~-'F1"7,"'If~" 'i , , . ..

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&hort title 1

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" Ma.netotellurici in th. a tern Town.hl~. ol.Quebec ,

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\ - , ~ut"or; 'Ch'rlltopher .chlid S'terl.nd Uall.. ~

, ~

Th 1 e or Thes il: M'an.tofeJl ur 1 ClS' 1 n th~ ,f',.~ t orn 'nu~n~hlp~ , 5 j , "

of' Qub.c: ..

. , Oepaft.ent) Minin, and ~.t.l1ur.lc.l en.tn.e~l~a.

De,re., ; Pli. D. ' \ " Il

A ".,n.tot.JlQric Survey h.. been ms dt- ln tht Rich.ond, Quebec .r.. to investikate ~hetber the tarit \..,

\. ,

PQ~itive .r.y~ty ano 1y thert Il due to an uplift l,n . .

the mantle,. FteJd equlplllent 'W" de51In.~ . nd the data

In"ty~~d on diaitl COM,utert ul1n. 'Power $pectrl,lll anal-. \

Y'~~" .. C,tah1,y cOflplx ne.r,-,urface structure ha~ co .. -pl1cated the i~t.~pret.tton. To .odl the' structure.

'. -.. . a finit. elem.nt nu rical appro.ch t5 dev.toped for .aA-

.. .fie t 0 tell url cs.

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. a~~' MAGN8TOTlL~ICS

.. IN TRI \.. BASTI!tN ,TOIMSflI'S 1 . ,

; ~} OP ~UI'IC

, . . , . . ....

. . " Chrl.t-.h.r R. S, Ha'1U " a. Se (St .. P X. ) t 1ilJ. (~11).' N, ~

1

",

,

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, '.

(M~Gl11) )

A 'th i. ,ubatt'.d to th.PaultyOf Gr.du.t.'Stu61e. _ .n~ R r~h. 111. patti.1 fulf.l .. at of ta. l'tqul,r."ft~.

, " ~ " for tlM ,1'.' of' ~etol" of 'bl1010ptay. : . .'

Pe,art .. nt of Ntaia. a.4 Meta~llc.t Ift,l Ti., McGlll UIat ....... ity. ~.tr lt Qu .... c.

'. .

Mard 1911 , ,

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'l''''''JIJ)!II''';).,~~ . '+, l!'

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'. ~ 'A C k N Q W L P. 0 G B M B N T S

1/ r

)

t No th 1. la sol.1y the reluit 01 work by ono n. It i. thtou.h co-op.r.tlon' with other., and throu,h

/

th.ir dvl~o and h,lp, that such wrk t. co.pleted. , , . T)\C' Authar ha ny p.ople,to th'nk for thelr contributions: 1 J / ~ ., '" ......--- .

. '. 'Ors_, t.P. Geldart .nd W.M. ,Telford. for rell' .... ch dlr-,1 ...

.,ctlon and ftnanei.l ~,upport . ...

'-~ \'" ~

"

1 Or. ,. Silvester of.~he Dep.rt.ont of Blectrlcal Hnaln- ~

'.

oerlna for '.n lntrd~ctton to. the rlnl te elepont' "othod

Ors. P.ft . Ser.6ft 'and B.R.' Niblett of Ilo.inlon Obscrvu" , , "

tory, (or f.ln.nci.~ support._ technie.l '.dvlce, field equip

aeftt. office sp,c and co.puter ti . .... ~

Me.~rs. A.M. lo11y, F . Jones, J.A. Slankl! and W.J .

Scot t L,Jrduate students. {or h.l'p and advlce

'M ,rs . Adrian

."

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T A\ L Il F CON T fl N T S. , . '\"' ....

ABSTRACT

AC KNOWl.HDGBMJ!NfS ;

l'AR 1. Ji Of COI-4TltNTS . .

Not~' on' the Presenta', ion oC 'Vector,

\

, ., "'-

v

. ,.~

il

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t v

viii

xltl 1

Nore on the NtaMbetln4 of ~~c'tiOn, .!quatjonl, an,1 111 au r~~ " Not.o on Sola. Syllb-ols U!e~ in Thil Th"!l i"

CIIA PT f. R ON,F. 1 NT RODH CT t ON

1.1 Purpq:\e . . l.} Ilistoricai Review of ~he M netotelluri~ Mctho~

1.3 1 Geo~olY of tbe Are. ' , t.4 Pt-tvlotts (;eophYlical WOJ;k

.' CUAPTI! R TWO Til EOR y .. , ~

2,. lin t rocSuc t ion,

2.2 Nalne~otJlurlc5 , ....,

l.3 A Nov.l Tethaique for,~lnetot.llurlc Modol) hg . .' ,L4 . Th.e ,Fini te ~l ... nt Nethod

. CHAPTF.1t TURE! .. PIBLD EQUIPMBNt

Introduct 10n, .' r

C

"" 3.2 Th.'Marl 2 S,lt '. . . .. '> ,

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c _

~ l' ~ - .

xi-li

xi li

1

2

l

11

11

21

'22

, 51

51

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s.! 'urther. Co ... nts, on Field sy.te .. l " _

, . ,CHArTHR FOUR PI BLD WORK

4~1 Introduction

4.2 ,1961 field Work r

. '"

\,

CHArTER FJV! -~ANALYSIS A;HD INTSRPRETATION .. . S.l Hand' C.lculaUc\n. 'on M,.ne'tote}Juru natta l-. \ , 'S \ Z ~()'.puter An.1Yli~C)r Ma.netotellu''rlc nat. S _,3 Further A~aly.l. 0'- tb. COllptlted' Relul ts .

\ S.4 MOdellina the NOTth-South Line

S. S Correlation with Gr.vlt~ ~nd Na, ... etls Data , ,

dtAPTpR SIX ~'CONCLUSIONS

. 6.1 'General'

b.2, The, Contribution. of This Thest, ~

6.3 Suaaesti~n. for Further Work

,

SU'lestionsl for Malftetotellutic Depth Soundin, , . , . in '~re.s ~( C~.plex N.rlutf.te btololY

.. - .. APP~HDIX " EXPRnSSJNG DtFfERENftAL OPElAtORS . .

lN TRJAHGULAR CO~ORDtNATES

APP'EN-Orx 8 .. CORRECTIONS TO PAPERS ON lHFINIT! 41J

SERIIS SOLUTIONS a

APPENDIX, C" .. PlELO BQUIPJGNT USID IN Il66 AND 19~1 , .

C. r Mark 'A S,st .'

vi

54 -

60 .'

60

" . 65

al, ~)

108

.134

lA4

,151'

1$2

153

154,

, 158

164

171

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C.,Z The Mark 18 51.te .. \. ~'PSNDIX D .. 1'112 -STRI' CHART DIG.lTJZER

APPBNOIX ,H THB.1966 AND 1'67 fllLD SEASONS

'APP8HDIX, P D. c. USrSTIVITY' dl . ..

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201

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PI GURBS .\

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'4

Map 0 f the Struc tur.l CeololY of the Ba. tern

TownthJp. of. Qu,bec, and adjointnl,area.

Ceolo.lcal Nap of the Eastern Townships of

, Quebec

1 ~ :5 "e1'o ... net 1 c: Total Pield Nep 0 f the Eu tern . . Town.hl pt of Quebec

1. 4 8()UIUer lGravhy Ano.aly N.p of the eastern Twft.hi p. of Qu.bec. and adj oinl n, are a5

~

4

1. S , Geolo.ical ProU le t alonl the line AA' , , aho # the Bouauer, Gravi ty a10n. thh line

- Fdlte el ... nt .. thod: 2. 1 coap.rison of the fini te

el ent .olution wi tb that of d' Erceville \

and kun.tl

2. l Pini te e l ... nt tbl:: dla.r sho"ina ho" ., the dylte proft te' wa. dlvided Into tri angu-

1ar .l ..... t.s

.... 1 2- :\ P1.ni te .l ... nt .. thod: cOllpari,lon of the {ini te

eleaent solution vith Rankin', (1962)

2. 4 Field Cue '1: d'lllr showin, how t~e profile

.as dlvlcled lnto trlaDlular .1 ... nU

. .' . "j'fi _, ' . ", ,._' .1

vUi

4

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6

10

11

14 \

li

34

31

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r" ~ ........ , 'Tt: ") "',,-'>;"O..; "'t .,. ~ 1 ~ A ~ " ,

. "

1x

2. S PI.ld C Il: Co.parilon 01 finit. 'l nt

r.lult. with valu ob rv.d ln the fi. Id 43

Pl.ld ~.Ie '2: d~ ra bovin, bow th, profil.

v dtvld.d into trla~ul~r .1 lnt.

l. 7 / Pt'.ld Ca.e '2: co.parl.on of finit l nt

.. , r.lult. with valu ob rvld ln th. fi.ld

3. 1 Block dia,ra. ~ ,netot.llur~c T.cor~n,

IY' t Ma r1c 2

3. 2 FreqUlney re'ponsl of;, the Mark 2

rlco.rdin, Iyste.

