ABSTRACT
Laboratory analogue model techniques are used to d e m o n strate the validity of removing geomagnetic coast effects from coastal field site measurements through a vector s u b traction to yield the induction responses of anomalous c o n ductors alone for models of elongated anomalous conductors normal to a coastline. The case of elongated conductors n o r mal to a coastline has particular application to field site measurements in Nigeria where numerous anomalous conductive structures such as faults, shear zones, and sediment filled grabens have strike directions generally normal to the coastline. The laboratory measurements for these models are also used to examine the induction responses at sites between pairs of parallel conductors.
A laboratory analogue model of the Nigeria region, c o n structed to include a simulation of the local ocean b a t h y m e try and coastline contours, is used to study the geomagnetic coast effects for both uniform and non-uniform inducing source fields simulating the actual nighttime uniform field and the daytime electrojet field respectively. The analogue
sites through a vector subtraction of the model coast effect induction arrov>s from the field site induction arrows. The resulting difference induction arrows for nighttime field measurements are then interpreted as the induction responses of conductive structures associated with an array of faults, shear zones, grabens and sedimentary basins. It is also demonstrated that both the coast effects and the non-uniform source field effects can be removed from daytime field m e a s urements with the aid of induction arrows obtained from the measurements for the laboratory model which employs a non- uniform source field to simulate the electrojec. source field.
Examiners:
Dr. H.W. Dosso, Supervisor
Dr. J.T. Weaver, D e p a r t m e n t a l M e m b e r
Dr. G.D. Spence, Outjfside Member
Dr. P. van den Dfiessche,— Outaride Member
A b s t r a c t ... • ii
Contents . . ... » ... iv
F i g u r e s ... . vi
Acknowledgements ... xiii
Chapter I: INTRODUCTION ... 1
1.1 Electromagnetic Induction Within the Earth . . . . 1
1.2 Geomagnetic Depth Sounding and Magnetotelluric Studies ... 5
1.3 Modelling studies of EM I n d u c t i o n ... 12
1.4 The Geomagnetic Coast Effect ... 16
1.5 Mutual Coupling in EM I n d u c t i o n ... .. 18
1.6 EM Studies in Equatorial R e g i o n ... . 20
1.7 Summary of the Work in This Dissertation . . . 21
Chapter II: Laboratory Analogue EM Modelling... ... 24
2.1 The Analogue Modelling Conditions and Scaling F a c t o r s ... 24
2.2 The Laboratory Analogue Model Facility . . . 28
Chapter III: E M RESPONSES O F CONDUCTORS IN COASTAL REGIONS A N D REMOVAL O F T H E COAST EFFECT— LABORATORY ANALOGUE MODEL R E S U L T S ...34
3.1 EM Responses of a Constant Depth O c e a n ... 34
3.2 EM Responses of 3D Conductors Near an Ocean . . . 41
3.2.1 An Elongated Conductor Perpendicular to a Straight Coastline ... 41
3.2.2 An Elongated Conductor Perpendicular to a Straight Coastline at the Corner of a Right Angle Coastline Contour ... 48
3.2.3 A n Elongated Conductor at an Angle of 45° Relative to the sides of a Right Angle Coastline Contour ... 51 3.2.4 A Pair of Elongated Conductors
Perpendicular to a Straight Coastline - iv
3.3.1 A n Elongated Conductor Perpendicular to a
Straight Coastline ... 59 3.3.2 An Elongated Conductor Perpendicular to a
Straight Coastline at the Corner of a
Right Angle Coastline Contour ... 67 3.3.3 An Elongated Conductor at an Angle of 45°
Relative to the Sides of a Right Angle
Coastline Contour ... 70 3.3.4 A Pair of Elongated Conductors
Perpendicular to a Straight Coastline
C o n t o u r ... 73
3.4 Chapter S u m m a r y ... 75
Chapter IV: E M INDUCTION IN 3D CONDUCTORS— LABORATORY
ANALOGUE MODEL RESULTS ... 77 4.1 I n t r o d u c t i o n ... . 7 7 4.2 Induction Arrow Responses of a Single
C o n d u c t o r ... 78 4.3 Induction Arrow Response of Pairs of Parallel
C o n d u c t o r s ... 87 4.4 Chapter S u m m a r y ... 101
Chapter V: The Geological and Tectonic Setting of the
Southwest Africa Region ... 104 5.1 The Tectonics of the South Atlantic Ocean . . . 104 5.2 Geological Features in Southwest Africa . . . . 106 5.2.1 Fracture Z o n e s ... 107 5.2.2 Sedimentary Basins ... 109 5.3 Chapter S u m m a r y ... . 115
Chapter VI: Analogue Model EM Coast Effects in the
Nigeria Region ... 119 6.1 The Laboratory Analogue Model ... 119 6.2 Uniform Inducing Source Field ... 122
6.2.1 Model Magnetic Field Responses for the
Uniform Source Field ... 122 6.2.2 Model Induction Arrow Responses for the
Uniform Source Field ... 133 6.3 Non-uniform Inducing Source Field . . . 138
6.3.1 Model Induction Arrow Responses for
Uniform and Non-uniform Source Fields . . . 141 v
-E f f e c t s ... 147
6.3.3 Determination of the Source Field Effect . 151 6.4 Chapter S u m m a r y ... 153
Chapter VII: Interpretation of Field Site Induction Arrows in N i g e r i a ...155
7.1 I n t r o d u c t i o n ... 155
7.2 Model and Nighttime Induction Arrows ... 158
7.2.1 In-phase Induction Arrows ... 158
7.2.2 Quadrature Induction Arrows ... 162
7.3 Nighttime Difference Induction Arrows ... 165
7.3.1 In-phase Difference Induction Arrows . . . 167
7.3.2 Quadrature Difference Induction Arrows . . 175
7.4 Daytime Difference Induction Arrows ... 182
7.5 Chapter Summary . ... 185
Chapter VIII: Summary and Conclusions ... 188
8.1 EM Induction in Idealized Conductor Models . . . 188
8.2 EM Induction in the Nigeria R e g i o n ... 190
8.3 Suggestions for Further W o r k ...191
R E F E R E N C E S ... . 194
Appendix A: Model Induction A rrow Component Responses for Conductors near an O c e a n ... 222
Appendix B: Model Induction Arrows for Elongated Conductor Perpendicular to the Straight C o a s t l i n e ... 233
Appendix C: Model Induction A rrow Responses for Single and Pairs of Parallel Elongated Conductors 237 Appendix D: Nigeria Model Bx, By, Bz components for X-and Y - p o l a r i z a t i o n s ... 244
-Appendix F: Field Site, Analogue Model and Difference Induction Arrow Responses at Eleven Sites
in the Southwest Nigeria Region ... 264
Appendix G: Nigeria Model (Line Current) and Daytime Field Site Induction Arrows at Eleven
29 31 36 38 42 44 46 49 50 52 53 Laboratory analogue model facility ...
