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E lectrom agn etic Im agin g
o f D eep F lu ids
in
A rchean C rust
by
Jam es A. Craven
Geophysics Laboratory
D epartm ent o f Physics
U niversity o f Toronto
A thesis subm itted in conformity with
the requirem ents of the degree of
M aster of Science
in the University of Toronto
© 19S9 by J.A. Craven
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A ck n ow led gem en ts
I wish to gratefully acknowledge the guidance and advice of my supervisor
Dr. Dick Bailey. Throughout my two year's at the University of Toronto Dr. Bailey
has been extremely supportive and insightful. The two readers, (who are unknown
at the tim e this was written), are also thanked for their time and effort.
This thesis could not have been completed w ithout the software kindly provided
by Dr. Richard Sm ith and Lamontagne Geophysics. Many of the diagram s in this
thesis were drafted using the interactive graphics program authored by Dr. David
Boerner. I thank K hader Khan for his draft of the location map.
Several people contributed useful comments regarding tim e dom ain electro
magnetics. The discussions with Ben Polzer and Dr. Jim M acnae of Lamontagne
Geophysics Ltd. were enlightening. I thank them for the gift of their valuable time.
The dialogues with Dr. Ian Ferguson and M ark Everett were also invaluable.
Financial support for part of the work contained in this thesis has kindly been
provided by a research agreement with Dr. Bailey and the Geological Survey of
Canada. My own personal finances were provided by a University of Toronto Open
Fellowship and an O ntario G raduate Scholarship.
Finally, I m ust acknowledge and thank the enduring patience of Karen Devine.
In addition to the considerable support Karen gave me, she was always a willing
and thorough reader.
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A b stra ct
Depth Image Processing (DIP) of transient electromagnetic d a ta collected over
layered structures such as sedimentary basins has proven to be an effective and cost
efficient m ethod of imaging the electrical conductivity variation in two dimensions.
D ata collected over the Kapuskasing S tructu ra l Zone (KSZ) of the A rdieun Superior
Province in central Canada were DIP processed in an a ttem pt to determ ine the
structure associated w ith the resistive upper crust in the region. Two conductive
horizons beneath the overburden are imaged a t 2 and 5 km depth w ith conductances
of approximately 0.05 S and 0.15 S respectively. An increase in conductivity at
m id-crustal depths is also observed. T he shallower horizon is truncated in the
vicinity of the Ivanhoe Lake Cataclastic Zone (ILCZ). Both conductive horizons are
interpreted as saline fluids in a connected porosity. The saline waters are m ost likely
a m ixture of fluids w ith m any origins. T he fluids may be genetically related to such
phenom ena as prograde m etam orphic reactions during the creation of the extensive
gneiss domains in the region as observed in the deep well of the Kola Peninsula, the
uplift of the KSZ, infiltration from nearby sedim entary basins or meteoric influx.
The conductive zones show some correlation with seismic reflections interpreted
as “ram p and flat” style th rust planes. This correlation suggests the fluid-filled
porosity may be controlled by structures associated w ith the uplift of the KSZ. The
in terruption in the continuity of the 5 km deep layer is possibly due to a high-angle
fault, unseen by seismic m ethods, penetrating to m id-crustal depths in the region
of the ILCZ.
The d a ta collected across the KSZ were strongly contam inated by local galvanic
effects associated w ith an inhomogeneous overburden covering the region. To ap
proxim ate the contam inated data , synthetic channelling responses, generated using
inhomogeneous th in sheet algorithm s, were superim posed on a layered earth re
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sponse. The layered earth response used was th a t indicated by the D epth Imaging
and an inversion of the d a ta to a layered earth structure. The synthetic responses
were Depth Image Processed using single- and multi-fold geometries to investigate
the reliability of the conductivity estim ation from d a ta strongly distorted by gal
vanic effects. The results of the modelling show the image of the layered earth
structure may be distorted due to lateral variations in the conductances w ithin the
overburden tha t are com parable to cumulative conductance of the layered earth
model. Although the drastic change in conductivity between the overburden and
the gneiss (10—2 to 10-,i S /m ) cause a certain am ount of ringing in the numerical
differentiation to derive the apparent conductivities, significant artifacts are not
introduced into the imaged conductivities. These results dem onstrate the imaged
conductive horizons under the KSZ are the result of inductive effects in conductive
layers at 2 and 5 km depth.
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T able o f C on ten ts
1. Introduction .................................................................................................................... 12. Background to the Thesis .......................................................................................... 5
2.1 Archean Crust Near Kapuskasing, Ontario .................................................... 52.2 Electromagnetic Techniques for Crustal Exploration ................................... S2.3 The Electrical Nature of Archean Crust ...................................................... 142.4 The Transient Response In a Conductive earth .......................................... IS
3. D epth Image Processing .......................................................................................... 233.1 An Overview of Depth Image Processing .................................................... 233.2 Determining the Reference Depths ............................................................... 293.3 Depth Stacking .................................................................................................. 323.4 A Study of the Depth Resolution and Correction Routines ...................... 353.5 An Overview of the Program .......................................................................... 3S
4. Model Studies of Depth Image Processing ......................................................... 40
4.0 Introduction ...................................................................................................... 404.1 Single-fold Layered Earth Imaged Conductivity .......................................... 414.2 Multi-fold Layered Earth Imaged Conductivity .......................................... 454.3 Single-fold Thin Sheet Imaged Conductivities ............................................ 47
4.4 Multi-fold Thin Sheet Imaged Conductivities .............................................. 585. T he Conductivity S tructure Beneath the KSZ ................................................ 64
5.1 Imaged Conductivity Beneath the KSZ ......................................................... 645.2 Theoretical Fluid Distributions in Archean Crust ..................................... 665.3 Observed Fluid Distributions in Archean Crust ......................................... 695.4 A Model of Fluid Distribution Beneath the KSZ ....................................... 74
6. Conclusions ................................................................................................................... SOReferences ............................................................................................................................ 82Appendix A : The UTEM System and the KAP Survey .................................... S8
A.l The UTEM System ......................................................................................... S8A.2 The Kapuskasing Survey ................................................................................. 90
A ppendix B : The Program STAR ............................................................................... SOB.O Introduction ...................................................................................................... 93B .l Initial Tabulations ............................................................................................ 93B.2 Function Xnewres ........................................................................................... 95B.3 Subroutine Sigcalc ............................................................................................ 96
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C H A P T E R 1
IN T R O D U C T IO N
The Lithoprobe project in C anada has been directed towards understanding the
lithology, s tructure and processes of the crust and upper m antle w ithin C anada and
its surrounding waters. One of the Lithoprobe targets, the Kapuskasing S tructural
Zone (KSZ), is of special interest to earth scientists: it may be one of the few regions
of the globe where the deep crust has been tectonically exhumed for investigation
on the ea rth ’s surface. As an exposure of deep continental crust, the Zone provides
a means of calibrating geophysical and geochemical techniques used worldwide
to investigate the lower crust. Studies of the electrical conductivity in tectonically
stable regions have traditionally detected a rise in the conductivity a t lower crustal
depths related to increased conduction in either the deep crustal rocks or in volatiles
th a t exist w ithin a connected pore structure. Frontier electromagnetic work here by
Woods and Allard (1985) dem onstrated th a t the rise in electrical conduction often
observed in the lower crust is a phenom ena associated only w ith conditions such as
pressure, tem perature and volatile content a t lower crustal depths. Further natural
source investigation by K urtz et al. (1988) and Cavaliere et al. (1986) of the KSZ has
confirmed the homogeneous resistive natu re of the upper crust, although Mareschal
et al. (1988) report an interesting correlation between lithology and conductors in
the structurally complex region of the northern KSZ.
During the la tte r p a rt of 1987. the KSZ was investigated using a deep-pene
tra ting controlled source electromagnetic system (UTEM ). The UTEM experiment
area is shown in Figure 1.1 and in detail in Figure 2.1. The m otivation behind the
experiment was to investigate the nature of the conductivity in the region of the
boundary faults associated with the uplift of the KSZ. The m ethod used to derive
the conductivity structure from the UTEM d a ta is term ed D epth Image Processing
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2
(M acnae and Lamontagne 1987). This procedure is untested w ith d a ta affected by
galvanic channeling associated with a variable overburden. In this thesis I approach
this problem using numerical studies of simple overburden models to determ ine
the reliability of the imaged conductivities beneath the KSZ. I then in terpret the
imaged conductivities in terms of a possible porosity and tectonic history for the
Kapuskasing area.
