Earths Dynamic Magnetic Field: The State of the Art Comprehensive Model

1
Earths Dynamic Magnetic Field The State of the
Art Comprehensive Model
Terence J. Sabaka
Geodynamics Branch NASA/GSFC
with special thanks to
Nils Olsen
Danish Space Research Institute
2
Outline

• Introduction
• Data
• Parameterization
• Estimation
• Results
• Conclusions

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Electromagnetic Basics The Biot-Savart Law
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Major near-Earth Current Systems
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Nature of near-Earth Magnetic Fields

• Core

• Motion of conductive outer core fluid
• 30,000-50,000 nT
• Changes on order of centuries

• Ionosphere

• Dynamo layer between 100-140 km altitude in
  the E-region
• 10-50 nT at surface
• EEJ is from enhanced eastward current at dip
  equator

6
Nature of near-Earth Magnetic Fields

• Magnetosphere

• Magnetopause, tail and ring currents
• 20-30 nT at surface
• Broad scale, but rapidly changing

• FACs

• Connect ionosphere with magnetosphere at high
  latitudes in the F-region
• 30-100 nT during quiet times

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Nature of near-Earth Magnetic Fields

• Lithosphere

• Rigid portion of crust above Curie temperature
• Induced and remanent
• Up to 20 nT at satellite altitude

• Induced fields

• Time varying external fields influencing
  conductive material in Earth skin layer
• Magnitude depends upon inducing period

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Time Scales of Magnetic Fields from Various
Sources
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Terrestrial Magnetic Field Applications

• Orientation/Reckoning

• Used by satellites including GPS
• Navigation systems

• Geophysical prospecting

• Aeromagnetic surveys
• Towed by ships
• Military targets

• Deep Earth probing
• Space weather

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Comprehensive Approach to Modelling Terrestrial
Fields

• Method

• Parameterize fields from all major near- Earth
  sources
• Coestimate these parameters by solving an
  inverse problem
• Use satellite vector/scalar and ground- based
  observatory hourly-means data

• Advantages

• Optimal for frequency overlap
• More feasible than treating fields as noise

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Data Used for Modelling

• Satellites

• POGO 1965-1971, scalar only, elliptic
• Magsat 1980, vector, six months duration, only
  dawn and dusk, 450 km
• Oersted 1999-present, vector, 750 km
• CHAMP 2001-present, vector, 400 km

• Observatories

• Several hundred, continuous, but poorly
  distributed
• Vector hourly-mean values

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Recent Satellite Magnetic Mapping Missions
Oersted vector and scalar at 750 km
CHAMP vector and scalar at 400 km
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Permanent Magnetic Observatory Stations
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Maxwells Equations
Amperes Law
Absence of magnetic monopoles
Faradays Law
Gauss Law
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Potential Fields (zero J)
(Laplace Eqn)
(Internal)
(External)
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Absence of Monopoles
Internal n 0 term violates Maxwells
monopole equation at origin
O External n 0 term is constant, doesnt
contribute
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Spherical Harmonic Functions (Ynm )
n6, m0 n6, m3 n6, m6

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Toroidal Fields (non-zero J in
thin shells)
Vector potential
Toroidal only
Toroidal scalar

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Parameterizing Core and Lithospheric Fields

• Core

• Broad scale, dominates n 1-14
• Secular variation (SV) represented by cubic
  B-spline functions

• Lithosphere

• All spatial scales, but breaks from core Rn at
  about n 15
• Modelled as n 15-65
• Considered static
• Vector biases solved for at observatories

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Rn Spectrum of Internal Field

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Fluid Velocity at Core-Mantle Boundary

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External Field Current Systems
ionospheric current systems
magnetospheric ring-current
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Ionospheric Daytime Electron Density
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Parameterizing Ionospheric E-region Field

• Primary

• Assume currents flow in sheet at 110 km
• Use potential functions conforming to
  quasi-dipole (QD) coordinates defined by
  DGRF1980
• Diurnal and seasonal variation
• Solar activity via scaling by F10.7 cm flux

• Induced

• A priori 1-D conductivity model (4-layer)
• Infinite conductor at 1000 km depth

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Continuity Across E-region Sheet Current
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E-region Breathes with F10.7 cm Solar Flux
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Quasi-Dipole Chart at Surface from DGRF1980
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Parameterizing Magnetospheric Field

• Primary

• Distant currents not differentiated
• Potential functions in dipole coordinates
• Diurnal and seasonal variation
• Ring current activity via linear dependence of
  external dipole on Dst index

• Induced

• Same as for E-region
• Internal dipole also linear in Dst

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Dst Behavior Around Storm Main Phase on 18 Aug
1998
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Parameterizing Ionospheric F-region Field

• Magsat (vector only)

• Modelled separately for dawn and dusk
• Assume QD meridional currents
• Use toroidal functions conforming to QD
  coordinates
• Seasonal variation

• Oersted (vector only)

• Same as above, but single model with diurnal
  variation

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Ionospheric F-region Currents

• Field-aligned currents (FACs) connect
  ionosphere and magnetosphere in polar region
• Meridional currents associated with the
  equatorial electrojet (EEJ)

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Ionospheric F-region Currents
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The Principle of Least-Squares Estimation
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Estimation of CM Parameters via Iterative Gauss
Method

• Solves non-linear LS problems

• Fast convergence
• Cheaper than Newton method

• Allows for A priori information

• Smooth core SV
• Eliminate nightside E-region current
• Damp excursions from LT external dipole
• Smooth F-region current

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CM Fits to Observatory Hourly-Means
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CM Fits to Satellite Data
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CM Core Br at CMB at 2000

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CM Core F at Surface at 1980

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CM Core DF at Surface from 1980 to 2000

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CM Lithospheric Br at 400 km

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CM Ionospheric Z at Surface
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CM Magnetospheric Z at Surface on 22 Aug 1998
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CM F-region Jr from Magsat at Dawn and Dusk
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CM F-region J from Oersted at Noon
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Conclusions

• Present

• CMs are only models accounting for all these
  field sources
• CMs are separating fields in a consistent and
  plausible manner

• Future

• More realistic conductivity models
• Better treatment of magnetospheric fields
• Increased use of CMs for applications