3,.3 Coapar lion of fr.qu.ncy 'I.ponse.: th. re.

pon of th urinl' syst and the res

ponle to aD a,.r.,. 11~.alnetlc field

4. l 1968 Field S on: .ap Ihowin. the location'

of Itation.

S. 1 M'ln.tot.lluTicJ: hand calcul.tion.

s. ~. 1 Hand ana1y,1.: dia,r ... hows how polslble error. o~cur in pickln, .lnu.oid. for

S. 2. 2

hand an.ly. il)

Hand an.1y.l.: th. r'lult. wh.n plottinl. Jf .n '1'ror ln pietin, a .lnu.oid

~',s~' .. 1.,

45

41

S2

ss

57

63

66

69

71

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s. ~

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St.

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U.n" a".ly.l': r.tlo of U,. '1aPlltude. of -~

th. v.rth:-,l ~(ull'o".nt of th _"t'h' n.l\Var.atiun. " . tv.en W!tkh Quebttl'

.nd a) a('kburn, Ont.rlo

i' .

Haftd .nalyal.: bar .r.ph uf th, rat10 of th~

.."rttudo. of tb. v.rti\'al \oapon\.1\t 01 A"

th ,,,.th' fl.ld vart.tion. betw n flc-ht -'atlo", and Rla(kburn

tiand .n~) Yli. : l'ha., " (oapart.on. bet"een the rv~rtl~.l co.ronont of th, netle (l.l~ .

vara,tton. at field .t.tlon. and at ~l.rk-

. x

r

14 .

70

bu", "

"and .n.ly.l.~ pha.o collparl.o". bot" " the

vertical cOIIpon.nt. 01 the .alnetlc fi.ld

var'atlon. at th. Il.ld~.tatlon. and at

IHlckburn /-,

Ma,netotellurlcal dt,ltal co.puter ~.ly.,. 81

~Ift.tot'llurle.: dl.ltal ~o8put.r a".ly.l . o

Coh.~nc. includ.d \ 1104

S. .. Ph ~o, ... rl.~n.: dliitai tOllput., ,ana1y.t.

Coh ... elle. i ne 1 u.s.ct 109 . ...

S. 10 . , C"'a" 1 10ft of "I".lot.' ha .. ! ."cI cl. c. rel 't,, , )

, ti ri ty .... ul t. for al1 .l.h~ f'_ld 1 tat lo".

U6

1 .. if.

~,

,.

"

S .11

, ."

...

, - , ..

( Contoured plot. of Z and 1: ratio r ults

a. a fuftctlon of horizontal dlsplac eftt

and perlod , ,

1111 ,

S.12 Con~oured ptots of,.a.netotellurlc resulta

5, 13

S.14

a Cunetion of horizontal displace nt .

and perlod (nFtke Resiltivit:y" plot!')

Contoured plots of .aanetOtellurie re!ults a8

CURetton of horizontal displ.cemnt and

urake depth lt

finite ele nt .odel of the . anetie north '

south line. Ihowin. how the profile wai

dlvided into tr4lftlle.

5.15 Ma,netotelluric.: .a.netle north~south li~e \

l24

13S

140

. Co.parlton of apparent re.i.tivItUes as . ! ~ , .

observed and .s .odelledo' 142

S.16 Gr.vi ty: anetie nbrth-Iouth 1 ine "

A ,uaa~,ted'profile ~o fit the'aravity

data, and the netotel1urie .odet

5.17 Aero ,netic profile: .alftetlc north,outh

llne

8. 1 aankin' olution to netotelluric effect of ,.

dyk.: revi d BIH curY.~

C. 1- 8~Ok dia,ra. of .alne~ot.~luric recordin,

" sy.t , Mark lA

'N ~ ........ ..

14S

166

172

! "

"

C. 2

C. 3

C. 4

\

c. s

,. C. fi

D. l

'. ~

l' t. 2

F. 1

" Sche.a~lc dia.ra. '01 the telluTlc a.pliflers

us~d ln the Mark lA and 11 .yst s 1

Frequency re.pDns. o(ONark lA\an~8 tel1urics recordlnl syst.~s

174

118

Frequency r~sponse of Mark lA .a,aetici recordina 180

p

Block dia.r oC ,netic. recordlna 5yste_

Mark la . 1-83

Freque~y respons~ 01 Mark 11 a~ettc~ recor~

ding syste. ' '187

t Oiagra. of the Do.inton Obs.rvatory strip chart

/-diKitizer. as IIOdtfied 190

1966 Fleld Selson: p showlna tbe location,

. of stations 194

, 1967 Pield Se.son: pshowinl~the locations

of stations 191' ...

.. D. C. Retiltivlty CU"_' 204

. < '.

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,-,

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..

~otc on the PresentatiQn of Vectors , ,

Vector. are shown in it.llcs. Thu'S'. , 1. a

'vector.

~otc on the Nu~erin of Sections ..

,

Src t ions. and fiaures are nullbered'

by chapter.

"h ft'

Sections cc.ss

Equations (cc.sl.nn)

Fi lures (CII{.'"

.c Js the chapter nu"er , cl

55 is the section nullb.r

la is the Iroup nu.ber ~f Eilures havina a

co-.on caption

f } denotes that the ite. i. option.}

,and 'nn is a sequence nuaber

. Sote on Jo.e, SrllbolS !Sed ln This Thesis

Pa apparent reslitivlt1

'xl i 1

l, .~

Ens , cOIlpO" t of the ,electrlc f..i:.l1l lA Uat ..... tt(; ,

north-south direction (Borth positive) . , .

~.w li~e Ens' Oftly,in t-~ t dtrectlon.< ... , po.itiye)

lt cOllp .... t of th. Mpet'ie flelcl variatioft tft tbe' ,~

. f . , ",

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, CHAPTER /JME

t N T R 0 n u ~ T t~o N

1.1 Purpo58,

The purpose of th!s thesl. va. to .stablish

whether the pTonounced positive gravit y .no~aly 1~ the

Rich.ond'Irea of 'the Ea'trn Townships of Quebec i. . .... .

caused br 'an upllft in the crult/.antle lnterftce. and

if th~ be'the caS,8., to obt.ln a value for the reststivity

0(' th,e upt>e'r '.antle. 10 thi n~. it v decided ~o carry

out 1 wlde-band low-frequency .a.netotellurlc depthsoun-.

d.ina .x~.rh,ent in tbe area. lit ! .... '

. . ' The .aanetbtellurlc ~urv.y is descrl.d here: ' in' addl t ion t the fi l'st applict l~n of the fini te ol nt

numerical technique to .cd.l11nl ... ft~totellul'~c, 15

presentod a5' i t was de,veJoped t.o llt ln int.,.,reftn. tbe

, re;~l ts. f

" Much experi.nce was I.i~.d in the, deilin. deve1

op.ent~ .na aodiflc.~lon.of th. la.tl'ua.ntatlon. In f.ct, the equip nt wa. ftot con.ld.r.d to b. one huadT perceat

reliabl. Dritl1' tihe tlal rd flelcl Oft; fOT thl. 1"'~Jon

onl" the la.t re.ult. are 1y.ecl .. a iat"Pl'eted

. . J ; ~M

, .

" , .

, ' ' "

'"~- r---~~"'f-, 11",

t ~"'~y:. or -\tl~'Q""r,,\ >l''~~'''' "'_',~

"

here. ..," , \

. 1.2 Historie.! Revlew of the Wa,MtOttllurlc" Mfthod

~iblett (1967) and 'Swift (1967) have reviewed"

tlte deve':1t1pment of the lIagnetotelluric thod# ln 1953

Cagniard published ti\e deCinlt.l.,e paper on the theory of ~

the technique ; he, presented ~he-ore.tical resul t, for the

orthogonal eloctro netlc field co.p0ftnts at the surface , of a horizontally layered earth ... Various writers have

\

shawn "that ther. are resirictions on the applicabi~ity of

the Cagniard theory:

(a) the source JIU.t be a plane-incident "a1re ,

(b l the .. pli tude of the incident w.ve' a, t be cons tant

over a horitontal distan~e equlvalent to at least ORe ,kin

depth in the g~ound (Wait (195.), Wait (1962), Prie.'