.60 '
H U D SO N
B A Y
JAMES
IPAUCA BELT
‘00°— - 9 6 °
ABTT1BI BEL]
AREA.
400 7 2 'km 76
8 0 °92' 84“8 8 °
F ig u re 1.1 T he Archean Superior Province of C anada and surrounding geological regions. T he Kapuskasing Uplift (KU) represents the change in m etam orphic grade across th e the Kapuskasing S truc tu ra l Zone. After Percival and M cG rath (1986).
C hapter 2 is a review of the background to this thesis. The geological and
geophysical investigations of the KSZ and the western Abitibi Belt are reviewed.
Archean crust around the world as revealed by regional electrom agnetic investiga
tions is summarized. The theory of the electromagnetic tim e dom ain response of
a conductive earth is also discussed. C hapter 3 presents a discussion of the image
processing procedure wherein I investigate the effect certain processing techniques
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3
may have on d ata collected in extremely resistive environm ents overlain by thin
conductive glacial deposits.
The d a ta collected for the KSZ survey is strongly contam inated by the effects of
shallow heterogeneity in the overburden. These effects are investigated in C hapter
4 by D epth Image Processing of synthetic d a ta for a model consisting of a simple
heterogeneity within a th in overburden. The synthetic d a ta is generated using the
numerical technique of Smith and West (1987). The exam ination of the effects of
shallow heterogeneity on Depth Image Processing is broadened by utilizing the prin
ciple of superposition. The superposition of the channeling response in the shallow
inhomogeneity upon a background response associated w ith the decay in a layered
earth provides a good approxim ation to the d a ta collected a t Kapuskasing. The
layered earth synthetic d a ta are based on a model w ith conductances as estim ated
by the inversion and the Depth Image Processing techniques. The synthetic data
created using the superposition are Depth Image Processed to determ ine the stabil
ity of the conductivity estim ation by the image process in the presence of shallow
heterogeneity over a layered earth . The imaged conductivities derived from the
synthetic d a ta dem onstrate conductive layers m ay be observed beneath a variable
overburden and th a t false layers generated in the imaged section are insignificant.
The KSZ Depth Image Processed (D IP) section is presented in C hapter 5. Two
sub-horizontal conductive layers are imaged at 2 and 5 km beneath the surface.
The conductances of the two layers are 0.05 S and 0.15 S respectively. These values
are in agreement w ith an inversion to a layered earth perform ed by Ben Polzer of
Lam ontagne Geophysics Ltd. using the m ethod of Polzer (19S6). The DIP section
dem onstrates the shallow conductor is truncated in the region of one of the main
boundary faults, the Ivanhoe Lake C ataclastic Zone (ILCZ), while the lower layer is
perhaps continuous under the KSZ and into the Abitibi Belt. As other EM studies
in the area have shown, the upper crust in the region of the KSZ is extremely
resistive w ith a resistivity of the order 105-6M fi m.
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4
In C hapter 5 I analyse the possible interpretations of the shallow conductors
under the KSZ. The favored interpretation of a saline pore fluid in a low perm eability
crust relies on argum ents based on theoretical and observed fluid distributions in
Archean crust. The seismic in terpretation by Geis et al. (1989) reveal the deep
crustal rocks of the KSZ may have been uplifted along “ram p and flat” style thrusts.
The correlation of the locations of the th rust surfaces and the conductors beneath
the KSZ suggests porosity and therefore the fluid distribution under the KSZ is
structurally controlled and is probably related to thin skin uplift in the Kapuskasing
area.
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C H A P T E R 2
B A C K G R O U N D TO T H E T H E SIS
2.1 A rchean C rust N ear K apuskasin g, O ntario
Pre-2.5 Ga. rock units are found to varying extents in all m ajor continen
tal masses. These regions axe typically composed of high-grade gneiss belts and
low-grade greenstone belts (W indley 1984). Based on a variety of geological and
geochemical criteria, the ancient orthogneiss terrains are probably tectonically ex
hum ed portions of the Archean lower crust. The actual mode of emplacement or
formation of the granulites is still a debated issue (Taylor and M cLennan 1985,
Windley 1984), bu t Kroner (1986) expects the lithological heterogeneity in present
lower crust to be reflected in th a t of the exposed sections. The relationships between
the low and high grade rock assemblages can be used to classify Archean terrains
(Kroner 1986). The structural grain of certain high-grade terrains axe similax to
those of the nearby greenstone belts. The gneisses in the Zimbabwe craton and
those of the Pikwitonei granulites in M anitoba are typical examples. The other
type of association is characterized by high-grade terrains th a t, accordingly, pos
sess individual structural tra its unobserved in the low-grade terrains. Examples of
these high grade “mobile” belts include the Limpopo belt of southern Africa and
the Kapuskasing S tructural Zone (KSZ) of the Superior Province of C anada (Figure
2 .1 ).
A wealth of literature exists on the Archean crust near Kapuskasing and the
summaxy given here is based largely on the clear review of Percival and C ard (1986).
The KSZ is a N N E-trending belt of aeromagnetic and gravity anomalies and ex
posed high-grade gneisses, th a t in terrupts the lateral continuity of the Michipicoten
and Abitibi belts in the southern portion of the Superior province and the Quetico
and O patica belts to the north. The Michipicoten belt is comprised of dom inant
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2.1 : Archean Crust Near Kapuskasing, Ontario 6
metavolcanic rocks of variable composition and of intercalated sedim entary units
(Goodwin 1962). Intruding the southeast portion of the M ichipicoten belt, the
Wawa domed gneiss terrain is characterized by paragneiss and mafic gneiss in com
plex interference patterns w ith structural wavelengths of 20-25 km. Tonalitic rocks
of the Wawa belt were emplaced ca. 2700 M a at the m argins of the supracrustals
dated a t 2749-2696 Ma. To the east of the KSZ are the low-grade supracrustals
and plutonics of the Abitibi greenstone belt. Volcanics are clearly the dom inant
lithology in the Abitibi (Goodwin 1982) and formed 2725-2703 Ma ago (Nunes and
Pvke 19??).
The Kapuskasing Uplift, defined by Percival and M cG rath (19S6), corresponds
to the eastw ard transition cf low-grade m etam orphic rocks of the Wawa and Quetico
belts to the high-grade am phibolites and granulites of the KSZ. Based on geological
and geophysical considerations, the KSZ was divided by Percival and M cGrath
(1986) into three tectonic blocks which from north to south are: the Fraserdale-
Moosonee block, the Groundhog River block and the C hapleau block. The deep
geophysics of the Chapleau block has received the m ost a tten tion to date and forms
part of the Uplift studied herein. The Chapleau block is comprised predom inantly
of orthogneiss w ith m inor paragneiss and mafic gneiss. The block also includes at
least two anorthosite complexes of deep-seated origin (Bursnall 1988). Granulite-
grade m etam orphism , not exposed in the Chapleau block, is manifest only in the
Quetico and Wawa belts and the Fraserdale-M oosonee block ''Percival and M cG rath
1986). Delimiting the eastw ard extent of the KSZ is the T'':mhoe Lake Cataclastic
Zone (ILCZ), proposed by Percival and C ard (1983) tn ’ i he surface expression of
an east-verging, listric th rust ram p active between 1.7 and 2.9 G a ago (Percival and
Krough 1983, Parrish 1988). T he ILCZ, only a few kilometres wide a t the most,
is comprised of b rittle faults and th in seams of cataclasite and mylonite (Percival
and C ard 1986). Geobarometric calculations by Percival (1983) indicate the th rust
exposed approxim ately 20 km of vertical succession.
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2.1 : Archean Crust Near Kapuskasing, Ontario
Ap
/A ft ,, *p .
