Interactions between aeromagnetic data and electromagnetic induction in the earth

/

Interactions Between Aeromagnetic Data and

Electromagnetic Induction in the Earth

by

Adrian P. Hitchman, B.Sc. (Hons), Grad.Dip.Ed.

A thesis submitted for the degree of Doctor of Philosophy

of

The Australian National University

Author's Declaration

Except as noted throughout the text and in the acknowledgments, the research described in this thesis is solely that of the author.

~I~

KL~,_J

ADRIAN

P.

Contents

List of figures

.

List of tables _Xlll

...

Frequently-used symbols and notation _xv

Abbreviations

..

XVll

Acknowledgments

.

XIX

Abstract

.

XXI

Chapter 1 Introduction ₁

Chapter 2 _{The geomagnetic field 5}

2.1 _{Earth's magnetic field}

_.

_.

2.2 _{The main field . . . .}

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_.

_.

_.

2.2.1 Main-field modelling _{. .}

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_.

2.2.2 _{Origin of the main field}

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_.

2.3 The crustal field • • • • .. • • 0 • •

.

.

2.3.1 Mapping _{the crustal field}

_.

_.

_.

2.3.2 Origin _{of the crustal field}

_.

_{. .}

2.4 The daily variation . . .

.

.

.

2.5 _{Magnetic storms and substorms . .}

_.

2.5.1 _{Indices of magnetic activity}

_.

_.

_.

_.

_.

_.

2.6 Pulsations . . .

_.

2.7 Induced fields .

.

_.

_.

2.7.1 _{The induced fields of rock magnetisation . 21}

CONTENTS V 2. 7.2 The induced fields of EM induction in Earth . . . 21

Chapter 3 Electromagnetic induction in Earth

3 .1 The coast effect . 3.2 Array studies ..

3.3 Possible conductors . .

Chapter 4 Aeromagnetic surveying

23

23 24 28

32

4.1 Surveying practice . . . 32

Chapter 5 Data analysis procedures

5.1 Time series analysis 5.2 Spectral analysis . .

5.2.1 Discrete Fourier transforms 5.2.2 Power spectral density . 5.2.3 Transfer functions . .

5.2.4 RRRMT Fourier transform convention

5.2.5 Transfer-function and induction-arrow errors

35

35 . . . 37 37 38 40 42 42

Chapter 6 Micropulsations and the coast effect - CICADA97 44

6.1 Instrumentation . 6.2 Station locations 6.3 Data collection 6.4 Data analysis .

6.4.1 Processing raw data 6.4.2 Transfer functions 6. 5 2D forward modelling . .

Chapter 7 An Sq signal in aeromagnetic data 7 .1 Data description . . . .

7 .1.1 Aeromagnetic surveys 7.1.2 Crossover misfits . . . .

7.2 Methods of recovering the quiet daily variation 7.2.1 The quiet daily variation as a Fourier series

45 46 46 . . . . 48 . . . . 48 . . . 49

55

63

.

7.2.2 _{The quiet daily variation from data binning} 7._{3 Measuring induction effects . . . .}

7.3.1 The diurnal-residual index (2) 7.3.2 _{The diurnal-ratio index (A)} 7.3.3 Phase discrimination .

7.3.4 _{Estimating errors .} 7.4 Data analysis . . . .

7 .4.1 _{Clarence-Richmond .} 7.4.2 Frome . . . .

7.4.3 _{Medusa Banks-Port Keats .}

Chapter 8 A global total-field Sq model 8.1 The WDCA/SQl model

8._{2 The total-field model ..}

CONTENTS

74 78 82 83 83 84

85 85 88

89

94

94

97 8.3 _{Comparison of modelled total-field variations and other data for Australia . 99}

8.3.1 _{Upper-mantle conductivity study} 8.3.2 AWAGS Sq study . . .. . . 8.3.3 _{Southeastern Australia array study .} 8.3.4 _{Aeromagnetic base-station records}

Chapter 9 Magnetic amphidromes 9.1 _{Basis for the amphidrome effect .} 9.2 An amphidrome parameter

9.2.1 Mathematical basis .

.

.

..

9.2.2 _{Amphidrome predictions for Australia} 9.3 Examples of the amphidrome effect in data

9.3.1 CICADA97 data .. . . .. . . . 9.3.2 _{Southeastern Australia array study .} 9.3.3 _{AWAGS disturbed-field study . . . .}

9.3.4 Murray _{Basin aeromagnetic base-station data} 9.3.5 SWAGGIE data .. . . .

.

Chapter 10 Induction information from total-field data

.

.

. . 0 • • • • .

.

.

.

.

.. 101

. 103 . . 106 .. 111

115 . 116 . . 121 121 122 123 . 123 . 124 . 127 130 135

CONTENTS

10.1 Mathematical groundwork

10.1.1 Vertical-field transfer functions from total-field data 10.1.2 Total-field transfer functions . . . .

10.1.3 The amphidrome parameter, re-visited . . 10.2 Murray Basin aeromagnetic base-station data 10.3 SWAGGIE data . . . .

10.3.1 Anchored magnetometers 10.3.2 Floating magnetometers .

Chapter 11 Conclusions and future work 11.1 Micropulsations and the coast effect 11.2 An Sq signal in aeromagnetic data 11.3 A global total-field Sq model

11.4 Magnetic amphidromes . .. .

11.5 Induction information from total-field data 11.6 Concluding remarks . . . .

Appendix A Number of each day of the year

Appendix B CICADA97 transfer functions and induction arrows

Appendix C Base-station records

Appendix D Singular value decomposition

..

Vll

148

. . 148

. 150 . 151 . 151 . 155 . . 155 . 157

159

. 159 . 161 . 163 163 . 164 . . 165

166

167

183

190

Appendix E Recovered quiet daily variations, and the diurnal-residual in

-dex (3)

E. l Clarence-Richmond survey . E.2 Frome survey . . . . . . . .

E.3 Medusa Banks-Port Keats survey . .

192 .. 193

. 207 . . 213

Appendix F Linear regression analysis of recovered variations, and the diurnal-ratio index (A)

F .1 Clarence-Richmond survey . F .2 Frome survey . . . .

F.3 Medusa Banks-Port Keats survey .