The detectors and recording equipment. . . . The cross-section of the model ocean (a) in a
resistive host earth, all underlain by a conductive substratum (c) at depth Zc . . . . The in-phase and quadrature induction arrow
responses V along a traverse perpendicular to the coastline for periods of 1-90 min. . . Plan view of a model of an elongated conductor
(embedded in the host earth) perpendicular to a straight c o a s t l i n e ... In-phase and quadrature induction arrows for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline for W=5 k m ... In-phase and quadrature induction arrows for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline for W=100 k m ... Plan view of a model of an elongated conductor
(embedded in the host earth) perpendicular to one coastline at the corner of a right angle coastline contour. . . ... In-phase and quadrature induction arrows for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a right angle coastline contour for W-5 k m ... In-phase and quadrature induction arrows for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to :he straight coastline at the corner of a right angle coastline contour for W=100 km. . „ . . Plan view of a model of an elongated conductor
(embedded in the host earth) at an angle of 45° relative to the two sides of a right angle coastline c o n t o u r ...
-relative to the sides of a right angle
coastline contour for W=100 k m ... . 5 5 3.11 Plan view of a model of a pair of elongated
conductors (embedded in the host earth)
perpendicular to a straight coastline. . . . . 57 3.12 In-phase and quadrature induction arrows for
traverses T l f T2, T3 over the model of a pair of elongated conductors perpendicular
to the straight c o a s t l i n e ... 58 3.13 The in-phase and quadrature Vy and D y for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the
straight coastline for W=5 k m ... 60 3.14 The in-phase and quadrature V y and D y for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the
straight coastline for W=20 k m ...61 3.15 The in-phase and quadrature V y and D y for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the
straight coastline for W=50 k m ... 62 3.16 The in-phase and quadrature V y and D y for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the
straight coastline for W=100 k m ... 63 3.17 The in-phase and quadrature V x and D x for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the
straight coastline for W=50 k m ... 65 3.18 The in-phase and quadrature V x and D x for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the
straight coastline for W=100 k m ... . 6 6 3.19 The in-phase and quadrature V y and D y for
traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a right
angle coastline contour for W=5 k m ... 68 ix
-traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a right
angle coastline contour for W=100 k m ... 69 3.21 The in-phase and quadrature Vy and D y for
traverses Tl, T2, T4 over the model of the elongated conductor at an angle of 45°
relative to the sides of a right angle
coastline contour for VW=100 k m ... 71 3.22 The in-phase and quadrature V x and D x for
traverses Tl, T2, T4 over the model of the elongated conductor at an angle of 45° relative to the sides of a right angle
coastline contour for W=100 km. . ... 72 3.23 The in-phase and quadrature Vy and Dy for
traverses Tl, T2, T3 over the model of a pair of elongated conductor perpendicular
to the straight coastline for V?b=5 km and
Wd=20 k m ... 74 4.1 Plan view of a model of an elongated conductor
(embeded in the host earth). The conductor width W will vary, but the depth extent
will be 5 km for all c a s e s ... 79 4.2 The in-phase and quadrature Vy (y-component of
the induction arrow responses of the conductor) for traverses Tl, T2, T3 over the model of the elongated conductor for
W-5 k m ... 80
4.3 The in-phase and quadrature Vy (y-component of the induction arrow responses of the
conductor) for traverses Tl, T2, T3 over the model of the elongated conductor for
W=100 k m ... 82 4.4 Empirical curves of the in-phase and
quadrature maximum response Vm as a function of period for conductor widths W=5, 10, 20, 50, 100 km for traverses Tl,
T 2 , T 3 ...83 4.5 Empirical curves of the in-phase maximum
response Vm as a function of distance from the end of the conductor for conductor
-86
88
89 90 92 93 95 97 response V m as a function of distance fromthe end of the conductor for conductor widths W=5, 10, 20, 50, 100 k m ... Plan view of a model of a pair of elongated
conductors (embeded in the host earth). The width Wb=5 km is held constant while W<j is varied. . . ... The in-phase and quadrature Vy for traverses
Tl, T2, T3 over the model of a pair of elongated conductors for Wb=5 km and Wd=5 km. The distance between the conductors is S=50 k m ... ... The in-phase and quadrature Vy for traverses
Tl, T2, T3 over the rondel of a pair of elongated conductors for Wb=5 km and Wd=5 km. The distance between the conductors is S=100 k m ... The in-phase and quadrature Vy for traverses
Tl, T 2 , T3 over the model of a pair of
elongated conductors for Wb=5 km and Wd=100 km. The distance between the conductors is S=50 k m ... The in-phase and quadrature Vy for traverses
Tl, T2, T3 over the model of a pair of
elongated conductors for Wb=5 km and Wd=100 km. The distance between the conductors is S=100 k m ... Empirical curves of the In-phase maximum
response V m as a function of period for traverses Tl, T2, T3 over the model of a pair of elongated conductors for Wb=5 km and W(j=5, 10, 20, 50, 100 km for S=50, 100 k m ... ... Empirical curves of the quadrature maximum
response V m as a function of period for traverses Tl, T2, T3 over the model of a pair of elongated conductors for Wb=5 km and Wd=5, 10, 20, 50, 100 km for S=50, 100 k m ...