Jtl
Av
A m g
F ig u re 2.1 T he Archean Superior Province near Kapuskasing, O nt. separa ted by the Ivanhoe Lake C ataclastic Zone (ILCZ). T he geological symbols are. in order o f appearance in the stra tig raphic column for the region; Ap: quartz-rich paragneiss, Amg: mafic gneiss, Asa: Shawm ere A northosite, Av: m etavolcanics, Atx: xenolithic tonalite-gneiss, A ft : flaser-tonalite, Adm: diorite-m onzonite intrusive complex, Ag: massive granite, g ranodiorite. T he locations of the twelve large loops are indicated by black lines. The survey line along which the recordings were m ade is marked by the thick line extending eastw ards across the Kapuskasing S truc tu ra l Zone and into the western portion of the A bitibi Belt. (A fter Percival 1983).
As noted eaxlier, a large database of geophysical m easurem ents exist for the
region, w ith the deeper geophysical studies being centred prim arily on the Chapleau
block. T he gravity signature of the KSZ, modelled by Percival and M cG rath (1986),
indicates the structu ral history of the Zone is characterized by a complicated series
of norm al and th rust events. A pilot reflection survey undertaken by Cook (19S5)
provided some evidence for a westward . >ing projection of the ILCZ. Prelim inary
results from a detailed seismic reflects -urvey (Geis et al. 19SS) confirm the obscr-
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2.2 : Electromagnetic Techniques for Crustal Exploration 8
vations of Cook (19S5) and indicate the ILCZ is comprised of numerous sub-parallel
refectors. Crustal-scale seismic refraction in terpretations by Boland and Ellis (1988)
(Figure 2.2) and Wu and Mereu (19S8) clearly dem onstrate a quasi-layered litho-
logical succession beneath the region interrupted by an upwarping in the velocity
contours beneath the Uplift, consistent with the th rust hypothesis of Percival and
Card (1983). Boland and Ellis also note a distinct low velocity zone in the Abitibi
subprovince at a depth of approximately 6-12 km. The Moho is situated a t a depth
of approximately 48-52 km and is deepest southeast of the Zone. Percival and Green
(1988) suggest this is a result of ductile vertical thickening at depth to compensate
for horizontal shortening during uplift. The various electromagnetic studies of this
area will be discussed in Section 2.3 in light of world-wide studies of the electrical
nature of Archean crust.
g 20A?
•7.0•7.0
•7 j6
60F igure 2.2 Seismic refraction velocity contours, in km /s, benea th the C hapleau Block from Boland and Ellis (1988). T he upwarp of lower c rustal velocities is indicated by the darkened contours.
2.2 E lectrom agn etic T echniques for C ru sta l E xp lora tion
For a variety of reasons, the electrical s truc tu re of continental crust distant
from areas of active tectonism is currently the subject of intense study. The electri-
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2.2 : Electromagnetic Techniques for Crustal Exploration 9
cal conductivity represents a param eter of the earth th a t varies dram atically with
bulk composition and can be m easured using a variety of sophisticated techniques.
The variations with depth and lateral extent of crustal conductivities are determined
using both natural and controlled source electromagnetic (EM ) m ethods. The na tu
ral source techniques, such as geomagnetic depth sounding (GDS) ('Ichmucker 1964,
1970) and the m agnetotelluric m ethod (M T) proposed by Cagniaxd (1953), use fluc
tuations in the ea rth ’s magnetic field as the source, while the controlled source
m ethods use artificial source fields. The energy of pulsations in the ea rth ’s field are
considerably stronger than those of man-made sources and thereby perm it a greater
depth of investigation; however, controlled sources offer the advantage of a known
source-receiver configuration which typically lowers the possibility of interpreting
an anomalous source-field pulsation as an anomaly in the earth. In addition, us
ing controlled sources allows the in terpretation to ignore large-scale channeling of
currents induced outside the region being investigated. Electromagnetic techniques
can be used in a depth-sounding mode recording vertical contrasts of resistivity be
neath a “station” ; or, if more than one site is occupied, lateral variations in crustal
resistivity are determined.
Under certain conditions, controlled sources can ietrate to large depths.
M ethods th a t inject current directly in the ground, such as the current dipole
m ethod popularized in the 1960’s by Keller (1966), will achieve significant pene
tration into a conductive earth (see for example de Beer et al. 1982). O ther sources
couple magnetic fields w ith conductors in the earth inductively and generate “vor
tex” currents in the earth th a t will be responsive to deeper structure in more re
sistive terrain. The inductive m ethods can be further subdivided into two classes:
those where m easurem ents are m ade ir the “frequency dom ain” and those where
they are made in the “tim e dom ain” . Tim e-dom ain m easurem ents of the induced
or “secondary” fields are perform ed after an ab rup t discontinuity in a “prim ary
excitation. The discontinuity is generally either an impulsive or step function in
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2.2 : Electromagnetic Techniques fo r Crustal Exploration 10
time. The UTEM system developed by Lamontagne (1975) and West et al. (1985)
m easures the step response fields while the SIROTEM system (Busseli and O ’Neill
1977) measures e.m .f. voltages induced in the receiver. Because tim e dom ain mea
surem ents are affected by the past history of the transient, where the early time
signal is affected by inhomogeneous overburden, the la te tim e signal will also be
distorted. Because the overburden effects along the tim e dom ain survey line pre
sented in this thesis are so pronounced, new techniques axe presented in C hapter
4 to assess the distortion. Examples of frequency dom ain inductive devices include
TURAM and the various airborne EM systems (Pem berton 1962). By selecting
various source frequencies, the depth of investigation in the frequency dom ain of
the fields can be varied. Longer periods can be used to m onitor greater depths.
Of course, this skin-effect of EM waves in conductors is also obeyed by the n a tu
ral source fields used in the GDS and M T techniques. Each m easurem ent in the
frequency dom ain is an independent estim ate of the e a rth ’s response function; but,
again because of the diffusive natu re at typical frequencies of the EM fields, it is
difficult to ascribe a particular depth to any m easurement.
The interpretation of EM sounding da ta from Shield areas is typically per
formed using one- or two-dimensional modelling schemes on d a ta th a t is least af
fected by three-dimensionality. M ost researchers acknowledge the electrical com
plexity of the upper crust based on the obvious d isturbed s ta te of the physical
geology, bu t this geological complexity is difficult to determ ine from the d a ta due
to the resolution of the geophysical m ethods used. For M T, even though it responds
well to conductive horizons, effects due to a th in m oderately resistive layer can be
difficult to separate from the large-scale diffusion of MT fields in a very resistive host
such as a craton. This idea is illustrated by the behavior of the one-dimensional M T
sensitivity function for a half-space as derived by Gomez-Trevino (1987) based on
the work of Oldenburg (1979) and linear perturbation theory. The perturbation in
apparent conductivity as a function of frequency of oscillation of M T fields, 8aa(uj).
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2.2 : Electromagnetic Techniques fo r Crustal Exploration 11
due to a small change in conductivity a t depth z is defined by
y.0cr0 and cra is the conductivity of the half-space. The kernel
of equation (2.1), K ,\i t , represents the sensitivity of noise-free d a ta to a small
perturbation in the host conductivity, 6
2.2 : Electromagnetic Techniques for Crustal Exploration 12
Shown in Figure 2.3 is the MT kernel function for a half-space norm alized by
the value at the surface; the depth is normalized by the skin depth. The real part
of the kernel function is a direct measure of the sensitivity of the m agnetotelluric
apparent resistivity whereas the imaginary p a rt is, to within a scaling factor, a
m ensuration of the weighting effects on the phase. Both curves clearly illustrate
the m agnitude of the integrated effects th a t can occur when depth sounding; each
independent estim ate of the earth ’s response function is affected by the conductivity
distribution as a whole. A simple model can be used to illustrate this effect on
normal M T data . Figure 2.4 shows the M T response to a thin relatively conductive
layer, representing a fracture zone, in a block of 1 Mfi m m aterial w ithin a 100
fi m lower crust and a conductive overburden. In order for the th in layer to be
detectable in the resistive host there m ust exist a resistivity contrast of three orders
of m agnitude. Due to the skin effect of EM wave propagation in conductors, the
desired inform ation in the response is contained a t frequencies of approxim ately 10
Hz. A high frequency response such as this would be difficult to discern from noise
in the d a ta caused by small-scale inhomogeneities th a t commonly d istort telluric
fields (Groom 1988).