217

Vlll

CONTENTS

Appendix H SWAGGIE transfer _{functions and induction arrows 256}

A pp end ix I Reprint 1

Appendix J Reprint 2

Appendix K Reprint 3

References

270

272

277

List of figures

1.1 Summary of data used in the CICADA project.

2.1 Components of Earth's magnetic field . .

2.2 Satellite-derived geomagnetic spectrum.

3.1 Parkinson's preferred plane.

3.2 Significance of the preferred plane. 3.3 The original 'Parkinson: arrow. 3.4 A \YA.GS station locations. .

3.5 -~ustralian conductivity anomalies.

3.6 Electrical conductivities of some Earth materials.

3. 7 Representative skin depths. . . . .

2

7

11

25 26 26 27 29 31 31

4.1 The magnetic anomaly map of Australia. . . 33

6.1 CICA.DA97 station locations. . . .

6.2 Occupation periods for the CICAD_--\.97 stations.

6.3 \--ariations used to recover CICA __ DA.97 transfer functions. 6.4 Real CIC_illA.97 induction arrows. . . . .

6.5 Quadrature CICA.D_r\97 induction arrows. 6.6 CIC_illA.97 induction-arrow errors.

6. 7 Real TPS::VIE induction arro\\-s. . . 6.8 Quadrature TPS:\IB induction arrows.

6.9 2D model of the CICA.DA97-line conducthity structure. 6.10 2D-model real response. . . . .

6.11 2D-model quadrature response.

47 48

51 52

53

54

56

5""'

.jg

X _{LIST OF FIGURES}

6.12 2D model response with increasing period .. . . 62

7.1 _{Aeromagnetic survey locations. . . . . .}

7.2 _{Aeromagnetic crossover-misfit frequency distributions.}

7.3 _{Relationship between ap index and crossover-misfit magnitude.}

7.4 Relationship between Kp index and crossover misfit. . . . .

7 .5 _{Relationship of time between line and tie measurements, and}

crossover-misfit magnitude. . . .

7.6 _{Crossover point formed by the intersection of lines and ties.}

65

66

68

69

70

73

7. 7 _{Quiet daily variations represented by a Fourier series and recovered from}

'same day' crossover misfits. . . 7 4

7.8 Quiet daily variations _{recovered by data binning from 'same day' crossover}

misfits. . . . .

7. _{9 Compartmentalisation of the Clarence-Richmond survey.}

7 .10 _{Recovered indices for the Clarence-Richmond survey.}

7.11 Location of Flinders conductivity anomaly.

7.12 _{Compartmentalisation of the Frome survey.}

7.13 Recovered indices for the Frome survey. . .

7.14 _{Compartmentalisation of the Medusa Banks-Port Keats survey.}

7.15 Recovered indices _{for the Medusa Banks-Port Keats survey.}

7.16 _{Thick sediments in Medusa Banks-Port Keats survey area ..}

78

86

87

88

89

90

91

92

93

8.1 WDCA/SQl observatory locations. . . 95

8.2 Sq variations _{derived from the WDCA/SQl model. . 98}

8.3 Daily range of modelled total-field variations. . . 99

8.4 Annual _{average total-field daily range for the globe. . 100}

8.5 Annual average total-field daily range for Australia. . . 101

8.6 Upper-mantle conductivity study stations. . . 102

8.7 Sq variations for h(t), d(t), z(t) and

f

8.8 Daily range of total-field Sq variations _{for the line of AWAGS stations . . . . 104}

8.9 AWAGS total-field Sq pattern. . . 105

8.10 1971 array stations. . . . .

8.11 Sq variations _{from the 1971 array study.}

106

LIST OF FIGURES XI

.

8.12 Total-field Sq ranges for the 1971 magnetometer array. . 110

8.13 Plots of quiet daily variations recorded by aeromagnetic base stations. . . . 113

9 .1 Temporal magnetic field changes in relation to the main field.

9.2 Preferred plane in relation to a region of high conductivity.

9.3 Relationships between magnetic field components.

9 .4 Prediction of amphidromic locations in Australia. .

9.5 CICADA97 vertical-field power spectra estimates ..

9.6 CICADA97 total-field power spectra estimates.

9.7 Magnetic-field variations from the 1971 array.

9.8 SSC amplitudes from AWAGS.

9. 9 Location of the Murray Basin.

9 .10 Aero magnetic base-station data from the Murray Basin.

9 .11 Expanded time series from the Murray Basin.

9.12 Power spectra for the Murray Basin sites.

9.13 Location of the SWAGGIE experiment. . .

9.14 Locations of the SWAGGIE floating magnetometers.

9.15 Total-field time series for deployments of the anchored magnetometer.

9.16 Power spectra for anchor-mag variations. . . . .

9.17 Total-field time series for deployments of the floating magnetometer.

9.18 Expanded floater-mag time series.

9 .19 TMI image for the Eyre Peninsula.

9.20 Power spectra for floater-mag variations . . .

117

119

. 120

. 123

. 125

. 125

. . 128

. 129

. 130

132

. 133

. 134

. 136

. . 138

. 139

. 141

. 143

. 144

145

146

10.1 Vertical-field induction arrows for Murray Basin sites, determined from

total-field variations. . . 152

. 154 10.2 Total-field induction arrows for Murray Basin sites ..

10.3 Vertical-field induction arrows for anchor-mag sites, determined from

total-field variations. . . 156

10.4 Vertical-field induction arrows for floater-mag sites, determined from

total-field variations. . . ₁₅₈

..

Xll _{LIST OF FIGURES}

C.l Base station records for the aeromagnetic surveys. . . . . 183

E.l Numbering _{of compartments for the Clarence-Richmond survey .. 193}

E.2 _{Quiet daily variations for the Clarence-Richmond survey area using Fourier}

sen es. . . . . . ₁₉₃

E.3 Quiet daily variations for the Clarence-Richmond survey area using data

binning. _{. . . . . . 200}

E.4 Numbering _{of compartments for the Frome survey. . . . . . . . . . . . 207}

E.5 Quiet daily variations for the Frome survey area using Fourier series. . 207

E.6 Quiet daily variations for the Frome survey area using data binning. . 210

E.7 Numbering _{of compartments for the Medusa Banks-Port Keats survey. . 213}

E.8 Quiet daily variations for the Medusa Banks-Port Keats survey area using

Fourier series . . . 213

E.9 Quiet daily variations for the Medusa Banks-Port Keats survey area using

data binning. . . 215

F.l Linear regression analysis of quiet daily variations for the Clarence-Richmond

survey area using Fourier series . . . 217

F.2 Linear regression analysis of quiet daily variations for the Clarence-Richmond

survey _{area using data binning . . . 224}

F .3 _{Linear regression analysis of quiet daily variations for the Frome survey}

area using Fourier series . . . . ₂₃₁

F .4 Linear _{regression analysis of quiet daily variations for the Frome survey}

area using data binning . . . . . 234

F .5 Linear regression _{analysis of quiet daily variations for the Medusa}

Banks-Port Keats survey area using Fourier series. . . 237

F .6 Linear regression _{analysis of quiet daily variations for the Medusa}

Banks-Port Keats survey area using data binning. . 239

G.l Murray Basin total-field _{transfer function and induction arrow plots . . . 245}

