nuraddeen usman · katsina ii), halima usman and hadiza usman during the trial moment of my life...

AUTOMATIC INTERPRETATION OF

MAGNETIC DATA USING EULER

DECONVOLUTION WITH MODIFIED

ALGORITHM

NURADDEEN USMAN

UNIVERSITI SAINS MALAYSIA

2018

AUTOMATIC INTERPRETATION OF

MAGNETIC DATA USING EULER

DECONVOLUTION WITH MODIFIED

ALGORITHM

by

NURADDEEN USMAN

Thesis submitted in fulfilment of the requirements

for the degree of

Doctor of Philosophy

April 2018

ii

ACKNOWLEDGEMENT

All praises are due to Allah (S.A.W) Who spare my life up to this moment

and destined me to pursue this PhD program. May the peace and blessing of Allah be

upon Prophet Mohammad (S.A.W), his companions and those that followed them up

to the day of resurrection. I’m in short of words to appreciate the solid upbringing,

support and guidance I received from my parent, may Allah reward them abundantly.

Special thanks to my supervisor Professor (Dr) Khiruddin Abdullah, my

mentor who makes my dream to become true. His vast knowledge, tolerance,

humility, hardworking and decades of experience in academia have helps me to

achieve my aim. May Allah (S. A. W) keeps him (and his family members) healthy,

accept his prayers and forgive all his shortcomings. I also appreciate the support I

received from my co supervisor in person of Professor (Dr) Mohd Nawawi. I

appreciate the effort I received from Dr. Amin Esmail Khalil for his enomous effort

to improve my manuscripts. The efforts of Arisona Arisona, Fathi Al-hamadi and

Talha Anees are highly appreciated. I thank all the staff and students of Geophysics

unit, Universiti Sains Malaysia who help in one way or the other in the course of

carrying out this research.

I acknowledge the moral, financial and spiritual support I received from the

entire members of Alhaji Usman Koguna’s family. To my parent, Alhaji Usman

Koguna and Hajiya Tamagaji Usman Koguna, may Allah for give them and reward

them with Jannatul Firdaus, without your support I would have never achieved this

dream. The assistance I received from my brother, Alhaji Aminu Usman (Kogunan

Katsina II), Halima Usman and Hadiza Usman during the trial moment of my life will

never be forgotten. I thank you very much for your support. I also remain indebted to

iii

my wife and children for their patients and understanding to stay away from them

during my academic pursuit, I highly appreciate it. I acknowledge the support I

received from my step mothers, right from my primary school to date.

For Umaru Musa Yar’adua University Katsina, I appreciate the opportunity

given to me to serve my people and pursue higher degrees. I remained resolute, loyal

and steadfast to render service as enshrined in the condition of service of the

university. I thank the management of this great University for given me full

sponsorship to pursue PhD exploration geophysics program. Special thanks to Dr.

Bashir Muhammad Gide, Dr. Sama’ila Batagarawa, Dr. Nura Liman Chiromawa and

Dr. Abdullahi Abdulrahaman who introduced me to Universiti Sains Malaysia where

I fulfilled my destiny.