In some cases, the electrical complexity of the upper crust can be determ ined.
Clearly, the more stations per unit area in a survey, the more likely one can map
out large-scale lateral and vertical variations in the conductivity structure. Jones
(1986), using a numerical model, illustrates th a t current fl«-«»•;nsc across the electrical
strike of a body (which presum ably parallels the geologic;r ike) and encountering
a resistivity contrast of three orders of m agnitude, can create a considerable geomag
netic anomaly. A notable example of these effects is drawn from K urtz et al. (1986)
who, using spatially intensive high-frequency M T m easurem ents, discerned a struc
turedly high, presum ably wet fracture zone. T he im portance of such studies is clear.
Conductive zones corresponding to fluid flow in fractured upper crustal lithologic
units can affect a variety of phenom ena pertinen t to the crust: the feasibility of
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2.3 : The Electrical Nature o f Archean Crust 13
1 0 6
1: no con d u cto r 2: .005 S' conductor 3: .05 S
o 1
907560453015
10 " 4 10 ~ 3 10 “ 2 10_1 1 0 ° 101 102 103 104 P eriod ( s )
F ig u re 2.4 M T apparen t resistivities and phases of typical Archean crust, i.e. a 1 M fl m block beneath a 10 m thick .1 S overburden and above a 100 f2 m lower c rust a t 25 km. Curves 2-4 represent the effects of introducng a conductive layer a t 2 km depth .
long-term storage of nuclear waste, the dissipation of heat in the crust, deformation
and m etam orphic rates, and the mechanisms of in trap la te seismicity, to nam e but
a few.
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2.3 : The Electrical Nature of Archean Crust 14
2 .3 T h e E lectrica l N a tu re o f A rch ean C rust
Due to the small num ber of electromagnetic surveys th a t have been performed,
the electrical nature of Archean crust is poorly understood. The Russian terrains,
such as the Baltic Shield, are the m ost intensively studied and are, for the most
p art, very resistive w ith resistivities as high as 106 D m (Zham aletdinov and Se
menov 19S5). Conductive layers in ancient sequences are thought to represent
graphitic or sulphidic schists w ithin interbedded prim ary sedim entary sequences
(Zham aletdinov 19S3). The Archean Presvecokarelide basem ent of eastern Finland,
investigated by the GDS technique (P ajum paa 19S5), is more resistive than the over
th rust Svecokarelide block. M T in terpretations across the same area in Finland, as
sum m arized by Korza (1985), are sim ilar to those for the Russian studies.
The M T survey by Cull (1985) across the G auler-N ullarbar Block of south-
central A ustralia d e le te d a conductive layer (700 D m - 8500 Q m) in a resistive
host at approxim ately 4 km depth. The conductive layer is associated by Cull (1985)
w ith the Archean Redan Group. In contrast, earlier m easurem ents by Everett and
Hyndm an (1968a.b) across a small portion of the Yilgarn block in southwestern
A ustralia did not detect any large-scale conductive features. The Archean Kaapval
craton in southern Africa exhibits upper crustal resistivities of 104-105 D m (van
Zijl 1977). The neighboring Limpopo gneiss belt is characterized by less resistive
values a t 2500-6700 D m to 25 km depth (van Zijl 1977).
The KSZ, whose tectonic origin is likely similar to th a t of the Limpopo belt,
does not display a low resistivity layer at upper crustal levels (K urtz et al. 1988).
At mid to lower crustal depths there is a suggestion of electrical anisotropy or
of the presence of a conducting slab (100 fl m). Various surficial features in the
region have been m apped electrically (K urtz et al. 1988, C houteau et al. 1988) and
a conductive zone associated w ith the ILCZ has been modelled as a moderately
conductive feature extending to approxim ately 600m depth (K urtz et al. 198S). A
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2.3 : The Electrical Nature of Archean Crust 15
prelim inary UTEM sounding (K urtz, pers. comm.) across the KSZ confirmed the
extremely resistive nature of Archean crust in the area (105-106 fim , first observed
by Woods and Allard, 19S5) and, in addition, indicated a shallow conductive feature
is dipping to the west beneath the ILCZ. The high resistivity of the KSZ has also
been observed in the Superior Province by Duncan et al. (19S0) and Strangway et
al. (1984). This observation implies, as noted by Woods and Allard (1985). that
the conductivity structure in this region is not related to lithological character.
Because this thesis is centred upon the conductivity features beneath the KSZ.
the electrical structure of continental crust will be discussed in the context of stable
cratons. A review of the electrical nature of the lower continental crust is pertinent
to this thesis as it is believed the rocks of the KSZ represent ancient mid-lower
crustal m aterial. Reviews by Jones (1981), Shankland and Ander (1983). and Haak
and H utton (19S6) are all in general agreement as to the widespread occurrence of a
zone of relatively low resistivity (100-1000 Sim) below about 20 km depth and above
the Moho. The statistical evaluation of electromagnetic techniques by Edwards et
al. (1981) shows th a t the depths of such crustal conductivity anomalies are well
resolved. Further, as Haak and H utton (1986) note, because a variety of m ethods
indicate anomalous values in the lower crust, their existence cannot be seriously
questioned.
In consideration of the laboratory work by Lebedev and K hitarov (1964) on the
influence of water on the conductivity of granite a t elevated tem peratures. Hyndman
and H yndm an (1968) suggested th a t the crust a t the base of Paleozoic mobile belts
is satu rated w ith water. Hyndman and Hyndm an (1968) rule out partial melting
of crustal rocks as an explanation for anomalous conductivities due to the low
heat flows of the areas they considered. Laboratory work on rock properties led
Brace (1971) to model conductivity in crystalline rock, under crustal pressure and
tem perature conditions, as a function of porosity and water content in a m anner
similar to th a t of Archie (1948) for sedim entary stra ta . In such a model, the bulk
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2.3 : The Electrical Nature o f Archean Crust 16
conductivity of a m aterial, a , is given by
a — aap4>m, 2.1
where o p is the conductivity of the fluid (in this case, w ater) in , the porosity (ratio
of void to rock volume), and a and m are empirically determ ined constants. Such
a relation is generally term ed Archie's Law and it can be expressed in a variety of
manners: for example, equation 2.1 assumes th a t the porosity is completely occupied
by the fluid. Brace (1971), using this relation and expected values for lower crustal
porosities, could not reconcile his calculated resistivities w ith those inferred from
geoelectric measurements. Incorporation of a conductive saline solution into Brace’s
model enabled Dvorak (1975) to calculate conductivities more appropriate to the
lower crust. Brines were shown by Quist and M arshall (1968) to be conductive
at up to 400 M Pa and 800°C. The laboratory m easurem ents of Lee et al. (1983),
detailing the variation of conductivity w ith confining pressures of up to 400 M Pa
in Lewisian gneisses perm eated by a saline solution, also lend support to Dvorak’s
model. Olhoeft (1981) proposes th a t free water in the lower crust might be present in
quantities of a few wt. percent based on the electrical properties of granite. Sulphur,
known to be conductive as a liquid, is also conjectured to enhance conductivity
(Olhoeft 1981); but as for other proposed conductive m aterials, such as graphite
and hydrated minerals, Shankland and Ander (1983) cannot accept th a t there are
extensive am ounts of these m aterials deep w ithin the crust. Shankland and Ander
(1983) also favour free water contained in a fracture porosity. Haak and H utton
(1986) note th a t the lateral changes in conductivity of the lower crust (see, for
example, Jodicke et al. 1983) could be due to local variations in available free water.
Gough (1986) believes th a t ductile flow increases the connectivity of the pore spaces
dram atically at m id-crustal levels resulting in the higher conductivities measurable
for the lower crust.