H.l SWAGGIE anchored _{magnetometer vertical-field transfer function and}

in-duction arrow plots. . _{. . . 258}

H.2 SWAGGIE floating magnetometer vertical-field transfer function and

List of tables

2.1 Conversions for Kp and ap indices. . . 20

4.1 Typical specifications for aeromagnetic surveys. . . 34

5.1 Percentage of a normal population within intervals about the mean. . . 36

5.2 Complex components of transformed discrete frequencies.

6.1 Magnetometer recording periods . . .

6.2 CICADA97 station location details ..

7.1 Aeromagnetic survey specification. . .

7.2 AGRF95 secular variation for aeromagnetic surveys.

8.1 WDCA/SQl observatories. . . .

8.2 Station locations for the 1971 magnetometer array.

8.3 Total-field Sq ranges for the 1971 magnetometer array.

8.4 AGSO aeromagnetic base-station locations. . . .

8.5 AGSO aeromagnetic base-station mean daily ranges.

9.1 Transfer functions for the 1971 magnetometer array.

9.2 Location of anchored magnetometer deployments ..

9.3 Location of floating magnetometer deployn1ents.

9.4 Reference stations for floating magnetometer deployments . .

10.l Murray Basin declination and inclination values. . ..

10.2 Anchor-mag AGRF declination and inclination values.

10.3 Floater-mag AGRF declination and inclination values.

A.l Number of each day of the year.

.

39

45

47

64

71

96

107

. 109

112

112

126

137

142

142

153

155

157

. 166

_...

.

XIV _{LIST OF TABLES}

B.l CICADA97 AGRF declination values. . . . . .

B.2 Transfer _{functions and induction arrows for the CICADA97 stations.}

G.l Murray _{Basin total-field transfer functions and induction arrows. . .}

. . 168

. 169

. 242

H.l SWAGGIE anchored magnetometer vertical-field transfer functions and

in-duction arrows. . . . 257

H.2 SWAGGIE floating magnetometer vertical-field transfer functions and

Frequently-used symbols and

notation

Symbol Description A

B

D

d(t) d(w) F

f

f(w)

f

H

h(t)

h(w)

I

p

Q

q

r

T

X

x(t)

x(w)

y

y(t)

y(w)

horizontal magnetic-north transfer function (dimensionless) horizontal magnetic-east transfer function (dimensionless) declination of magnetic field (0

, positive east)

temporal variations in D (nT) Fourier transform of d(t) (nT.s) total magnetic field (nT)

temporal variations in F (nT) Fourier transform off (t) (nT.s) frequency,

f

=

horizontal magnetic-north component (nT) temporal variations in H (nT)

Fourier transform of h(t) (nT.s) inclination of magnetic field (0

, positive down)

horizontal geographic-north transfer function (dimensionless) horizontal geographic-east transfer function (dimensionless)

indicates quadrature (out of phase) component, when used as a subscript indicates real (in phase) component, when used as a subscript

period, T

=

1-

horizontal geographic-north component (nT) temporal variations in X (nT)

Fourier transform of x(t) (nT.s)

horizontal geographic-east component ( nT) temporal variations in Y (nT)

Fourier transform of y( t) (nT.s)

.

Symbol

z

z(t)

i(w)

f3

8

K,

µ

µo

</>

CJ

p

Description

vertical component (nT)

temporal variations in Z ( nT)

Fourier transform of z(t) (nT.s)

amphidrome parameter

skin depth, 8

=

Ii§;

magnetic susceptibility (dimensionless)

magnetic permeability (H.m-1₎

magnetic permeability of a vacuum (41r x 10-7_{H.m-1 )}

dip latitude (0 )

electrical conductivity, CJ= p-1 (S.m-1)

electrical resistivity, p

=

w angular frequency, w

=

2;

( Other symbols are introduced in the text, as required.)

Abbreviation AGRF

AGRF95 AGSO ANU AWAGS

BBB

BLN

CICADA CICADA97 CDM

CLC CMB CNB CSE CSIRO CWN DGRF DRS EM EPA FCA FUSA GDS GPS IGRF IMF

Abbreviations

Meaning

Australian Geomagnetic Reference Field AGRF model for epoch 1995

Australian Geological Survey Organisation Australian National University

Australia-Wide Array of Geomagnetic Stations Bombay Bridge, CICADA97 magnetometer station Barellen, CICADA97 magnetometer station

Clarifying Induction Contributions to Aeromagnetic DAta line of 3-component magnetometers, deployed during 1997 Clyde Mountain, CICADA97 magnetometer station

Coolac, CICADA97 magnetometer station core-mantle boundary

Canberra magnetic observatory Continental Slope Experiment

Commonwealth Scientific and Industrial Research Organisation Currowan, CICADA97 magnetometer station

Definitive Geomagnetic Reference Field Durras, CICADA97 magnetometer station electromagnetic

Eyre Peninsula conductivity anomaly Flinders conductivity anomaly

Flinders University of South Australia geomagnetic depth sounding

global positioning system

International Geomagnetic Reference Field interplanetary magnetic field

XVlll

Abbreviation

-LT

MHD

NSW

0TH

PPM

PSD

RRRMT

RSES

SODA.

