tauxe |first=Lisa |title=Paleomagnetic Principles and Practice |publisher=[[Kluwer]] |year=1998 |isbn=0-7923-5258-0 |ref=harv}}
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| * {{cite journal |first1=J. N. |last1=Towle |title=The Anomalous Geomagnetic Variation Field and Geoelectric Structure Associated with the Mesa Butte Fault System, Arizona |journal=Geological Society of America Bulletin |volume=9 |pages=221–225 |year=1984 |doi=10.1130/0016-7606(1984)95<221:TAGVFA>2.0.CO;2|ref=harv |issue=2|bibcode = 1984GSAB...95..221T }}
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| * {{cite journal |first1=James R. |last1=Wait |author1-link=James R. Wait |year=1954 |title=On the relation between telluric currents and the earth's magnetic field |journal=Geophysics |volume=19 |pages=281–289 |doi=10.1190/1.1437994|bibcode = 1954Geop...19..281W |ref=harv |issue=2}}
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| * {{cite book |first1=Martin |last1=Walt |author1-link=Martin Walt |year=1994 |title=Introduction to Geomagnetically Trapped Radiation |publisher=[[Cambridge University Press]] |isbn=978-0-521-61611-9|ref=harv}}
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| {{Refend}}
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| ==External links==
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| * ''[http://www.agu.org/sections/geomag/background.html Geomagnetism & Paleomagnetism background material]''. American Geophysical Union Geomagnetism and Paleomagnetism Section.
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| * ''[http://geomag.usgs.gov National Geomagnetism Program]''. [[United States Geological Survey]], March 8, 2011.
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| * ''[http://www.geomag.bgs.ac.uk BGS Geomagnetism]''. Information on monitoring and modeling the geomagnetic field. British Geological Survey, August 2005.
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| * William J. Broad, ''[http://www.nytimes.com/2004/07/13/science/13magn.html?ex=1247457600&en=e8f37e14d213ba16&ei=5090&partner=rssuserland Will Compasses Point South?]''. [[New York Times]], July 13, 2004.
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| * John Roach, ''[http://news.nationalgeographic.com/news/2004/09/0927_040927_field_flip.html Why Does Earth's Magnetic Field Flip?]''. National Geographic, September 27, 2004.
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| * ''[http://www.pbs.org/wgbh/nova/magnetic/ Magnetic Storm]''. [[Public Broadcasting Service|PBS]] [[Nova (TV series)|NOVA]], 2003. (''ed''. about pole reversals)
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| * ''[http://www.psc.edu/science/Glatzmaier/glatzmaier.html When North Goes South]''. Projects in Scientific Computing, 1996.
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| * ''[http://www.phy6.org/earthmag/demagint.htm The Great Magnet, the Earth]'', History of the discovery of Earth's magnetic field by David P. Stern.
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| * ''[http://www-spof.gsfc.nasa.gov/Education/wmap.html Exploration of the Earth's Magnetosphere]'', Educational web site by David P. Stern and Mauricio Peredo
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| * ''[http://blackandwhiteprogram.com/interview/dr-dan-lathrop-the-study-of-the-earths-magnetic-field Dr. Dan Lathrop: The study of the Earth's magnetic field]''. Interview with Dr. Dan Lathrop, Geophysicist at the University of Maryland, about his experiments with the Earth's core and magnetic field. 7 - 3 - 2008
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| * [http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html International Geomagnetic Reference Field 2011]
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| * [http://www.vukcevic.talktalk.net/Global%20Mag%20Anomaly.gif Global evolution/anomaly of the Earth's magnetic field] Sweeps are in 10 degree steps at 10 years intervals. Based on data from: The Institute of Geophysics, [http://www.ethz.ch/index_EN ETH Zurich]
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