-quadrature zero response locations at a distance Y from the major conductor d as a
function of period for S=50 k m ...99 4.15 Empirical curves of the in-phase and
quadrature zero response locations at a distance Y from the major conductor d as a
function of period for S=100 k m . ... 100 5.1 The evolution of the earth continent (from
Irving, 1983 by p e r m i s s i o n ) ... 105 5.2 Locations of the major fracture zones off
shore near the southwest Africa region
(adapted from Sibuet and Mascle, 1978). . . . 108 5.3 A three dimensional model of top basement in
the Benin Basin (adapted from Omatsola and
Adegoke, 1 5 8 1 ) ... 112 5.4 A geological cross section of the Ise graben
in the Benin Basin determined by boreholes near the coast (adapted from Ornate ila and
Adegoke, 1 9 8 1 ) ... 113 5.5 The major geological features in the southwest
Africa (including Nigeria) r e g i o n ...117 6.1 Simplified map of the modelled south-west
Africa region including the ocean
bathymetry and the locations of the eleven
(1-11) field sites in south-west Nigeria. . . 120 6.2 The locations of the six traverses along which
model measurements were carried o u t ... 123 6.3 The in-phase and quadrature magnetic field
components along traverses over the model at 20 min for X-polarization. Solid and dashed lines show the responses over the
ocean and land respectively. ... 125 6.4 The in-phase and quadrature magnetic field
components along traverses over the model at 20 min for Y-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 126 6.5 The in-phase and quadrature magnetic field
-respectively... 128 6.6 The in-phase and quadrature magnetic field
components at 10-120 min along traverse NI for Y-polarization. Solid and dashed lines show the responses over the ocean and land
respec t i v e l y... 129
6.7 The in-phase and quadrature magnetic field components at 10-120 min along traverse N6 for X-polarization. Solid and dashed lines show the responses over the ocean and land
respe c t i v e l y ... 130 6.8 The in-phase and quadrature magnetic field
components at 10-120 min along traverse N6 for Y-polarization. Solid and dashed lines show the responses over the ocean and land
respec t i v e l y ...131 6.9 The in-phase and quadrature Vx and Vy along
traverses N1-N6 at 20 min. Solid and dashed lines show the responses over the ocean and
land respectively... 134 6.10 The in-phase and quadrature Vx and Vy
responses along traverses NI. Solid and dashed lines show the responses over the
ocean and land respectively... 136 6.11 The in-phase and quadrature Vx and Vy
responses along traverses N6. Solid and dashed lines show the responses over the
ocean and land respectively... 137 6.12 The in-phase and quadrature induction arrows
for traverses N1-N6 over the model at 20
m i n ...139 6.13 The locations of the line current source and
the travrrse along which model measurements
were carried o u t ... 140 6.14 The Vx and Vy responses for the layered earth
model for uniform (U) and line (L) current
s o u r c e ... 142
-for uni-form (U) and line (L) current
s o u r c e s ... 143 6.16 The Vx and Vy responses for the conductor
model for uniform (U ) and line (L) current
s o u r c e s ... 144 6.17 The Vx and Vy responses for the
Nigeria/conductor model for uniform (U) and
line (L) current s o u r c e s ... 145 6.18 The Vx and Vy responses along traverse T for
the Nigeria/conductor model for the uniform (U) source field and for the
Nigeria/conductor model response minus the layered earth model response for the line
(L) current source f i e l d ... 148 6.19 The Vx and Vy responses along traverse T for
the conductor model for the uniform (U) source field and for the Nigeria/conductor model response minus the Nigeria model
response for the line (L) current source
f i e l d ... 150 6.20 The induction arrows at sites near the
conductors for the Nigeria/conductor model for uniform (solid lines) and line current
sources (dashed l i n e s ) ... 152 7.1 The locations of eleven field stations in the
Nigeria survey region. The site IPE was
used as a reference s t a t i o n ... 156 7.2 Analogue model and nighttime field site
in-phase induction arrows for 15 and 20 min. . . 159 7.3 Analogue model and nighttime field site
in-phase induction arrows for 30 and 60 min. . . 160 7.4 Analogue model and nighttime field site
quadrature induction arrows for 15 and 20
m i n ... 163 7.5 Analogue model and nighttime field site
quadrature induction arrows for 30 and 60
min. ... 164 7.6 The x- and y-components of the field site, the
168 169 176 177 184 192 223 224 225 226 The in-phase difference arrows at 15-20 min
together with the major geological features in the Nigeria region. „ ... The in-phase difference arrows at 30-60 min
together with the major geological features in the Nigeria r e g i o n... The quadrature difference arrows at 15-20 min
together with the major geological features in the Nigeria r e g i o n... The quadrature difference arrows at 30-60 min
together with the major geological features in the Nigeria region. . . . . ... The in-phase model (M), field ( F ) , and
difference (D) induction arrows for daytime and nighttime measurements at field site A W A for 20 and 15 min. El and E2 are the arrow error margins for the daytime field m e a s u r e m e n t s ... Summary of proposed fault and graben
extensions in the present w o r k ... The in-phase and quadrature Vy(ab) and Vy(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline for W=5 k m ... The in-phase and quadrature Vy(ab) and Vy(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline for W=100 k m ... The in-phase and quadrature Vx(ab) and Vx(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline for W-100 k m ... The in-phase and quadrature Vy(ab) and Vy(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a right angle coastline contour for W=5 km. . .