SODA3

SODA4

SOMEx

SSC

SvVAGGIE

T11I

TPSlvIE

T\V

UT

\\\Y\Y

Meaning

local time

magnetohydrodynamic

New South Wales

ABBREVIATIONS

One Tree Hill, SWAGGIE-array land magnetic station

proton-precession magnetometer

power spectral density

Robust Remote Reference MagnetoTelluric, software package Research School of Earth Sciences, ANU

Study of Ocean Dynamo Action, EM induction experiment

SODA-experiment seafloor magnetometer station

SODA-experiment seafloor magnetometer station

Southern Ocean Magnetometer Experiment

sudden storm commencement

Southern Waters of A.ustralia Geoelectric and

Geomagnetic-Induction Experiment

total magnetic intensity

Tasman Project of Seafloor Magnetotelluric Exploration

Twosome, _{SvVAGGIE-arra:y seafloor magnetic station}

universal time

Acknowledgments

Heartfelt thanks go to my family, Melissa, Emily and Sara, for their unwavering

sup-port. My return to student life has had a variety of implications for us. It has been an

extremely rewarding time, for all of us, though was not without some costs. The

success-ful conclusion of this research is founded on the selfless and generous concordance of my

family. Thankyou!

Ted Lilley, my supervisor, has been a thorough and thoughtful guide throughout my

candidature. Most of the strands of the CICADA project have grown from Ted's seminal

ideas. His keen insight and appreciation of the broad issues have helped bind this

wide-ranging project into a cohesive unit. I have appreciated Ted's generosity with his time and

energy, and I have benefited enormously from the depth and breadth of his understanding.

Ted, my sincere gratitude.

Peter Milligan, AGSO, has been an active collaborator in the CICADA97 line of

mag-netometers. He contributed the instruments which formed the backbone of the exercise,

and has been enthusiastic in participating in the fieldwork, and processing and analysis

of these data. Peter also assisted in the practicalities of obtaining the three aeromagnetic

datasets provided by AGSO for the development and testing of the crossover-analysis

tech-niques. This was a time-consuming task which Peter undertook willingly. Additionally,

Peter has been a regular sounding board for new ideas and developments in most aspects

of this project.

I am pleased to acknowledge the contribution to this research of members of my

ad-visory panel, Prof. David Green, Prof. Brian Kennett, Malcolm Sambridge, Jean Braun

and Peter Milligan, particularly at the time of my mid-term appraisal.

Liejun Wang introduced me to UNIX when I arrived at RSES, and provided

wide-ranging assistance throughout the time we overlapped as students. Terry Lee made his

PC available on many occasions, an island in a sea of Macs and UNIX!

To colleagues in the Seismology and Geomagnetism Group, led by Prof. Brian Kennett,

I am grateful for regular assistance with computing, technical and scientific issues.

.

xx ACKNOWLEDGMENTS Antony White and Graham Heinson, Flinders University, have contributed data (SODA3

and SODA4), and the suite of programs used to decode, de-tilt, rotate and time-correct

data from the Flinders-designed seafloor and land magnetometers.

The WDCA/SQl model, which forms the basis for the total-field model developed in

this project, was provided by Wally Campbell, WDCA/NOAA, as were the programs for

recreating Sq variations from the line of AWAGS stations. Wally has given generously of

his time and suggestions during visits to Canberra.

Prof. John Weaver, Victoria University, Canada, provided the 2D forward modelling

program used in Chapter 6, and, with Ashok Agarwal, gave ready assistance in response

to questions relating to its implementation.

The RRRMT _{software, used for determining transfer functions in this research, was}

pro-vided by Alan Chave, Woods Hole Oceanographic Institution.

Charlie Barton, Peter Hopgood and Andrew Lewis, Geomagnetism Section, AGSO,

made available observatory data covering periods of magnetometer field-deployments.

I thank the Executive Director of AGSO, Neil Williams, and the head of the

Air-borne Geophysical Mapping Group, Peter Gunn, for permission to use AGSO

aeromag-netic datasets.

Aeromagnetic base-station data for the Murray Basin were provided by Steve Mudge,

formerly with RGC Exploration, and Grant Donnes, UTS Pty Ltd.

Jon Whellams answered many initial queries about Ib-'I£,X, xfig, xvgr and GMT. He

kindly contributed the Ib-'I£,X style files used to produce this thesis. ·

The production of many figures in this thesis has been accomplished using the Generic

Mapping _{Tools (GMT) package [Wessel and Smith, 1991, 1995].}

My _{experience has been enriched by attendance at a number of conferences and}

work-shops. I am grateful to the Research School of Earth Sciences, the ACT branch of the

Australian _{Society of Exploration Geophysicists, the US Dept. of Energy, the International}

Association of Geomagnetism _{and Aeronomy, and the American Geophysical Union, for}

financial assistance which made such attendance possible.

The opportunity to have been a research student in the fertile environment of RSES

is appreciated. I _{gratefully acknowledge the receipt of an ANU PhD scholarship, which}

made it financially possible.

The Australian National University

July 1999

Abstract

Magnetic mapping activities seek to identify patterns of the crustal magnetic field as it

changes spatially in response to geologic structures. The crustal field is, essentially,

con-stant with time, but can change significantly over short distances. It is significant for many

reasons, particularly for its ability to indicate the presence of geologic features otherwise

hidden by soil, vegetation or water, especially such features as might be associated with

minerals and hydrocarbons.

As mapping exercises are conducted, time-dependent changes of the geomagnetic field

occur, originating from electric currents flowing both outside and within Earth. These

temporal variations of the field have timescales ranging from thousands of years down to

less than a second.

Research into electromagnetic (EM) induction in Earth has shown that temporal v

ari-ations of the magnetic field may also be non-uniform, spatially. The CICADA* project

grew out of the recognition that such spatial non-uniformity should have significant

im-plications for mapping exercises. It has investigated the consequences of spatio-temporal

geomagnetic variations, in relation to total-field data; and has sought the extent to which

total-field data may contain information on the origins of this spatial inhomogeneity. These

investigations have involved the analysis of new and existing datasets, using both new and

established techniques.

The coast effect is well-known in geomagnetism. However, little has been known of

its implications for the total field. New data, from the CICADA97 experiment across the

coast of NSW, indicate significant modification of total-field variations near coastlines, at

all periods. 2D forward modelling of seawater works well at long periods, and local 3D

effects become important at short periods ( of order seconds).

Procedures developed for analysing aeromagnetic crossover misfits have yielded esti

-mates of the magnetic diurnal variation for the surveyed area. The methods have been

tested on three different aeromagnetic datasets, from different parts of Australia. The

* _{Clarifying Induction Contributions to Aeromagnetic DA ta}

.

..

XXll ABSTRACT

results suggest the use of modern aeromagnetic datasets as sources of additional geologic

information, due to the responsiveness of these 'diurnals' to electrical conductivity

struc-ture. The ubiquity of aeromagnetic-survey data thus opens the possibility of their use in

reconnaissance mapping of conductivity structure.

