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Magnetic fields induced in the solid Earth and oceans
Alexei Kuvshinov & Nils Olsen
Danish National Space Center, Copenhagen, Denmark
• Predicting magnetic signals induced in 3-D conductivity Earth by various sources
- Sq and EEJ
- Geomagnetic storms
- Ocean tides and global circulation
• Possible utilization of 3-D predictions in geomagnetic field modeling
• Conclusions
Forward problem formulation and 3-D Earth’s model
ext
Calculate EM field induced by a given j (t , r , , ) in Earth’s model of a given  (r , , )
Governing (Maxwell’s) equations:
1
o
  B   (r , , )E  jext (t , r , , )
B
E  
.
t
Existing numerical solutions:
Fainberg et al., 1990;
Tarits, 1994;
Everett & Schultz, 1996;
Martinec, 1999;
Uyeshima & Schultz, 2000;
Tyler et al., 1999, 2002;
Koyama et al., 2002;
Kuvshinov et al., 2002; 2005 (VIE approach)
Yoshimura & Oshiman, 2002;
Hamano, 2002;
Weidelt, 2004;
Velimsky et al., 2005
Basic 3-D conductivity model:
S ( , )
 b (r )
Conductance
Varies from 0.1 S up to 35000 S
 b (r )   (r,, )
3D magnetic fields due to Sq current system
Source: Sq of 21 March 2000 (from CM4; Sabaka et al.,2004)
Sea level
Altitude of 400 km
3D Br (inducing + induced parts)
Ocean effect (up to 12 nT)
Ocean effect (up to 6 nT)
Magnetic fields due to equatorial electrojet (EEJ)
Source: EEJ of 21 March 2000 (from CM4)
Sea level
Ocean effect (up to 4 nT)
Altitude of 400 km
Ocean effect (up to 1 nT)
Magnetic fields due to geomagnetic storms
Source: storm of 5-6 November, 2001
Sea level
Ocean effect (up to 80 nT)
Altitude of 400 km
Ocean effect (up to 30 nT)
Magnetic fields due to geomagnetic storms (contd.)
Z at HER for selected storms
Olsen & Kuvshinov, 2004
Z at coastal obsrvatories for storm 13 July 2000
Magnetic fields due to ocean tides
Movement of sea water through the main field:
Source:
Jext   S U  B
M2 tidal model by Egbert & Erofeeva (2000)
Predictions from Kuvshinov & Olsen (2005)
Magnetic fields due to ocean tides (contd)
Magnetic effect of oceanic M2 tide as seen by CHAMP
Observed
Predicted
Tyler, Maus & Luhr, 2003
Magnetic fields due to ocean tides (contd.)
Tidal correction for MF4 model
Tides
Period, days
M2
0.5176
S2
0.5
N2
0.5274
K2
0.4986
K1
0.9973
O1
1.0758
P1
1.0027
Q1
1.1195
The spectrum of the magnetic residuals over
the Indian Ocean before (black) and after
(red) subtracting our predictions from 8
major tidal constituents (Maus et al., 2005).
Magnetic field due to ocean circulation
Ocean circulation velocities (ECCO model)
Source
Jext   S U  B
 0
• The magnetic signals are largely
influenced
by
the
Antarctic
Circumpolar Current (ACC).
Br at 430 km
• The largest signature is in Br with
peak-to-peak values of order 3 nT.
Manoj et al., 2005
Possible utilization of 3-D predictions in geomagnetic field modeling
• Signals due to ocean flows – subtracting the 3-D predictions from the data
Bexp ,refined  Bexp  Bocean flows
• Signals of magnetospheric origin – decomposition of Dst = Est + Ist (Maus &
Weidelt, 2004) using 3-D conductivity model
• Signals of ionospheric origin – replacement of 1-D responses by 3-D ones
Conclusions
• 3-D induction effects contribute much to near-Earth magnetic field
• These effects can be predicted with required accuracy and detail by using
modern numerical solutions
• 3-D predictions can be readily incorporated into modern geomagnetic field
modeling schemes