-A . 6 A . 7 A . 8 A . 9 A . 10 B.l B.2 B. 3
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a
right angle coastline contour for W=5 km. . . 227 The in-phase and quadrature Vy(ab) and Vy(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a
right angle coastline contour for W=100 km. . 228 The in-phase and quadrature Vx(ab) and Vx(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to the straight coastline at the corner of a
right angle coastline contour for W=100 km. . 229 The in-phase and quadrature Vy(ab) and Vy(a)
for traverses Tl, T2, T3 over the model of the elongated conductor at an angle of 45° relative to the sides of a right angle
coastline contour for W=100 k m ... 230 The in-phase and quadrature Vx(ab) and Vx(a)
for traverses Tl, T2, T3 over the model of the elongated conductor at an angle of 45° relative to the sides of a right angle
coastline contour for W=100 k m ... 231 The in-phase and quadrature Vy(ab) and Vy(a)
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to
the straight coastline for W=5 k m ... 232 The in-phase and quadrature induction arrows
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to
the straight coastline for W=10 k m ... 234 The in-phase and quadrature induction arrows
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to
the straight coastline for W=20 k m ... 235 The in-phase and quadrature induction arrows
for traverses Tl, T2, T3 over the model of the elongated conductor perpendicular to
the straight coastline for W=50 k m ... 236
-the model of -the elongated conductor for W~10 k m ... C.2 The in-phase and quadrature Vy (y-component of
the induction arrow response of the
conductor) for traverses Tl, T2, T3 over the model of the elongated conductor for W=20 k m ... C.3 The in-phase and quadrature Vy (y-component of
the induction arrow response of the
conductor) for traverses Tl, T2, T3 over the model of the elongated conductor for W-50 km. . ... C.4 The in-phase and quadrature Vy for traverses
Tl, T2, T3 over the model of a pair of elongated conductors for W&=5 km and Wd=10 km. The distance between the conductors is S=50 k m ... . C.5 The in-phase and quadrature Vy for traverses
Tl, T2, T3 over the model of a pair of elongated conductors for Wb=5 km and W<j=20 km. The distance between the conductors is S-50 k m ... , C.6 The in-phase and quadrature Vy for traverses
Tl, T2, T3 over the model of a pair of elongated conductors for Wb=5 km and Wd~50 km. The distance between the conductors is S-50 k m ...
D.l The in-phase and quadrature magnetic field components along traverses over the model at 10 min for X-polarization. Solid and dashed lines show the responses over the ocean and land respectively... D . 2 The in-phase and quadrature magnetic field
components along traverses over the model at 12 min for X-polarization. Solid and dashed lines show the responses over the ocean and land respectively... D.3 The in-phase and quadrature magnetic field
components along traverses over the model
238 239 240 241 242 243 245 246 - xvii
D.5 D. 6 D. 7 D. 8 D.9 D. 10
0.11
dashed lines show the responses over the
ocean and land respectively. . ... 247 The in-phase and quadrature magnetic field
components along traverses over the model at 30 min for X-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 248 The in-phase and quadrature magnetic field
components along traverses over the model at 60 min for X-polarization. Solid and dashed lines show the responses over the
ocean and land respectively. ... 249 The in-phase and quadrature magnetic field
components along traverses over the model at 120 min for X-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 250 The in-phase and quadrature magnetic field
components along traverses over the model at 10 min for Y-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 251 The in-phase and quadrature magnetic field
components along traverses over the model at 12 min for Y-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 252 The in-phase and quadrature magnetic field
components along traverses over the model at 15 min for Y-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 253 The in-phase and quadrature magnetic field
components along traverses over the model at 30 min for Y-polarization. Solid and dashed lines show the responses over the
ocean and land respectively... 254 The in-phase and quadrature magnetic field
components along traverses over the model at 60 min for Y-polarization. Solid and dashed lines show the responses over the
-at 120 min for Y-polariz-ation. Solid and dashed lines show the responses over the
ocean and land respectively... 256 E.l The in-phase and quadrature Vx and Vy along
traverses N1-N6 at 10 min. Solid and dashed lines show the responses over the ocean and
land respectively... . 258 E.2 The in-phase and quadrature Vx and Vy along
traverses N1-N6 at 12 min. Solid and dashed lines show the responses over the ocean and
land respectively... 259 E.3 The in-phase and quadrature Vx and Vy along
traverses N1-N6 at 15 min. Solid and dashed lines show the responses over the ocean and
land respectively... 260
E.4 The in-phase and quadrature Vx and Vy along traverses N1-N6 at 30 min. Solid and dashed lines show the responses over the ocean and
land respectively... 261 E.5 The in-phase and quadrature Vx and Vy along
traverses Nl-Ni at 60 min. Solid and dashed lines show the responses over the ocean and
land respectively... 262 E.6 The in-phase and quadrature Vx and Vy along
traverses N1-N6 at 120 min. Solid and dashed lines show the responses over the
ocean and land respectively. . ... 263 F.l The x- and y-components of the field site, the
analogue model, and the difference
induction arrow responses at field site
E R U ... 265 F.2 The x- and y-components of the field site, the
analogue model, and the difference
induction arrow responses at field site
O B A ... 266 F.3 The x- and y-components of the field site, the
analogue model, and the difference xix
-A W -A ... 267 F.4 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site I G B ...
the
268 F. 5 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site O K I ...
the
269 F.6 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site E J I ...
the
270 F.7 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site A G B ...
the
271 F. 8 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site I K O ...
the
272 F. 9 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site BAD. . . ...
the
273 F. 10 The x- and y-components of the field site,
analogue model, and the difference
induction arrow responses at field site I F E ...
the
274 G.i Analogue model (line current) and daytime
field site in-phase induction arrows for and 20 m i n ...
15
276 G.2 Analogue model (line current) and daytime
field site in-phase induction arrows for and 60 m i n ...