iv

TABLE OF CONTENTS

Acknowledgement

ii

Table of Contents

iv

List of Tables

x

List of Figures

xii

List of Symbols

xxi

List of Abbreviations

xxiv

Abstrak

xxvi

Abstract

xxviii

CHAPTER 1 – INTRODUCTION

1.1 Background

1

1.2 Problem statements

7

1.3 Research question

11

1.4 Research objectives

11

1.5 Novelty of the study

12

1.6 Scope and limitation of the study

12

1.7 Thesis outline

13

CHAPTER 2 - LITERATURE REVIEW

2.1 Introduction

15

2.2 Magnetic susceptibility

15

2.2.1 Magnetic elements

17

2.3 Reduction of magnetic observations 17

v

2.3.1 Diurnal variation correction

18

2.3.2 Geomagnteic correction

18

2.3.3 Reduction to the pole and equator

19

2.3.4 Applications of magnetic method

20

2.3.5 Limitations of magnetic method

20

2.4 Euler homogeneity

21

2.4.1 Previus work

23

2.4.2 2D Euler deconvolution

25

2.4.3 3D Euler deconvolution

27

2.4.4 Differential similarity transform

28

2.4.5 Euler deconvolution using gravity tensor gradient

31

2.4.6 Extended Euler deconvolution

32

2.4.7 Euler deconvolution of higher derivatives

33

2.4.8 Analytical Euler (AN-EUL)

34

2.4.9 Euler deconvolution of analytic signal

35

2.4.10 Depth estimation using tilit derivatives

36

2.4.11 Related literitures

36

2.4.12 Drawbacks of the reviewed technique

41

2.5 Research Gap 41

2.6 Filtering of Euler deconvolution solution

42

2.7 Accuracy assessment

43

2.8 Chapter summary

47

vi

CHAPTER 3 - RESEARCH METHODOLOGY

3.1 Introduction

49

3.2 The present technique (AUTO-EUD)

51

3.2.1 Description of the technique

52

3.2.2 Data inversion

54

3.2.3 Filtering using AUTO-EUD

56

3.2.4 Plotting of Euler solution 57

3.3 Synthetic models

58

3.3.1 Enhancement filter assessment

68

3.3.1(a) Sphere and box model

70

3.3.2 Validation using synthetic models

72

3.3.2(a) Assessing the effect of inclination on AUTO-

EUD

72

3.3.2(b) Accuracy assessment of AUTO-EUD using

synthetic models

80

3.3.2(c) Effect of interfernce

84

3.3.2(d) Effect of noise

87

3.3.2(e) Effect of window size

88

3.3.2(f) Comparison between AUTO-EUD and CED

91

3.4 Validation using field model

92

3.4.1 Multiple sources field model, Leister (UK)

93

3.4.1(a) Comparison between total field and RTP results

94

3.4.2 Concrete wall field model, Leister (UK)

94

3.5 Application of AUTO-EUD to magnetic data of Nevada basin,

USA

96

3.5.1 Description of some part of Nevada basin, USA

96

3.5.2 Geology of Nevada, USA 96

vii

3.5.3 Data description 99

3.5.4 Data processing 100

3.6 Application of AUTO-EUD to Seberang Jaya, Malaysia 101

3.6.1 Description of some part of Sebarang Jaya, Malaysia 101

3.6.2 Geology of Sebarang Jaya, Malaysia

101

3.6.3 Data acquisition

102

3.6.4 Comparison between measured and computed vertical

derivatives of total field

104


105

3.7 Application of AUTO-EUD to Upper Benue Trough, Nigeria

105

3.7.1 Description of some part of Upper Benue Trough, Nigeria

105

3.7.2 Geology and tectonics of of Upper Benue Trough, Nigeria 106

3.7.3 Data acquisition

108

3.7.4 Data pre-processing

109

3.7.5 Reduction to the equator

110


110

3.7.7 Data filtering

111

3.8 Chapter summary 111

CHAPTER 4 - RESULTS AND DISCUSSIONS

4.1 Introduction

113

4.2 The present technique

113

4.3 Synthetic models

116

4.3.1 Enhancement filter assessment 116

4.3.1(a) Sphere and box model 117

viii

4.3.2 Validation using synthetic models 138

4.3.2(a) Assessing the effect of inclination on AUTO-

EUD

138

4.3.2(b) Accuracy assessment of AUTO-EUD 171

4.3.2(c) Effect of interference 177

4.3.2(d) Effect of noise 182

4.3.2(e) Effect of window size 184

4.3.2(f) Comparison between AUTO-EUD and CED 197

4.3.3 Structural index of synthetic models 200

4.4 Field model 201

4.4.1 Multiple source field model 201

4.4.1(a) Comparison between total field and RTP data 202

4.4.1(b) Inversion output result after filtering 206

4.4.2 Concrete wall field model 208

4.4.3 Structural index of field models 210

4.5 Application of AUTO-EUD to magnetic data of Nevada basin,

USA

212

4.5.1 Comparison between estimated position and geology 217

4.6 Application of AUTO-EUD to magnetic data of Sebarang Jaya 221

4.6.1 Measured and computed vertical derivatives 224

4.6.2 Comparison between CED and AUTO-EUD 227

4.7 Application of AUTO-EUD to magnetic data Upper Benue Trough,

Nigeria

228

4.7.1 Reduction to the equator of total aeromagnetic intensity 229

4.7.2 Analytic signal of total aeromagnetic field intensity 230

4.7.3 Analytic signal of RTE of total aeromagnetic field

intensity

231

ix

4.7.4 Comparison between the AUTO-EUD outputs inverted

using total field and it’s RTE data

232

4.7.5 Comparison between CED and AUTO-EUD

238

4.8 Structural index of application site

240

4.9 Chapter summary

242

CHAPTER 5 - CONCLUSION AND RECOMMENDATIONS

5.0 Introduction

243

5.1 Conclusion 243

5.2 Limitation and sources of error

245

5.3 Recommendations

245

REFERENCES

246

APPENDICES

LIST OF PUBLICATIONS

x

LIST OF TABLES

Page

Table 1.1 Geophysical methods 2

Table 2.1 Magnetic susceptibility of rocks and minerals 16

Table 2.2 Structural index of magnetic source 22

Table 2.3 Grading scale of synthetic models 46

Table 3.1 Dimension of the targets of multiple sphere model 84

Table 3.2 Dimension of the targets of complex model 2 86

Table 3.3 Description of the targets in the field model 94

Table 4.1 Summary of the result (Profile AA’) 118

Table 4.2 Summary of the result (Profile BB’) 118

Table 4.3 Summary of the result (Profile CC’) 119

Table 4.4 Inversion and filtering output of isolated box model 140

Table 4.5 Inversion and filtering output of isolated contact model 144

Table 4.6 Inversion and filtering output of isolated cylinder model 148

Table 4.7 Inversion and filtering output of isolated dike model 152

Table 4.8 Inversion and filtering output of isolated sphere model 157

Table 4.9 Inversion and filtering output of complex model 1 164

Table 4.10 Inversion and filtering output of slanted box model 167

Table 4.11 Inversion and filtering output of infinite box model 172

Table 4.12 Inversion and filtering output of multiple cylinder model 174

Table 4.13 Inversion and filtering output of multiple sphere model 176

Table 4.14 Solutions of complex sphere model after filtering 178

Table 4.15 Estimated parameters of concrete wall model

180

xi

Table 4.16 Estimated parameters of two cylinder model 184

Table 4.17 Solutions of finite box model using different windows 186

Table 4.18 Result of combined two sphere and cylinder model 195

Table 4.19 Average inversion result of two sphere model

198

Table 4.20 Total field inversion result of multiple source field model

204

Table 4.21 Reduction to the pole of field model inversion result

204

Table 4.22 Total field inversion result of multiple source field model

after filtering using 4 parameters

207

Table 4.23 Inversion result of concrete wall model after filtering

209

Table 4.24 Statistics of solutions obtained from the inversion of total

field derivatives

216

Table 4.25 Statistics of solutions obtained from the inversion of RTP

derivatives

216

Table 4.26 Comparison between CED and AUTO-EUD

216

Table 4.27 Correlation coefficient (R) of the profiles analysed

227

Table 4.28 Inversion result of Sebarang Jaya site using CED and

AUTO-EUD

227

Table 4.29 AUTO-EUD solution (SI deviation = 0.2) summary of the

depth to the magnetic basement source indicating depth

interval and percentage obtained from the number of

solution from the RTE of total field

237

Table 4.30 AUTO-EUD solution (SI deviation = 0.2) summary of the

depth to the magnetic basement source indicating depth

interval and percentage obtained from the number of

solution from the RTE of total field

237

Table 4.31 Statistics of the inversion result using AUTO-EUD and

conventional Euler (Program) deconvolution technique

239

xii

LIST OF FIGURES

Page

Figure 3.1 Flow chart of the methodology for the application site and

aeromagnetic grid

50

Figure 3.2 Figure 3.2: Description of data inversion and filtering

procedure

53

Figure 3.3 A plane of box model indicating directions of some

magnetic element

60

Figure 3.4 A section of box model indicating the coordinate system

60

Figure 3.5 A section of contact model

62

Figure 3.6 Plane of horizontal cylinder model indicating directions of

the magnetic element

64

Figure 3.7 A section of horizontal cylinder model

64

Figure 3.8 Plane of dike model indicating directions of the magnetic

element

66

Figure 3.9 Section of a dike model

66

Figure 3.10 Plane of sphere model indicating directions of the magnetic

element

67

Figure 3.11 Section of sphere model indicating directions of the

magnetic element

68

Figure 3.12 Sphere and box model

71

Figure 3.13 Three Profiles (AA’, BB’ and CC’) on Sphere and box

model

71

Figure 3.14 Base map of isolated box model

73

Figure 3.15 Base map of isolated contact model

74

Figure 3.16 Base map of isolated cylinder model

75

Figure 3.17 Base map of isolated dike model

76

Figure 3.18 Base map of isolated sphere model

77

xiii

Figure 3.19 Base map of complex model 1

79

Figure 3.20 Slanted finite box model

80

Figure 3.21 Base map infinite box model

82

Figure 3.22 Base map of multiple cylinder model

83

Figure 3.23 Multiple sphere model

84

Figure 3.24 Base map of complex model 2

85

Figure 3.25 Base map of concrete wall model

87

Figure 3.26 Base map of two cylinder model

88

Figure 3.27 Base map of finite box model showing the true position of

the target

89

Figure 3.28 Base map of finite box model showing the true position of

the target

91

Figure 3.29 Base map of two sphere model indicating true position of

the target

92

Figure 3.30 Base map of multiple source model

93

Figure 3.31 Base map of concrete wall model

95

Figure 3.32 Geological map of Nevada

97

Figure 3.33 Survey stations super imposed on base map of geotechnical

site

103

Figure 3.34 Layout of GEM gradiometer system

104

Figure 3.35 Map of Nigeria showing the location of Upper Benue

Trough

106

Figure 3.36 Geological map of the study area

108

Figure 4.1 Anomalous magnetic field (nT) of sphere and box model

117

Figure 4.2 Anomalous magnetic field (nT) of a box and sphere model

with Profile AA’, BB’ and CC’

118

Figure 4.3 Vertical derivative of the field

120

Figure 4.4 Vertical derivative (dz) of Profile AA’

120

xiv

Figure 4.5 Vertical derivative (dz) of Profile BB’

121

Figure 4.6 Vertical derivative (dz) of Profile CC’ 121

Figure 4.7 Horizontal derivative in x-direction (nT/km) of the field

122

Figure 4.8 Horizontal derivative in y-direction (nT/km) of the field

123

Figure 4.9 Total horizontal derivatives (nT/km) of the field

123

Figure 4.10 Total horizontal derivatives (nT/km) of Profile AA’

124

Figure 4.11 Total horizontal derivatives (THDR) of Profile BB’

124

Figure 4.12 Total horizontal derivatives (THDR) of Profile CC’

125

Figure 4.13 Analytic signal (nT/km) of the field

126

Figure 4.14 Analytic signal (AS) of Profile (AA’)

126

Figure 4.15 Analytic signal (AS) of Profile (BB’)

127

Figure 4.16 Analytic signal (AS) of Profile (CC’)

127

Figure 4.17 Tilt derivative (nT/km) of the field

128

Figure 4.18 Tilt derivative (nT/km) of Profile AA’

129

Figure 4.19 Tilt derivative (nT/km) of Profile BB’

129

Figure 4.20 Tilt derivative (nT/km) of Profile CC’

130

Figure 4.21 Tilt angle

130

Figure 4.22 Total horizontal derivative of tilt derivative (nT/km) of the

field

131

Figure 4.23 Total horizontal derivative of tilt derivative (nT/km) of

Profile AA’

132


Profile BB’

132


Profile CC’

133

Figure 4.26 Laplacian of the field (nT2/km

2)

134

Figure 4.27 Laplacian Profile AA’

134

xv

Figure 4.28 Laplacian Profile BB’

135

Figure 4.29 Laplacian Profile CC’

