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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
Anomaly associated with
buried metallic materials
Computed magnetic field
produced by bedrock
Results obtained from
inverse modeling
Bedrock configuration
determined from gravity survey
Where are the drums and
how many are there?
Locating Trench
Boundaries
Theoretical model
Examination of trench for
internal magnetic anomalies.
actual field data
Gilkeson et al., 1986
Trench boundaries - field data
Trench Boundaries - model data
Gilkeson et al., 1986
Locating abandoned wells
Abandoned Wells
From Martinek
Abandoned Well - raised relief plot of
measured magnetic field intensities
From Martinek
Falls Run Coal Mine Refuse Pile
Magnetic Intensity
Wire Frame
Gochioco and Ruev, 2006
40
30
Site 3 2:34
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Site 3 2:39
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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
The text uses 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
monopole
vs.
Toxic Waste
dipole
The earth’s main magnetic field
Measuring the Earth’s magnetic field
Proton Precession Magnetometers
Steve Sheriff’s Environmental Geophysics Course
Tom Boyd’s Introduction to Geophysical Exploration Course
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 Elements
Magnetic north pole: point where
field lines point vertically downward
The compass
needle points to
the magnetic
north pole.
Geomagnetic north pole: pole associated with the
dipole approximation of the earth’s 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
Today’s Space Weather
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
Diurnal variations
http://www.earthsci.unimelb.edu.au/ES304
/MODULES/ MAG/NOTES/tempcorrect.html
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
N
S
Magnetic fields are fundamentally associated with
circulating electric currents; thus 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
M  pl
Thus
p
and A  kFE
p  kAFE
where
yielding
The cgs unit for pole
strength is the ups
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, more ambiguously, as F
dyne
1
 an Oersted
ups

 dyne
Force
H


  

 pole strength  ups
 p  ups
H
(or
F
)


  2 2
 r  cm
ups
thus 1 Oersted  1 2
cm
p  Fr 2 yields  p  Oersted-cm2
Note also that 1 Oersted = 105 nT
&
1 nT = 1 
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 (per unit pole) is simply
m
r
As we have done repeatedly with the force, we divide it
by unit mass, charge or pole to obtain
m
" F" 2
r
an acceleration, electric or magnetic field intensity.
Doing the same with the potential yields a
potential per unit pole strength, or just
m
V
r
Most importantly, working with potentials offers us some
simplification since the denominator is in r and not r2. It offers
useful simplification when characterizing the dipole field.
Basic Magnetic Unit and Vector Concepts
Problem - At a point 20 cm from the center of a thin magnetized
rod 40 cm long and equidistant from its ends, the magnetic field
is 500 nT. What is the pole strength in Oersted-cm2?
Sign conventions imply that the test pole is positive.
HR=2Hx=500nT
UNITS - nanoteslas, ups, Oersteds …..
105
Given H R  2 H x
what is H x ?
HRX = 500nT
Then, what is H+ or H-? Once we know this,
we can then determine the pole strength.
H = p/r2
so p = Hr2
Bring questions to class Tuesday
after Thanksgiving break –
November 28th
We will meet in the 310