(1962) l.

(cl ~here ther. are aniso~ropic layers. the apparent resls-

tivity .. y be eonsiderably diEE.Tent froa the expeted.

(Pr.us and Petr (1969}).

"0- At tbe'ti_ of "ritlAI; the Iapetotet'lurlc Mtho4 ls

... nder att.ck EToa a theoietical viewpoin\; .,".elally vith.

rea.rd to the nature oE the loutce field; however, a pra,-

.. tic apptoach still .se ... 'justlfied. [Macl4en and Helloft

(1964) l ,

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1~ -'. 1 ~-""' ..... ~~~"'j~ ~' l Jr ;. ,.~~ l' ~"'" ~ ~ ]' "*''''. 1

..

1.] Th~r'GeoloIY ot the Arca ~ p

Fitzpatrlck h~s revieved the aoo10lY. Tvo

',eo1011cal _ap' are presented. Fiaure l~l stresses

, structure and coatS Cro. Inn and Ar,un*Weston (1967);

in Fiaure 1.2 the rock type~ and thelr aaes ar shown;

this p is ,iai1ar to the one in ~it%pattik's thesis.

As sua,ested by Da.lnion Obs~rv.tory personnel, tbe line

Jndie.tint the Richao~ Fault {ra. northeast of,Asbestos \

to Beaucevil1e and the equivalent~part of th~ St. Francis

Thrust line have been o.itted. ( F.tzpatrick states:

. ...., , "For 1001oliea1 purpose!. the Eastern T~wnshi'ps

can be split into two parts: the Lowlafids 'of ,the St. Law-

rence'west olJLo,an's L'ine .nd the ar~UI of,.etallOrphoscd .. ' rocks 1yinl betweon this line and the United States border.

tlThe ,eo10&y of the Lowlal1ds re,ion i5 descrlbed ,

by Clark (1947) in a veTy leneral report ..

"The ,eolo,y of various sections east of LOlants

Line has been studied by v.rious .ut~ors . The proble.

of lnte.~atinl the findin,s of these vartous aen i9 alaost

iapossiblo due to the wide Tana~ of opin~ons expressed .

to the struct,ure and .tr.ti,raphy of the re.ion.

Lowl,nd. Th. reaioft 1. ,ently folded"into broacl .yn-, ' Q.. ..

cline vith i"ts axis ruMina approxi tely down t,he, ceJ.:'tre

of the Lowlanc1s. Th. plun._ of the lolel 1. tow'rd the L , ~

,",~,~,~t(J

r

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f,tl

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Il' 'lit . J

...-A ,

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0

Pal'e LI .. ,

M.p of tb. Structur.r Geolo,y of the

E tara townships of Quebec. and ad,ointft. a..... ,.

.'

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(after taae. and Ar.un~W ton (196)

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'rt. UW 4'rHr---------__________________ ~------------~~----~----~_,4 - '

,

." .... .. . .. . ..... t, ..... ' '" ." ,

Granite

if

.... ONdl ... 'O" ct "' avote.nie 'OC".

E:Z1 MoUe ond "Ii,ameaflc 1" ."., ......

ra ..... 1.1

. ~ t~ ... ,l ..."J.t}.:\~m~\lililiii

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6eolog1,.1 Mep of the Eastern Townshlp. of' Queb.c:

(aEter Flt~p.tylck (1953)

fi

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, 1

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r' 1.

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8 .1,.

north st at th. soutb en4 and tow.rd the s~o~t At the .~ " ~

north end! It li, tb.n, *" eloftlated b.sin , The tblck-1 t. ~

ness of s.di .. nts in ~ ftorthern p.rt of the b.~ .s to be of the order of 7000 feot whllst in the .outhern

section the depth to t~. Preca.brlan b.so.ent ~y e.ceed

10000 feet in pl.~es.

"The oftly iln.oua rock. present in the 'Lowlands

are those .. tina up ih& cores of the Montetoai.n Hills. ~

.,Roaion East or'Lol " Line A description is COM-ti .. plic.ted by the tack of .&re en~ ( .an,J ... the

t. v.rlous ,eSlollst. whG h.ve .. pped the .te .

"

"The .st striklnl r ture ln [the C .. bro-Ordo .. vieian rock,sJ $ the an~~inorlua tunnin. the who!e

l~nlth of the TOWDlhip

~ . ,~

(

"The oldes. rocks in th. reaion .re el ther the ; \

The l.t ter .... ~_~ Sutton schists or the Tibbet Hill ichists. unde"l le the Oak Hi II serie. This fo .... tion. is trace-

able fro. the unite States bord.r to .' point north .nd

west of Th.tfor Mine here lt .e~ to ~ls.ppe'r. pos- , .ibly due to the~ asterly pluaae of the fol. axis. The

axis of t~ ... la ~.ylt1 ano.aly colnclde. vith th!. fora;

.tion.

"fb. latruslve iaaeo~' rock. fOUDd in tbe ar

..:.../ 1 \ .\

,q :. ti

lt,., I~. !

",

'"

.~

"".' !

IF'W' ,r" , ,,". , '

"~. , ~~"

, ,.'

fl.' Il ~, 1''1

"

'/

~-.--, ~~""""",, ~ ~

~, , ~ . ., ", . '1"-" .~'~._'~ ! ..... ,I .,~"~ .. ;r~.!' "'", ....... ' ~ . -' , . . . ~\

, !

..

/

f.l1 lnto three b~ad cateaof't : ~nt.re.l.n tyJ. -'of un-kftOwn post-Devonian ,',., tbe .1~~",~~ . lr1~1'U.lfes oE po~.t ..

,Devonien ale, and the .aflc, ultra.lfic, and ~.l.t.d sil

icebus rocks .. It is the intr~sive. which are, respon-

t ihle for thtr bult of ttl. arlvi ty ~no l lei oc:c:urrl'na,' i,~ . \"' the relien . ~

1 r UThe fic, ultr .... fie, Ind .related lille.ous

rcftks .re exposed' on t~"'ou~hern fl.-nk of the. Sut ton

,

,."ticline", . Tbe l.araest bodies of ultra fie ~ock in

the Eastern\rovnships occur in the Thetford Mines area ... \-. (

-) Reli,onal Struc:t~re The MOSt ob.viou. st ructurll Ieat",r. ~

in the Eastern Townlhip. il Lo._,,'s Li.ne. Thil Z-one .of , ~

(aultin, dips to the .outh.ast ,nd . the vertical dllp~ ,

lace.ent is not'likely to exceed 5000 feet and .. y be as

) s 11 es 0.200 reet. r-"-

tt The Ric.h.ol)d fau!t is nearly vertical and

the "e~ side ltas .ovec! up relative to the t."

1.4 Pt.viou! G.ophyslc'l ~OIk i

. Cravity. aero.aanetle and around' ,netle IUrv.y .

h."e be,en c.rried ot ln the ar . Fi,ure. 1.3 l,' ,a ,.ro-1.'

.a,netic .. p.of'th~ B ter~ Townships. ~oapl1.d fro. th. ~ . ~ C.olo,lcal Surv.y of C.nada one .. inch-to-one-al1e serie .

Fiaure 1.4" is Iouluer Gravit y "p, taken f10. Fltzpatrick l ."

. ), l,l, . . '~,', r ~II."

, '

..

,:r '~

~

~ , ,~

\

'\

. '

,. '. , ~\ ,

i'

" , l' ;l

1 1 . ~

(

ft> , "

l't", ''li'' 'It"'. '''', "'QI" , , '

.~

Plaure 1.3

A~ro n.tt( Totll Fle14 Map of th I: t.rn Townahlp. o( Quebec

1 r,ro. G.otoltcll Surv.y of CanRda ata)

,\

c' .

, '

1 .

.

" r

,

,)

'J '4 J,j "j

l,'

1~ \',1 \ ;

- ~.

"

1 .......

Fiaure 1. 4

'.'

. '

..