135

Figure 4.30 Enhancement filters along Profile AA’

136

Figure 4.31 Enhancement filters along Profile BB’

137

Figure 4.32 Enhancement filters along Profile CC’

137

Figure 4.33 Anomalous magnetic field intensity (nT) of a box model

(a) I = 0(b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

141

Figure 4.34 Depth solutions super-imposed on AS (nT/km) of a box

model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

142

Figure 4.35 Anomalous magnetic field intensity of a contact model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

145

Figure 4.36 Depth solutions super-imposed on AS of contact model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

146

Figure 4.37 Anomalous magnetic field intensity of cylinder model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

149

Figure 4.38 Depth solution of a cylinder model super-imposed on AS

for:

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45°(e) I = 60°

(f) I = 75° and (g) I = 90°

150

Figure 4.39 Anomalous magnetic field intensity of dike model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

153

Figure 4.40 Depth solutions super imposed on AS of dike model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

154

Figure 4.41 Anomalous magnetic field intensity of sphere model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I =75° and (g) I = 90°

158

xvi

Figure 4.42 Depth solutions super imposed on AS of anomalous

magnetic field intensity of sphere model

(a) I = 0°(b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

159

Figure 4.43 Anomalous magnetic field intensity of complex model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

162


magnetic field intensity of complex model

(a) I = 0°(b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

163

Figure 4.45 Anomalous magnetic field intensity of slanted model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

168


magnetic field intensity of slanted box model

(a) I = 0° (b) I = 15° (c) I = 30° (d) I = 45° (e) I = 60°

(f) I = 75° and (g) I = 90°

169

Figure 4.47 Anomalous field (nT) of infinite box model

172

Figure 4.48 Depth solutions of infinite box model super imposed on

AS (nT/km)

173

Figure 4.49 Anomalous field (nT) of multiple cylinder model

174

Figure 4.50 Depth solutions of multiple cylinder model super imposed

on AS (nT/km)

175

Figure 4.51 Anomalous magnetic field (nT/km)

176

Figure 4.52 Depth solutions super imposed on AS (nT/km)

177

Figure 4.53 Anomalous magnetic field (nT) of complex model 2

179


179

Figure 4.55 Anomalous magnetic field (nT)

181


181

Figure 4.57 Anomalous magnetic field of two cylinder model

183


magnetic field with10% noise with Gaussian distribution

183

xvii

Figure 4.59 Depth solutions of finite box model using the window size

of 5×5 grid points super-imposed on AS

187


of 7×7 grid points and convolution window of 7 units

super-imposed on AS

187


of 7×7 grid points and convolution window of 11 units (all

SI)super-imposed on AS

188



super-imposed on AS

188



super-imposed on AS

189



super-imposed on AS (all values of N)

190



super-imposed on AS (-0.44≤N≤0.44)

191



super-imposed on AS (0.45≤N≤1.44)

191



super-imposed on AS (all values of N)

192



super-imposed on AS (-0.44≤N≤0.44)

192



super-imposed on AS (0.45≤N≤1.44)

193

Figure 4.70 Anomalous magnetic field (nT) of two sphere and cylinder

model

195

Figure 4.71 Depth solutions super-imposed on AS of anomalous

magnetic field (nT) of two sphere model inversed using

window size 9×9 grid points (cw = 9 units; SI dev = 0.2;

error = 1% and threshold of AS)

196

xviii


magnetic field (nT) of two sphere and cylinder model

inversed using window size 13×13 grid points (cw = 13; SI

dev = 0.2 error = 1 and threshold of AS = 2)

196


magnetic field (nT) of two sphere model inversed using

window size 21×21 grid points (ws = 21; SI dev = 0.2;

error = 1 and threshold of AS = 2)

197

Figure 4.74 Anomalous field of two sphere model

199

Figure 4.75 Estimated position (obtained from inversion using a

commercial software, CED) super imposed on AS

199

Figure 4.76 Estimated (obtained from inversion using AUTO-EUD)

super imposed on AS

200

Figure 4.77 Total field (nT) of multiple source field model

203

Figure 4.78 RTP of multiple source field model

203

Figure 4.79 Depth solutions (obtained from inversion of the total field)

super imposed on AS (nT/m) of total field of field model

205

Figure 4.80 Depth solutions (obtained from inversion of RTP of the

total field) super imposed on AS (nT/m) of Reduction to

the pole of field model

205

Figure 4.81 AS (nT/m) of total field of field model (after filtering)

207

Figure 4.82 Total magnetic field intensity of the field model

209

Figure 4.83 Depth solutions of buried walls model super imposed on

AS

209

Figure 4.84 Total magnetic field (nT) of some part of Nevada

213

Figure 4.85 RTP of total magnetic field (nT) of some part of Nevada

214

Figure 4.86 Analytic signal (nT/km) map of the total magnetic field

214

Figure 4.87 Analytic signal (nT/km) of RTP

215

Figure 4.88 Depth solutions (from the inversion of total field

derivatives using AUTO-EUD) super imposed on analytic

signal (nT/km) map of the total magnetic field

215

xix

Figure 4.89 Depth solutions (from the inversion of RTP data

derivatives using AUTO-EUD) super imposed on analytic

signal (nT/m) of RTP data

216

Figure 4.90 Depth solutions (from the inversion of RTP data

derivatives) super imposed on analytic signal (nT/m) of

RTP data

218

Figure 4.91 Range of valued of the estimated depth solutions (obtained

from the inversion of total field data)

218

Figure 4.92 Depth solutions (obtained from the inversion of total field

data) super imposed on geological map of the study area

219

Figure 4.93 Range of valued of the estimated structural index (obtained

from the inversion of total field data)

220

Figure 4.94 Total magnetic field intensity map of application site

222

Figure 4.95 Depth solutions (application site) super imposed on AS

(nT/m)

223

Figure 4.96 Solutions of structural index super imposed on AS (nT/m)

of Sebarang Jaya, Malaysia

223

Figure 4.97 Measured vertical derivatives (gradiometer reading) of

application site

224

Figure 4.98 Computed vertical derivatives of application site

225

Figure 4.99 Computed vertical derivative (contour lines) of application

site superimposed on measured vertical derivative with

three selected profiles (AA’, BB’ and CC’)

225

Figure 4.100 Profile AA’: Measured (Meas) and computed (Comp)

vertical derivatives of application site

226

Figure 4.101 Profile BB’: Measured (meas) and computed (comp)


226

Figure 4.102 Profile CC’: Measured (Meas) and computed (Comp)


226

Figure 4.103 Total aeromagnetic magnetic field intensity (nT) of some

part of Upper Benue Trough

228

Figure 4.104 Reduction to the equator of total aeromagnetic magnetic

field intensity (nT) of some part of Upper Benue Trough

230

xx

Figure 4.105 Analytic signal (nT/km) of total aeromagnetic magnetic

field intensity of some part of Upper Benue Trough

231

Figure 4.106 Analytic signal (nT/km) of RTE of total aeromagnetic

magnetic field intensity of some part of Upper Benue

Trough

232

Figure 4.107 AUTO-EUD depth solutions super-imposed on AS of total

field map, SI deviation = 0.2, the maximum acceptable

regression error was10%, the threshold value of AS was

0.005 nT/m, the centre of convolution window was 13 and

negative SI values are rejected

234

Figure 4.108 AUTO-EUD depth solutions (obtained from RTE data)

super-imposed on AS of RTE map, SI dev = 0.2, the

maximum acceptable regression error was10%, the

threshold value of AS was 0.005 nT/m, the centre of

convolution window was 13 and negative SI values are

rejected

235

Figure 4.109 AUTO-EUD depth solutions super-imposed on AS map, SI

deviation = 0, the maximum acceptable regression error

was10%, the threshold value of AS was 0.005 nT/m, the

centre of convolution window was 13 and negative N

values are rejected

236

Figure 4.110 Lineament obtained from AS super-imposed on AS (nT/m)

map

240

xxi

LIST OF SYMBOLS

A Angle between positive x-axis and magnetic north (0° to 90°) of dike

model

a order of differentiation

B Background field/ base level of the total magnetic field

c Magnetic constant

Partial differentiation

δ: 90 - I

d dip

d1 Depth to top of the structure of contact model

d2 Depth to the bottom of the structure of contact model

E True model parameter

Estimated model parameter

f field

F Force

f(x) Observed field at x

General function

H magnetizing field

h depth of the element (box model) below the level of observation

I inclination of the geomagnetic field

i Positive and negative in the Northern and Southern Hemisphere

respectively

Ip Polarization

effective inclination of cylinder model

real inclination of cylinder model

xxii

k Magnetic susceptibility

K Dipole moment

L1 direction cosine characterizing polarization vector of the volume

element (box model)

