Global Electrical Conductivity
and
Magnetic Satellite Induction Studies
Steven Constable
Catherine Constable
Scripps Institution of Oceanography
sconstable@ucsd.edu
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http://mahi.ucsd.edu/Steve/MDAT/
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Contents:
• Background: Earth conductivity
• Background: EM induction
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• Some satellite results
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Why mantle electrical conductivity?
• Highly senstitive to phase transitions
• Sensitive to mantle temperature
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• Influenced by volatiles and trace materials
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Conductivity of Earth materials:
Conductivity σ has units of S/m.
Electrical resistivity ρ has units of Ωm.
Silicate minerals are semiconductors σ = σo
A
−
e kT
Shankland, Peyronneau
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& Poirier (1993)
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A simplified Earth:
water, gabbro, granite
olivine + pyroxene
garnet + spinel
m
k
0
7
6
silicate perovskite +
magnesio-wustite
m
k
0
0
9
2
liquid iron
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inner core
outer core
lower mantle
crust
upper mantle
solid iron
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60°C
127°C
227°C
394°C
727°C
Shankland, Peyronneau
1727°C
Silicate perovskite and olivine
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& Poirier (1993)
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Olivine, spinel, and perovskite:
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Xu et al (2003)
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Mixing olivine and spinel:
Conductivity, S/m
10 0
10
HS+
-1
α = 0.1
σ = 0.05 S/m
HS-
10 -2
σ = 0.01 S/m
Allowable region
olivine
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Spinel volume fraction
0.8
spinel
0.9
1
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10 -3
0
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Volatiles in the mantle?
Karato
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Nature (1990)
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Electromagnetic Induction:
Faraday’s Law states that a time-varying magnetic field induces
electric currents in conductors.
∂B
∇×E=−
∂t
Secondary magnetic fields created by these currents appose the
primary magnetic field.
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So, conductors attenuate magnetic fields.
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Skin depth:
zs = 2/(ωµσ)
In practical units
zs ≈ 500 m 1/(σf ) ≈ 500 m ρT
Thus 100 s period signal over a 100 Ω m earth has a skin depth of 50 km.
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Skin depth can be a very useful indicator of energy penetration, but be
careful!
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Density, acoustic velocity, magnetization, and conductivity are the few
physical properties are available for remote sensing, but resolution differs:
Radar: wave equation (same as seismics)
2E
∂
∂E
∇2E = µσ
+ µ 2
∂t
∂t
Inductive EM: diffusion equation
∂E
= µσ
∂t
Gravity, Magnetics, Resistivity: potential fields
∇2 E
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∇2 E = 0
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A time-varying magnetic field:
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A time-varying magnetic field:
Grand Spectrum
Reversals
Cryptochrons?
Amplitude, T/√Hz
Secular variation
?
?
Annual and semi-annual
Solar rotation (27 days)
Daily variation
Storm activity
Quiet days
10 kHz
1 second
1 minute
1 hour
1 day
1 month
Schumann resonances
1 year
1 thousand years
10 million years
Powerline noise
Radio
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Frequency, Hz
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A space-varying magnetic field:
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Using induction to measure Earth conductivity:
• Magnetotelluric (MT) method
Measure electric and magnetic fields
• Geomagnetic depth sounding (GDS) method
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Measure horizontal and vertical magnetic fields
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Magnetelluric method:
ρ(ω) =
T Ey (ω) 2
2πµ Hx (ω)
E
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B
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Geomagnetic depth sounding:
-
+
i
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ρa = f e
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Egbert and Booker: MT and GDS responses
MT
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GDS
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Egbert and Booker: Models
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Satellite GDS:
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Field geometry for satellite GDS:
Write the observed field as the gradient of a scalar potential,
B(r, θ, φ) = −µo∇V (r, θ, φ)
∞ l
m ao l+1
r l m
m
V (r, θ, φ) = ao
il
Pl (cosθ)eimφ
+ el
r
ao
l=1 m=−l
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m (t).
with internal coefficients im
(t)
and
external
e
l
l
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Keeping only the P10 contribution and with r, θ, φ in geomagnetic coordinates
0 ao 2
r 0
0
0
V1 (r, θ, φ) = ao i1
P1 (cosθ)
+ e1
r
ao
r
1
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or
0
a 3 0
Br = −e1 + 2i1
cos(θ)
r
0 0 a 3 Bθ = e1 + i1
sin(θ)
r

  e01
−cos(θ) 2( ar )3cos(θ)
Br

  =
Bθ
i0
sin(θ)
( a )3sin(θ)
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BUT.... magnetic satellites measure more than just induced fields.
Have to remove:
The main (core) field, and its secular variation.
The crustal field due to remanent and induced magnetization.
Ionospheric currents (daily variation)
Field aligned and meridional currents, and seasonal variations.
Equatorial electrojet.
Coupling and induction of the above.
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for which we use CMP3 (Sabaka et al., 2000; 2002) on Magsat.
