Earth's Magnetic FieldBy convention, the "north-seeking" pole corresponding to that at the north end of a compass needle is called the positive pole, and the "south-seeking" pole is referred to as the negative pole The lines of force are directed o utward from a positive (i.e., north) pole and inward to a negative (i.e., south) pole."P. V. Sharma Geophysical Methods in Geo logy, 2nd Edition. Note that this means the Earth's north magnetic pole is a negative po le , because the positive "north-seeking" end of a co mpass needle is attracted toward it. The lines of force re ferred to would be the force o n a positive "test monopole" of unit strength. yGilbert (1500s) recognized Earth's field was similar to a dipole's y1838, Carl Friedrich Gauss proved 95% of Earth's magnetic field is internal, approx. 5% external Earth's field is sum of 3 parts: 1.External Magnetic Field2.Anomalous Induced Magnetic Field 3.Main Magnetic Field1. External magnetic field yabout 1-5% of total field ybiggest secular variation is diurnal, with an amplitude of tens of nT yalso a seasonal variation, i.e., diurnal variation greatest in summerystrongest at equatoryall suggest role of sun 1. EM (UV and x-rays) ionizes particles in ionosphere 2. Sun's tidal force produces cyclic wind currents in ionosphere, which in turn produces electrical currentsoionosphere directly produces 2/3 of observed diurnal effect; induced currents in Earth contribute about 1/3 magnetic storms: external field occasionally variable over minutes, at hundreds of nT or more (magnetic storm)
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
By convention, the "north-seeking" pole corresponding to that at the north end of a compass
needle is called the positive pole, and the "south-seeking" pole is referred to as the negative pole
The lines of force are directed outward from a positive (i.e., north) pole and inward to a negative(i.e., south) pole." P. V. Sharma Geophysical Methods in Geology, 2nd Edition.
Note that this means the Earth's north magnetic pole is a negative pole, because the positive"north-seeking" end of a compass needle is attracted toward it. The lines of force referred to
would be the force on a positive "test monopole" of unit strength.
y Gilbert (1500s) recognized Earth's field was similar to a dipole's
y 1838, Carl Friedrich Gauss proved 95% of Earth's magnetic field is internal,approx. 5% external
Earth's field is sum of 3 parts:
1. External Magnetic Field
2. Anomalous Induced Magnetic Field 3. Main Magnetic Field
1. External magnetic field
y about 1-5% of total field
y biggest secular variation is diurnal, with an amplitude of tens of nT y also a seasonal variation, i.e., diurnal variation greatest in summer
y strongest at equator y all suggest role of sun
1. EM (UV and x-rays) ionizes particles in ionosphere
2. Sun's tidal force produces cyclic wind currents in ionosphere, which in turnproduces electrical currents
o ionosphere directly produces 2/3 of observed diurnal effect; inducedcurrents in Earth contribute about 1/3
magnetic storms: external field occasionally variable over minutes, at hundredsof nT or more (magnetic storm)
reports useful to predict when not to conduct surveys o 27 day cycles (sunspots rotate with Sun) o fixed-station recording magnetometers provide data on field variability
(e.g., Alaska)
[3/28/20001 propagation forecast based on sunspot activity]
o produced by electrical currents in ionosphere consisting of particlesionized by solar radiation
o South dip pole (I = -90o), approximately at 66 deg S, 143 deg E, fieldstrength 0.7 Oe (70,000 nT)
o magnetic equator: 0 deg inclination contour line; for best-fit dipole field, itis a great circle "tilted" 11o from geographic equator; "real" magneticequator depends on current field values but is shown schematically below
Spherical Harmonic Analysis of Earth's Field
y because magnetic field is conservative and, for a monopole, follows same 1/r 2 dependence as gravity, it, too, obeys Laplace's equation
o Q: Why not just use, say a Fourier series to represent Earth's field? I.e.,what is advantage of using spherical harmonic analysis, Legendrepolynomials, yada yada...