30
277 G. 3 Analogue model (line current) and daytime
field site quadrature induction arrows for
15 and 20 m i n ... ... 278
-I am greatly indebted to my supervisor, Dr. H.W. Dosso, for encouraging me in my studies and for suggesting this research problem. His generous support, valuable advice and guidance, the patient chats and discussions are very much appreciated.
I would like to thank Dr. Z. Meng, Dr. J. Chen, Dr. X. Pu and Dr. A.K. Agarwal for helpful suggestions and useful d i s cussions.
I would also like to thank my wife Connie for all her love, support, and understanding over past years.
The financial support in the form of a University of V i c toria Fellowship, and a research assistantship provided by my supervisor Dr. H.W. Dosso is gratefully acknowledged.
-1.1 Electromagnetic Induction Within the Earth
The distribution of electrical conductivity within the Earth can be studied using the phenomenon of electromagnetic induction. The electromagnetic responses observed on the Earth's surface consist of an external field with its origin outside the Earth, in the ionosphere and magnetosphere, and an internal one arising from electric currents induced by the external field. At different periods, the responses contain information about the electrical structure at d i f ferent depths. Thus, by analysing these electromagnetic responses measured at the surface of the Earth, one can deduce the structure within the Earth.
Electromagnetic induction studies can be considered in two major groups (Price, 1964): (i) global studies, involv ing the properties of the Earth as a whole with average induced current systems of world-wide extent; (ii) regional studies which arise in the interpretation of anomalous fea tures of usually rapid geomagnetic fluctuation in terms of local conductivity distribution.
Global EM Induction
The global induction studies regard the properties of the Earth as a whole and are concerned with the average values of the electrical conductivity distribution over regions having dimensions comparable with those of the Earth. The electrical conductivity, o, is often treated as some smooth function of latitude, longitude and distance from the centre of the Earth (r, 0, $)• The electromagnetic response is dependent upon the form of the external field, expressed in terms of spherical harmonics, and upon the electrical s t r u c ture of the Earth.
Early global induction studies dealt with special cases only. The case of a sphere of constant conductivity was studied by Lamb (1883). The fields of external and internal origin were separated by Schuster (1889) using the method of spherical harmonic analysis. Further applications of Lamb's solution were made by Chapman (1919) and Chapman and W h i t e head (1922). Lamb's solution was extended by Price (1930, 1931) and Chapman and Price (1930) to include aperiodic fields. Lahiri and Price (1939) were the first to apply a theory of electromagnetic induction in a non-uniform sphere in which the conductivity is a function of its radius. They concluded that the Earth's conductivity increases sharply at a depth of several hundred kilometers.
the conductivity is mainly a function of the depth (Riki- take, 1966). However, since the early 1 9 5 0 's it has been noted that in some regions the vertical component of the geomagnetic variations at periods shorter than a few hours varies considerably even over distances as small as tens of kilometres (Honkura, 1978). Such a geomagnetic variation can be accounted for neither by an external field nor by induction in a laterally uniform earth. It can be reason ably interpreted as indicating the existence of a lateral heterogeneity in conductivity. Induction in thin sheets and shells with lateral changes in conductivity was studied by Price (1949). Rikitake (1961) treated the problem of induc tion in such non-uniform shells by considering the mutual induction between a conducting shell and the conducting upper mantle for daily magnetic variations of the earth's external EM field. Bullard and Parker (1970) studied a p a r ticular model consisting of a conducting mantle, a non conducting crust-mantle layer and a layer of conducting sed iments of variable thickness. A good review of global electromagnetic induction was given by Roberts (1986).
Regional EM Induction
Regional electromagnetic induction studies are concerned with limited regions of the Earth and variations in c o n d u c
tivity over horizontal and vertical distances of the order of several hundreds of kilometers. On this scale the c u r v a
ture of the Earth can be neglected. The Earth is treated as a semi-infinite half-space with some variable distribution of conductivity. The inducing fields for various types of geomagnetic disturbances are frequently of global dimensions and are then treated as uniform over the region being s t u d ied.
A flat earth model was studied analytically by Price (1950) for a semi-infinite uniform conducting half-space and an arbitrary inducing source field. A uniformly layered earth model was considered by Tikhonov (1950) and Lipskaya (1953) later. Cagniard (1953) provided a definitive a n a l y sis for two-layered and multi-layered earth models. His method has since become known as the MT method. Wait (1954) and Price (1962) showed that Cagniard's results are valid only if the electromagnetic field is uniform over a h o r i z o n tal distance of at least one skin depth 6 (S=[T/(nna)
where T is the period, p is the magnetic permeability and o is the conductivity) of the conducting medium. Weaver (1973) reviewed the principal features of electromagnetic induction for a multi-layered earth by various source fields. Recent reviews of regional electromagnetic induction studies have been given by Haak and Hutton (1986), Kaikkonen (1986),
and Schiffmacher (1988), Hjelt (1988), Gough (1989, 1992), Schwarz (1990), and Hjelt and Korja (1993).
1.2 Geomagnetic Depth Sounding and Maqnetotelluric Studies
Geomagnetic Depth Sounding (GPS)
Investigation of a conductivity anomaly may be carried out by means of geomagnetic depth sounding (GDS) based on geomagnetic variation anomalies characterized by anomalous vertical fields and sometimes by anomalous horizontal ones as well. A geomagnetic variation of external origin may be regarded as being approximately spatially uniform at m i d latitude regions. For such a uniform inducing field, no vertical magnetic field will be observed in an earth of homogeneous conductivity. Conversely, any observed vertical field will be related to current concentrations due to either non-uniformity of the source, or non-homogeneity of the conductor. In the present discussion, a uniform inducing source is assumed. In GDS studies, the three simultaneously measured components of the geomagnetic field (in time domain) are denoted here by Cartesian B x and By for the orthogonal horizontal components to the Earth's surface, and B z for the vertical component. Rikitake and Yokoyama (1953) appear to have been the first to explicitly state m a t h e m a t i
cally the relationship between the vertical and horizontal components of the magnetic field as:
Z = yH + XD (1.1)
where Z, H f and D are the traditional symbols for the d o w n ward, northward, and eastward magnetic components, respec tively, and y an<3 X are called Rikitake-Yokoyama constants. It is usual to consider only a limited range of frequencies, which is equivalent to filtering the time functions. It is also possible to interpret equation (1.1) as indicating a plane in which the magnetic variations are confined. This was first noted by Parkinson (1959, 1962) when he studied local induction at coastal sites in Australia. This plane has sometimes been called the "preferred plane" or Parkinson plane (Gregori and Lanzerotti, 1980). An arrow, called the Parkinson vector, can then be derived by projecting a vector which is normal to the Parkinson plane onto the Earth's s u r face. Another arrow representation called the Wiese vector was introduced almost simultaneously by Wiese (1962). It is essentially the same as the Parkinson vector except for a 180° difference in direction.