The review of crustal conductivity in conjunction with seismic velocities by
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2.3 : The Electrical Nature o f Archean Crust 17
Jones (1981) shows basement rocks tend to exhibit a predom inantly resistive nature,
at least to a depth of 20 km. If indeed the theory of Brace (1971) is valid, then as
Gough (1986) points out, neither fluids at hydrostatic pressure nor a compressive
horizontal stress regime will perm it a fracture porosity at upper crustal depths
to develop, thus ensuring th a t measured resistivities reflect the properties of an
insulating rock rather than those of a conductive pore fluid. The problem with these
explanations is two-fold. Firstly, there is increasing m icro-structural evidence at all
m etam orphic grades of a m etam orphic porosity concom itant w ith a high pore fluid
pressure, P f (Fyfe et al. 1978, E theridge et al. 1983). Furtherm ore, a compressive
stress regime can become tensile if the pore fluid pressure is strong enough. This will
cause either tensions! or shear failure (depending on the local differential stress),
even if the stress on a regional scale is compressive. Secondly, there is unequivocal
evidence for the existence of concentrated brines to considerable depths based on an
extensive database of geochemical analyses taken from groundwaters in deep holes
from around the globe and collated by Frape and Fritz (1987). Supporting both
points I have raised are the startling revelations of the Kola deep hole in Russia
(?????, 19??). D ata from the Kola hole clearly dem onstrates th a t the presence of
fluidized fractures (macro and micro) in the upper crust is a common feature and
extends their observed depth to somewhat over 10 km. It would seem then tha t
anomalous zones due to conductive brines in a fracture porosity, should they indeed
exist in the upper crust, are generally not being imaged by conventional methods.
Such an observation does not seem unreasonable in light of the MT sensitivity
analysis discussed earlier. My suggestion is th a t these fracture zones exist in the
upper and possibly middle crust, b u t the im plication is th a t the resistivity contrast
they present is low, suggesting limited pore connection. The natu re of porosity in
Archean crust, as revealed by the Kapuskasing UTEM experim ent, is discussed in
detail in Chapter 5.
A new approach to crustal electromagnetic exploration is presented in this
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2.4 • ' The Transient Response in a Conductive Earth 18
thesis, th a t of imaging the crust using a large loop inductive source developed
at the University of Toronto by Lamontagne (1975) and used to date prim arily
by the mining industry for relatively shallow m apping and depth-sounding. The
system measures the to tal field at up to 20 delay times after repeated steps of a
prim ary field. By measuring the total field, signal-to-noise ratios are considerably
improved over m ethods th a t measure secondary fields alone. Further enhancem ents
to the ratio are gained by stacking the d a ta obtained by loops situated over and
to either side of a receiver site; i.e. multi-fold coverage. A more detailed overview
of the system (UTEM ) is provided in Appendix A as are the param eters used to
penetrate to m id-crustal depths. In general, as mentioned earlier, such depths are
generally untenable using controlled sources, bu t by virtue of 2 km 2 source loops and
a resistive, low-loss country rock in which the currents induced in the earth should
diffuse downwards quickly, these depths are attainable. Such a technique presents a
novel way of avoiding some of the difficulties inherent in o ther m ethods, and because
the scale of the induced currents is relatively small, contrasts in resistivity, due to
the local existence of fluids, will be more am enable to m apping and interpretation.
2.4 T h e T ransient R esp o n se in a C on d u ctive E arth
After an abrup t discontinuity in the source or prim ary field, the am plitude
of a secondary magnetic field and the change w ith tim e in the am plitude, consti
tu te the ea rth ’s step and impulse responses respectively. In transient EM studies,
the response is m easured a t various times after the discontinuity using a variety of
source-receiver configurations summarized by Spies (1980) and M acnae (1988). Due
to the diffusive nature of the fields, outside the loop the sign of the response varies,
complicating the in terpretation in inhomogeneous environm ents (Spies 1980). Al
though in-loop measurements are not characterized by a sign reversal, they are not
necessarily as sensitive to conductive structures as are the outside loop measure-
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2.4 : The Transient Response in a Conductive Earth 19
ments. This can be observed in Figure 2.5 where the difference in the step response
of a 2-layer model and an equivalent model w ith a th ird conductor inserted a t depth
is plotted. The UTEM system measures the step response by transm itting a tailored
triangular waveform and using a coil to m onitor the m agnetic fields. Although the
time ra te of change is measured, the response is a true step response due to the
nature of the source waveform. For the following discussion, the term “response-"
implies, unless otherwise clearly stated, a tim e-dom ain step response; bu t does not
necessarily exclude the impulse response, as the two are simply related.
8
6
S '^ 4
CO (S
2<
0
_ 2-1 .5 - 1 . 0 - 0 . 5 0 0 .5 1.0 1.5
F ig u re 2.5 T he difference between the step response of a 2-layer model and th a t of an equivalent model with a conductor em bedded a t dep th . T he ord inate is the distance of the receiver from the loop centre scaled by the loop w idth. T he two-layer model consists of a .1 S overburden over a 1 M Q m half-space. T he em bedded conductor, located a t a d ep th of 2 loop widths, has a conductance of .01 S.
For exploration projects where conductive bodies im plicate economic mineral-
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2-4 • The Transient Response in a Conductive Earth 20
ization, the phenomena of electrical current-gathering, generally from a non-resistive
half-space and into a more conductive target, presents an in terpretations! problem.
This problem arises because existing interpretive tools typically calculate the re
sponse as though a sphere or a thin conductive p late (as the ore body) is fully
encompassed in a perfectly resistive host rock or half-space. T ha t is, the modelled
response is based solely on the pretext th a t only vortex or eddy currents Eire present
in the body. If the host rock conductivity is approxim ately zero, or if the electrical
contrast between the host Emd body is small (and there axe not extenuating circum-
stsmces such as a conductive overburden), then the simple model is reasonable and
successful (Lodha 1981). W here the electrical contrast between the body and the
half-space is sufficiently small, the half-space response can, according to McNeil et
al. (1984), “delay, distort and reduce the vortex component in comparison to the
free-space comp one' These effects are manifest in the frequency domain as dis
tortions in the pha ;e and am plitude measurements (for comments on this topic, see
•Jones 1983 and Hanneson and West 1984). In the tim e domEiin, channeling appears
in the response sis an initial attenuation of the response th a t diminishes a t later
times (Lam ontagne 1975). If the background conductivity is sufficiently high, the
attenuation can persist to later times. Channeling also causes a certain am ount of
tim e shift th a t diminishes w ith decreasing host conductivity.
The “smoke-ring” sinalogy of Nabighian (1979) for downward and outw ard cur
rent m igration in a conductive half-space (Lewis and Lee 1978) has greatly improved
target/half-space discrim ination. Smoke-ring dissipation is faster in a resistive envi
ronm ent; therefore, a resistive half-space is dom inated by a faster decay compared
to th a t in a relatively conductive half-space. This effect is illustrated in Figure
2.6 by the slow and rapid decays of the surface H® th a t occur over conductive and
resistive half-spaces respectively. C urrent-gathering occurs only in discrete conduc
tors (K aufm an 1978) anu presents an obvious “sta tic” response (Dickson and Boyd
1980) w ithin the response of a dispersing background current system. Kaufman
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2.4 : The Transient Response in a Conductive Earth 21
(1978) showed th a t the late-time response of discrete two-dimensional conductors
can be approxim ated by a series of exponentials. Spies’ (1980) investigation of the
problem of stationary signal discrim ination concluded tha t, depending on the con
ductivity contrast, a certain time-window exists after prim ary excitation where the
response of the conductor is separable from th a t of the half-space. A case history, re
ported by Staples (1984), dem onstrated th a t for certain interm ediate to late times,
a conductive half-space response subtracted from the m easured response enabled
a simple p late model in freespace to effectively reproduce the sta tionary signal of
the conductor. A dhidjaja and Hohmann (1988) provide num erical evidence that
the discrim ination window is larger for the step response com pared to th a t of the
impulse response, and illustrate the late-tim e decay of two-dimensional conductors
is be tter represented by a power law than an exponential.
K.
3?
-200
K.
ij"
200
100
-1 0 0
-200 1.60.6 1.0
F ig u re 2.6 T he norm alized step response of a conductive (a) and a resistive half-space (b) w ith conductivities of 10- s and 10-2 S /m respectively.
