Transcript Crustal magnetization

Crustal magnetization
Kathy Whaler
University of Edinburgh
Why study the Martian Magnetic Field?
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
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:
B 
1
Bc
( ) ( )

B
Bc

η
• Hence any methods developed to treat
vector data will work with minor
modifications on scalar data
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
– difficult to use scalar data
Martian magnetic field
• The internal magnetic 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
Data and Technique
• Low-altitude coverage is sparse, suitable for
analysis to degree 50 globally.
• Spatially varying magnetization, linear
combination of Green’s functions relating
predicted magnetization to observed magnetic
field.
• Minimize RMS magnetization within the
Martian crust.
• Data by data information matrix is sparse
(preconditoned CG).
• Damping controls relative importance of fit and
RMS magnetization.
Methodology
• Relate a magnetic field satellite
measurement to the magnetic field or
magnetization in the crust, e.g.
B (r )  ˆl .  H(r , s).M(s)dV
( )
( )
j
j
r j V
j
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
Methodology
• Express the model as a linear combination
of the data kernels
2
M
• Find the multipliers that minimize e.g. V dV
so-called minimum norm solutions
• Hence model continuously-varying
functions, either downward continued B, or
M within the crust
Numerical considerations
• Minimum norm solutions require solving a databy-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
• Calculation parallelises effectively
• Use iterative conjugate gradient algorithm on
resulting sparse system
• Improve convergence by Jacobi preconditioning
Green’s function showing how the surface magnetic field
contributes to a satellite measurement at 400km altitude.
Solid/dashed line: vertical/horizontal component
Its interpretation
A magnetic chronology
Interpretation caveats
• Residuals to our model are strongly
non-normal: external fields and
unmodelled sources
• Varying misfit by a factor of 3 alters the
RMS magnetization by two orders of
magnitude: model does not constrain
magnetization strength, only direction
Comparison with other magnetization models
•Discrete model of magnetization (Langlais et al., 2003):
correlation coefficients are in excess of 0.8.
•Ideal body theory (Parker, 2003) demonstrates that
magnetization must be at least 4.76 A/m for a 50 km thick
crust.
•Ten isolated bodies described by Arkani-Hamed and Boutin
(2003): Five of their ten paleomagnetic poles are within 30º of
our poles. The others are at angular distances of 32º, 41º, 59º,
66º and 69º.
Power spectra for downward continued Magsat model
(diamonds) and aeromagnetic compilation (crosses)
over Africa
This rendition of the
North American
compilation has had
wavelenths longer
than 500 km replaced
with the
Comprehensive model
(Sabaka et al., 2002),
utilizing a technique
developed by Ravat et
al. (2002). The data is
on a 1 km grid
projected with a
spherical transverse
Mercator. The grid
size is 8901 by 8511.
Inversion for
magnetization
directions based on
satellite and nearsurface data
Depth-independent magnetization
• Satellite data ‘see’ magnetized crust as a thin
sheet
•  no point in trying to resolve depth
dependence
• Allowing depth variation seems to cause
problems when integrating aeromagnetic data
• Almost finished implementing code to calculate
M constant with depth through magnetized layer
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