In a related analysis, Schmucker (1964, 1970) extended equation (1.1) from the time domain to the frequency domain by using Fourier transformations, to obtain
where B z , Bx , and By are the Fourier transformations of the vertical and two horizontal magnetic components for a time variation of the form exp(iwt). The coefficients a and b are period dependent transfer functions, and are in general c o m plex. The a and b transfer functions can be determined by using three magnetic field components for two independent polarizations of the regional source field. In the case of field data processing statistical methods are used to m i n i mize the error A(e.g., Everett and Hyndman, 1967).
The transfer functions a and b characterize the p o l a r i z a tion and period dependence of the electromagnetic response of an anomalous conductor in the Earth, that is, dependence of the anomalous response on the direction in which an inducing magnetic field varies. For instance, in a purely two-dimensional case, anomalous B z variations will not be observed on the Earth's surface for the B-polarization case, whereas for the E-polarization case a striking anomaly is
expected.
The transfer functions are usually displayed by plotting on a geographical m a p in terms of a two-dimensional vector (ar , b r ) and (a*, bjj, corresponding to the real (in-phase) and imaginary (quadrature) parts of the transfer function. To maintain the custom of plotting arrows that point towards
the better conductor, the directions of the arrows are reversed to (-ar , - b r ) and (-ai, -bjj following the sign convention of Lilley and Arora (1982) for time-varying fields of the form exp(iwt). In the case that the fields are described by exp(-iwt), only the signs of the in-phase response need be reversed.
The behaviour of both the in-phase and quadrature induc tion arrows has been examined in many electromagnetic induc tion studies. In general, the behaviour of the in-phase arrows is well understood, with most people reporting that the in-phase arrows point towards the zones of high e l e c t r i cal conductivity. Only for special cases, for which the depth of burial of the conductive body is more than one skin depth in the less conductive host, is the in-phase arrow (though small) found to point away from the conductive body (Jones, 1986; Hu et al., 1989). The behaviour of the q u a d r a ture arrows, however, is found to bt more complex than that of the in-phase arrows (e.g., Rokitvansky, 1982; Nienaber et al., 1983; Chen and Fung, 1985; Agarwal and Dosso, 1990, 1993). One of the controversial behaviors of the quadrature arrow is the sign reversal. For an ocean model, at s u f f i ciently short periods, the quadrature arrow near the coast is seen to point away from (rather than towards) the c o n d u c tive ocean. The magnitude of the arrow then decreases to zero with increasing period. With a further increase in
towards the conductive ocean) and increases in magnitude to some maximum value, then again decreases. The period at which the quadrature arrow is zero and in-phase arrow is maximum is known as the characteristic period T c (Rokityan- sky, 1982). This behavior has frequently been observed in earlier analogue model experiments at the University of V i c toria (Hebert et al., 1983a,b for the Newfoundland coastal region; Hu et al., 1989 for a seamount; and Meng and Dosso, 1990 for the Japan-China region), in sea-floor field data
(Delaurier et al., 1983), in an analytic study (Weaver, 1987), and in numerical model studies (Chen and Fung, 1985, 1987). Agarwal and Dosso (1990, 1993) have studied reversals of the quadrature arrow in some detail for 2-D numerical models of a conductive plate in a resistive host. They s u g gested that the behavior of the quadrature arrow behavior could in some cases serve as an aid in locating the conductive-resistive interface. For 3-D models, the behavior is expected to be more complex, with the quadrature arrow rotating over a period range to accomplish a reversal. The response would be expected to be even more complex if in addition multiple conductive bodies were present.
Maqnetotelluric (MT) Studies
Induced electric fields observed on the Earth's surface should contain some information on the underground c o n d u c tivity structure. Observations of both the electric and magnetic fields are used in magnetotellurie (HT) studies of regional conductivity distributions in the Earth. This method was first introduced by Cagniard (1953). As in GDS s t u d i e s , a uniform inducing source field is assumed for studies in mid-latitude regions. The external m a g n e t i c fields penetrate into the ground and induce electric fields and magnetic fields. At a survey site, three magnetic field components Bx , By, Bz , where x usually denotes north (geo graphic or geomagnetic), y denotes east, and z denotes v e r tically downwards, whereas only two horizontal electric field components Ex , Ey are measured In the analysis, those measurements in the time domain, are then transformed into the frequency domain through Fourier transformations.
The horizontal electrical and magnetic components are related by the complex M T impedance tensor:
Ex II zxx zxy Bx
Ey zyx Zyy By
1
The so-called apparent resistivities (pa ) can be o b t ained by taking anti-diagonal elements Zxy and Zyx in the impe dance tensors,
In a ID problem, when the conductivity varies with depth alone, the M T impedance tensor reduces to the simple form:
In a layered earth, for a model in which the conductivity increases with increasing depth, the apparent resistivity decreases with increasing period, and the phase lies between 45° and 90°. By contrast, for the model in which the conduc tivity decreases with increasing depth, the apparent resis tivity increases with increasing period, and the phase lies between 0° and 45°. The M T method has advanced to the stage at which ID MT data are well understood and conductivity- depth profiles can be determined using a variety of inver sion methods (e.g., Niblett and Sayn-wittgenstein, 1960; Parker, 1980; Parker and Whaler, 1981; Fischer and LeQuang, 1981; Schmucker, 1983; Constable et al., 1987; Dosso and Oldenburg, 1991; and Weaver and Agarwal, 1993), each of which involves a fundamentally different philosophy.