A model, developed as part of this research, describes global patterns of total-field

Sq variations, apparently for the first time. The model has been used to show the

latitu-dinal and seasonal dependence of Sq variations. The model possesses a range of features,

such as the strong local effects of the equatorial electrojet, and, on either side, regions of

low-amplitude Sq variations (here termed the diurnal doldrums).

It has been realised that spatially non-uniform magnetic fluctuations, arising from EM

induction, enter total-field fluctuations in a way which is also spatially non-uniform. A

mechanism which could cause suppression of total-field fluctuations has been identified.

This mechanism is one of destructive interference between the vertical and horizontal

components of the fluctuating field. A place of ideal complete suppression has been termed

a magnetic amphidrome. A quantitative amphidrome parameter has been developed, based

on the transfer functions of EM induction in Earth. The predictive power of amphidrome

considerations has been tested.

Additionally, techniques have been tested which use temporal variations of the total

field, and remote-reference horizontal variations, to derive information on transfer

func-tions at the total-field site. The techniques have been demonstrated with aeromagnetic

base-station records, and then tested with novel data from floating magnetometers, both

anchored on the continental shelf and free-floating over the deep ocean. Magnetic signals

Chapter

1

Introduction

Magnetic methods have been used for geologic mapping since the 17th century

[Paras-nis, 1979], and modern techniques of measuring Earth's magnetic field using instruments

mounted in aircraft can be traced back to the 1940s. During the intervening years

aero-magnetic surveying has become a refined and successful means of mapping the magnetic

character of Earth's crust efficiently and accurately. With the passage of time there has

been a trend toward greater resolution in aeromagnetic data, brought about by demands

for greater geologic detail and facilitated by rapidly advancing technology. As the

res-olution of geologic detail increases the relative effect of sources of error also increases.

The study of data-contamination sources is, therefore, an essential part of the ongoing

development of high-resolution aeromagnetics.

Non-uniformity of magnetic field variations across a survey area is a source of significant

error in aeromagnetic data. Such non-uniformity is particularly pronounced where geologic

structures have heterogeneous electrical properties. This gives rise to highly variable

induced magnetic fields, which result in a complex pattern of magnetic field variations

across a survey area.

The CICADA project, described in this thesis, investigates the interplay between

spa-tially non-uniform magnetic-field variations and total-field magnetic-mapping data. The

project explores two questions, they are:

1. How do spatially non-uniform magnetic-field variations affect the spatio-temporal

measurements of magnetic-mapping exercises?

2. To what extent can evidence of electromagnetic induction in Earth be recognised in

total-field data?

The CICADA project links two well-established fields of scientific pursuit, those of

2 110" ~ -10" t-20<> ::,;_: -30<> <$-❖•

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~:.i::-.'

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"'

;:s e

II' "'

'!<

120~ _130°

~

0

~

•

~

e ₉

"

•

~

• e

• #

b

•

"

.

-,,.,-,

(

v·-

-

.; \

~

• _J

( '-,.._

-0 ~

V

140"

Data timeline

1980

y x; \

d e

\ / 1990 160" ··. ~~ ~.~ ~

20 . .,

- ::f::

" ~ b

-30" . J

-40"

..

160"

I•

b a c f

~ ! ! /

2000

Figure 1.1: Data sources for the CICADA project have included (a) the

CICADA97 line of 3-component magnetometers, (b) three AGSO

aeromagnetic surveys, (c) the SWAGGIE experiment, (d) the

AWAGS experiment, (e) a line of AWAGS stations, (f) base-station data from aeromagnetic surveys in the Murray Basin, and, (g) an array study in southeastern Australia.

the potential for investigation is broad. Consequently, the investigations described herein

are wide-ranging. In some cases, established methods have been adapted for application

to total-field data; in others, new techniques have been developed and tested. The project

has involved collection of new data, the application of new techniques to existing data, and

comparison of new predictions of magnetic-field behaviour with archived data. Figure 1.1

shows the data sources used in this project.

The particular topics investigated have developed in a logical sequence from the original

3

One of the first intentions of this research was an investigation of the coast effect at

short periods. This aspect of the project was made possible by enhancements to instru

-mentation which have occurred in recent years. The impetus for this investigation came

from the interest in aero magnetics of accurate removal of short-period variations from

spatio-temporal data. A line of 3-component magnetometers, stretching from inland, and

across the coast to deep ocean (Figure l. la) was deployed. Data from these instruments

were analysed using methods based on traditional EM induction studies, and enhanced to

provide additional total-field information.

An allied investigation sought to determine the extent to which evidence of EM

induc-tion effects could be found in misfits at crossover points in aeromagnetic surveys. Datasets

for this research were provided by the Australian Geological Survey Organisation (AGSO).

The datasets were from surveys flown over the continental shelf, where induction effects

could be expected to be strong; over a known intra-continental conductivity anomaly,

where induction effects are more subtle; and in an area where no previous conductivity

anomalies have been identified (Figure 1.1 b). This aspect of the research has involved the

development of new techniques for analysis of crossover misfits, which have been tested

on the 3 datasets provided.

It became evident during this last investigation that quiet daily variations of the total

magnetic field had differing character in different parts of Australia. This observation was

difficult to confirm, however, because there appeared to be no published investigations of

the spatial dependence of quiet-daily variations of the total field. This seemed to be so,

notwithstanding commonly available information on global patterns of variations in field

components. To investigate patterns of total-field variations, an existing model, derived

to represent quiet variations in magnetic-field components over the globe, was extended

to also represent the total field. The model has been used to investigate the dependence

of total-field variations on both latitude and season. The modelled variations have been

compared with new and archived Australian data (Figure 1.ld,e,g).

Evidence of low-amplitude variations in the Sq model formed a natural background

to an investigation of the possibility of reduced-amplitude variations at shorter periods.

Careful consideration of EM induction effects on total-field variations led to the descrip

-tion, for the first time, of circumstances under which amplitude reduction results. Places

exhibiting this phenomenon have been called 'magnetic amphidromes'. Predictions of

. amphidromic locations for Australia have been checked against new and existing data

(Figure 1. la,c,d,f,g). This topic brings into focus the importance of base-station position,

relative to the magnetic mapping area, in terms of the spatial uniformity of temporal

4

Associated with the _{investigation of EM induction effects on total-field variations has}

been the use of temporal variations, _{recorded by base stations, as a source of information}

on conductivity structure. Total-field variations _{have been used with horizontal variations}

from a nearby reference station, _{to derive induction arrows. The broad application of these}

methods would make possible wide-ranging _{reconnaissance of continental conductivity}

structure using the base-station data produced in modern magnetic mapping.