L2 direction sine characterizing polarization vector of the volume element

(box model)

M Magnetization

m magnetic induction

N Structural index

n direction cosine vector of the earth’s field (box model)

n Degree of homogeneity

O’ Origin

∫

magnetic flux

Adjacent distance from the observation point to the depth to the top of

the dike model

Ro’p vector originate at O’ towards P

r Radius between the poles

Vector directed from the source point to observation point

S the cross-sectional area of cylinder model

operator of the differential similarity transform

: effective total intensity of cylinder model

T Tesla

t Number of observations

xxiii

u Inclination

v Declination

ui Set of variables

w Width of the sheet

x observation point along x

x0 Position of source in x direction

Xi Independent variable in MLR

y0 Position of source in y direction

Yi Dependent variable in MLR

y observation point along y

z observation point along z

z0 Position of source in z direction/depth

Coordinate of the volume element d

ρ Density of magnetic flux

β0 intercept of dependent variable

βi Slope of regression/ coefficient of variable

εi Regression error

∆T(x) Total magnetic intensity at x

Permeability of free space

µ 1+K

τ threshold value of Euler depth solutions

θ the azimuth angle of box model

strike angle of the structure measured clockwise from north of contact

model

∆n Absolute error

xxiv

LIST OF ABBREVIATIONS

AN-EUL Analytical Euler

AS Analytic Signal

AAS Amplitude of Analytic Signal

AS_tot Analytic signal of total field

AS_rtp Analytic signal of RTP data

AUTO-EUD A technique of magnetic data interpretation for the fully

automation (AUTO) of Euler deconvolution (EUD) relation

CED Conventional Euler Deconvolution

cw distance from the centre of convolution window

dz Vertical derivative

DST Differential Similarity Transform

ED Euler deconvolution

fd declination of the ambient field

ft Feet

IAF Integrated and Automated Filter

IGRF International Geomagnetic Reference Field

Lap Laplacian

md declination of magnetization

MLR Multiple Linear Regression

Ng Geographic north

nT Nano Tesla

Oe Reduction to the equator

Op Reduction to the pole

THDR Total Horizontal Derivative

xxv

RTP Reduction to the pole

RTE Reduction to The Equator

S.I International System of Units

SI dev Deviation of structural index from the integer value

SD Standard Deviation

TA Tilt Angle

TD Tilt derivative

THD_TD Total horizontal derivative of tilt derivative

TDR Tilt Derivative

TMI Total Magnetic Field Intencity

USGS United States Geological Survey

ws Window size

2D Two dimensional

3D Three dimensional

pmic Micro scale clustering

pmac Macro scale clustering

xxvi

PENAFSIRAN AUTOMATIK DATA MAGNETIK MENGGUNAKAN

KAEDAH DEKONVOLUSI EULER DENGAN ALGORITMA TERUBAH

SUAI

ABSTRAK

Dekonvolusi Euler konvensional mempunyai lima parameter yang tidak

diketahui untuk diselesaikan iaitu lokasi sumber (x0, y0 and z0), medan latar belakang

(B) dan indeks struktur (N). Antara lima perkara yang tidak diketahui ini, indeks

struktur dipilih secara manual oleh pengguna. Input manual indeks struktur ke dalam

persamaan Euler menjadikan teknik ini semi-automatik dan tafsiran menjadi

subjektif. Untuk menangani masalah ini, penyelidikan ini bertujuan untuk

mengautomasikan teknik dekonvolusi Euler dan memperkenalkan teknik penurasan

untuk membezakan penyelesaian yang boleh dipercayai daripada output

penyongsangan. Ia juga merupakan sebahagian daripada objektif kajian ini, untuk

menilai kesan kecondongan teknik baru dan menyiasat ketepatan algoritma yang

diubahsuai. Regresi linear berganda digunakan untuk menyelesaikan lima parameter

hubungan dekonvolusi Euler yang tidak diketahui untuk data magnetik bergrid.

Untuk menyediakan penurasan yang berkesan, enam penuras dianalisis untuk

memilih yang terbaik yang akan digunakan sebagai bantuan untuk penuras

penyelesaian Euler. Kriteria lain yang digunakan untuk penurasan output

penyongsangan ialah jarak dari pusat tetingkap konvolusi, sisihan indeks struktur dan

ralat regresi. Kriteria ini disepadukan, automatik dan digunakan untuk memilih

penyelesaian yang boleh dipercayai dari output penyongsangan. Kesan kecondongan

pada teknik ini dinilai menggunakan kajian model sintetik (mudah dan gabungan) dan

model lapangan. Setiap model disimulasikan menggunakan kecondongan yang

xxvii

belainan (0°, 15°, 30°, 45°, 60°, 75° dan 90°) dengan parameter lain yang tetap.

Terbitan bagi setiap set data dikira dan disongsangkan. Penyelesaian yang boleh

dipercayai dipilih dan hasilnya dibandingkan. Untuk data sebenar, keputusan

tersongsang dan terturas dari jumlah medan dan data yang dikurangkan kepada kutub

juga dibandingkan. Kajian model sintetik dan lapangan atas sumber magnet

digunakan untuk menunjukkan keupayaan algoritma yang diubah suai untuk

menyelesaikan lokasi sumber dan sifat sasaran. Hasil songsangan (fail) terdiri

daripada 5 parameter yang tidak diketahui yang terdapat dalam persamaan

dekonvolusi Euler. Isyarat analitik didapati mempunyai banyak kelebihan terhadap

penuras yang dianalisis dan ia dipilih sebagai salah satu kriteria (sebagai tambahan

kepada tiga kriteria yang disebutkan) untuk penapisan. Hasil model sintetik

menggunakan kecondongan yang berlainan adalah sama. Hasil yang diperolehi dari

penyongsangan jumlah medan dan data yang dikurangkan kepada kutub dari model

medan pelbagai sumber juga adalah sama. Anggaran kedalaman min yang diperoleh

dari penyongsangan jumlah medan dan data yang dikurangkan kepada kutub bagi

data aeromagnet Nevada adalah 801 dan 787 m masing-masing. Keputusan yang

diperolehi daripada analisis data Nevada telah memperkuatkan hasil yang diperolehi

daripada pemodelan sintetik. Dalam kebanyakan ujian dijalankan, algorithma yang

diperkenalkan menentukan kedudukan sasaran dengan kejituan yang baik dan teknik

ini tidak bergantung pada kecondongan. Teknik ini adalah mod cepat tafsiran data

magnetik dan mudah dilaksanakan kerana ia melibatkan terbitan tertib pertama

medan tersebut.

xxviii

AUTOMATIC INTERPRETATION OF MAGNETIC DATA USING EULER

DECONVOLUTION WITH MODIFIED ALGORITHM

ABTRACT

The conventional Euler deconvolution has five unknown parameters to be

solve which are the location of source (x0, y0 and z0), the background field (B) and the

structural index (N). Among these 5 unknowns, the structural index is to be manually

selected by the user. The manual input of structural index into the Euler equation

makes the technique to be subjective and semi-automated. The objectives of this

research are, to automate Euler deconvolution equation and introduce a filter for

discriminating reliable solution from the inversion output. It is also part of the

objectives of this research, to assess the effect of inclination on the new technique

and investigate the accuracy of the introduced algorithm. Multiple linear regression

was used to solve the five unknown parameters of Euler deconvolution relation for

gridded magnetic data. To provide an effective filtering, six filters were analysed in

order to select a best one that would be used as an aid for filtering Euler solutions.