In a 2D model of the Earth, where the axes of the c o ordinate frame are aligned parallel (x) and perpendicular
In 2D MT studies, it is becoming common to undertake more thorough tria.l-and-error forward modelling of the data (e.g., Kurtz et al., 1986, 1990; Jones and Craven, 1990), and recent advanced 2D inversion methods are very promising (deGroot-Hedlin and Constable, 1990; Smith and Booker, 1991; Oldenburg and Ellis, 1993; Agarwal et al., 1993; Raiche, 1993).
In a fully three-dimensional (3D) earth model where Z takes on the general form as expressed in Eq. 1.3 above, MT data are not well understood. Due to prohibitively high c o m putational costs, full 3D modelling (if possible) is usually undertaken only for representative structures, not to model actual field data. Approximate 3D studies, such as thin- sheet methods, have been developed and used for modelling continent-ocean boundaries (e.g., Dawson and Weaver, 1979; Ranganayaki and Madden, 1980; Weaver, 1982; Mckirdy et al., 1985; Agarwal and Weaver, 1989; Fainberg et al., 1993).
1.3 Modelling studies of EM Induction Analytical and Numerical Modelling
The variations of conductivity in the Earth have also been studied using analytic modelling techniques. D'Erce- ville and Kunetz (1962) considered a model for two media of
ly with a uniform inducting source field. A similar model was studied by Weaver and Thomson (1972) for induction by an external line current. Ramaswamy and Dosso (1973) studied a model for a horizontal magnetic dipole buried in a two-layer earth. Ogunade and Dosso (1977) studied a model of a c o n ducting sphere embedded in a two-layer earth with an o v e r head vertical magnetic dipole source field. Geyer (1972) studied the effect of a dipping contact of two homogeneous media. The model with more than one vertical contact has also been studied by Wait (1982) and Weaver et al. (1985).
Analytic modelling techniques are generally only suitable for certain idealized structures with simple geometry. Many numerical modelling techniques have been developed for s t u d ying more complex structures. For example, the finite d i f ference 2D program of Jones and Pascoe (1971) and Brewitt- Taylor and Weaver (1976); the finite difference 3D program of Weaver and Pu (1988), Pu et al. (1993); the staggered grid finite difference 3D program of Smith (1994); the finite element 2D program of Lee and Morrison (1985) and Wannamaker et al. (1987); the 3D integral equation of Hoh- mann (1975), Wannamaker et al. (1984), Lee et al. (1989); the thin sheet model for uniformly conducting half-space by Vasseur and Weidelt (1977), Dawson and Weaver (1979),
Ranga-nayaki and Madden (1980)/ Dawson et al. (1982), and Dawson (1983); 2D thin sheet layered medium model by Mckirdy and Weaver (1984); 3D thin sheet layered medium model by Mckirdy et al. (1985), finite (3D) body in layered medium by Best et al. (1985), Gupta et al. (1987, 1989).
Analogue Modelling
Laboratory analogue modelling methods have been developed to the stage where they are particularly useful in studying actual 3D geophysical problems. The theory of analogue scale modelling has been developed by Sinclair (1948), Strangway (1966), Ward (1967), and Frischknecht (1971). Dosso (1966a) developed a laboratory analogue modelling facility employing graphite plates to simulate conductive structures, and brine solution to simulate a resistive host earth. The graphite- brine conductivity contrast is of the correct order for m o d elling a wide range of realistic induction problems. These include the studies of idealized conductive structures such as vertical faults and dykes (Dosso, 1966b; Charters et al., 1989), conductive spheres and cylinders embedded in a resis tive host earth (Ogunade et al., 1974; Ogunade and Dosso, 1977, 1980,1981; Ramaswamy and Dosso, 1977), islands s u r rounded by an ocean (Ramaswamy et al., 1975, 1977), island- continent-ocean channels (Nienaber et al., 1976, 1977a, 1 9 7 7 b ) , cape and bay coastlines (Chan et al., 1981a;
1989). Inducing source fields that have been employed in the laboratory electromagnetic induction studies include approximately uniform fields (Dosso, 1966a; Nienaber et al., 1976), non-uniform fields of line currents (Dosso, 1966c; Dosso and Jacobs, 1968; Ogunade and Dosso, 1981), fields of vertical and horizontal magnetic dipoles (Dosso, 1969; Ramaswamy et al., 1972; Thomson et al., 1972; Ramaswamy and Dosso, 1973,1975,1978; Hibbs et al., 1978), and a vertical line current source to simulate lightning induced Schumann Resonances (Heard et al., 1985). Magnetic field variations induced by ocean waves have also been simulated using m e r c u ry as a conductive fluid (Miles et al., 1977; Miles and D o s so, 1979,1980). As well, 3D models of realistic coastal conductivity structures have been used to examine the effects of complex continental coastlines, for example, in the Vancouver Island region (Nienaber et al., 1979a, 1979b, 1980, 1982; Ramaswamy et al., 1980; Chan et al., 1981b), in the eastern coastal region of North America (Dosso et al., 1980b), in the British Isles region (Dosso et al., 1980a; Nienaber et al., 1981), in the Assistance Bay region (Heard et al., 1983), in the Queen Charlotte Islands region (Chan et al., 1981c, 1983), in the Newfoundland region (Hebert et al., 1983a, b), in the Hainan Island region of China (Hu et
al., 1983, 1984), in the Tasmania region (Dosso et al., 1985; Parkinson et al., 1988), in the Bohai Bay region of China (Meng et al., 1990), and the Japan-Korea-China region (Meng and Dosso, 1990; Dosso and Meng, 1992), and in the New Zealand region (Chen et al., 1990, 1993).