For a layered earth , the smoke-ring analogy is readily applicable as shown by
the num erical calculations of Hoversten and Morrison (1982). Individual current
rings do no t readily form in each layer; the smoke rings form sm eared relatives of
their conductive half-space counterparts. The plots of Hoversten and M orrison show
that the highest current densities are confined to the neighborhood of the most
conductive layer; th a t is. the rings’ downward progression is re tarded and their
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2-4 ■' The 'IYanaicnt Response in a Conductive Earth 22
lateral progression enhanced by a conductive layer. To obtain these results, the
algorithm of Morrison ct al. (19G9) was used, whereby a simple recursion relation in
the wavenumber and frequency domains (W ait 1962) is transform ed to the space
time domain. Although rapid schemes exist for such a transform ation (Holladay
19S1), and also for direct inversion to a layered earth model (Nekut 19S7, Polzer
19S6. and B arnett 19S4), their prohibitive cost, for d a ta collected using a m ultitude
of stations and source loops, is now a m ajor influence in the development of new
approaches to time domain interpretation.
In addition to the inverse methods, forward modelling techniques provide an
other means of obtaining the earth 's conductivity structu re from the transient re
sponse. Although they would be time consuming as one searched for the appropriate
model to fit the data, they provide useful insights into the two- or three-dimensional
EM diffusion process. Integral equation or scattering techniques (A dhidjaja and
Hohmann 19SS) quickly provide useful inform ation regarding only small-scale inho
mogeneities and would therefore be ineffective for crustal-scale EM investigations.
The advantages of finite element (FE) m ethods applied directly to the pertinent
differential equations in two dimensions are clear: they employ efficient banded m a
trices and perm it a larger model param eter set. Unfortunately, due to the large
size of the matrices, FE techniques are generally cost prohibitive when modelling a
dataset as large as th a t collected across the KSZ.
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C H A P T E R 3
D E P T H IM A G E P R O C E S S IN G
3.1 A n O verview o f D e p th Im age P ro cessin g
W ithin a geophysical framework an image can be defined as a m athem atical
reflection of an energy source about a physical boundary th a t functions as a m irror.
Because images reproduce the effects of the boundary in a physical system thereby
reducing the m athem atics to a simpler form, the use of im age theory is common
to m any of the sub-disciplines of geophysics. Images of a point seismic source
facilitate the calculation of norm al and dip moveouts and are useful when dealing
with the m ultiple reflections often, but not exclusively, observed in m arine studies.
Image theory is also a useful com putational tool in d.c. resistivity interpretation.
The disturbing potential (from th a t of the half-space value) caused by planar or
spherical boundaries between conductive regions is calculated using images of the
source current electrode. In addition, resistivity type-curves over a layered earth
can be simply calculated by treating each interface between the layers as a m irror
reflecting both real and image point current sources. T he potentials of the images
can be sum m ed to obtain a simple expression for the d isturbing potential of the
layers.
Image theory is a powerful tool in the in terpretation of electrom agnetic in
duction phenomena. Sommerfield (1897), reproduced in G rant and West (1965),
presented a solution of a dipole field over a dipping th in sheet of infinite strike and
dip (half-plane) in term s of image dipoles. The solution over a horizontal sheet was
investigated earlier by Maxwell (1891). At t = 0 the secondary field due to a step
in a dipole source located above the sheet, or by extrapolation due to a step in a
loop source, is represented by w hat Maxwell (1S91) term ed a “negative"’ image sit
uated at the reflection point on the opposite side of the sheet. A “negative” image
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3.1 : A n Overview o f Depth Image Processing 24
loop has the same physical dimensions as the source loop, b u t the current flow is
reversed. To satisfy the thin sheet boundary conditions (see G rant and West, 1965,
p. 49S) a t t > 0 the solution for the secondary field is given by
H ’ ( t > 0 ) = H* (3.1)
where H s( x , y , z ) is the solution a t t = 0, 5 is the conductance of the sheet and
f i0 is the perm eability of freespace. From equation (3.1), the step response can
be thought of as the result of a negative image descending from an initial depth,
- = 2h, w ith a constant velocity of where h is the depth of the sheet. (Figure
3.1). The decay of the secondary fields will therefore be faster over a resistive sheet.
T h in Shaw l w*h
F ig u re 3.1 Schem atic representa tion of image locations beneath a sheet a t d ep th , h t after a step in the source loop curren t.
The use of image theory towards a be tter understanding of the response over a
conductive half-space is only a recent development. W ait and Spies (1969) present
a simple form ulation whereby reflection due to the presence of the half-space is
representable by a complex series of exponentials. They show the half-space can be
replaced by an image of the source a t complex depth, s + a , where a = (1 — i)6
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3.1 ; A n Overview o f Depth Image Processing 25
and 6 is the skin depth. The work of Nabighian (1979) suggests a reasonable
approxim ation of the eddy current p a tte rn in a uniform half-space is th a t of a
simple current loop with the same shape as the source loop which moves downward
after the step in the prim ary like the Maxwell th in sheet image, b u t which also
slows and increases in size w ith depth. The current filaments therefore represent
the well-known smoke rings blown by the transm itter. The downward slowness of
the rings is given as
d t / d z = y j —cr(i0t (3.2)
where a is the conductivity of the half-space. To invert a synthetic half-space
response to derive an approxim ation to the half-space conductivity it is necessary to
fit the fields of descending smoke-rings to the synthetic data , calculate the slowness
of the smoke rings and to solve for the conductivity using equation (3.2).
M acnae and Lamontagne (1987) sought a basis function com putationally sim
pler than the expanding smoke rings of N abighian from which to approxim ate the
eddy-current distribution in the uniform half-space as a function of tim e. The cen
tra l concept to the technique proposed by M acnae and Lam ontagne (1987) is an
image packet. W hereas a receding negative image is an exact solution of the thin
sheet problem , a descending packet of images was found by M acnae and Lamontagne
to be a good approxim ation of the half-space response. The packet is characterized
by fourteen images of the source loop, each w ith the same shape as the source, but
w ith individual current am plitudes. The num ber of images, their currents, and their
vertical d istribution within the packet were fixed by inverting the step response of
a variety of half-space synthetic data, subject to the constraint th a t the sum of the
currents in the images equalled the step in the current of the source loop. The syn
thetic studies of M acnae and Lam ontagne dem onstrated an em pirical relationship
between packet depth, h, and the conductivity of the half-space
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3.1 : A n Overview o f Depth Image Processing 26
The packet depth has been term ed the reference depth by M acnae and Lamontagne
and is a m easure of the effective penetration of the induced eddy currents in the
half-space. If the packet depth is tracked w ith tim e the slowness of the packet
penetration into a half-space, given by
d t / d h = y /2 a po t = a p 0h, (3.4)
provides an estim ate of the conductance to the depth h. An estim ate of the half
space conductivity can also be recovered from the reference depths as
1 ( f ta = — -jTj. (3.o)
fj,0 d h 2
The fourteen point im age-distribution represents the best compromise between
time to calculate the fields of a descending packet and error when fitting the cal
culated fields to a synthetic half-space response (M acnae and Lam ontagne, 1987).
Listed in Table 3.1 are the current am plitudes of the fourteen images th a t comprise
the packet relative to the source current am plitude, and the depths of the images
w ithin the packet relative to a reference depth of unity located a t a fractional depth
of zero. Figure 3.2 is a schematic cross-section of a typical packet a t a reference
depth of 1000 m based on the inform ation in Table 3.1.
The th rust of the work of M acnae and Lam ontagne (1987) was to provide
a simple and accurate means of estim ating the apparent conductivity of a layered
earth . Equation (3.5) not only works for the case of a uniform earth , bu t if the packet
is collapsed onto the reference depth so th a t it forms a single image, i .e.a Maxwell
Image, equation (3.5) will also work for the extrem ely non-uniform case of the thin
sheet. This suggests th a t the slowness gradient, is in general a reasonable
estim ator of conductivity, and th a t an inverse m ethod to extract inform ation from
d a ta collected over layered earths can be based on such an estim ator.
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3.1 : A n Overview o f Depth Image Processing 27
T ab le 3.1 A m plitudes and fractional dep ths o f th e fourteen images th a t com prise the packet. A m plitudes and dep ths are given relative to th a t of the prim ary excitation and the reference dep th , h, respectively.