Other criteria used for filtering of the inversion output are distance from the centre of

convolution window, deviation of structural index and regression error. These

criterions are integrated, automated and used for selecting more reliable solutions

from the inversion output. The effect of inclination on this technique is assessed

using synthetic (simple and combined) and field model’s studies. Each model is

simulated using different inclinations (0°, 15°, 30°, 45°, 60°, 75° and 90°) with other

parameters kept constant. The derivatives of each data set were computed, inverted,

more reliable solutions are selected and the results were compared. For real data, the

inverted and filtered results from the total field and it’s reduced to the pole data were

xxix

also compared. The synthetic and field models studies over magnetic sources were

used to demonstrate the ability of the modified technique to solve for the source

location and nature of the target. The inversion (file) result comprises of 5 unknown

parameters contained in Euler deconvolution equation. The inversion can be achieved

by prescribing the window size which is the only choice a user has to make. Analytic

signal is found to have so many advantages over the filters analysed and it is chosen

as one of the criteria (in addition to the three mentioned criteria) for filtering. The

results of synthetic models using different inclinations are about the same. The result

obtained from the inversion of total field and it’s reduced to the pole data of multiple

source field model are about the same. The mean depth estimates obtained from the

inversion of total field and reduced to the pole data of aeromagnetic data from

Nevada are 801 and 787 m respectively. The results obtained from the analysis of

Nevada data have further corroborated the result obtained from the synthetic

modeling. In most of the tests carried out, the introduced algorithm located the

position of the target with good precision and the technique does not depend on

inclination. The technique is fast mode of magnetic data interpretation and easy to

implement as it involves first order derivatives of the field.

1

CHAPTER 1

INTRODUCTION

1.1 Background

Now a days geophysical methods are widely applied to investigate subsurface

of the Earth in order to explore geological structures of economic interest (in most

cases) in areas of hydrology, solid minerals (Arisona et al. 2016), hydrocarbons,

engineering, archaeological, geothermal studies (Khalil et al. 2017), geo-hazard

assessment, geochemical (Yang et al. 2015) and environmental studies (Loke et al.

2013; Yang et al. 2015). The choice of geophysical methods over other techniques is

partly due their nondestructive nature and cost effective in large area investigation.

Geophysical survey can be carried out on land, from the air or over water because of

the improved sensitivity of the measuring instruments. The speed of operation from

air geophysical survey is another feature that attracted many Earth scientists to these

techniques. The use of geophysical methods permits geophysicist to investigate the

conceal features beneath the Earth’s surface. These features appear in the form of

anomaly due to different physical properties in the subsurface that need to be

interpreted in to its geological relevance. The methods are Seismic, Electrical,

Ground penetration radar, Transient electromagnetic (TEM), Gravity and Magnetic

method among others.

Geophysical methods are classified as those that make use of the natural field

of the Earth e.g. gravity and magnetic methods, and methods that require the input of

artificially generated energy, e.g. seismic reflection and electrical methods. The

geophysical surveying methods, measured parameters together with their respective

operative physical properties are shown in the Table 1.1. It is the operative physical

2

property that determines the specific use of any method. Thus for example, seismic

or electrical method are suitable for locating water table because saturated rock may

be distinguished from dry rock by its higher seismic velocity and higher electrical

conductivity. Nevertheless, other considerations also determine the type of methods

employed in a geophysical exploration program. For example, reconnaissance

surveys are often carried out from air because of the high speed of operation. In such

cases the electrical or seismic methods are not applicable since these require physical

contact with the ground for the direct input of energy.

Table 1.1: Geophysical methods (Kearey et al., 2002)

Method Measured Parameters Operative Physical

Properties

Seismic Travel times of reflected/ refracted

seismic waves

Density and elastic moduli,

which determine the

propagation velocity of

seismic waves

Gravity Spatial variations in the strength of the

gravitational field of the Earth

Density

Magnetics

Spatial variations in the strength of the

geomagnetic field of the Earth

Magnetic susceptibility

Electrical

-Resistivity

-Induced

polarization

-Earth resistance

-Polarization voltages or frequency-

dependent ground resistance

-Electrical conductivity

-Electrical capacitance

Self-potential Electrical potential

Electrical conductivity

Electromagnetic Response to electromagnetic radiation

Electrical conductivity and

inductance

Radar Travel times of reflected radar pulses

Dielectric constant

Measurement of geomagnetic field can be used to determine the structure of

the Earth since many rocks have magnetization. Magnetic method can be used as a

tool for detecting shallow structure of local, regional and global scales. With the aid

3

of techniques used for the inversion of magnetic data (Gerovska, and Bravo 2003;

Gerovska, et al. 2010;Cooper, 2014; Cooper and Whitehead 2016; Salem, 2007), it is

possible to determine the horizontal and vertical position of concealed metallic

objects in the near vicinity of the earth’s surface in addition to the delineation of

deep-seated structures. The advantages of magnetic method include its ability to

detect near surface weak magnetic signal produced by the buried objects and its

relative ease of operation.

The choice of a geophysical method to locate a particular geological structure

depends on its mineral content. Some of the reasons for choosing the magnetic

method are:

i. This method is widely used in mineral and petroleum explorations,

engineering, environmental, geothermal and global applications.

Magnetic method is the most versatile of geophysical prospecting

techniques.

ii. Magnetic measurements are made more easily and cheaply than most

geophysical measurements (Telford et al., 1990).

iii. In order to understand this field (geophysics) very well, magnetic

method needs to be studied since the study of the Earth’s magnetism is

the oldest branch of geophysics.

iv. Magnetic method is one of the methods that use the natural field of the

Earth, unlike some other methods that requires the artificially generated

field. It is therefore provide room to understand the variation of a

certain phenomenon on the Earth.

v. Aeromagnetic maps of most of the areas around the globe are available

for free or at nominal amount.

4

Aeromagnetic survey is carried out in order to detect rocks or minerals that

have abnormal magnetic properties which can be identified by causing anomalies in

the geomagnetic field. It is fast, cost effective and accessible technique used for

regional geological mapping, mineral and petroleum exploration (Chinwuka, 2012).

Euler deconvolution can assist in the interpretation of aeromagnetic data by

indicating the nature of the basement topography (undulating), depth and the

direction of steepness. Overburden thickness of the sedimentary sediment is very

essential in hydrocarbon exploration.

Generally, potential field data interpretation can be categorized into three

sections; forward modeling, inverse modeling, data enhancement and display

(Blakely, 1996). Modeling is an essential aspect of geophysics because it can be used

to predict a particular geological structure based on known model parameters. It can

also be used to determine feasible subsurface distribution of physical properties of

the target. The former and latter processes are known as forward and inversion

modeling. Mathematical modeling can be divided into three main groups which are

analytic, empirical and numerical models. Analytical modeling applies to simple

cases only and it provides error free solution. Analytical modeling is a vital tool used

in potential field data inversion. In general, modeling of geophysical data is

addressed in terms of depth to simple magnetic or gravity sources. Modeling leads to

a distinct inversion techniques as a result of non-uniqueness nature of the causative

sources.

The difficulties attached on seeking an inverse solution are:

i. Scientifically, error is present in all the measurements collected due to

instrumental and systematic error.

5

ii. The presence of sub-surface features that are not properly addressed by

a model

iii. Superposition of close features. However, these effects can be

constrained by using geological map and borehole information.

There are so many depth estimation techniques that assist geophysicist in

potential field data interpretation such as Werner deconvolution, source parameter

imaging (SPI), source location using total field homogeneity, depth from extreme

points, tilt depth and so on. In addition to the mentioned manual or automatic/semi-

automatic depth estimation techniques, Euler deconvolution is powerful technique

designed to analyze large amount of potential field data. It has been applied

extensively in delineating geologic boundaries (Hsu et al., 1996; Ugalde and Morris,

2010; Barbosa and Silva, 2011), and locating geothermal sources or hot springs

(Nouraliee et al., 2015); and is combined with other geophysical methods to ensure

enhanced interpretation of subsurface geology. It is one of the techniques that can be

used to provide fast means of data interpretation. Euler deconvolution technique uses

field and its derivatives in the system of linear equation in relation to the source

coordinate to estimate depth and location of anomalous source. This technique can

assist geoscientist by indicating portion of interest which can then further be

analyzed in detail. Some of the justifications on the need of depth estimation

technique are:

i. Large amount of potential field data sets (especially magnetic and

gravity methods) have been collected using aeroplane, ships and

satellites in regional/global scale. These data sets need to be process

and interpreted in to its geological relevance.