As part of the LITHOPROBE project (Clowes et al., 1984; Kurtz et al., 1986; Clowes et al., 1992) and EMSLAB (EMSLAB, 1989, Kurtz et al., 1990), an analogue model of the s u b d u c t ing Juan de Fuca plate region, including a simulation of conductive substructure associated with the subducting plate was constructed at the University of Victoria and m e a s u r e ments were used to aid in the interpretation of field m e a s urements (Dosso and Nienaber, 1986, Chen et al., 1989; Dosso et al., 1989; 1990; 1992). These analogue model results, when compared with field site measurements, clearly d e m o n strated the importance of the dipping conductive s u b s t r u c tures on the observed electromagnetic field responses in regions of lithospheric plate subduction.
1.4 The Geomagnetic Coast Effect
In induction in coastal regions, enhanced electric c u r rents flow in the conductive ocean, resulting in large v e r tical magnetic fields near the coast. This phenomenon has been called the coast effect (e.g., Parkinson, 1959, 1962;
and Jones, 1979; Gough and Ingham, 1983; Gough, 1989). Some of the important characteristics of the coast effect are summarized here; 1) there is a sharp enhancement in the v e r tical to horizontal magnetic field ratio as the coastline is approached (Meng and Dosso, 1990; Chen et al., 1990, 1993); 2) the coast effect depends on the polarization of the inducing source field, for example, the coast effect should be seen most effectively for a polarization parallel to the coastline (the so-called E-polarization case), since in this case electric currents flow parallel to the coast (Chen et al., 1990); 3) there exists a characteristic period (Tc ) at which the in-phase induction arrow is maximum, and q u a d r a ture induction arrow is minimum. At sufficiently short p e r i ods, the inland quadrature induction arrow near the coast is seen to point away from the coast (Agarwal and Dosso, 1990, 1993); 4) if the ocean is underlain by a conductive substra tum, both in-phase and quadrature responses near the coast would be decreased significantly, caused by reduction in the intensity of electric currents in the ocean due to e l e ctro magnetic coupling between the ocean and the conductive sjbs-
tratum (Dosso and Meng, 1992).
Coast effects have been studied in detail using laborato ry analogue modelling methods (e.g., Dosso, 1973; Meng and
Dosso, 1992; Chen et al., 1993), and by numerical methods (e.g., Fischer and Weaver, 1986; Weaver, 1987; Agarwal and Weaver, 1^39; Dosso and Meng, 1992; Agarwal and Dosso, 1990, 1993).
1.5 Mutual Coupling in EM Induction
Induction arrows, characterizing induced current c o n c e n trations, may be employed to study anomalous conductors in the Earth. In the case of measurements in coastal regions, it would be very helpful if the coast effect could be removed before interpretation of the field data. Such a removal has been studied and employed by subtracting the coast effect induction arrows (measured in the laboratory with the aid of an analogue model) from the field m e a s u r e ments at sites in coastal regions (e.g., Hebert, et al.,
1983a,b; Meng et al., 1990; Meng and Dosso, 1990; Chen et al., 1990, 1993). The resulting 'difference arrow' (field site arrow minus the model coast effect arrow) is then regarded as an indicator of local conductive anomalies in the region, such as a buried conductive geological feature. Such a technique for removing the coast effect is, however, approximately valid only with the condition that the mutual coupling between the ocean and the anomalous conductors is sufficiently small. Wolf (1983) investigated the mutual
which the anomalous conductor was located some distance from the ocean, and the coupled case in which the anomalous c o n ductor was overlain by the ocean, both models were underlain by a conductive substratum. His results indicated that s i m ple subtraction for the additive case may be promising if the separation distance of the anomalous conductor and ocean was sufficiently large, but for the coupled case, strong mutual induction effects would lead to erroneous interpreta
tion. Weaver and Agarwal (1991) employed a thin sheet numer ical model to study electromagnetic induction in a rectangu lar surface anomaly near a coastline, and concluded that in certain regions the induction arrow is not simply the resul tant of the component for the coast effect and the component for the anomalous conductor individually, unless the ocean- anomalous conductor separation distance is sufficiently large so as to have negligible coupling through mutual induction and the redistribution of the charge accumulations on their boundaries. Dosso and Meng (1992) used 2D n umeri cal models to calculate electromagnetic induction for sub surface anomalous conductors in continental and island coastal regions, then determined constraints on ocean- conductor separation distances that would permit, to within an acceptable approximation, a simple subtraction of the
coast effect response. Their studies show that if the ocean-conductor separation distance is at least as great as the coast effect response range Yr (defined to be the range where the coast effect |BZ/By| is decreased to a value of 0.2 ■, then the coast effect can be removed by simple sub traction to yield a response, approximately that of the c o n ductive anomaly alone. Their results were applied to inter pret the field measurements in the Japan-China region (Meng and Dosso, 1990; Dosso and Meng, 1992) and in the New Zea land region (Chen et al, 1990, 1993).
1.6 EM Studies in Equatorial Region
The Equatorial Electrojet (EEJ) is a phenomenon which has been of interest to geomagneticians for more than three d e c ades. Onwumechilli (1959a) first reported the results of magnetic field measurements on either side of the magnetic equator in Nigeria. Using such ground based measurements, it was possible to study the altitude, the width extent, and the current density of the EEJ (Onwumechilli, 1959b; Ogbuchi and Onwumechilli, 1963, 1964). These parameters are now known to vary with the season of the year and the level of solar activity. The location of the EEJ varies with longi tude, being south of the geographic equator in South America and the Pacific regions, and north of the geographic equator in the Africa and Asia regions.
