1 Modeling of the Geomagnetic Field at the Core Surface Bryan Grob Institute for Geophysics, ETH Zurich.

1

Modeling of the Geomagnetic Field at the Core Surface

Bryan Grob

Institute for Geophysics, ETH Zurich

2 Departement/Institut/Gruppe

Outline

1. Introduction and Aims2. Data - the U.S. Maury Collection3. Methodology 4. Results and Conclusions


1. Introduction and aims


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


1.2 Aims

Deduction of field morphology at CMB in form of maps of

Detailed analysis of the U.S. Maury Collection


2. Data - U.S. Maury Collection

Woodruff et al., 2005


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!!


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‘


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‘


2.2 The brilliant idea/data provenance His method:

ABSTRACT LOG

Definition of ‘abstract log‘:added extra log sheet prior to actual log pages


2.2 The brilliant idea

Woodruff et al., 2005


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!


2.3 Data analysis

Organisation:


2.3 Data analysis

Spatial distribution of complete Maury Collection (MC):

outliers (total: 42 of 78,409) => 0.5 ‰

return route

Inbound route


2.3 Data analysis

Temporal distribution of complete Maury Collection (MC):

Onset American Civil

War (1861)


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


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


2.3 Data analysis

Test for accuracy of ‘point data‘ against gufm1 (Jackson et al, 2000): D [°] D [points]

##

‘point data‘ are retained!


2.3 Data analysis

Test (complete MC) against gufm1 (Jackson et al, 2000)

#

(Jackson and Walker, 2000)

What about Central Limit Theorem??


2.3 Data analysis

Verification of Laplace distribution:


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)


2.3 Data analysis

Temporal residual distribution (MC):


2.4 Final data sets

1820.mod 1855.m

od

2 criteria:1)good data

coverage2)as far appart as

possible


2.4 Final data sets

Distribution of 1820 final data set

Distribution of 1855 final data set


2.5 Reduction to epoch

Data are reduced to discrete epochs 1820 and 1855


3. Methodology


3.1 Boundary conditions/prelimnary assumptions Magnetic vaccum outside Earth‘s surface Mantle => insulator Gaussian assumed errors


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


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:



Dissipation norm (Gubbins, 1975):

Norm in terms of least-squares:

=> regularization matrix

Errors:



Combination (=> objective function):

Iterative solution:

data kernel matrix =


4. Results and Conclusions



Effectiveness criterion:

Data subset statistics:

Jackson et al, 2000: 1.16

Jackson et al, 2003: 1.97



1820 model

red: flux out of core, blue: flux into core; color interval: 100 T



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



Tracing of drifting patches:

D1D1

D3 D3

1820 1855

D2

D2

Feature Drift rate----------------------------D1 0.46°/aD2 0.50°/aD3 0.31°/a



Decay of axial dipole:

Decay: 1.4% in 35a

Slope: 13nT/a (ref. value: 15.46nT/a)



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

1 Modeling of the Geomagnetic Field at the Core Surface Bryan Grob Institute for Geophysics, ETH Zurich.

Documents

data analysisdeclination

maury collection woodruff

maury collection3

maury collection2

data analysis organisation

abstract log sheet

matthew fontaine maury

geomagnetic field