1 modeling of the geomagnetic field at the core surface bryan grob institute for geophysics, eth...
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Modeling of the Geomagnetic Field at the Core Surface
Bryan Grob
Institute for Geophysics, ETH Zurich
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Outline
1. Introduction and Aims2. Data - the U.S. Maury Collection3. Methodology 4. Results and Conclusions
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1. Introduction and aims
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1.1 Introduction
Modeling of the geomagnetic field at the CMB from historical data • expansion of magnetic potential in spherical
harmonics• Solve resulting non-linear inversion problem
New data set used in geomagnetic modeling• U.S. Maury Collection• Analysis of new data set
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1.2 Aims
Deduction of field morphology at CMB in form of maps of
Detailed analysis of the U.S. Maury Collection
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2. Data - U.S. Maury Collection
Woodruff et al., 2005
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2. Data - U.S. Maury Collection2.1 Biographical sketch
Wikipedia, 2009
Matthew Fontaine Maury (1806-1873) Birth in Virginia, death in Lexington Became midshipman at 19 => started studies of the sea
and navigation At the age of 33 => stagecoach accident
=> severe damage of knee and hip=> from now on unable to undertake further sea voyages
1842: officer-in-charge of ‘Depot of Charts and Instruments‘=> intensive studies of old logbooks and charts=> Brillant idea!!
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2.1 Biographical sketch
Wikipedia, 2009
1843: publication of first wind and current charts(Wind and Current Chart of the North Atlantic, Sailing
Directions and Physical Geography of the Seas and Its Meteorology)
1853: first International Hydrographic Conference in Brussels
‚Pathfinder of the Seas‘
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2.2 The brilliant idea/data provenance His idea:
having a great fleet of volunteers, collecting data on their voyages
His strategy:distribute new logbooks for free against hand in of completely filled out ‘abstract log‘ sheet or in Maury‘s own words: ‘You are expected in conformity with the agreement as per the foregoing receipt to send to the Observatory the abstract [logs] of every voyage you may make until the charts are completed. Vessels that fail to return
abstract [logs] will forfeit their claims to the charts‘
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2.2 The brilliant idea/data provenance His method:
ABSTRACT LOG
Definition of ‘abstract log‘:added extra log sheet prior to actual log pages
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2.2 The brilliant idea
Woodruff et al., 2005
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2.2 The brilliant idea/data provenance
Abstract logs contains information about:- date, hour- latitude, longitude- currents, pressure- temperature (air & water)- form/directoion of clouds- duration of fog/rain/hail/snow - magnetic variation (= declination (D))
oceanographic parameters
=> TOTAL: 78,409D observations!
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2.3 Data analysis
Organisation:
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2.3 Data analysis
Spatial distribution of complete Maury Collection (MC):
outliers (total: 42 of 78,409) => 0.5 ‰
return route
Inbound route
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2.3 Data analysis
Temporal distribution of complete Maury Collection (MC):
Onset American Civil
War (1861)
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2.3 Data analysis
Declination reported in two different units:• Degrees & minutes (convential)
Accuracy: 1/60 = 0.02°
• Points- 32 point compass rose- Accuracy:
1/10 point = 1. 13°
32 points = 360°1 point = 11.25°
Wheeler, 2005
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2.3 Data analysis
Data testing against gufm1 (Jackson et al, 2000):
• normalized residuals: best estimate (gufm1)
prediction error
obersvation
• assigned prediction errors :
Errors are assumed gaussian
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2.3 Data analysis
Test for accuracy of ‘point data‘ against gufm1 (Jackson et al, 2000): D [°] D [points]
##
‘point data‘ are retained!
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2.3 Data analysis
Test (complete MC) against gufm1 (Jackson et al, 2000)
#
(Jackson and Walker, 2000)
What about Central Limit Theorem??
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2.3 Data analysis
Verification of Laplace distribution:
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2.3 Data analysis
Spatial residual distribution (MC):
Residuals < 10 sigma (# obs 77,065)
Residuals < 3 sigma (# obs: 65,662)
Residuals > 20 sigma (# obs: 598)
Residuals > 50 sigma (# obs: 50)
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2.3 Data analysis
Temporal residual distribution (MC):
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2.4 Final data sets
1820.mod 1855.m
od
2 criteria:1)good data
coverage2)as far appart as
possible
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2.4 Final data sets
Distribution of 1820 final data set
Distribution of 1855 final data set
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2.5 Reduction to epoch
Data are reduced to discrete epochs 1820 and 1855
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3. Methodology
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3.1 Boundary conditions/prelimnary assumptions Magnetic vaccum outside Earth‘s surface Mantle => insulator Gaussian assumed errors
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3.2 Core field modeling
Magnetic potential expanded in spherical harmonics:
Spherical harmonic expansion truncated at L=14
Downward continuation of observations=> spherical harmonics with large l are amplified
Non-linear inverse problem
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3.2 Non-linear inverse problem
Solved by damped least-squares parameter estimation
Goal: smoothest model for given fit to data
Strategy: find model vector m that minimizes both misfit to data and spatial norm
Non-uniqueness and instabibility resolved by regularization (norm, which measures model complexity)
Associated forward function:
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3.3 Non-linear inverse problem
Dissipation norm (Gubbins, 1975):
Norm in terms of least-squares:
=> regularization matrix
Errors:
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3.3 Non-linear inverse problem
Combination (=> objective function):
Iterative solution:
data kernel matrix =
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4. Results and Conclusions
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4. Results and Conclusions
Effectiveness criterion:
Data subset statistics:
Jackson et al, 2000: 1.16
Jackson et al, 2003: 1.97
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4. Results and Conclusions
1820 model
red: flux out of core, blue: flux into core; color interval: 100 T
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4. Results and Conclusions
1855 model
red: flux out of core, blue: flux into core; color interval: 100 T
High intensity, high latitude flux patchesReversed flux patchesActive AtlanticQuiet Pacific
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4. Results and Conclusions
Tracing of drifting patches:
D1D1
D3 D3
1820 1855
D2
D2
Feature Drift rate----------------------------D1 0.46°/aD2 0.50°/aD3 0.31°/a
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4. Results and Conclusions
Decay of axial dipole:
Decay: 1.4% in 35a
Slope: 13nT/a (ref. value: 15.46nT/a)
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4. Results and Conclusions
Prospects for model improvement:• Data:
1) increase coverage2) Correct for altitude
• Solution finding process: o Damping parameter o Minimization of L2 rather than L1 norm
• Model type: 1) Usage of time-dependent model