BouJUer Gravit y Ano.aIy Map of the Eastern Townships of Quebec. and adjoininl are.s "

(aft~r FitzpatTick (19S3)) (

/b

1

-, '

l 'l;.!. ___ _ ,',.-:::~ ~,.' a _

11

, A

" "'

, t

r

')

'. ';-'" \ . "" , . -. '! , ~~ {:. "

~' '. , , , ,.

"

" w BOUGUEA GRAVITY ANOMALfES

'N MILLtGALS SCAl~ Cl 5.0 KM

1 -

fi ..... 1.4 ('. " ! \

; f . , ~ Vl fi ~ "

l, ,

,. ~ f'

..

;\

~ ~. ~ .. ' .. ~. \.' -

... -thesis l'

1.... --"', -- ~~ ..

13

It viii be noted that elonga(ed. aeroManetic an-.

o.'lies coincide vith the axis of the Sutton anticJin and

wi th the RichllOnd fault. -)IS0, the gravi ty peak Whi.

"

o

Il "

, ," " "1,..,

, (

-'

Fl,ure 1.5

Geolo,lcal profl~ alon. t~. ,lin. A-At, s.u, tecl by Pltpatrlck t19~3 also, the Bou,uer aravity alona th!. e.

, .

r

The 11ne AA ais shawn in Fi,uTes 1.1 anil 1 .;.,

(drawina talten ,roa Pitzpat.rick (1953)]

. ,

. ~ ,",'

, .

- ..

. ' .' . '

. "

, .. -

. ; .~ j - '-~ .. i c ..

"

:.