y if purely dipolar, but tilted, g10, g1
1, h1
1 would be only non-zero terms
In other words the best-fit (tilted) dipole field, at r = a (radius of Earth), as discussedearlier, can be analyzed in terms of spherical harmonics:
y B0 is strength of best-fit dipole at magnetic equator
y as mentioned above axis of dipole is tilted about 11 degrees to spin (geographic)axis, dipole moment is 8 x 1022 Am2, N pole approximately at 79o N, 71o W, Spole approximately at 79o S, 109o E
Non-Dipole Field
y Non-dipole field is just Earth's total (main) field minus tilted dipole field
y shows four major anomalies (quadrupolar) y can be constructed from spherical harmonic coefficients by setting g1
0, g11, h1
1 = 0
Secular variation
y one of the few "solid Earth" phenomena that change significantly over ahuman lifetime
y data go back to at least 1500s! Rregular observations of magnetic field madesince 1540 at London, later Paris (figure from McElhenny)
y data go back to at least 1500s (London Observatory) y change about 50 - 150 nT/year most places (see gs, hs) mostly related to non-
dipole field y westward drift: non-dipole field drifts about 0.2 deg longitude per year
o produces decreases and increases at some localities o indicates that core rotating more slowly than mantle/crust
y dipole field changing also; decreasing 1/2000 per year
International Geomagnetic Reference Field (IGRF)
y IGRF is just the main field as defined by spherical harmonic coefficients (external field
excluded)y it is a reference field in the sense that in exploration work, which is concerned with the
shallow crustal induced field, we subtract IGRF from measured field values in a region,to remove a regional field
y to express the secular variation in the Earth's main field, a new set of constants in the spherical harmonic expansion of the field are made from thelatest magnetic data, at 5 year intervals, and time-rate-of-change in field at
end of the 5 year interval is computed for extrapolating into the future. y for exploration field work, it is important to subtract the IGRF for the time period thedata were collected
y example: to find field in June, 2003 (2003.5), extrapolate by using IGRF2000values for 2000.0 plus secular terms for 2000.0 times 3.5; to find field in 1994,interpolate between 1990.0 and 1995.0 coefficients
y example:
Model: USGS90 Latitude : 35 N
Date : 10/6/93 Longitude: 97 W Elevation: 300.000 m
D I H X Y Z F
deg min deg min nT nT nT nT nT
--- --- --- ---- ----- ----- ---- ----- -----
6 3.0 64 14.1 22914 22787 2414 47474 52715
Model: USGS90 Latitude : 35 N
Date : 10/6/83 Longitude: 97 W Elevation: 300.000 m
D I H X Y Z F
deg min deg min nT nT nT nT nT
--- --- --- ---- ----- ----- ---- ----- -----
6 56.3 64 16.5 23199 23029 2802 48149 53447
Field Elements
y Earth's field can be separated into
vector components:
y where F is the total fieldintensity, and X, Y, Z and Hare the north, east, vertical
and horizontal components,respectively
y inclination: angle field makeswith horizontal ("dip")
where Um is magnetic
colatitude; Jm is magnetic
latitude y declination: angle horizontal
field makes with true north y X, Y and Z can be found from
|F| (magnitude of total field) and declination, D, and inclination, I
y define a quantity (analogous to power in seismology) called mean square field per
harmonic degree:
y gotten by adding up square of terms of all orders, m, for each degree l. y for lower order terms (e.g., 10 or less, as in IGRF), use IGRF coefficients
y for very high order (short wavelength) terms ( ), use Fourier analysis of field strength from aeromagnetic data (great-circle airborne magnetic survey at 3km altitude)
y note that above illustration based on Magsat datay Another illustration of spectral roll-off y strong roll-off of low-degree terms indicates a deep source y downward continuation of low degree terms (1-8) indicates the spectrum would
be white (no roll-off) at 0.47a y therefore, long wavelength terms generated in outer core
y further evidence for outer core source: o dipole and non-dipole components change in direction and magnitude with
time o motion is of order 0.2o per year (~20 km/yr) o major non-dipole features move westward, hence called westward drift o this is ~105 times rate of mantle convection o thus implies origin in fluid core
y less rapid roll-off indicates a much shallower source, out ~10 km of crust
y paramagnetism: weak susceptibility possessed by most materials y diamagnetism: weak negative susceptibility (e.g., halite, anhydrite, H2O) y ferro- and ferrimagnetism: magnetite, pyrrhotite, ilmenite, hematite, etc.)
Curie temperature
y above about 500-700 oC, minerals cease being ferromagnetic (about what depthis this?)
y since para- and diamagnetism are weak, must attribute low degree componentsof field to electric currents
y mantle is poor electrical (and thermal) conductor, so currents are in Fe/Ni outer core
Mineral Formula Curie Temperature
magnetite Fe3O4 578oC
maghemite KFe2O3 675
o
C hematite EFe2O3 680oC
Source of High Degree/Order Components of Magnetic Field
y must have had external field to kick this off (Sun, especially in T-Tauri phase),but now self-sustaining
y magnetohydrodynamics: especially difficult because flow of conducting core inpresence of its own field gives rise to the currents causing the field, but then wehave:
Lenz's Law: the induced currentwill appear in such a directionthat it opposes the change thatproduces it
y this means the core mustdo work to maintain thefield
y the work turns into Jouleheating in core (I2R) ==> P
= IE, E = IR, ==> P = I2R
y where does work (energy)come from?
o estimated 109 - 1011 W required; for comparison:
earthquakes:1012 W
Earth's totalheat flux:4x1013 W
o precessional torqueexerted on core bymantle probablyinsignificant
o latent heat of fusion from solidifying core: crystallization drives convection
o radioactivity drives thermal convection y thermal convection must provide significantly more heat than
in order to be efficient y
40K is only radioactive isotope compatible with core materials y would require 0.1% K in core (equivalent to 67% of K in a chondritic Earth)