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Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation...

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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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Page 1: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Martian and terrestrial Satellite Magnetic Data: Crustal

magnetization and downward continuation models

Kathy Whaler

University of Edinburgh, UK

GEST Visiting Fellow

Page 2: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Plan

• Satellite data available

• Methodology

• Downward continuation

• Link to aeromagnetic data

• Magnetization

• Mars

• Further work

Page 3: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 4: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 5: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 6: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Green’s function showing how the surface magnetic field contributes to a satellite measurement at 400km altitude. Solid/dashed line: vertical/horizontal component

Page 7: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 8: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Trade-off curve of solution versus residual norm. The choice of preferred solution is somewhat subjective.

Page 9: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 10: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 11: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Total field anomaly projected onto main field at

1km above the Earth’s surface

Page 12: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 13: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Power spectra for downward continued Magsat model (diamonds) and aeromagnetic compilation (crosses) over Africa

Page 14: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 15: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 16: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 17: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 18: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 19: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 20: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 21: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 22: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

Green’s function showing how the surface magnetic field contributes to a satellite measurement at 400km altitude. Solid/dashed line: vertical/horizontal component

Page 23: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 24: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 25: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 26: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 27: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 28: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 29: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 30: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 31: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 32: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 33: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 34: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 35: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 36: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 37: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 38: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.
Page 39: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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

Page 40: Martian and terrestrial Satellite Magnetic Data: Crustal magnetization and downward continuation models Kathy Whaler University of Edinburgh, UK GEST Visiting.

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


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