Download Magnetic Field Variations

http://www.geo.wvu.edu/~wilson/geo252/lect12/mag2.pdf
Environmental and Exploration Geophysics I
Magnetic Methods (I)
tom.h.wilson
[email protected]
Department of Geology and Geography
West Virginia University
Morgantown, WV
Locating Trench
Boundaries
Theoretical model
Examination of trench for
internal magnetic anomalies.
actual field data
Gilkeson et al., 1986
Locating abandoned wells
Abandoned Wells
From Martinek
Falls Run Coal Mine Refuse Pile
Magnetic Intensity
Wire Frame
Magnetic monopoles
Fm12 
p1 p2
4 r122
1
p1
r12
Fm12 Magnetic Force
 Magnetic Permeability
p1 and p2 pole strengths
Coulomb’s Law
p2
Fm12 
p1 p2
4 r122
1
F
1 po
Ho  o 
pt 4 r 2
Force
Magnetic Field
Intensity often written
as H
pt is an isolated test pole
F
1 pE
" FE" 

pt 4 r 2
We will use F instead of H to represent magnetic field
intensity, especially when referring to that of the Earth (FE).
The fundamental magnetic element is a dipole
or combination of one positive and one negative
magnetic monopole. The characteristics of the
magnetic field are derived from the combined
effects of non-existent monopoles.
Dipole
Field
The earth’s main magnetic field
Source of Protons and
DC current source
Proton precession generates
an alternating current in the
surrounding coil
M
GF
f 
F
2L
2
Proton precession frequency (f) is directly
proportional to the main magnetic field intensity F. L
is the angular momentum of the proton and G is the
gyromagnetic ratio which is a constant for all protons
(G = 0.267513/  sec). Hence -
F  23.4874 f
Magnetic north pole: point where
field lines point vertically downward
Compasses point
to the magnetic
north pole.
Geomagnetic north pole: pole associated with the
dipole approximation of the earth magnetic field.
61000
F (nanoteslas or gammas)
60000
59000
58000
57000
56000
55000
54000
53000
1900
1920
1940
1960
Date
1980
2000
Inclination (degrees)
72
71
70
69
68
1900 1920 1940 1960 1980 2000
Date
W
declination (degrees west)
-9
-8
-7
-6
-5
-4
-3
-2
1900 1920 1940 1960 1980 2000
Date
Magnetic Elements for your location
Magnetic Field Variations
Magnetic field variations
generally of non-geologic origin
Long term drift in magnetic declination and inclination
Magnetic fields like gravitational fields are not constant.
Their variations are much more erratic and unpredictable
Today’s Space Weather
Real Time Magnetic field data
In general there are few corrections to apply to magnetic data. The
largest non-geological variations in the earth’s magnetic field are those
associated with diurnal variations, micropulsations and magnetic
storms.
The vertical gradient of the vertical component of the earth’s magnetic
field at this latitude is approximately 0.025nT/m. This translates into
1nT per 40 meters. The magnetometer we have been using in the field
reads to a sensitivity of 1nT and the anomalies we observed at the Falls
Run site are of the order of 200 nT or more. Hence, elevation
corrections are generally not needed.
Variations of total field intensity as a function of latitude are also
relatively small (0.00578nT/m). The effect at Falls Run would have
been about 1/2 nT from one end of the site to the other.
International geomagnetic reference formula
The single most important correction to make is one that
compensates for diurnal variations, micropulsations and magnetic
storms. This is usually done by reoccupying a base station
periodically throughout the duration of a survey to determine
how total field intensity varies with time and to eliminate these
variations in much the same way that tidal and instrument drift
effects were eliminated from gravity observations.
Anomalies - Total Field and Residual
The regional field can be removed by
surface fitting and line fitting
procedures identical to those used in
the analysis of gravity data.
Magnetic susceptibility is
a key parameter, however,
it is so highly variable for
any given lithology that
estimates of k obtained
through inverse modeling
do not necessarily
indicate that an anomaly
is due to any one specific
rock type.
N
S
Opposites attract
N
S
S
N
Magnetic fields are associated fundamentally with
circulating electric currents, so that we can also
formalize concepts like pole strength, dipole moment,
etc. in terms of current flow relationships.
Cross sectional area A
+
pl = n iA
pl is the dipole moment
l
Units of pole strength
-
 niA 
 p      ampere  meter
 l 
I=kF
I  kFE
I is the intensity of magnetization and FE is the ambient
(for example - Earth’s) magnetic field intensity. k is the
magnetic susceptibility.
The intensity of magnetization is equivalent to
the magnetic moment per unit volume or
M
Magnetic dipole
I
V moment per unit volume
and also,
I  kFE .
M pl

I
V
V
Thus
p
and A  kFE
p  kAFE
where
yielding
M  pl
p  kAFE
Recall from our earlier discussions that magnetic
field intensity
p
H or F  2 so that
r
p  Fr 2
Thus providing additional relationships that
may prove useful in problem solving exercises.
For example,
F
kFE A
r2
What does this tell us about units
of these different quantities?
We refer to the magnetic field intensity
as H or ambiguously by some as F

 dyne
Force
H


  

 pole strength  ups
1
dyne
 an Oersted
ups
 p  ups
 H (or F )   2   2
 r  cm
thus 1 Oersted  1
ups
cm 2
Force varies inversely as the square of the distance
between charges, masses or poles. It has the general form
F
m1m2
r2
Potential on the other hand refers to the energy available to
do work and is the integral of the force times displacement.
V    Fdr   
m1m2
dr
2
r
What is this integral?
m1m2
V    Fdr    2 dr
r
Remember the general power rule for integration
n
r
 dr 
1 n 1
r C
n 1
Since n is -2, n+1 = -1 so that the potential V is simply
m
r
As we have done repeatedly with the force, we express it
in terms of force per unit mass, charge or pole to obtain
m
F 2
r
where F is acceleration, electric or magnetic field intensity.
We can do the same with the potential writing it as the
potential per unit pole strength, or just
m
V
r
Note that working with potentials may offer us some
simplification since the denominator is in r and not r2.