Am plitude Fractional D epth
-0.0916 -0.3880.4352 -0.370
-0.0975 -0.234-1.4940 -0.181-1.1175 -0.1181.1914 -0.0182.5356 0.0482.3283 0.1011.4719 0.166
-2.1069 0.324-1.9642 0.406-1.0817 0.4670.5682 0.5420.6433 0.902
The conductivity in equation (3.4) was assum ed to be constant w ith depth. If
the conductivity changes w ith depth of penetration , the slowness at the reference
depth, h, is given by
d t / d h = f (TfXodh. (3.6)Jo
Thus, an estim ate of the difference in cumulative conductance from one estim ate of
the reference depth to the next can be made. In order to improve the fit of synthetic
layered earth responses to the descending image packet, M acnae and Lam ontagne
incorporated the concept of a packet width. This w idth, as defined by the fractional
depths of the first and last entries in Table 3.1, was varied sm oothly by M acane
and Lam ontagne as the packet descended to provide the best fit of the synthetic
response to the fields of the descending packet of images. The smallest permissible
w idth w e i s zero; the m axim um useful w idth was 1.5 times th a t defined by the entries
in Table 3.1.
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3.1 : A n Overview o f Depth Image Processing 28
D epth Image Processing no longer utilizes a packet w ith a variable w idth as
the inform ation extracted from layered earth m edia using a packet w ith a constant
w idth provides a robust estim ate of the conductivities (Ben Polzer, pers. comm.).
Because a strict analytical relationship between packet w idth and layered earth
structu re does not exist, the w idth of the packet appropriate for the d ata is derived
empirically. I have found th a t by comparing the actual measured step response
to th a t of the responses of the descending packet for different packet widths, a
reasonable estim ate of the proper packet w idth can be obtained. W hen comparing
the responses, the d a ta m easured outside the loop should be closely reproduced by
the response of the descending packet because the outside loop response is strongly
enhanced by inductive coupling of conductors a t depth.
500
J t 1000
U 15000)
2000- 3 - 2 - 1 0 1 2 3
F ig u re 3.2 An exam ple of the half-space image packet for a reference d ep th of 1000 m constructed from the values given in Table 3.1. T he ord inate is the ra tio of the image am plitude to th a t o f the primary.
The cumulative conductance of layered earth models w ith strong conductors at
dep th was extremely well reproduced using the slowness gradient estim ator (Mac
nae and Lamontagne, 19S7). W here the cumulative conductance increased only
m arginally due to resistive layers in the models the estim ator tended to smooth
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3,2 : Determining the Reference Depths 29
the estim ated conductances. This is not entirely unexpected because the horizontal
eddy current flow generated in a layered earth is not significantly perturbed in resis
tive layers. An apparent conductivity profile can be constructed using the reference
depths beneath each station as
1 i tz n — rrr- (3. /)Ho
The goal of Depth Image Processing is therefore an accurate determ ination of the
reference depths, h , under each receiver position by fitting a descending packet of
images to the observed secondary fields.
3.2 D eterm in in g th e R eference D ep th s
A datum in TJTEM studies refers to a secondary field m easurem ent a t a cer
ta in delay tim e for a particular receiver position and for a particu lar loop. The
secondary field m easurem ent is normalized using standard channel one norm aliza
tion to reduce the effect of local galvanic channeling and system atic errors due to
chaining inconsistencies (Appendix A). It is the normalized response th a t is used
during the fit to the response of the image packet. The com putation and tabulation
of the responses due to the descending packets are discussed in A ppendix B .l.
To derive the imaged conductivities, an estim ate of the reference depths as a
function of tim e are required beneath each receiver position. To reduce the num ber
of calculations in later processing steps, an initial estim ate of the reference depths
beneath each loop is obtained. Subsequent processing tasks use these initial esti
m ates as starting points in their search for the best-fit packet depths b .eath each
receiver; and therefore, the determ ination of the initial reference depths is quite
im portant. The initial estim ates of the reference depths beneath each loop for a
particular delay time are found by selecting the depth of the packet, w ith the de
sired w idth as discussed earlier, from the tabulated responses (see Appendix B .l)
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3.2 : Determining the Reference Depths 30
th a t minimizes the square of the misfit error for all receiver positions. The error,
for d a ta given as O ij and tabulated function responses given as T}k, is defined as
e? = (Oi j - Tj k f ( 3 .8 )
where
i = 1 . . . nt , the num ber of delay times
j = 1 . . . ns, the num ber of stations
k = 1 . . . nk , the num ber of tabulated reference
depths (typically 201).
A plot of ef versus the table depth indices for one station is provided in Figure 3.3
where the depth range of the table is the same as th a t used in Figure B .l. A simple
interpolation of the table depths is perform ed at the location in the tables indicated
by the m inim a of ef to refine the initial depth estim ates. Care m ust be exercised
to avoid spurious local m inim a for the late UTEM delay times (curves 12-1) due to
m atching of the increase in the step response m easured by the receivers outside the
loop to decreasing values in the tabulated functions.
W ithin a layered, conductive earth , the change of the penetration depths d u r
ing the tim e interval between two UTEM channels m ust possess a positive slowness.
Irregularities in the depth progression due to 2- or 3-D bodies could generate physi
cally meaningless negative slownesses. The initial estim ates of the reference depths
under each loop are corrected to ensure there exists a positive increase in the con
ductance w ith depth. The goal of the depth correction is to ensure the d istribution
of the depths provides a conductance which does not fall below some minim um
plausible value, /?; th a t is,
* ( £ ) > * (3.9)
A simultaneous constrain t on the late time depth d istribution ensures the late time
slowness does not change beyond some reasonable fraction of its initial value. Most
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3.2 : Determining the Reference Depths 31
106
1 0 4
CM
1 0 2
10 °
1CT21 51 101 151 201Table Depth
F ig u re 3.3 T he prefit erro r given in equation (3.8) for the 20 UTEM delay tim es for a single loop over a sim ple layered earth model. T he erro r is p lo tted against the logspaced tabu lated reference depths. T he best fit reference dep th s for each UTEM delay tim e are taken a t the location of the minima.
layered earth models studied satisfied the two inequalities in under twenty iterations:
if the num ber of iterations required to satisfy the inequalities rose much higher
th an twenty, then slight alteration of the w idth of the packet selected for the fitting
procedure usually reduced the num ber considerably.
The estim ated reference depths under each loop are used to calculate nominal
slowness values beneath each loop at each delay time. The slownesses are used to
determ ine correction term s to the table values described in more detail in Appendix
B.2. The corrections have little effect on the processing of the models in this thesis
and are not discussed further. The m ain purpose of the estim ated reference depths
beneath each loop is to serve as the initial search point in the tables to locate the
best-fit packet depths beneath each receiver at each UTEM delay tim e and thereby
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20
'4 —1
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3.3 : Depth Stacking 32
reduce the tim e spent searching through the tables. T he table-search a ttem pts to
locate a valley in the error as a function of packet depth th a t is in the neighborhood
reference depths beneath each receiver for each loop are also checked to ensure the
resultant conductances are monotonically increasing.
3.3 D ep th S tacking
For each station, severed reference depth estim ates are available a t each tim e
because each station has measured the eddy currents associated w ith several trans
m itter loops. The object of the depth stacking is to reduce the m ultiple sets of
reference depths for each station to a single “stacked” estim ate for each station
at each time. The weighting function used not only uses the estim ates from the
different set of the reference depths, but it also incorporates the depths of station
positions of neighboring stations within a window. Using I to represent the sets
of reference depths of the various loops, j to represent the receiver positions for a
particular loop I, and x to represent the position of a station w ithin window centred
at Xj the weighting function is given as
prim ary field, p lo tted versus depth is shown in Figure 3.4 for stations at various
distances from the loop. Estim ates far from the loop, curve 6, where the step re
sponse is more sensitive to layered conductors are strongly weighted by the prim ary
field term in equation 3.10. The first term of equation 3.10, shown m Figure 3.5 is
of the initial estim ate of the reference depth. Interpolation of the fitting error curve
between the tabulated response depths is used to refine the depth estim ate. The
(3.10)
H i ( r , h x ) is the prim ary field of the Ith d a ta loop at the reference depth and position
of the window location. The th ird term in the weighting function, the square of the
a geometric factor th a t drops off sharply for increasing h j and for distance from the
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3.3 : Depth Stacking 33
centre of the window. Note th a t the weights require an a priori knowledge of the
reference depths beneath each station, h j . To provide a rough estim ate of these, a
“prelim inary stack” is done using weights
G x [ ^ ] _1 [fT '(*,/»x) ]_1 (3.11)
where G x is a generic station weight input a t the s ta rt of the program . The resulting
prelim inary stacked estim ates of h j are used above in equation 3.10 (known as the
m igration stack).
