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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. Plan. Satellite data available Methodology Downward continuation Link to aeromagnetic data Magnetization Mars - PowerPoint PPT Presentation
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Martian and terrestrial Satellite Magnetic Data: Crustal
magnetization and downward continuation models
Kathy WhalerUniversity of Edinburgh, UK
GEST Visiting Fellow
Plan
• Satellite data available• Methodology• Downward continuation• Link to aeromagnetic data• Magnetization• Mars• Further work
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
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
Methodology
• Relate a magnetic field satellite measurement to the magnetic field or magnetization in the crust, e.g.
V jjjjdVB )(.),(.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
Green’s function showing how the surface magnetic field contributes to a satellite measurement at 400km altitude. Solid/dashed line: vertical/horizontal component
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
Trade-off curve of solution versus residual norm. The choice of preferred solution is somewhat subjective.
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
Total field anomaly projected onto main field at
1km above the Earth’s surface
Power spectra for downward continued Magsat model (diamonds) and aeromagnetic compilation (crosses) over Africa
Green’s function showing how the surface magnetic field contributes to a satellite measurement at 400km altitude. Solid/dashed line: vertical/horizontal component
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
BBB1B
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
)(P1
)()2)(1(
12)( 220
20
3
ll
l
lM
aRll
laC
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
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
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