;'1

li M

\ . a, -z .. 6-\.1 Q

~~~

~ ~ ~ ~~~ ~\t., r Ll l, 1: " ~;,

~i ~{ ~'

0

''-

- -.~_4, , -.

\ ,

, 1

OIII.YlI ,OUIII MOIIA""

"'..-.1 .

. ,'i

. .

'.

" h-'~ 1

~. " "

~ ~f ~:! f' ' 'J '

\"

. '

,l., \

CHAPTER T_O

-

T Il.E Q:R ~

2.1 Introduction

finito eleaent aethod as' a teqmiqu!, for sol,vina the dif-." ... ,~

.... , -.' . lerentiel equatio",' produced. Cunes 'are UU::l\#ded to ,

~ 110

show the coarison .betven this -.ethod and Infinite series'-

solutions for certain geo.etrie,. r '\ .

\

2.2 Ma&netotellurics

The electroaaanetic equatlon, that .ust alw~y~

be satisfied are the Maxwell equations and associated con- ,

tinuity conditions. At .aanetotelluric frequcncies, the, 'lit ' "

.clettric displaceaent curtent 3D/at 15 nora.lly very auch

smaller than the conduction urrent J, and ~y salely b. JI.

neglected. Under th!! assuaption, the ,Maxwell equations

assume the, s iapl t fied for.

curl 6 - - aS,at cur1 - J

in ter.' of the COnYeDtiOna~y ... ~ls,' vector J. the aentraI fora of Oh.' s Law.

-\

(2.2.1)

(2.2.2)

..

(2 .. 2.S)

.'." .... _~~ i

..

, . l'

'\

. , ,

'\

, , , ,

,-, 1r.

f ~ . ~' ,

'" ,

,

f

c ,

,l, + j."'1418 0 .. (2.2.8) , The th ... tical essence of the pTobl ls therefore to

solve the diffusion equatioA (2.2.8), subjec't to the con-

dition of a given at the .arth's surface.

"

A2E~rent Resistivitx ' The field decays with depth l~

!act, it d~cre.ses to IVe of the surface value in the

flrst a Iz/lJtfMJ .eters .. wher. a il the' s~in depth.

Let us define the propa,ation conl~ant cl

jwuoo ; this 15 a ,ood approxl tlon at netotelluric

frequencies. The refractive index of a ~diu. i5 inversely

proportionl to K. Sinee the propa,atiQn coftstn~ lS nUM-

~rially auch greater in the ,round th.n in the air, waves ,

incident upon the earth at Any anale a're re.fracted allaost -verticaUy downward.

We wi Il now deri ve the for.ura for, the apparent

resistlvlty produced by wav,'r~fr.ction at the earth's

surface. W, consider a horizontal electric ~leld at the

earth' s surface in the x di rection. Thul

.. 1( z A e

. 15 a two-di.ensional soluti'otl of .quation -(2.2.7)

J

CA is an arbitrary constant.)

beco.e.

In tvo di~nsions, equ.~ion (2.2.1)

. ,',,,.

",;< .,

'.'

..

.. ... {

~~j , .;;

v",

J/:\' , ,l, .-, '-'. ~ ~~ ,

"

~'

;~

't'~ .. ~-.,:. .. l" ... .,..~

r:,};-'- -- --

f' f Ir !,. 1...,

" ~ "

'j '.

l ,

, "

"

ext'''t. tN"blett (1161) J . , ...

l' '-

. ~ '.caUie very few ,lolo.leal fo~.tloD' are ~.11

, approxl.at,.d by Ihap tba' Ind th .... l... to el lcal . . anl1yt le tr t .. "t ..... rieal Mtlrocl. have b.e. ,ainln, .

pTo.lnence ln .a,ft.tot.11arie ~d.lll.,. Th. obJect

of th ctlo~ la to add ne. nu.erlcal tetbRlque \

ta tho alr.ady'in U". and by ... n. of Illu.tree!., Iaples to ahoi its u

It will, be IS'UM" h.r. that 'ollly two-di".lioul

structure thlt la to '.Y. h In, Inflnlt. l..th la .. the strlke (or V, dlr.ctlon .r. to b. cl 1t vith. It

. will furtheT b. Issuaed that th. electro.al tlc .ourees

ln quest'ion are such '1 to r"ult Ira l1a,al'ly polarlaed plane w.av noral1ly lncld."t at th atth. surf.ce.

Thts. a uaptlo", have b .... wle1.t, u ct ln pr.vioUi wort

and. whll. they .r. op'" to eritlel in certai" "'~pect ,

they nev'l'thele PP'lr to furnl.h u ful .od.la for

ft_rous probl.... Purth.nore. ,th'y .r. IlOt- funda .... tal . to the .. thod ,.d.,erib.d, but clo ,p."'lt .irect co.,.rl.on

vJ tb rl1er " ... rlcai t.chaiq .... Ilace ,reel l, the

u.ptlon. ha be.a ua br th .orteT' ref.r~ to below.

-~~ . , , ~~q

i '-

,\'" ~. ,

,1

, , '" . {~

1

r,'

~ ! 1

.' .. ~ ",.,.. "". "' .. ,

1

o

2 ,Tb 1alte BI .... ' Me,t04

.The fir.t att .,t at a " ... rical a,proach to thl, Arobl wa ... de by Nev (1.57). who u d flnlte-

. ' dltf.rfn~. approxt .. tlon to equation (Z.2.1), Unfortun-

ately. a. Swift (19S1) ha. ~lftt.d oUll thls tr.at.ent of

,boundary ,condition. wa. Il,correct. Iy ployift. 8 tran.-

'.isslon line .. a1011 to th. el.ctro.arnetlc pro.l Swift

succeed.d in fo~lattn. the bo~dary cond~tlon. correctly.

and in .. a1uatin. th. eff.et of a two-dl .. nlional 'discon-

tinul ty.

ln cODAectlon with th are oth.r .nu.erlcal t.ch-

niques. certain analyt!c solutions ar. ot .ajor interest .1

For" the ca of a w.v. polariled wlth p.ral-

leI to the ttrit d'Erc.ville and lunetz (1962) solved

the proble. of '" outeroppln, (au} t (actually a vertical

contact) ov.rlyln, (a) an Infinitely re.l.tive and (b) an 1nilni Utly concJuc.tiv ",b.tl"atua. Wht le thelr .olutlon - appear, to be correct, the ,oblt.hecl paper ~.ontain 0 .. . typoaraphlcal er1'or. ln the fo ... l ; th 81". detalled ln

\

Ap~ftdix 1. Rankin (1162) .01 cI the c of-ln o"'tcrop-

pill, dyle over (a) a.~ lafla1t.ly .... l.tiv. Ulci (h) an lnfla--

ltely (oftductl~e substrat... Hl olution .pp r. to b ~.

tt.ntlall, correct, thou,h tb.r .... to b. aOli typo".,'-

ical el"rol'" 1ft th. publl.h .. for.ul... Furth.~r ...... /O~ , r

th,_ ,raph ,,. ... te. ta. Hl tb.1' play.leall, r l1'abl." "'t

'l' .. ,. VI,,", . ....... ~ 1".".:"'';, ,

, , .

, ./

'.

", .' ,

! \

.J

. yo',

: l

,: .. 1 ~ r ..

n~

" ~\~"

_.- ~.,... --_.. \

"

, l,- ~

~ 1

~. j,I,;~ ~, . , ~

'i*'~ ~, '. ~# ~\t:~ "

'y,"""'" ~"W;, ,u:, ~,.. '1. J "~' .

1>'

."", .. ~~ "~

. " l '

~ "

24 ~

g

Here the f k .~e as yet/to be deterain~d coefficients.

To find thelr .alues. equatioD (2.'4.2) will be aultip11ed p

by each aeaber function in tum. and inte,rated over the

entire problea reliou. Thus we obtain the N equations

i 1.2, ... ,N (2.4.3)

. The first integtal in equation (2.4.3) aay be converted

" using Green's tbeorea, into a sy .. etric for., so that (2.4.3)

AlI boundary intearals tbat .ay be expected fra. Green's

theore. vanish identically, since it il assuaed throughout

that aIl functions satisfy the required bou~ary conditions.

, Equation (2.4.4) Y be viewed'as constituting

one line taken fro. the aatrix equation

. (5 + jT) F 0 (2.4.S)

wbere S is a square a.trix whose typial ele'ent i5 aiven by

an6 T is square trix -ltb eleaents \

, '

, . ~'-'. < ,t)! ~"

[

1) , '

" . ..tll:_

" "

F represents eol~ vector lublualnl aIl the co.fflci~tl

f k

l? ( Next. it will be assu.ed that aIl bounderles

within the'proble~to be solved y be well approxi.ated bye straight-line s nt., i.e., that aIl fini te sectlons of

the rroble. re,ion fora aeneral polYlons. In th1. cllse" ,

the entire reaion can alwaYI be subdivided into-a set of

triangles. ,Fro. th. co.putationa! point of view, it 15

convenient to choole the approxi.atina funetions sa th~t (a) they form a co.pl~te fa.ily of polynoala1s o~so.e

degree n on .ach tri.nale. nd (b) 'each funetion assua.s non-,

~ro value on only one trian,le. A suitable chorce i5 , il,

the set of Sewton-Cotel intrpolat\on polyno.ials within

.cach .ri~nglc (~il~ester(1970)] ; for the.e it i5 possible

to calculate th~ correlpondin, Sand T aatrices in a form

which retains its validity for trlanal.~ of Any shape (Sil-

o vester (l969a) 1. It i. usual to ter ach trianaular

subrg,ion a fini te ele!!nt J The application of fini te

ele.ents to probleas Qf .1ect~oaala.tlc. ha. 10 far been

confineJ to real or Heraitian .elf-adjoint operators, for