Novel total-field data recorded _{by magnetometers in floating buoys are also analysed in}

a number of ways. An important feature to be identified _{is the magnetic signal generated}

Chapter

2

The geomagnetic field

The first recorded observations of the effects of a magnetic field are attributed to the

Greek philosopher Thales who lived in the 6th century BC [Merrill et al., 1996]. These

observations were of the tendency of lodestone ( a highly magnetic form of magnetite) to be

either attracted or repelled from other samples of the same species. Similar observations

are recorded in Chinese literature between the 3rd century BC and 6th century AD.

By about the 1st century BC the Chinese had used these properties of lodestone to

fashion the first compass. It _{consisted of a lodestone ladle, free to rotate on a smooth}

non-magnetic base, which always tended to align itself in the non-magnetic north-south direction.

With time the compass became more refined so that by the 12th century it was in wide

use in China and by the 13th century in Europe.

It _{is reputed that, while en route to America in 1492, Christopher Columbus observed}

that the compass usually did not point to true north but aligned itself at some angle to it

[Rikitake and Honkura, 1985]. This angle could be either to the east or west of true north,

depending on location. Columbus had observed the declination of the magnetic field. The

German cleric, Georg Hartmann, in 1544, noticed that a magnetic needle, free to rotate

vertically, aligned itself at an angle to the horizontal plane. Hartmann was the first to

observe the inclination of the magnetic field.

William Gilbert, physician to Queen Elizabeth I, made a detailed study of the magnetic

field associated with a magnetised sphere, in the 16th century. He published his research in

De M agnete. Based on his observations, Gilbert concluded that the entire Earth possessed a magnetic field.

Sir Edmond Halley, in the early 18th century, compiled the first chart of the declination

of the magnetic field and noticed that the magnetic field tended to drift westward with

time.

In the early 19th century Carl Friederich Gauss undertook an important analysis of

6 _{2.1. Earth's magnetic field}

global magnetic field data and deduced that Earth's magnetic field was the combination

of fields originating both within Earth and outside it.

2.1

Earth's magnetic field

It is now well known that Earth is surrounded by a magnetic field which is actually a

combination of fields arising from a number of sources. At any location, the field may be

completely described by its total intensity (F), its declination (D) and its inclination (I).

Figure 2.1 describes these and other components of Earth's magnetic field.

As shown in Figure 2.1, _{in addition to its principal components, Earth's magnetic field}

may also be described by its horizontal intensity (H), northward intensity (X), eastward

intensity (Y) and vertical intensity ( Z).

Simple mathematical relationships exist between the total field and its components.

These include the following [see, for example, Chapman and Bartels, 1940, Chapter l]:

H

=

(2.1)

z

X - HcosD (2.3)

y

_-

_(2.4)

p2 - H2+z2

_(2.5)

p2 _{- x2}

₊

₊

_(2.6)

It should also be noted that, as indicated in Figure 2.1, the directions of positive axes

are defined as northward, eastward and vertically down. Consequently, over most of the

southern hemisphere, where _{the magnetic field is generally directed out of the Earth, both}

the inclination and vertical component of the field have negative values.

Time-dependent _{changes in a field component, from some defining epoch, are denoted}

h(t), x(t), y(t), z(t) and f(t), for the H , X, Y, Z and F directions, respectively. All

changes are in nT. In this _{thesis, time-dependent angular changes in declination, D, are}

also represented in nT, by d( t), defined as

d ( t)

=

where d' ( t) are the _{angular changes in declination, in degrees [ see Chapman and}

Bar-tels, 1940, Chapter 1]. _{The changes are taken to occur in the direction perpendicular to}

that of H , that is, in _{the magnetic-east direction. Easterly changes in declination have}

nT-equivalent values which _{are positive, westerly changes are negative. The following}

2 .1. Earth's magnetic field

-Z

Up

' - - - " l '

' '

y

' I '

'

'

' ' ' I ' '

r - - - - -

I

x1

' ' ' '

F

True North

H

True East

Figure 2.1: Components of the magnetic field of Earth. The orientation of the

vertical_ field, which results in both Zand I having negative values, describes the southern-hemisphere magnetic field direction.

8

Chapter 1]

h(t) d(t) x(t) y(t)

f

==

+

==

=

=

+

=

+

2.2. The main field

(2.8)

(2.9)

(2.10)

(2.11)

(2.12)

in which D and I are epoch values of the declination and inclination, respectively.

For the purposes of subsequent discussion ( Chapter 8), it is useful to define dip latitude

at this juncture. The dip poles are locations at Earth's surface where the time-averaged

inclination of the magnetic field is 90°, and the dip equator is the line about Earth along

which the inclination is 0°. The dip latitude, </>, is an angular coordinate relative to the dip

equator and is related to the inclination ( or dip), I, by the dipole field equation [Merrill

et al., 1996, p. 94]

tan I

= 2 tan

As _{has been previously mentioned in this section, the magnetic field measured at any}

location in the vicinity _{of Earth is the vector sum of a number of fields that have various}

origins. These cornponent fields are described below.

2.2

The main field

Earth's main _{field contributes close to 99% of the total geomagnetic field ( about}

50000 nT) [Parkinson, 1983, Table

l].

secular variation is _{used to describe temporal changes of the main field. The period of}

this variation is thousands of years. In addition, the main field has undergone complete

reversals in direction every million years _{or so, on average. Evidence for these reversals is}

contained in the magnetic _{record of rocks formed at mid-ocean ridges [Vine and Matthews,}

1963], lavas extruded from volcanoes and in seafloor sediments.

2.2.1

Main-field

modelling

Mathematical models may be developed which represent the spatial nature of Earth's

main field. In fact, two separate models are necessary to represent both the magnitude

and secular variation of the main field.

There _{are many sources of data which contribute to a model of main-field magnitude.}

2.2. The main field 9

for example] data, satellite, aeromagnetic and marine magnetic data are commonly used.