6

ii. The thickness of the sedimentary section and depth of ore bodies (that

contains magnetic minerals) are highly interested in hydrocarbon and

mineral exploration respectively.

iii. Euler deconvolution technique (Thompson, 1982) has been popularly

used by Chevron Oil Companies and within the Gulf, EULDPH is also

applied by Durrheim (1983), Corner and Wisher (1989) to determine

magnetic markers in search for gold in Witwatersrand Basin.

In addition, Euler deconvolution technique does not assume any geological

model, but it requires (prior knowledge of the rate of decay of the field of a particular

source) structural index which gives the nature of the geological structure. The

anomaly source is considered as singular point that consists of elementary potential

field distribution such as point poles or dipoles. An anomaly is considered as the

field caused by local variation in the geomagnetic field given rise by a singular point

of source. With the aid of Euler homogeneity relation, magnetic method can be used

to delineate the presence of metallic structures in the subsurface. Therefore, some of

the advantages of this technique are speed of operation, ability to interpret large data

sets and its implementation is less tedious.

The conventional Euler deconvolution (Thompson 1982; Reid et al 1990;

Ugalde and Morris 2010; Barbosa and Silva 2011; Oruç and Selim 2011; Chen et al.

2014) has 5 unknown parameters which are the location of source in x, y and z-

directions (x0, y0 and z0), the background field and the structural index (N). Among

these 5 unknowns, N is to be manually selected by the interpreter/user. An interpreter

has to solve the equation using different N and finally select the best set of solution.

The interpreter is left with the decision that has the highest impact on the depth

7

solutions: which N should be chosen? Much of the interpreter’s efforts will be

exhausted on choosing the solution produced by the appropriate structural index.

1.2 Problem statement

i. The manual input of structural index into the Euler equation makes the

technique to be semi-automated. This makes the procedure too

subjective (Interpreters can make different decisions), tedious and time

consuming. Moreover, the geology of the earth is comprises of different

structures (it is very complex) which may not be fitted by a fixed N.

Hsu (2002) stated that the use of wrong N can cause bias on depth

estimate and scattered solution on target’s locations. Therefore, the used

of fixed structural index may not estimate the parameters of different

sources in the real geology with desired accuracy.

One of the disadvantages of conventional Euler deconvolution is

that the interpreter/user has to select N manually. This property is a

setback to one of the most important attribute of the technique which is

fast means of interpreting large volume of data. However, attempts

made to address this problem using Differential Similarity Transform

(DST) (Stavrev, 1997; Gerovska and Arouzo-Bravo 2003; Grerovska et

al. 2010) and other related techniques that does not require the use of

structural index (Mushayandebvu et al., 1999, 2001; Nabighian and

Hansen, 2001; Salem and Ravat, 2003; FitzGeral et al, 2004; Keating

and Pilkington, 2004; Salem et al., 2007) surfer some drawbacks. DST

is less implemented because of the complexity involved in operation

(Reid and Thurston, 2014). According to Florio et al., 2006, the

8

estimation of N using AS (Salem and Ravat, 2003) could lead to error.

Tilt depth (Salem et al., 2007) technique uses higher order derivatives

(Reid and Thurston, 2014).

A procedure for solving five unknown parameters (including the

structural index) of magnetic anomaly using Euler deconvolution that

can be implemented without the use of complex mathematics, the use of

analytic signal and higher order derivatives is missing in the literature.

Multiple linear regression (MLR) methodology can be used to

solve positions (x0, y0 and z0) of magnetic source, background (B) and

structural index (N) simultaneously. The use of multiple linear

regression to solve the unknown parameters of Euler deconvolution

technique of magnetic anomaly is not available in the geophysical

literature. Unlike the past works, this technique allows the use of first

order derivatives, the inversion is independent of analytic signal (AS)

and it does not involve complex mathematical operations. It is simple to

apply and the derivatives are computed directly from the total field grid.

ii. Euler deconvolution treats the potential field sources as consisting of

elementary points with different parameters (such as N) as such large

number of solutions is usually obtained and it needs effective filtering

technique. Because of the complicated nature of the Earth subsurface,

some of these solutions are spurious/artifacts caused by interference of

other sources. Many studies have been carried out to address this issue

and they come out with different procedures in determining the correct

solution. Reid and Thurston (2014) has advocated that when depth and

9

N of the source are to be estimated simultaneously, rigorous means of

data filtering is required to choose the valid solutions.

The use of standard deviation of estimated depth and clustered

solutions had been the preferred means of selecting valid solutions

(Thompson, 1982; Reid et al., 1990, Grerovska et al., 2010). Other

researchers used various traditional filtering techniques (FitzGerald et

al., 2004) to discriminate the most accurate solutions. However,

rigorous filtering technique still remained one of the challenges of using

Euler deconvolution technique. Euler deconvolution method is built

based on the potential field and its derivatives; so, the accuracy of Euler

deconvolution method relies largely on the derivatives. Thus, Euler

deconvolution solutions should be filtered based on the area of the data

to be convolve, rather than focusing on the sprays of solutions. It is

crucial to study how potential derivatives based filters can be used as an

aid of choosing the correct range of depth solutions. The coupling

problem that exists between depth and structural index can be avoided

by identifying and using the locations immediately above the source

body’s critical points (Reid and Thurston, 2014).

iii. The pattern of magnetic anomaly depends on its position on the earth

surface. The same structure placed at different geographical locations

would give different anomaly’s shape because of the variation in

magnetic latitude. The dipolar nature of the magnetic field causes

distortion in the anomaly’s shape and as a result of this effect, error will

be introduced to the data and there by affecting the estimate of the

anomaly’s location (Araffa et al, 2012). While the use of RTP is

10

recommended to be applied on the data prior to the application of Euler

deconvolution (Thompson, 1982), other researchers (Reid et al., 1990)

are of the opinion that it should not be applied.

However, this problem remain unsolved, no attempts have been made

to investigate this effect on Euler deconvolution related techniques.

Also, no inclination’s assessment was carried out on the present

technique. The use of synthetic models and real data is very essential in

understanding the effect of inclination of the introduced technique.

Because, the introduced technique is not available in the literature,

evaluating the effect of inclination will definitely be added or otherwise

to the strength of the technique.

iv. The limit of the accuracy of depth estimation technique from magnetic

data is well established in the literature (Breiner, 1973; 1999). The

accuracy of conventional Euler deconvolution (Thompson, 1982; Reid

et al., 1990) and other related techniques have been evaluated. The

traditional approach for evaluating the performance of Euler

deconvolution technique has been the use of deviation from a certain

referenced value (mean).

However, in this research where a new approach is introduced, its

accuracy remains unknown. Moreover, the accuracy of interpretation

techniques determines its applicability in various geophysical

applications. Therefore, there is need to assess the present technique in

order to know its accuracy. Synthetic modeling using different models

such as box, contact, cylinder, dike and sphere can be used to assess the

accuracy of the introduced technique. In this case, the theoretical basis

11

of the technique can be established. The assessment can also be carried

out using field model data and the site where the detail geological

information of the area is known. In addition to the deviation of the

parameters, percentage of minimum/maximum error permits easier

assessment of the output parameters.

1.3 Research question

i. Which approach shall be adopted to automate Euler deconvolution

technique?

ii. What are the criteria for choosing valid Euler solutions?

iii. What is the effect of inclination on AUTO-EUD?

iv. How accurate is AUTO-EUD?