which the pl"oje-ction ae'thod us~d in. equa5iOft. (2.4.1) to

(2.4.7) above reducel to the aaylel,h-Ritz aethod. Such

operators are encountered, fot_exaaple. in wav.Juide prob-

.~ .' , "

.'

(

i ,",

t 1

\.

,-

leas lCsendes and Silvester (1970)J or, in non-linear

fo~. in electtic .achine ... ly.is (Chari and Silvester

(1970) 1. The coaplex d~ffusion operator of equation

(2.2.8), however, 15' not Heraitian. 50 that the above

procedure 15 in effeet equivalent to the classical Gale~-

kin lIethod. The re.artable point, indeed, 15 that the

26

eleaentary Sand T .. triees vhich result, are identically

the sa.e in either case. For this res50n, their detailed

derivation will not be dealt vith here ; the reader is

referrep to the appropriste literature. [Silvester {1969a)j

The Application of the 80undary Conditions at the Surface

operator equation (2.2.8) and its trix representation

(2.4.5) are both hoaogeneous equations. vith boundary con-

ditions iaplicitly included in the choiee of the trial fun-}

ction set. ln order tO'perait easy co-,utationl solu-,. , tIon, it is necessary to teeast (2.4.5) in such a fora as

to exhibit the boundary constraints explicitly.

ln the develop~nt Above, the trial funtions

have b~en selected to be interpolation fURetions. That

is to say, there exists vithin the problea relion a set of \ , .. , 1

,interpolatio~ points Pi such that each function 1s exactly

zc.ro at .11 pp1nts Pl" except ODe; there".l.(P.) ;: 1. " t 1

Thus" t,he coefficients fi 1ft, ei\uations (2.4.1) to (2.4.7)k' '.- ' are physiclly identifiable as th~~al values of ~ at A

set of points. This fact perait. eas, ifttroductio~ of

;i

,.

\

~.'" , ,

"-

;' .

,-.,; .. --." -r- .. '

;r; ~"' ~.,~ \" .

21

. the bound.ry conditions .1 the .arth's surf.ce. For the

proble. dealt vith here, the Yalue.of H la tat.n as,fixed

" ' at the surf.ce i in the .. trix r.presentation (2.4.S), the correspondin, Itat ... nt i5 tbat aIl ft correspondina to

surface interpolation points aust have exactly the aiven

value Qf surface H.

Suppose the interpolation points. and correspo-

ndingly the 'trial functiQns. a.e nuabered in luch a sequ-. Q

en ce as to hVe ail points below the surface counted first.

and ail surface poi~ts subsequently. Suppoae thero are o

M below-surface points and N-N surface points. The .. tri-,

ces of equ.tion (2.4.5) .. y tb.n be vritten in the parti-

t ioned fora

t j :: 0

(2.4.8)

y

in which Fl is the M-ve~tor cont.inin, aIl UDconstrained

fi' and F2 is the (N-Ml-vetol" whose co~nentl are fixed ~

at the prescribed values of H alonl the surfa~e. Matrices t

S and T, of course, are partitioned 50 as to be confo~le

with th!s partitioninl of F.

EliainatiA, FZ' thre obtatns

_ ...... .". JotIt,. i

28

( 5 ... j T ) F 1 1 1 1 1

t- j T ) F 1 J, 1

(2.4.9)

that 15 to say. the aiven b9undary values o~ the potenti.l -

{unetion H are translated into an eqivalent source den-

sity funetion by the aatrix - (S ~ j T ). 11 11

It is quite

convenient to arranae co.putationai details of tbe thod

50 as to construct the right-hand sida of equatlon (2.4.9) J'v

directIy, without any need to wTi~e down the full Sand T

matrices of equation (2.4.5). For tion of' the .atri~es th l~... and their storase in ~he coaputet, are arran-' . ,ed in a .anner very si.ilar to th4t described for the homo-

geneous waveguide ~roble. [Silvester (1969b)J, to which

the interested readei is ref.rred.

Recovery of the Surface Solution ;

Solution of equation

(2.4.9') produc.es the coefficient vector FI' froll which the

fieJd distribution i5 e85ily reconstTucted. However, this , ,

15 not a solution of auch i .. ediate practical value, sinee

only surface measureaents ar~ normally useful for geophys-

ieal purposes. In the'S-polarized case under conslder-

ation here, the transvers~ surface electric fi~ld Ex i~

found by deterainina the surface curr.nt density J x Croa

equation (l.2.J) IS

(2.4.10)

and subsequen,ly calculatina the cOfrespondi~1 el.etric

field coaponent frQa Oh.'s lav (2.2.3) as , ,

~ J"'J ... ,

. ,~

..

"""1f"~~-:J t. --~-"-"""'~i _o. "'~';"'-".I!If!'!~ "J ~ t\, ,-:.. . 1 ~. '. L , n

, '":.,b

~ ~ ~

~

21 .

B li! Ifl. x (l'IF (2.4.11)

It _l,ht be observed in thi. connection th.~ althQuah field

a.asureaents refer to the electric field value, the surface \ ,

, current density has certain repr.sentational advantages.

Because the Maxwell equations requi re continui,ty oE curfent

dens i ty across ail interfaces and other a.terial disc,on-, .

tinuitieS . the nuaeric.l value; ot, J,x are usually of the ..-

saae order of magnitude throUlhout the proble. rel10n, while

values o~ Ex y vary widely. depending on ~he local con-

ductivity. Exaaination of. the curvel publ1.bed by Ilankin ~ \', f \

[1162) or dtEr.~eville and kunetz (1962) shows the consequent

di{ficulty= it is alaost iapossibl&,to ehoose graphieal

scales 50 as not to obscure the local behaviour in hiah-

con~uctivity relions, while retainl~1 neilhbourina reltOfts

.of lov ~onductivity.

Sinee the solutions for H obtained fro. the fiRite

element method are invariably polynoalals. the differenti-

.tion indlcated in equation (2.4.10) ts car~i.d,out without , difficulty, resultin. in a polyno.ial ~xpresslon for J;. ln faet. for ~rianaular finit. ete.ents it 15 pqsslble

to perfora aIl such diEterentlatioRs on tbe f .. i1r of inter-, ~

. ) pol.tion polyno.ials in luch a fora a. to have the results . . essentially independent of th. sb.pe of the tflanl1e. Heace

the differentlations, jUlt' llt. the for.ation of fini te

J-. . ,

p

'-~ ,. :~ "

'--"

~ .... ~l 1

.,' \t'I'"

. , . ;-\"

) 30 tl nt ttl~.s. c.n b. t,bul,t 1ft th. fora of .. trlc,s'

valid for aIl c only-i.quiri., aultipl1eat!on. to b. )

c.rri.d out in th. solution of any .,.eille probl

The .ath ... tleal d.tails of eOIl.tr'ktlftl th.

nec.ssary interpol.tion polyno.~.ll and fo~lftl th 1.-. ent.ty aattte.' S and.T have b .. n Itat in d.tail .lae

} , where. ,lSilv.st\r (lg69.) l T~. cliff.r.nti.tion tric . . however, , are new; their elev.lop nt 1. S~OWft ln App.n4lx A.

Co.parlson vith Infinit. S.rie. Solutt~ns.

The author has co.par.d tb. finit 1 nt thod i

vith'data co.put.d frQM tb. foraul pr ent.cl by d'Erc.-

ville and ~un.tl (1962)'and Rankln (1962). 'l,ure. 2.1.1 .

and 2.1.2 are curv showin, the ch.ok I.alost d'Erc.vill.

and Kunetl. The lolid Iln.s . r.pr ntina th. luflnit.

, s,eries solut ion. end wb.te the 10lst. t.,.. of the .eties , exceeds 10. 6 of th. su.. It will b n that the linlt_

.1.Ment .. thod produc'I r.asonable d.ta ln th. r'llon around

the fault, wh.r. the Infinite ri IOlut~on fal1' to con-

verae. The points plot~ed froa th. finit l . nt solution

areat the interpolation points; as .. ntio~.d above. th

valu.s ar. the CO~fflCi.ftt. of the polynoal.11 ."roxl.atlD,

Jx/Hy '

Fl.ur. 2.Z show. bo. tk. 4yk. profil. wa. div!'e.

'1 ~., .

'j .,

r 1 , "

" ~ 1 :~ .. ' .-t,'1

~. "_ il. { .

.'

. .

r , .. c't

, , .

Piaures 2.1.1 to 2.1.2

\

)

,

Finite ele nt aethod: \ Co~.rl.on of the finite eleae*t solution with th.t' of d'ETceville an41unetl(1962)