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Residuals (Magsat - CMP3) for 100,000 data:
400
Total field CMP3-Dst residual, nT
300
200
100
0
-100
-200
0
20
40
60
80
100
120
Geomagnetic colatitude
140
160
180
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-300
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Fits to an individual pass:
50
Br
0
0
-20
Bθ
-40
-60
40
60
80
100
120
Magnetic colatitude
140
-50
40
60
80
100
120
Magnetic colatitude
140
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Br and Bθ, nT
Br,θ residuals, nT
dusk # 332
20
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RMS residuals to 900 dawn and 900 dusk passes
dusk
5.30 nT
8.40 nT
6.05 nT
11.16 nT
6.64 nT
107689
6.15 nT
11.03 nT
5.47 nT
19.53 nT
6.57 nT
99301
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Bθ
Bφ
Br
CMP3 Bθ
CMP3 Br
N
dawn
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Timseries of individual i and e estimates:
50
Int, Ext field, nT
Dusk passes
0
50
100
150
1979.8
50
1979.9
1980
1980.1
1980.2
1980.3
1980.4
1980
1980.1
Year number
1980.2
1980.3
1980.4
0
50
100
150
1979.8
Red - external
Blue - internal
1979.9
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Int, Ext field, nT
Dawn passes
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Satellite Dst (red) and observatory Dst index (blue):
20
Dst index (blue) and Satellite Dst (red), nT
0
-20
-40
-60
-80
-100
-120
1980. 1
1980.11
1980.13
1980.14
Year number
1980.15
1980.16
1980.17
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1980.12
IPPS IN
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-140
1980.09
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The agreement is statistically good:
40
20
0
Satellite Dst, nT
-20
(Sat. Dst - Dst index):
-40
std. deviation = 5.7 nT
-60
mean = 2.4 nT
-80
(+25 nT from CMP3)
-100
-120
-120
-100
-80
-60
-40
-20
Dst index, nT
0
20
40
60
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-140
-140
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Spectra of Dst and satellite Dst:
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Power in Dst estimated from ground and Magsat
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Use multi-taper time series analysis to obtain the transfer function between
e and i.
10
10
Power, nT 2
10
10
10
10
3
red - external
blue - internal
solid - dusk
dashed - dawn
2
1
0
-1
-2
0
2
4
6
Frequency, cycles/day
8
10
12
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10
4
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Coherence2 between e and i.
1
red - dusk
blue - dawn
0.9
0.8
Coherence 2
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
4
6
8
Frequency, cycles per day
10
12
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0
0
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Dusk passes have more power, better coherence. Use band averaging and
coherence weighting of transfer function to estimate
i1
Q1 =
e1
Convert Q1 to complex admittance c using
l − (l + 1)Ql
c=a
l(l + 1)(1 + Ql )
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(a is the radius of Earth and l = 1 is the order of the spherical harmonic
expansion).
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1400
1200
1000
This study
real
Olsen (1999b) Magsat response
C (admittance), km
800
600
400
200
0
imag.
-200
-400
1 day
4.5
5
5.5
6
Log Period, s
6.5
1 year
7
7.5
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-600
4
1 month
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3000
This study
2500
Schultz and Larson (1987) Honolulu
Olsen (1999a) European Observatories
2000
C (admittance), km
real
1500
1000
500
0
imag.
-500
1 day
3
4
5
6
Log Period, s
1 year
7
11 years
8
9
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-1000
1 month
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5
10
4
10
3
10
2
10
1
Surface conductance
8300S = 3 S/m x 2770m
1400
1200
1000
10
10
10
800
0
600
Admittance, km
Conductivity, S/m
10
-1
-2
400
200
0
200
400
600
-3
500
1000
1500
Depth, km
5
5.5
6
6.5
Log (Period, s)
2000
2500
7
3000
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4.5
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Dynamics of a dense lower mantle layer (Kellogg et al. (1999) Science,
283, 1881):
O c e a n ic
nd
I s la
t
nen
i
t
n
Co
Mido
cea
nR
idg
e
Ba
ck
Ar
c
0 km
670 km
?
Ma
nt
le
Co
re
D"
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2900 km
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Internal fields as a fraction of external field:
0.4
0.35
0.3
0.25
0.2
0.15
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0.1
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Average latitudinal dependence removed:
0.4
0.35
0.3
0.25
0.2
0.15
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0.1
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Turn CRUST 5.1 into conductivity map:
0.03 S/m
sea level
0.5 S/m
0.5 S/m
2km
3.2 S/m
0.8 S/m
0.001 S/m
7km
0.02 S./m
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50 km
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Global conductance map:
10000 S
1000 S
100 S
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10 S
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Improvement in time domain fits observatory data (Velimsky and Everett):
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-10
-5
0
5
10
100% x (χ23-D - χ21-D)/χ21-D
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Improvement to Oersted data (Velimsky and Everett):
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100% x (r23-D - r21-D)/r21-D
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-15
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Conclusions:
Electrical conductivity provides important information on temperature,
volatiles, and phases in the mantle
Even short magnetic missions provide broad spectrum EM responses
using modern methods
Satellite data identify both shallow and deep features not seen in observatory data sets
(Copies of the paper and talk can be obtained from
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http://mahi.ucsd.edu/Steve/MDAT)
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Where next?
Surface conductivity needs to be well understood before 3D mantle conductivity can be mapped
Comprehensive model is a very important tool for induction
Time domain is likely to be a good, maybe even the best, way to image
3D mantle structure
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Data analysis should include higher order internal fields and surface
conductivity a priori
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