Download LECTURE 11: MAGNETIC SURVEYS Magnetic surveys use

GG304 Lecture 11
3/10/11
1
LECTURE 11: MAGNETIC SURVEYS
Magnetic surveys use observations of magnetization variations among crustal
rocks to make inferences about crustal structures. Net magnetization in rocks is
r
the vector combination of both remanent magnetization ( Mr ) and magnetization
r
induced by Earth’s present-day magnetic field ( Mi ).
r r
If the Königsberger ratio Qn = Mr Mi >>1, then crustal
! observations can be
interpreted as remanent magnetism (oceanic
basalts).
!
If Qn << 1, then crustal
magnetism is induced, is oriented parallel to the Earth’s
!
field, and crustal minerology determines the magnitude (e.g., hematite).
!
Flux-gate magnetometer (1nT, vector magnetometer). Two coils are wrapped around 2 ferromagnetic strips. AC current is applied through a
primary coil wrapped oppositely around the two
strips. If a magnetic field is present, a secondary
coil senses the induced field.
Proton-precession magnetometer (1 nT, total
field). Hydrogen protons spin in an applied a
magnetic field, and precess due to torque from
background magnetism. The field is given by
B = 2"f # p ; f is the precessional frequency and
" p = 2.675 # 108 s$1T $1 is the gyromagnetic ratio.
!
!
Absorption-cell magnetometer (0.1 nT, total field). The light absorbed and
emitted by some gasses (e.g., caesium) depends on the magnetic field because
of electron precession: B = 2"f # e where " e ~ 1800" p .
Clint Conrad
!
!
11-1
University of Hawaii
GG304 Lecture 11
3/10/11
2
Magnetic surveys involve measuring the magnetic field, making known
corrections and comparing those measurements with the International
Geomagnetic Reference Frame (IGRF, a model of Earth’s field to degree n=10).
Measurements are made on land or using airplanes or boats (proton precession).
The measurement device must be separated from the airplane or boat.
Magnetic gradiometers measure differences in the magnetic field between two
absorption cell magnetometers a fixed distance apart (e.g., on a rod). Near a
magnetic body, "B between the sensors will be large.
Corrections for magnetic measurements
!
Diurnal variation. Earth’s magnetic field
has day-night variations associated with
interactions between the solar wind and
ionosphere; they can be removed using
concurrent observations at a base station.
Altitude corrections are determined from gradients of the dipole field:
µ m 1+ 3cos2 "
The total magnetic field is given by: Bt = Br2 + B"2 = 0
4#
r3
"Bt
µ m 1+ 3cos2 %
3B
= #3 0
=# t
The vertical gradient is:
4
"r
4$
r
r
!
This ranges from 0.015 nT/m at the equator to 0.03 nT/m near the poles.
!
Latitude corrections are determined from the northward gradient of Bt
1 #Bt µ 0 m #
3B sin$ cos $
"
=
1+ 3cos2 $ = " t
4
r #$ 4%r #$
r 1+ 3cos2 $
(
)
This range from 0 at the equator and poles to 0.005nT/m at mid-latitudes.
!
Topography corrections may be important (for large magnetized topography).
Clint Conrad
11-2
University of Hawaii
GG304 Lecture 11
3/10/11
3
A magnetic anomaly arises from a magnetization contrast ΔM. The anomaly
depends on the shape and depth of the contrast and on the orientation of the
shape, and on the orientation of the inducing magnetic field. The magnetization
contract may arise from remanent magnetization (oceanic crust), or variations
in the susceptibility k of a body relative to the background susceptibility k0.
For an inducing field F, the magnetization contrast is:
(
)
"M = k # k0 F
The total magnetic field (FT) is the vector sum of Earth’s field (FE) and the field
!
due to a magnetic anomaly (FA). Thus FT = FE + FA. Breaking each field into
vertical (Z) and horizontal (H) components gives:
(F
E
+ FA
2
) = (Z
2
E
) (
+ Z A + HE + HA
)
2
Expanding, removing the small squared terms, and using FE2 = ZE2 + HE2 gives:
"Z %
"H %
FA _ meas = Z A $ E ' + HA $ E ' = Z A sin I + HA cos I cos (
!
# FE &
# FE &
!
()
FE
Measured
! Anomaly
() ( )
FT
FA
where α is the angle between HA and
magnetic north (HE) (the component of
HA in the magnetic north direction is
the only horizontal component that
adds to HA). FA_meas is thus the measured
total anomaly field. Thus, the horizontal
(HA) and vertical (VA) components for
the anomaly field contribute differently,
depending on the inclination of the
Earth’s field.
Clint Conrad
11-3
University of Hawaii
GG304 Lecture 11
3/10/11
4
To estimate the anomaly at the surface, it is useful to consider the anomaly due
to a sheet (or rod) extending infinitely deep (analogous to a monopole at depth
d1), and then subtract the anomaly due to another monopole of opposite sign at
a deeper depth d2. Since the deeper monopole is farther away, it has a smaller
influence, but it does change the observed field.
For inclined fields, it is useful to
remove the skewness of the magnetic
anomaly using reduction to the pole.
In this method, the anomaly is
recalculated for the case of vertical
magnetization. For remanent magnetization, FA must be parallel to FE.
Clint Conrad
11-4
University of Hawaii
GG304 Lecture 11
3/10/11
5
The depth of the magnetic anomaly
can be inferred from the shape of
the anomaly (Peter’s half-slope
method). The depth is given by:
z = d k where 1.5<k<2.0 (approx).
d is the “half-slope distance”
(for vertically-oriented fields).
!
This method works for I~90°;
accuracy decreases as I decreases.
Poisson’s Relation simplifies prediction of magnetic anomalies by
relating them to gravity anomalies
(Δgz). Poisson showed that the magnetic potential W due to a verticallymagnetized body (magnetization
contrast ΔMz) is given by:
µ % #M z (
W= 0'
*#gz
4" & G#$ )
where Δρ & Δgz are density
!
contrast & gravity anomaly
Then the gravity anomaly for a buried sphere "gz =
1
z
W = µ 0"M zR 3
3
z2 + x2
(
)
3/2
4#
z
G"$R 3
3
z2 + x2
(
(
(
)
3/2
becomes:
)
2z 2 # x 2
$W 1
3
which gives "Bz = #
= µ 0"M zR
5/2
$z 3
z2 + x2
!
)
Then vertical magnetic field over a buried horizontal cylinder can be determined:
z2 # x2
1
z
$W 1
2
3
!
! gives "Bz = #
W = µ 0"M zR 2
which
= µ 0 "M zR
2
2
$z 2
z + x2
z2 + x2
(
!
Clint Conrad
(
(
)
11-5
!
)
)
University of Hawaii