martian and terrestrial satellite magnetic data: crustal magnetization and downward continuation...
TRANSCRIPT
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Martian and terrestrial Satellite Magnetic Data: Crustal
magnetization and downward continuation models
Kathy Whaler
University of Edinburgh, UK
GEST Visiting Fellow
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Plan
• Satellite data available
• Methodology
• Downward continuation
• Link to aeromagnetic data
• Magnetization
• Mars
• Further work
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Satellite data - Earth
• Earth– POGO (1960s and 1970s): scalar field – MAGSAT (1979/80): vector– Ørsted (current): vector (high altitude)– CHAMP (current): vector, but I’ve just worked
with scalar data so far
• Need to extract small crustal anomaly field from data dominated by the main field
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Satellite data - Mars
• Mars Global Surveyor– current– vector– aerobraking phase provided data as low as 120km
above surface– used data in the 120-600km altitude range
• No main field– field is due to remanent magnetization of the crust
and external field
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Methodology
• Relate a magnetic field satellite measurement to the magnetic field or magnetization in the crust, e.g.
V jjjj
dVB )(.),(.ˆ)()()( sMsrHlr
r
where (η) denotes the component, rj is the satellite datum position, s positionwithin the magnetized crust, H a known geometrical function, and M magnetization
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Green’s function showing how the surface magnetic field contributes to a satellite measurement at 400km altitude. Solid/dashed line: vertical/horizontal component
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Methodology
• Express the model as a linear combination of the data kernels
• Find the multipliers that minimize e.g. so-called minimum norm solutions
• Hence model continuously-varying functions, either downward continued B, or M within the crust
dVV
2M
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Trade-off curve of solution versus residual norm. The choice of preferred solution is somewhat subjective.
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Numerical considerations
• Minimum norm solutions require solving a data-by-data system of equations - too big
• Reduce by:
– expanding in terms of data kernels at a limited number of points
– taking advantage of peaked nature of data kernels - matrix effectively sparse
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Total field anomaly projected onto main field at
1km above the Earth’s surface
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Power spectra for downward continued Magsat model (diamonds) and aeromagnetic compilation (crosses) over Africa
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Green’s function showing how the surface magnetic field contributes to a satellite measurement at 400km altitude. Solid/dashed line: vertical/horizontal component
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Scalar data
• The anomaly field is a tiny fraction of the main field generated in the core, Bc
• Thus we can linearize the relationship between the scalar and vector fields:
• Hence any methods developed to treat vector data will work with minor modifications on scalar data
)(c
η
)(
c
BBB
1B
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Further work
• Investigate mis-match in power between satellite and aeromagnetic data
• Covariance and correlation length of crustal magnetization:– Is there a continent-ocean contrast?
– Compare the global value with the formula μ
= cos(angular separation between 2 points), Rl = power in
magnetic field at degree l, γ = a/(a+h) and h is
magnetized layer thickness)(P
1
)(
)2)(1(
12)(
220
20
3
ll
l
lM
aR
ll
laC
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Martian magnetic field
• No core field - internal magnetic field due to remanent magnetization
• The field amplitude is surprisingly high
• The field is much stronger over the heavily cratered region south of the dichotomy
• Greater external field contamination in the horizontal components
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Further work
• Why large amplitudes at North pole?
• Improve data sets, especially suppression of external fields, and better characterization of data uncertainties
• Compare downward-continued magnetic field with spherical harmonic and equivalent dipole models
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Conclusions
• Satellite data have provided a new perspective on the magnetic fields of both Earth and Mars
• The long wavelength crustal magnetization of both planets aids structural and tectonic interpretation