These multiple sources help to ensure a global and detailed coverage of data. The data on

which a secular variation model is based is much more restricted. Accurate estimates of

secular variation are available only from observatory and, perhaps, repeat-station

measure-ments. This availability limits coverage to continental regions, and significantly biases the

dataset to those parts of the globe best endowed with observatories. Verhoef and Williams

[1993] describe a method for estimating the secular variation at sea using crossover

dif-ferences in marine magnetic measurements. This was a major task which involved the

collation of a massive database of marine magnetic surveys. Estimates of secular variation

obtained in this way may indeed provide increased global coverage for secular variation

models, however, logistical constraints are likely to mitigate against the widespread use of

this method.

At 5-year intervals the International Association of Geomagnetism and Aeronomy

(IAGA) adopts global main-field and secular variation models from a raft of candidate

models [see Barton, 1997; Barton et al., 1992, for example]. The mathematical basis for

these models is spherical harmonics. A potential function is sought which provides the

best fit to the available data. Considering only the field originating within Earth, this

potential function has the form [Campbell, 1997, p. 19]

oo ( )n+l

V

=a~ ; Fo

[g~

+

where V is the magnetic potential, a is the mean radius of Earth ( 6371.2 km), r is the radial distance of the point of interest from the centre of Earth, g~ and

h":

coefficients which define the model, P represents a Schmidt quasi-normalised Legendre polynomial function, ¢ is the longitude, 0 is the colatitude, the index n is the degree of the model and m is the order of the model. The potential V is related to the X, Y and

Z components of the magnetic field by [Parkinson, 1983, p. 79]

that is

X

y

z

X

y

z

18V r 80

1 8V rsin0 8¢

8V

8r

oo

n ( )n+2

(d)

~

fo ;

(g~

+

0 P;'(cos 0)

oo

n (a)n+2

L L -

n= 1 m=O r Sln

oo

)n+2

~

J:=

0

- ; (n

+

+

(2.15)

(2.16)

(2.17)

(2.18)

(2.19)

10 _{2.2. The main field}

The degree and order for which coefficients are obtained determine the wavelengths of spatial variations _{which are represented by the model. At the equator, where Earth's}

circumference _{is approximately 40000 km, a model with coefficients up to degree, say, 10,}

represents _{spatial wavelengths down to} 40

?

°

0

₌

4000 km. Similar calculations may be

made _{for the order of a model, and equivalent wavelengths determined around a line of}

longitude. The highest degree and order appropriate for modelling Earth's main field has

been _{a topic of some contention [Barton, 1988].}

Langel and Estes [1982] derived a spherical harmonic model of Earth's internal field based on MAGSAT data, and computed a power spectrum using

n

Rn=

+

L (

+

m=O

for terms _{with degree 1 to 23. Figure 2.2 shows the power associated with each harmonic.}

The spectrum has two distinct components, on either side of n

=

[1982] conclude that harmonics with n

<

>

dominated by the main field, and those with n

>

<

by the crustal field. This separation of the main and crustal fields agrees closely with the independent analysis of Cain et al. [1974], which is presented graphically in Merrill et al.

[1996, Figure 2. 7].

The _{isolation of the main-field contribution from the crustal field is not necessarily}

as clean-cut _{as suggested by Figure 2.2, however, as there is overlap between the shorter}

main-field wavelengths and the longer crustal-field wavelengths [Jackson, 1996].

2.2.2

Origin of the

main

Specific _{details describing the origin of the main field are as yet unresolved, though}

there is _{broad agreement that magnetohydrodynamic (MHD) and electromagnetic}

induc-tion processes in _{Earth's outer core are responsible for its generation. Models which}

rep-resent the _{generation process need to account for the field's longevity, its secular variation}

and reversals, and its _{self-sustaining nature, within the constraints of geologically-available}

materials and physically-plausible processes within Earth.

Seismic evidence _{suggests the inner core of Earth is solid and surrounded by an outer}

liquid shell [Press _{and Siever, 1978, p. 428]. There is general agreement that iron is the}

main component of the _{core [Merrill et al., 1996]. At the temperatures of the core the}

electrical conductivity is expected to be high, though it is constrained to no better than an order of magnitude by surface measurement and inference [Roberts and Gubbins, 1987].

Movement _{of a good conductor through a magnetic field causes the induction of a}

2.2. The main field

CORE

o CRUST

O O ~ _ 0

0 0

c" X'Iif"j'k:,&:'r .. :,1

,, .,tin -s, '"<' .'.y.::;;:-' -:~:

Figure 2.2: Geomagnetic spectrum derive from MAGSAT data.

Rn

mean square contribution to the vector field by all harmonics of degree n, computed using Equation 2.21. After Langel and Estes [1982] and Barton [1988).

11

the liquid outer core in such a way that the induced fields become self-sustaining. A

number of possible mechanisms for motion in the outer core have been suggested [Roberts

and Gubbins, 1987; Merrill et al., 1996). One is thermal convection, driven by radiogenic heat emanating from the inner core and/ or by the latent heat of crystallisation, released as the inner core expands by freezing those parts of the liquid outer core closest to it. An

alternative suggestion is also related to the expansion of the inner core. It is thought that,

when the parts of the outer core nearest the inner core freeze, only the heavy component accretes to the inner core while the lighter fraction becomes buoyant and begins to move

toward the core-mantle boundary (CMB) [Bloxham and Roberts, 1991). This movement results in compositional convection in the outer core. A third possible mechanism is

thought to arise due to the different precession rates of the core and mantle in response

to the gravitational forces of the moon and sun. This differential motion results in shear

forces which act across the CMB and cause stirring of the core. There is conjecture that

12 _{2.2. The main field}

in the length of day [Backus et al., 1996].

Whichever _{mechanism, or combination of them, is responsible for the motion in the}

outer core, it is essential that the fluid moves with sufficient velocity to more than

compen-sate for the diffusing magnetic field it generates and, in fact, to increase the field-intensity

so that the dynamo becomes self-sustaining [Roberts and Gubbins, 1987].

Within _{such schema, it is suggested that the secular variation of the field is due to}

a combination of occurrences, each with different time scales. Secular variations of the

field with _{periods from 1 to 100 years may be caused by MHD waves in the outer core,}

whose mechanical energy is converted to magnetic-field energy. Secular variation of longer

duration may arise from free decay of the magnetic field in the temporary absence of

convection. _{Free decay times range from 100 years for high-order harmonics to 50000 years}

for the lowest harmonic [Merrill et al., 1996, Table 9.1].