10 °
- 2
- 4
- 6
-8
-1 0
201101 1511 51Table Depth
F ig u re 3.4 T he last term of the m igration stack weighting function p lo tted for the positions w ithin the window corresponding to the sta tion depicted in Figure B .l. and equivalent tab le dep th s of the prelim inary stacked depths. T he curves are normalized by the square of the prim ary in the centre o f the loop.
Once h j are established using the m igration stack they are halved to account
for the fact th a t although the process is imaging currents a t a depth of h the
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3.4 : A Study o f the Depth Resolution and Correction Routines 34
conductors are located at the m irror positions i.e.at h /2 . T he halved reference
depths are referred to as the imaged depths. Finally, the apparent conductivity
is obtained for each station by numerical double differentiation of the tim e as a
function of reference depth (equation 3.7). This numerically noisy and unstable
process has to be stabilized using the robust interpolation techniques perform ed by
subroutine S igcalc discussed in Appendix B.3.
-2
- 4
101 151 201Table Depth
F ig u re 3.5 The first term of the migration stack weighting function plotted for a window centred about the mid-point of the loop shown in Figure B .l. The weights are plotted as a function of hypothetical preliminary stacked depths expressed as equivalent table depths. The five curves represent the weights for positions within the window corresponding to the stations shown in Figure B .l. The weights depicted are normalized by the value of the weight at the centre of the loop.
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3-4 : A Study of the Depth Resolution and Correction Routines
3.4 A S tu d y o f th e D ep th R eso lu tio n and C orrection R o u tin es
The determ ination of the reference depths is performed using least-squares
matches to functions computed within a set range of depths. Because the tabulated
functions are calculated at depths logarithm ically spaced at discrete intervals, there
exists an element of non-uniqueness in the fit th a t is resolved to a certain extent
using simple interpolation techniques. Because of the compressed natu re of the
smoke rings a t early time, the step response far from the loop, i.e.in the so-called
far field, varies slowly with time. An analogous phenomenon is observed in the
tabulated functions depicted in Figure B .l as the slow decay from -200% in the
curves for stations far from the loop. As the centre of the diffusing current system
passes under a receiver, the step response rises to a m axim um th a t subsequently
falls as the current system continues its downward and outw ard progression. This
maximum can be observed in Figure B .l as a flat region in the curves w ith packets
at depths corresponding to interm ediate table depths.
If an error on a datum is larger than the change in the tabulated response
from one depth entry to the next, the range in the datum proscribed by the error
defines a region of packet depths th a t will fit the datum equally well. A grey-scale
diagram of the slope in the tabulated responses for the geometry and the packet
widths of Figure B .l is shown in Figure 3.6. Receiver positions are located a t the
top of the plot and extend across the diagram s from 0 to 2.5 loop d ia m e te r The
vertical axis is depth logarithmically spaced to 10 loop diam eters. Blank regions
illustrate where the slope in the tabulated values are less than a nom inal d a ta error
of 1% and therefore illustrate the range of reference depths th a t fit a datum with
1% error equally well. Black regions illustrate where the change in the table values
is 6 times th a t of a 1% error. A th in blank zone or "blind spot" swooping out
and away from the loop is the expression of the flat regions at the peaks of the
outside loop tabulated responses. Figure 3.6 dem onstrates the trade-off between
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3.4 : A Study o f the Depth Resolution and Correction Routines 36
the iesolving power of large and small packet w idths. The large w idth associated
w ith Figure 3.6(b) is more sensitive at greater depths than the zero w idth packet
of (a), but is less sensitive to the shallower inform ation. Both packet widths are
relatively insensitive to structure beneath the loop.
Figure 3.6 Simple sensitivity analysis of the two packet widths used in Figure B .l. The ordinates represent the receiver position out to 2.5 loop diameters and the abscissae represent depth increasing downwards on a log-scale to a tabulated depth of 10 loop diameters. Black levels indicate a change in the tabulated values at that depth of at least 6 times a nominal error in the data of 1%. The blank areas are representative of changes less than the error and thus are representative of poorly resolved areas.
The correction to the best-fit reference depths is performed frequently during
the processing sequence and therefore w arrants some attention. This routine might
be a distorting factor in the processing of the d a ta collected a t Kapuskasing due
to the insulating natu re of the Archean lithostratigraphic units and conductive
properties of the glacial overburden. Such an environm ent is closely approxim ated
by a thin sheet over an insulator. Because the constrain t imposed by equation (3.9)
imposes a minim um conductivity, there exists the possibility the correction may
introduce significant changes to the reference depths. This possibility is investigated
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3.4 : A Study o f the Depth Resolution and Correction Routines 37
by passing synthetic th in sheet d a ta through the depth correction using the same
low value of /?, ;0002, set during the processing of the Kapuskasing data. F igure 3.6
shows the imaged reference depths before (solid) and after (dashed) the correction.
The correction is far more significant at depths shallower than about 1 /2 the loop
dimensions; hence, it is not significant for any results below this depth. Of course the
actual depth estim ation is not as im portant to the calculation of the conductivities
as is the distribution with tim e of the reference depths. At shallow depths for the
th in sheet models one would expect irregularities in the conductivities and reference
depth estim ates and this is what is observed in C hapter 4.
500
.0758
.107.2000
.503.5000
.429
.60S
.857
1.21
1.72
2.42
SIN
Figure 3.7 Plot of thin sheet image depths before (solid) and after (dashed) depth correction for the first 12 UTEM delay times. The reference depths are one-half the image depths.
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3.5 : A n Overview o f the Programs 38
3 .5 A n O v erv iew o f th e P ro g ra m s
The Fortran-77 program to perform the depth and w idth fitting and the sub
sequent conductivity calculations is called S T A R , an acronym for Slowness Trans
formed A pparent Resistivities. P rior to running S T A R , ta,bles of the basis func
tions and other calculations are com puted as discussed in A ppendix B .l . The
table program s and the m ain program have been altered to run on the CRAY
X -M P/24. S T A R implements the transform ation of the d a ta to apparent conduc
tivities through a sequence of processing steps. Each step consists of related tasks
th a t are performed on either a whole line or station-by-station basis. W hole line
processing, such as estim ating the reference depths under each loop, takes into con
sideration the fit of all the stations for a single d a ta loop. After each step, there
is the option of storing the quantities calculated to perm it the re-start of S T A R
at the last complete step. The processing sequence for the IvSZ profile and for the
models studied in C hapter 4 is as follows:
P ro c e s s S te p # T ask
1) -set whole line mode on
-estim ate reference depths beneath each loop
-perform the depth correction
2) -set whole line mode on
-calculate slownesses beneath each loop
-calculate m inor corrections (Appendix B.2)
to table entries
-estim ate the depths beneath each loop
-perform depth correction
3) -set station-by-station m ode on
-calculate slownesses beneath each station
-calculate m inor corrections (Appendix B.2)
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3.5 : A n Overview of the Programs 39
to table entries
-estim ate the depths beneath each station
-perform depth correction
4) -set station-by-station mode on
-perform depth stacking
-perform depth correction
5) -set station-by-station mode on
-calculate conductivities beneath each station
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C H A P T E R 4
MODEL STUDIES OF DEPTH IMAGE PROCESSING
4.0 In tro d u ctio n
A strong conductivity contrast exists between the overburden and the meta-
morphic basem ent of the Ivapuskasing S tructural Zone. Due to a highly variable
composition, the overburden in the region under investigation is extrem ely het
erogeneous in term s of thickness and conductivity. The D epth Imaging Process
assumes the decay of a layered earth response can be fit to the response of a de
scend