The SQlid I1ne re fTO. the fo~.ul.e of d'Erceville .nd lun.tz; the circled point. J are valu at the fini te el ... nt laterpol-ation points. '

The plots are of the ratio of relative ~urrent den.ity'to anetic fi.ld - both ln .aptitude and pha.e.

Odt 1. the skin depth in tbe .edfu. to the left

f the f.ult; h 1. ,tbe a.pth te tbe tUbstf.tua.

\

L

t ... " ...

r

"

, ,

(

..

. t-

l "

, "

" "

" '"'

. -,

P.

...

,..---- RELAT1VE

o 0,

,a -9 P. . '

"-RS80

J

' ... " ..

0.2 0.4 XI" 'p: , 2

ft ... L'.1

..

"

.

4,:'

, 1

," ' .. ~ ~1

,1 , ,

, ,

\

f: ~

4

"

" .

, 1. 1 \ . " ~,

'" . , ~ ~

1

. -- '

\

4'" -';o;; ~ {: ."r . " - .-

/

!!t.. -Ii hT

(,.

.. Pt

t'

f'

,'.

0

0 li. 9 P.

'0

.. ,e.

.2

A

ft,.. "'.1

, , ~.' ~ V 1: (.. .~! '

/1

. ' .

-0 ...

" .4 ./n

"

"

" " ,. ,

:. , ,

\ .

,f , ,J

")

\:,'/

f: (, , ' f'

~\ ~ p ~

_. 11",

1

, ' ) --~---r- '

1:

,\

\

l' .... /4""-

.,

Plaure 2 .~2 J

Fiftite el nt tbod:

C

. .. \,

..

die,' re. Ihow1ft,. ho" the dyke profile V85 div ded lnto trienaute, ele .. nts

'" ~

l, ' ... po .....

, \

1-_, , i ,( ; .. ~ 1

en .. .II ~ ~ ...

Il

1 " -. 0 0.. " -f' a "'4 - ca.. - '1 ~ I:~ ,~

: ~

li. ,:~ ~"

L'"

.... : , '

,:': '.

"

.0ll(""l' "

\ .. j --,. -

i"to trlftlle~* It 1. '004 practlte to liait the

dl .. ~sloft' of th l .... t. to kalf a akin d.pth. and .v,n

less in .r of int.r'lt and/or rapld fl.ld chan,e.

S6

The field va~.tlon re thown ln 'liures 2.3.1 and 2.3.2.

Experience indlcate. thlt Dirichlet boun4.ry conditiona .... can be .pplied 11.1 tben one skin ,dlpth blyond the .re.

of interest: thui. th. horizontal extent of the .ode1 ne.d

not .reatly exceed the rl,lon wh.r. the ano ly 1. located.

ln rect. the bouadary here wa. tt x 2500 .. ter., or 0.035 skln depth. beyond the la.t data p01At.

, r-

Ther. li .0" cU.ctepancy bebee .. the flni te ele~ftt and inrlnit rte olutioft . \ 50 .. r onl

app.ar to be:

(a) the trienll.' dld not 'e.eI out or clown tnc)'ulh .kin

depths rro. the contact; , (b) the Infinite serie. 0lcl11ated rather than conver,in.

properly: curye 1 of Fi,ure 2.3.2 .how. thl. errect.

(c) the quertic polyaoalal fit wa. ftot~o( hlah enou.h

order to repr ent the chaDle. ift the field acro.s the

trian,le raithfully; .. {dl the particular ca,. wa. one for whlch the inflnite

seri approxl.at1on Rot accur.te.

It l, r.a411y .pp.r t that ln nature v.rtical

fau! ts and clylt Idoa, 1 f -r, 0 .. rl1. inflai t.ly eoa-. ' duet' or taflalttly re.l.~l~ __ ,trata. Tb c

" ,_1. _ ~ _ ; .",L ~.

"1~' -,.,-,."'~-, " (t

1

~ -~

~. , ' , , ~~ ~

-0

" " 'f

k'

" tI

(

.' '.

"

'.

"1l~~ ~t~ ", i: y~' ~r~ .-,rr~ .J." 1 'i':'1I9III!!IIr.'IIIIm>': "i, ..,<

... , ,~' f

\

"

.. Pliures 2.3.1 to 2.3.2

-FI,nite 'el at .. th04: 1 "

tCo..,artlon of tll. fiaite .l.ent, lolutfon ' wl th aankln', '(1H2). . .

. . The ,olid lia., are f~o, ... kia" to~l.e; the elrel.ct poiatl are value, at the finit. el ,nt iattrpol.tioa pol.tl~

17

The plots ~1".' of tb. :ratio of c:ur .... nt el .... ity to ~ ft.tlc fteld both ln ..,11tude and, ph

" The p. ri oeil are:

, ,

1 .11 . t. Z 7. ..c. 3 7100, t. . ' /

, ,

. ,

. ! , ". ~

:-r :,'

~ . ' :

~

. i"'-\ ~' ,

r .. 1

! . ,

f" f' , ,(i,

~

..

Co

1

. -

, ,

- "1/'" , .---\~~T-'"

....

-" . '

0

.01 4-

1

.OOS

....

2 f1-~I~t2~3-J~==::::::::::~::::::~ .001

// '/. -'jOO

A-160Am ~ tOoo I~OO 2000

x (M!TERS)

r.t ......... 1

, \

'1 ~

-= &II SO '~

cr ~ ..... " .. '" '. c -LaI

."

12 2

,'X (METERS)

. . . .

'"

l-"

..

'., , , ,

(-

40

. have.b n used to pro .. the .. thad .. th ... tical1y and

phy.ically, but the data pre ntect in Fi,ure. 2.4 00 2.i ar. of ~r.ctleal Inter.st. ln both these .... pl the .. shape of the .~lpbld. Ion. &ftd th. avetburd.n thickne'l

wer. deterainect by Slank!. (1970) froa availabl. drill-

hol. lo,s, structur.l.con.ideration., .nd fro. aod.llin,

by trans.lssion-lln. an.I~IY. Pi,ur.s 2.4 and, 2.6 show

how the proflle wa. dlvided into trian,les. The substra-f)

\ ' tua used in the Iyta and fault case. ha. b,en .li.inat.d.

The trian,le. axt.nd tO a d.ptb where the eff.cts of near-

surface inhoaoaeneitie. are ne,liaible. The ... netic

field Hy at that clepth Is .et to the value co.puted for a

horiJontal1y lay.reel earth haviR, tvo laterally infinite

Mdia i th!. is' re,areleel a. a pl'e.crlbed value.' and henee 15 inclueled in sub trix F2 of .qultion (2.4.8>.. ,In effect.

the host rock is .,su_ct to be of infinite dept,h ..

1 No atte.pt ha. be.ft .. de to i8prove the fit

-b.t en'.odel and observed curves by varylna le~etry.

Drill' 10&5 define the lones only in broad outline. , .

Thirci-order polyno.ial fi ts to the Hy field vere ..,ed for . \

al1 trian,ular el ... nts. This resulted in quadrati~

JI. polYl1oai 1 Interpolation to calcul. te th. v.lue It

.points p was done us inl .

l

~~.P '. t 'lft 11

.,'

( \

) \

.'

If.

.~;.

'.' "

, ,

r" '\j}- -'1:':, 1 ->;;-1('-' ~'('1.

. t,.

, Flau!'. Z .4

Fl'elcl C e '1: OS'ar how1"1 how th. ,profile . dlv'lded lnto tti.n.~l~r el ... nt .

The .ulph14. ton. 1 tippled.

( .... j

"

, ,

, '\1

.. ~

. ;

",~,;, , ; , . , ,r l ,fI, .. ,.!,

J

.. \

-

J

.... .. ----_ .... _----- ---.. "

\,.

'. ,1 ,

\ \

/ 1

,'~~--,-~~~~ ..

,;, T':"'" "~.""~" , ",

.i

,'-

.',

"

~~: ... r.

;.1(':" ~

'< ~,;K ,

~~',',e ~'" f , . . '

(

"e

. .

Figure 2.S

Field Case '1:.

\ '-; .'

, r

Coapari.on of finite .le nt results wi,th values observed in the field.

The' sulphlde zone ia stlppled.

Model values are 2Sfoot averales.

Frequeney 8 Hz.

.' /

1

. ,,.,.

(,

. ' ,

, r"'f."''"r ',1'"'' "-' il' r' rI' ''', ~ 'j

'j , ,

",

l1i ~~

)'1 '~

..

,J.

r ' .

)

) 44

MODEl VALUES 5 AVERAGED --x'xx x x X xxx x X xx ~~~ .. ~~~.. .

x

.;:~:: THEO/iETICAL /'~ODEL j;!l P SULPHIOES 20. nl'n !4If!

:l~~ P OVER$UROEN eoo am .til p HOST RQCK 2~OO Qm

{

,

"

r.""""l"'" ~~ .. \ , , ~. 1 1 ,. . .

,

b

plaure 2.6

6

Field CI'. 12: Diaar " showlna how th. profile was divided into triln,ul'ar . le nts.

The ,ulphide lone i, stippled.

..

l

'~

J .'~

'.

ft

~

" . , "

,'.s. .

(

8 &

,

..

.0

j'~F"=~""'lIii' ,-..~~., ,"F' v ''''i~;.: ~P',:~~~,~ ~ .. _~~~ '.' ... \ ~) ~ .... , h " -! ., ~"f.~'" ~

. -t

"

, '~ ~'"

,46 1

l~ \1

,~ . ,

. ,

" .

1 ,

"

"

Filure 2.7

Field ase 12: Co~.rilon of finite ele.ent results with values observed in the field . .. The sulphid."" zone is stippled.

'1

Model values are ~OO'oot avera.e .

Frequeney .. 8 Ht.

"' 1

, :W1i- _. L~ ~ r. ~ ~ l ","

t'iF"

47

~>t'

,l~~ ~ ~ . ,

" .1

"< ". '., '" 1

,.

(

)

'. ,/;."'",

~ .. l~:" ~~! l',/,t '.

'.~ .... ,,~"

\

MOD!L VALUES AVE~AGEO

Je x ' '\ --rl'lt

. 5+ooW ~ ~ ~ .' t l",' 1

~ 11: THO;TlCAL MOD~ ~ 200 P SUL:PHIOES ~ 1 01ft ' 0 e POVEABUROEN. lOOO Qin ' a p HOST ROCK. 2000 Atn'

,

SULPHIDES

PI ....... , l'

- .

. ..

, 1

\/-. ,

" '

-". , '

...,.":, ...........

where

4t 1

wheTe i 15 aodulo 3. Th. values frOli the .... 11 are .y.~

_.es 01 tlle inte.rpolat.d values oyer ZS- aacI lOO-foot " .

lengths ; this ut.s the. crudely coaparabl. vith Slaakis'

field .asure_nts which were tell oveT Juda .lect""'.

spreads. Much of t.he di ff.reDce- between .asurecl .. 4

theoretical curves ois ~h~ulht to be due to uacertainties