1.4 Research objective

An algorithm/procedure based on Euler’s homogeneity relation for fully

automation (hence the acronym, AUTO-EUD) of magnetic data interpretation is

presented in this research. Some of the objectives of this research are:

i. to automate Euler deconvolution equation in order to estimate the

horizontal coordinates (x0 and y0), depth, background (B) and structural

index (N) of a magnetic source,

ii. to propose a filter for discriminating reliable solution from the inversion

output of Euler homogeneity equation,

iii. to assess the effect of inclination on the introduced algorithm (AUTO-

EUD) and

12

iv. to investigate the accuracy of AUTO-EUD’s solutions using synthetic

and real magnetic data.

1.5 Novelty of the study

i. The introduced algorithm for solving the unknown parameters

of magnetic anomaly using multiple linear regression is not available

in the geophysical literature.

ii. The integrated and automated filter introduced in this study is

unique in the geophysical literature and therefore, it is a novel.

iii. This study has empirically deduced the structural index of a

box which is also not available in the literature.

iv. An application of the technique in engineering and

environmental site has been demonstrated. This application is rarely

found in the literature and it is therefore a new contribution to the

knowledge.

1.6 Scope and limitation of the study

The scope of this study is limited to forward modeling and inversion of 3D

magnetic field only. The accuracy of the introduced technique is determined using

synthetic models and field model data. The test of this inversion program using

synthetic model (in this research) is also limited to certain type of structures, namely

box, contact, dike, horizontal cylinder and sphere. These structures are designed with

the intention to simulate field with simple geologic structures. For synthetic and field

model data, the solutions provided by the introduced technique are compared to true

13

parameters of the models, whereas for real magnetic data, the depth solutions are

compared to thickness of rocks available in the literature.

1.7 Thesis outline

This thesis consists of 5 chapters. The first chapter introduces geophysical

prospecting methods and data interpretation with emphasize on Euler deconvolution.

The introductory chapter also presents problem statements, research questions,

objective of this study, novelty of the study, the scope and limitation of the study.

Other component of this chapter, although not the least, is significance of findings,

organization of the thesis.

The second chapter provides fundamentals of magnetic field and some

background of Euler’s homogeneity concept, which is the basis of Euler

deconvolution methodology. This chapter also includes the previous works to give

overview of how Euler deconvolution has evolved and modified through the past

decades, and also to sort out the research gap in Euler deconvolution methodology.

The third chapter presents the methodology used in this study and it consists

of (i) the introduction of the new technique using Multiple Linear Regression

methodology, (ii) the accuracy assessment of AUTO-EUD using synthetic modeling

and (iii) the accuracy assessment of AUTO-EUD using real magnetic data. This

chapter also explains how the solutions are filtered based on analytic signal and the

comparison between Conventional Euler Deconvolution (CED) and the present

technique (AUTO-EUD).

The fourth chapter presents the results of the forward modeling and inversion

of synthetic models as well as the inversion of real magnetic data of field models

application site. This chapter also discusses the accuracy of AUTO-EUD based on

14

the comparison between solutions from AUTO-EUD and the true models, and

between solutions and geological map. Besides these, the discussion also includes the

limitations of AUTO-EUD based on the results obtained.

The last chapter concludes the study by relating the findings to the objectives

of this study, emphasizing the significance of AUTO-EUD in locating the source of

magnetic field. This chapter includes some recommendation for future study as well.

15

CHAPTER 2

LITERITURE REVIEW

2.1 Introduction

This chapter introduces magnetic susceptibility and Euler homogeneity

relation as a depth estimation technique. An overview on the development of

Conventional Euler Deconvolution (CED) methodology through the past decades is

included in order to provide theoretical basis of the present algorithm. Introduction

on filtering and accuracy assessment of Euler deconvolution are presented.

2.2 Magnetic susceptibility

The quantity of magnetic moment per unit volume is called magnetization

(also called magnetization intensity, dipole per unit volume or magnetic polarization)

and it is denoted by a symbol M. It is the vector field that expresses the density of

permanent dipole moments contained in a magnetic material. The arrangement/line-

up of internal dipoles gives rise to a field M which is added to the magnetizing field

H. The S.I unit for magnetization is ampere per meter. For low magnetic fields

(Equation 2.1)

M α H

M = kH (2.1)

The constant in Equation 2.1 is called magnetic susceptibility (k), it is determined the

degree to which a body is magnetized. The total field including the effect of

magnetization is called magnetic induction (m) and it is given by (Equation 2.2)

m (H+M) (1+k) H

H (2.2)

16

The S.I and electromagnetic units for m is the tesla (T) and gauss (10-4

T)

respectively. Gamma ) is the unit of magnetic induction that is generally used for

geophysical work. The magnetic flux ( ) is given by (Equation 2.3)

= m.A (2.3)

Where A is a vector area. Thus

|m|

A and B are parallel, that is, m is the density of magnetic flux. The S.I unit for

magnetic flux is the Weber.

Magnetic susceptibility is the significant variable in magnetics. Although

instruments are available for measuring susceptibilities in the field, they can only be

used on outcrops or on rock samples and such measurement do not give the bulk

susceptibility of the formation. Table 2.1 lists magnetic susceptibilities for a variety

of rocks. Sedimentary and basic igneous rocks have the lowest and the highest

average values of magnetic susceptibility respectively:

Table 2.1: Magnetic susceptibility of rocks and minerals (source: Telford et al.,

2001)

Rock/mineral type Susceptibility (S.I Unit)

Range Average

Metamorphic

Schist

Gneiss

Slate

0.3-3

0.1-25

0-35

1.4

-

6

Igneous

Granite

Porphyry

Peridotite

Diabase

Pyroxenite

Diorite

0-50

0.3-200

90-200

1-160

-

0.6-120

25

60

150

55

125

85

17

Minerals

Magnetite

Pyrrhotite

Ilmenite

Clays

Graphite

Casiterite

Limonite

Pyrite

1200-19200

1-6000

300-3500

-

-

-

-

0.05-5

6000

1500

1800

0.2

0.1

0.9

2.5

1.5

Sedimentary

Dolomite

Sandstones

Limestone

0-0.9

0-20

0-3

0.1

0.4

0.3

2.2.1 Magnetic Elements

i. Inclination of the geomagnetic field: It is the angle between magnetic

north and the direction of the Earth field (Telford et al., 1990)

ii. Declination of the geomagnetic field: This is the angle between

geographic north and magnetic north (Telford et al., 1990).

iii. The angle of dip at a place: Is the angle between the direction of

earth’s magnetic field and the horizontal component of the earth’s

magnetic field in the magnetic meridian at that place

iv. Strike angle of the cylinder: Is the angle between the cylinder axis and

magnetic north

v. Azimuth angle: Is the angle between geographic north and horizontal

of a plane of box model.

2.3 Reduction of magnetic observations

The magnetic field readings measure from survey stations varies with time.

Diurnal effect and magnetic storms are the most significant causes of the changes in

magnetic field. This effect must be corrected from the data using appropriate

techniques. The short term, spikes and erratic changes in magnetic field are known

18

as micro-pulsations. These effects range from few to 100 nT in terms of intensity.

When these changes become large (amplitude and period), they are called magnetic

storm. It is a short term disturbances in the intensity of magnetic field associated

with sun spot activity and charged particles from sun. To achieve a successful

interpretation, the reduction has to be carried out to enhance and isolate the

contribution of the field due to concealed structure (Ismail, 2015). The correction or

reduction of magnetic data is necessary to remove all causes of magnetic variation

and noises from the observations other than those arising from the magnetic

anomalies in the subsurface.

2.3.1 Diurnal variation correction

Diurnal variation correction accounts for the temporal variation caused by the

electromagnetic radiation of the sun, which disrupts the geomagnetic field and thus

our survey, it can be checked by using two magnetometers with one acting as a base

station and recording the magnetic field every 1 minute or so, while the other would

be the primary machine to survey the area, however this method and magnetic survey

in general must not be used during magnetic storms (Sharma, 1997). After the

measurements, the primary machine readings would be time-synced with the base

station and then subtracting the results would give us the corrected readings.