Magnetic-field reversals may be caused by a cessation of convection, of longer duration,

which results in decay of the magnetic field. When convection recommences, the direction

of the newly generated magnetic field is dependent on the residual poloidal field in the core

[Merrill et al., 1996]. Recent studies have identified evidence of magnetic field excursions,

during which time substantial changes in direction have occurred, lasting between 5000

and 10000 years [see Langereis et al., 1997; Lund et al., 1998; Guyodo and Valet, 1999, for

example]. It is suggested that excursions result from reversals of the outer-core field, while

geomagnetic field reversals, in evidence in palaeomagnetic records, occur when both the

inner- _{and outer-core fields reverse [Gubbins, 1999]. The finite conductivity of the inner}

core _{has been found to be an important stabilising influence in modelling geomagnetic-field}

reversals _{[Hollerbach and Jones, 1993; Glatzmaier and Roberts, 1995a]. It is possible that}

the slow _{diffusion time of the inner core increases the time between full reversals of the}

field by a factor of 10 [Gubbins, 1999].

The _{first numerical three-dir.nensional model of core motions has recently been}

an-nounced [Glatzmaier and Roberts, 1995a]. The model is that of a self-exciting dynamo

which _{developed from a seed magnetic field and a random temperature distribution in the}

outer core. The _{mechanism for movement of the outer core is thermal convection, though}

with a somewhat higher _{energy input to compensate for the lack of a compositional}

con-vection mechanism in _{the model. The reported dipolar nature of the field, which also}

undergoes secular variation _{and spontaneous reversal [Glatzmaier and Roberts, 1995b], is}

2.3. The crustal field 13

2.3 The crustal field

Another internal contribution to the geomagnetic field is from the magnetised layer

which forms the outermost shell of Earth. The contribution is commonly known as the

crustal field ( or crustal anomaly field, or magnetic anomaly field), though some sources

may actually reside at greater depths in the lithosphere. No permanent magnetic effects

originate in the mantle because temperatures are too high [Merrill et al., 1996]. The

crustal-field contribution is evident as the near-flat portion of the spectrum in Figure 2.2.

2.3.1 Mapping the crustal field

Aeromagnetic mapping is an efficient and effective means of mapping the crustal

anomaly field [Bell, 1995]. Historically, aeromagnetic surveys have been used as an

ex-ploration tool to locate magnetite or economic minerals associated with magnetite [Gunn

et al., 1997b; Swiridiuk, 1998], and to map the geology by measuring its magnetite content

[Meixner and Gunn, 1997].

As surveys become more detailed their capacity to resolve more-subtle features is

enhanced [Mudge, 1996]. High-resolution aeromagnetic survey data are now used to assess

the structure and development of geologic provinces [Gunn et al., 1995b], to map

palaeo-drainage channels [Gunn et al., 1995a], regolith [Dauth, 1997], basement [Gunn et al.,

1997a], and to probe sedimentary basins for hydrocarbons [Iasky et al., 1997; Kivior and

Boyd, 1998].

The sophistication of data collection and processing procedures in high-resolution

aero-magnetics means that magnetic-field anomalies may be mapped exceedingly well. There

are, however, limitations on the spatial wavelengths of anomalies mappable by

aeromag-netic surveys. The lower limits are determined by the spacing between field measurements

as the aircraft flies over the terrain and by the spacing between adjacent lines. In the

direc-tion of the lines the shortest measurable wavelength is twice the sample spacing ( typically

about 7 m [Horsfall, 1997]), and in the perpendicular direction the shortest wavelength is

twice the line spacing (which may be as low as 20m for very-high-resolution surveys, or up

to 500m for regional surveys [Horsfall, 1997]). The upper limit of measurable wavelengths

is determined by the dimensions of the survey area, and is of the order of 100 to 200 km.

The lower-wavelength limit will decrease as lower aircraft speed, higher sampling rates

and closer line spacing are employed. The higher-wavelength limit would increase if survey

dimensions increased, however logistical considerations preclude any significant increases.

In any case, in designing aeromagnetic surveys, there is generally a trade-off between

de-14 _{2.3. The crustal field}

signed to map very short-wavelength anomalies, are usually very limited in their extent,

thereby _{lowering the long-wavelength limit of resolvable anomalies. Similarly,}

aeromag-netic surveys of a regional nature typically have a relatively high short-wavelength limit.

The specifications for a particular survey are determined by the anticipated nature of the

target anomalies, with resolution increasing as the specific survey purpose moves from

reconnaissance, _{through geologic mapping, to oil and mineral exploration [Horsfall, 1997].}

Insufficiently sampled data may result in missed geologic information, and misleading

anomalies due to aliasing [Bell, 1995].

The issue of the lack of resolution of long-wavelength anomalies by aeromagnetic

sur-veys _{has been brought sharply into focus by the recent publication of continental-scale}

images of the crustal anomaly field [Tarlowski et al., 1992; Hinze et al., 1988, for example].

The first generation of such images was simply a compilation of individual aeromagnetic

surveys, smoothed and stitched together at the edges, and lacked reliable information on

anomalies with wavelengths longer than the individual surveys [Arkani-Hamed and Hinze,

1990; Grauch, 1993].

Initial efforts to acquire the long-wavelength component of the crustal field have centred

on the use of long-traverse aeromagnetic lines [for Australian examples, see Wellman et al.,

1985; Tarlowski et al., 1996a]. More recently, the intermediate-wavelength components of

the satellite-derived magnetic field have been used as a surface on which to drape the

individual magnetic surveys for continental compilations [Whaler, 1994, for example].

Global maps of the magnetic anomaly field have also been produced from satellite data

[see, for example, Langel, 1990; Arkani-Hamed et al., 1994; Ravat et al., 1995; Langel and

Whaler, _{1996]. The global magnetic anomaly field is typically represented as a series of}

spherical _{harmonics (see Equation 2.14) of degree 15 to 60 [Arkani-Hamed et al., 1994].}

That is, _{the limits of anomaly wavelengths represented in global maps of the anomaly}

field are typically 700 to 2700 km. Such satellite-derived maps are important in their

own _{right as representations of the intermediate- to long-wavelength components of the}

anomaly field. Additionally, _{they are a valuable tool for levelling aeromagnetic surveys in}

continental and global [Reeves et al., 1998] compilation maps.

2.3~2

Origin of the crustal field

The _{crustal field results from the magnetisation of rocks due to the presence of magnetic}

minerals [Simpson, 1966]. This magnetisation has two broad forms, being either induced

or remanent magnetisation [Parasnis, 1979]. Induced magnetisation is dependent on the