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