Electromagnetic Imaging by James A. Craven...by Dr. Richard Smith and Lamontagne Geophysics. Many of the diagrams in this thesis were drafted using the interactive graphics program

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

R e p ro d u c e d with perm iss ion of th e copyright ow ner. F u r th e r reproduction prohibited without perm iss ion .

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


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.


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

- 1 - Draft: C H A P 1 Ju n e 20. 1989 19:55


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

Draft: C H A P 1 Ju n e 20, 1989 19:55


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.

Draft: C H A P 1 June 20, 1989 19:55


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.

Draft: C H A P 1 Ju n e 20, 1989 19:55


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

- 5 - Draft: C H A P 2 Ju n e 20, 1989 19:56


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.

Draft: C H A P 2 Ju n e 20, 1989 19:56


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-

Draft: C H A P 2 Ju n e 20, 1989 19:51!


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-

Draft: C H A P 2 Ju n e 20. 1989 19:56



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

Draft: C H A P 2 Ju n e 20, 1989 19:56


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).

Draft: C H A P 2 Ju n e 20, 1989 19:56

R e p ro d u c e d with perm iss ion of th e copyright ow ner. F u r the r reproduction prohibited w ithout perm iss ion .

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


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

Draft: C H A P 2 Ju n e 20, 1989 19:56


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.

Draft: C H A P 2 Ju n e 20, 1989 19:56


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

Draft: C H A P 2 Ju n e 20. 1089 19:56


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

Draft: C H A P 2 Ju n e 20, 1989 19:56



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

Draft: C H A P 2 Ju n e 20, 1989 19:56



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

Draft- C H A P 2 Ju n e 20, 1989 19:56


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-

Draft: C H A P 2 Ju n e 20, 1989 19:56


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-

D raft: C H A P 2 June 20, 1989 19:56


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

Draft: C H A P 2 Ju n e 20, 1989 19:56


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

D raft: C H A P 2 June 20, 1989 19:56


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.

Draft: C H A P 2 Ju n e 20. 1989 19:56


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

- 23 - Draft: C H A P 3 Ju n e 20, 1989 19:57


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

Draft: C H A P 3 Ju n e 20, 1989 19:57


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

Draft: C H A P 3 Ju n e 20, 1989 19:57



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.

Draft: C H A P 3 Ju n e 20, 1989 19:57



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.

Draft: C H A P 3 June 20, 1989 19:57



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

D raft: C H A P 3 June 20, 1989 19:57

R e p ro d u c e d with p e rm iss ion of th e copyrigh t ow ner. F u r th e r rep roduction prohibited without perm iss ion .

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)

Draft: C H A P 3 Ju n e 20, 1989 19:57


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

D raft: C H A P 3 Ju n e 20, 1989 19:57


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

Draft: C H A P 3 Ju n e 20, 1989 19:57

20

'4 —1


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

Draft: C H A P 3 Ju n e 20, 1989 19:57


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

D raft: C H A P 3 June 20, 1989 19:57


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.

D raft: C H A P 3 June 20, 1989 19:57

R e p r o d u c e d w ith p e r m is s io n o f t h e c o p y r ig h t o w n e r . F u r t h e r r e p r o d u c t io n p ro h ib i te d w i th o u t p e rm is s io n .

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

D r a ft C H A P 3 June 20. 1989 21:06

R e p r o d u c e d w ith p e r m is s io n o f t h e c o p y r ig h t o w n e r . F u r t h e r r e p r o d u c t io n p ro h ib i ted w ith o u t p e rm is s io n .


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

D raft: C H A P 3 June 20, 1989 21:06

R e p r o d u c e d w ith p e r m is s io n o f t h e c o p y r ig h t o w n e r . F u r t h e r r e p r o d u c t io n p ro h ib i ted w i th o u t p e rm is s io n .


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.

Draft: C H A P 3 Ju n e 20, 1989 19:57


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)

D raft: C H A P 3 June 21, 1989 17:53

R e p r o d u c e d w ith p e r m is s io n o f t h e c o p y r ig h t o w n e r . F u r t h e r r e p r o d u c t io n p ro h ib i ted w ith o u t p e rm is s io n .

3.5 : A n Overview of the Programs 39

to table entries

-estim ate the depths beneath each station


4) -set station-by-station mode on

-perform depth stacking


5) -set station-by-station mode on

-calculate conductivities beneath each station

D raft: C H A P 3 June 21. 1989 17:53


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

Documents

Electromagnetic Imaging by James A. Craven...by Dr. Richard Smith and Lamontagne Geophysics. Many of the diagrams in this thesis were drafted using the interactive graphics program