2.3.2 Geomagnetic correction

The earth’s magnetic field strength varies from 25000 nT at the magnetic

equator to 69000 nT at the magnetic pole. This correction is carried out by

subtracting the theoretical field from International Geomagnetic Reference Field

(IGRF). This theoretical value changes with time (Sharma, 1997)

19

2.3.3 Reduction to the pole and equator

Reduction to the pole (RTP) is an operation use to transform the magnetic

anomaly into an anomaly that would have been obtained if the measurements were

taken at the magnetic pole, the area where the magnetic inclination is vertical, with

the assumption that the source is magnetized by induction (Silva, 1986). This effect

causes asymmetry and lateral shift of the anomaly of measured total magnetic field

(Aina, 1986). It has some advantages when applied to magnetic data which include

simplification of the interpretation of anomaly, it removes dipolar nature of magnetic

anomaly and it changes the asymmetric shape of magnetic anomaly to its symmetric

form. The dipolar nature of the magnetic field causes distortion in the anomaly’s

shape and as a result of this effect, error will be introduced to the data and there by

affecting the estimate of the anomaly’s location (Araffa et al., 2012). For reduction to

the pole technique to be applied on magnetic data, the information about the

remanent magnetization is required. However this information is not available in

most areas. An alternative method to RTP is the reduction to the equator (RTE)

which transforms the magnetic measurement as the one that would be observed if the

anomaly were located at the equator.

The direction cosines of geomagnetic field vector are , m and n. the

geomagnetic field vector is assume to be parallel to the polarization vector, in this

case, the remanent magnetization is zero. u and v are the Cartesian spatial

coordinates of angular frequency given the reduction to the pole (Op) and equator

(Oe) operators as Equation 2.4 and 2.5 respectively:

) ){ ) ) } )

⁄ )

[ ) )]

(2.4)

20

) ) *{ ) ) } )

⁄ )+

[ ) )]

(2.5)

In Equation 2.4 and 2.5 above, j = -1. Both Op and Oe can be used as:

i. Find the Fourier transform of the measured field, apply Op/Oe on the

transformed field and obtain the inverse Fourier transform.

ii. Evaluate Op/Oe for various values of u and v for the inclination and

declination. Compute the inverse transform of various inclinations and

declination of the magnetic field. The output is the space domain

operator which can be convolved with the measured magnetic field.

The first approach is more accurate, however, it can only be applied to

relatively small areas. On the other hand, the second approach is less

accurate, the operator requires to be truncated to manageable

dimensions but it can be applied to maps of any size (Jain, 1988).

2.3.4 Applications of magnetic method

As for the applications of the magnetic survey, it can be used to map dikes

blocking groundwater flow in the subsurface, structural trends and basement

features. It can also be used for the detection of archaeological objects, buried metal

drums and investigations over landfills.

2.3.5 Limitations of magnetic method

The magnetic survey has some limitations, it can only detect ferrous materials

including volcanic rocks, its image resolution deteriorates quickly with the increase of

depth, and it becomes almost useless near buildings, vehicles, or areas with reinforced

concrete and where the ferrous materials or volcanic rocks are underlain by strongly

magnetic rocks (Zohdy et al., 1974).

21

2.4 Euler homogeneity

Euler Deconvolution method evolves from the Euler’s homogeneity

relationship (John, 1965); it is first initiated to solve 2D magnetic field by Thompson

(1982). In the homogeneity concept (Equation 2.6), a function f(u) is considered

homogenous of degree n if

) ) (2.6)

where u = (u1, u2, . . ., ui) is the set of variables with respect to the homogeneity of

the field f, t is a real number and n is the degree of homogeneity (Reid and Thurston,

2014). This function also satisfies the Euler’s differential equation given in Equation

2.7. as

) ) (2.7)

Equation 2.7 can be written in three Cartesian coordinates x, y and z form, such that

) ) (2.8)

and the partial differential equation then would be (Equation 2.9)

(2.9)

Based on this, the N is defined as (Equation 2.10)

(2.10)

According to the power law, the field’s fall off function for both f (u) and f (x, y, and

z) can be expressed in the form of (Equation 2.11)

f = C/rN (2.11)

22

where C is a constant which includes any factor that affects the field, r is the distance

between the source and the observation point. The degree of homogeneity explains

the rate at which the potential field strength reduces over increasing radius, and often

referred to as structural index (N) in the literature.

One of the advantages of Euler deconvolution is that no geological

assumption is required prior to inversion. However, some understanding of the study

area is necessary since N represents type of source that produces the field anomaly

(Thompson, 1982). Ideas about the geometry of the structure will elevate the

confidence in choosing the correct N. Besides this, the application of Euler equation

should be limited only to single-point sources, which give off potential field

conforming to Equation 2.10. Sources with homogenous magnetic field are listed in

Table 2.2.

Table 2.2: Structural index of magnetic source

Source Smellier model N

Sphere Dipole 3

Vertical/horizontal cylinder Line of dipoles 2

Dike/thin sheet Line of poles 1

Infinite contact - 0

In order to find the source location (x0, y0, z0), Equation 2.9 is then further

redefined as (Equation 2.12)

)

)

)

) (2.12)

where x, y, z are the observation point coordinates; x0, y0, and z0 are the source

locations;

are the potential derivatives; N is the structural index; B is the

background of field f (Thompson, 1982). Equation (2.12) forms the basis for the

methodology used in this research.

23

2.4.1 Previous work

Information that can be obtained from magnetic method can be used to

estimate the position of a concealed body if it has enough magnetization. Among the

parameters of the body that can be estimated is depth. Depth estimation techniques

are divided into manual and automated techniques. Some of the manual depth

estimation techniques include maximum slope, Peter half slope, half width, Sokolov

distance and Hannel distance (Samuel, 2017). The computerized techniques can be

further divided into 2; semi-automated and automated techniques. Euler

deconvolution belongs to a group of semi-automated techniques, in its operation, it

allows user to make choice of structural index. Numerous attempts have been made

to make it fully automated.

Examples of other automated techniques include spectral depth technique

Techniques for the estimation of depth to the bottom of magnetic sources has been

presented (Bansal et al., 2011; Nwankwo, 2015). The techniques used for detailed

analysis operates on limited amount of data and these are characteristics curve,

iterative or inverse curve matching.

There were so many computer-assisted interpretation techniques in the

literature that are belong to computerized class of depth estimation methods.

Automatic interpretation techniques have advantages of operating directly on the

recorded digital field data in addition to providing rapid means of analyzing large

amount of data. The technique for locating vertices of polygon model has been

presented (O’Brein, 1971). A technique based on vertical prism and thin plate

models was described by Koulomzine et al. (1970). Werner (1953) simplified

equation for the interpretation of two-dimensional thin dike. The position of the dike

could be obtained/ devised by choosing appropriate point along a profile. This

24

technique has been successfully applied in oil and mining companies as a result of

the advancement in Aero Service and further researches based on Hartman et al.

(1971). The analysis of magnetic discontinuities using derivatives (vertical and

horizontal) of the total magnetic field intensity was incorporated into Werner’s

equation (Hartman et al., 1971).

A depth estimation technique using statistical approach that makes use of

slope of the power spectral density has been presented (Vacqier et al., 1951). The

location of the boundary is obtained through the computation of the horizontal

gradient of the pseudo gravity that peaks over a vertical contact (Grauch and Cordell,

1987). For dipping contacts, the peak is somewhat offset (Thompson, 1982). Another

related technique is the use of analytic signal and total gradient with the peaks

directly over a contact model with arbitrary dip (Nabighian, 1972). Hansen et al.

(1987) has shown that the peak over a contact model using total gradient and analytic

signal were noisy estimator. Using this technique, the depth is obtained from the

breadth of the peak (Hansen et al., 1987). So many automatic processing techniques

that estimate both source location and depth have been presented. Naudy (1971)

introduced an approach similar to Werner deconvolution (Jain, 1976) that makes use

of prism and thin-plate models.

Euler deconvolution is a quick means of transforming field measurements

into location and depth estimates of the magnetic source. The technique operates on a

subset of data using a moving window in which the body coordinates are solved.

Intermediate bodies have non-integer structural index, the technique is only

approximate. The term Euler deconvolution was obtained by the analogy of Euler

equation with the established Werner deconvolution technique. In strong term, Euler

deconvolution is only valid for functions that are homogeneous. The field of most

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