Kathy Whaler University of Edinburgh, UK GEST Visiting Fellow

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

2. Plan • Satellite data available • Methodology • Downward continuation • Link to aeromagnetic data • Magnetization • Mars • Further work

3. 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

4. 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

5. Methodology • Relate a magnetic field satellite measurement to the magnetic field or magnetization in the crust, e.g. where(η)denotes the component, rj is the satellite datum position, s position within the magnetized crust, H a known geometrical function, and M magnetization

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

7. 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

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

9. 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

11. Total field anomaly projected onto main field at 1km above the Earth’s surface

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

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

28. 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

30. 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

31. 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

39. 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

40. 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