in profile geo .. try. Act.ually. the J x funct.ioD cpuld he

inte,rated over appropriat.e tntenals to yield a .ore pre-,

cise resul t.

1 t i s noteworthy that the fin'ite ele.at tech-

nique offers an ,valuation of the fiela at a coatiDuUll of

points ; thus field ..,.5ureMnts cu b. eO".1'IId with th.-

oretieal data wher er " uft_at, .,re .. ct.: .0 r.aard 'need be taken for the internai bounda .. ies of the "el ele-

aents. AIso the accuraey of the .olutioa fl.1el cu be '

check.d by

(a) runnina the c,.se vith two di ffereD~ orders of poly

no.lals (difiereoees wUI show re.ioDs --of lialteel ac.curacy).

and

(b) observina th. differeDces b.t .... field ".lues 'f ...

adjacent trtan.1es

.~~

.".Jo, "~,:tki.;~~:: ... -' .. i::...,-"".l~.&.w.~. , .. ::jil.~

(

,"

, , tf" " r .. ' J

. '

V'l"~.X .alue. fr;a ~"rl_ll !ch have only olle vertex

on the surf.e ~ peclally "11ab1 sbu:. th. d.erlv-.'

.tlve 1,1 evalueted .cros. the .lclcll. of the trlan,le " , ,

rlther th ... ,.10nl th. ..... Th. fit of the Hl' field 1$

better la th. '.idelle of tl"ianlle.

- - >--'---

r ."

,.

,',

50

"

\' , .

. ' ,

..

v' , "

. ,

CHAPTBR T H R B Il

F 1 B L D e~Q U 1 PME N'T

. 3.1 Introduction

, . ,This chaptel'"4eS''rlbes the equip.ent used durifil ., . .

1968. na.ely'the Mark 2 syste The M.rk lA and lB sys-, " .

tems are .e5cribe~ in Appendix C.

izer 'i5 delcl'lbed in Appendix D.

Th~ strip chart diait~

3. '2 The Ma l'If. 2. SIS te.

Figure l.1 i5 a block 41alr .. of the systeM.

- tu.,s ~f the syste. not .bown in the dilaTa are: -.

Fea

Medistor A-61RB .. plifter , relatively iMune to l1Ih~.nlnl , .'

differentlal lnput and output ,

Moseley 1100 ch~rt recorders

.. ink writina

. -60 db dynu't C ran,e 1

- Z .. fold chart

Do.in ion ObserY~.tory tel1uric pl i fiers

.. 26 db Iain ,

.. sina1e-ended input

ban4pal. ~.,llfi.rs ' .. flr.t-orI' active '"-

M r "\

\ '

\

fi&ure 3.1

.. , ,

- ..

Bloc~i.lr of gnetotelluric re~trding 5ySt , Matk 2. '

Power fro. Hydro-Quebec wa{ u5ed where avail.ble. ' .

. '

S2

"

..

\,

" l ,

~ , '1

J (

, fi ., \1 . l.' ;: () , 1

,~ , .. \ J,. \.

",.\~ Z;: ., \j '-'.i,l

V\ U W V\

Cl ,JI

." 1

-.II

an

i 0 ;/! ... CD

,,',

( ,

t . " " . ~ , . \.JI. )-

1 1 1 ...

". 1 .' 1 ('~I~ :)

l J \"

'''n :~ ,., 1"1 .r :.~ ;.Ali.

] et:

~f~ tooI~", g .... ~I .. ~

-",Jl

~J~ ~.12 ,-,,"n .... ~ l..t '" (.,~

'-" 'f" ~' ..

1

.. ,"--

. r

....

~: ex l ,-'

,f'- 1.11; ., n.":

~,-~

~!~t " L_' __ ------,--...

'li tt 4C ,1

Q ..1 j

'" "

~ , ' .. . ~ {l

2

~W'l "'- ' "'ct ~~ , f~~

't ~

\II

i~ 3X .... ..

---~~ ...

. .:

, \

~I

.-

1

low"pa fi 1 ter.

'.

.. S4

1 .. ,ob. lftput l.,.danc.

4 ca.ca.e. Re .tClion.

1 "Ioh. input l.,edanc.

r pon" oC aIl channel, ~ ....

3 db point. at 4 and S40 c~~

~ .ttentuation 01 6 db/octave at

10nl p.rlo.d.~. db/octave at short p.rlods

tran.l.torlled verslon of that

de.crlbed br S.r.on {19S1}

The .y. re.ponse t.'shown ln Pliure 3.2.*

3.1 Furth,r C~ .. ent. on Fi.ld Slst

,l,

ln des"lnina the ur ... nt .yat u d (or 'thl.

project. the pa.sband of the a.pl1ti.r a. cho n to be

the a. the (r.quency ran,. or inter t. It l~ now realll.d th.t thl. approach produt , an acceptable but not

~ptl.u. rec~rdtna sy.t.M.

. It i. 'lapo'rtant to U.it the dyniaic ranae v.r

whlch th. ch.rt recorders MU.t ,Ive r.adablt r.cord.. Th

equlp.utnt .t thne, "drlf.te""; r,'erence to Fi,ure 3.3. wllt.

d on~tratf that thl. pheno~non y'not have b.en d~lrtt ,

For SYlt Iccu .. acy checks. s 'i'". 6,1. . .

,,,,r~ _'01\. ~.!I, . " ":

, '

"

1

~,

! (~ ..

,

. .

l

, 1<

'" r

...

r--:-y. l ''Ti'"

)

Fr.qu,ny r.spon of the Mark 2 t~cordln. 8y.t

The ter. "Aver _ r .. o netic Field" h' dl!cua d ln the text

"

SI

"

, ' ,

'1, { '1);,

" \0,

,-, .... 14

~

RELATIVE' .GAIN (db) ..... . " 1 < ~ " t!P -~,

"

l "

" ~ , \ , "-l ~ , . , " , ,

/ J G) l:)", "h

i Pl'" \ '\ . , " 1 Ir 1(1) \, '. 1 \ " ~O

Ci). '\' \

~"" \ ~ ~~ \ - ~ "-0 0 n \ S ""'" :!!~ \ (1) ~ -", "'''' . < \ '" ,8 6~ \ z' ~ Ci) \ o ln _\ en ~

~8 \ \. \ , ~

\ \

~ r , " \-

1" ,~ ., , ,

L 1

"'1 ~I 1

6" 1 8,:, , .-1\)' '8 0. 0 RESPONSE TO AVERAGE

~ " GEOM~GNET'C FIELD (cfb)

.. ... 9S

Gwit1f'."Wyf,U'W H. ~ .. ~~_~~.1 ",~Ji!~'-~~~ ... j ~,-~~,~~~~:, ,r ':J

, . ,

-'1\ 1 .. ~-,

.. \

"

.If, 1

Comp.ri.on of fr.qu.ney te.pon : the rAt.ponse 01 the urina ,y.tea ("syste.'I) .~d the re.pon,. ta .n.aver'a. a.o ,netic fi.ld

Th, mea.utina ,yltea hll .eeond-crder Butter-worth hl,h-p.sa filterlna.

lhe "Re.pon.e to Averaa' Geo1lutan.tic Pi.let" i. what i. aetua11y recorded on pape .. chatts: i t il the "Aver e alo ,net! c Source Pi. ld-.5 (tltered by th. ct.Ylt."u.

c

- 1 \. , , ,.

(

..~:' . . "',

". ,'" ~\ " , '; ~

, .

,

SI

POWIR IN AViRAGI 110-......... --MAGNITIC lOUltel P1ILD

0.----... - __ ~"I'PON'I 10 AViltAGI

-40

t !-~o 1

-8

-100

~....... ___ ~O~1A(JNIT'C "II~D , ................ '\ 'IRIT' ................. --....

'" ORDIR ...."..

'" " , ,~ SVITIM . .

" RllPONS.

" \, MSPONS! TO AViRAGI--------t--. GlOMAGNITfe fJILD ~

PERIOD (NORMLIZED TO 1 08 POINT) ... \ l '

(

i ft ..... 1.1

,

, ,

t' Jlh:!.It~

~-~.

\ )

J

%4' i ; :,,'f4 4 ( ( - }4M Mh 4' ("i, OA '. , .

. 60

C lf-.A PTE R FOU R

FJELD 'WORI

4.1 ,Introduction

Magnetotelluric survey' vere conduc~ed duriRi

tbree successive yeats: 1966. 1961. and 1968. AlI data

which has been analysed was recorded dur!n, the two 1968

field trip~.

Appendix E.

Tbe first two field trips .re described in

4.1 1968 Field Work

In 1968 t~o field trips were de, using Do.in~

Ion Observatory, Tather than McCill. as a base. Recordings

werc .ade at thtee locations si.ultaneously: 'at a fild

statiob, at Blackburn, Ontario (near Ott.wa), and at Mont .. St. Hi la ~ re .

r'

At each field station, ,netic north-south (II),

.agnetle east-west (~). ,and vertical (~) anetie compon-

ents and hori~ontal ortho,onal telluric co.ponents'were

\recorded.,usin, the Mark 2 sy,stea. The olectrodes were . , separated by 300 to. 700 ~ters. The telluric lines we~e

surveyed usina a Wilde Tl transit equipp&d vith a tubular

co.pass, distances being co .,uted by the st.,lia.,_ethod.

The be.rin,s of the lines, were al1 vithin 20 .inutes of

,

'. ,l. \'r" , .

r"~-, ' . ~.

~f "

, l' .,

, l

,

J

.".

61

the dealr.d dlr.tlon. ,t th. vertical anal . of th. lin

tlhl not .x\:,ee,d thr de,r and wer. ulull1y l'fU than one . deKre~. ,~noul~ .'.ctrod wlr. drtvln lnto the Mround to .

u valut' of ~hree 110h wa. typlcal. Th. ,,1.,trod vore

mAintn!n the lni' 1.~trod. r l.tance beiow 10 kjloh \

th~rmal1~ lalae durlna the .~.er by burlal ln th~ around ; durln~ the winter .now cov.r dld the job.

!,:h{'ll'k h~ror leavinfOttawl. and 'fter r.turnlna . stne' .

WHV~~ havinM rerlod. betw n J ~d 1000 conds were used "'\

th~ lnl"Ument w 0.2 of d.c.~e. / ln th. Cleld, checktl

w~re made at thr ~r.qu.ncl'8. vi" 0.003,0.03, and 0.3

Ill, berort~ IUld ,fter record!na at .ach Itat,lon. For

t~11uric channel., the o,elilator output va. applled to

th., input of the te11urt, 1..,11 fler . ' Por .alnetiel, the

tluXlftte wa~ dl~conne~ted, and the sl.nal fd to th. input

of th~ band-raiS fllter.

r~(orded on Atrip charts.

Both input. and 4Utputs ver~'

The fluxl.te b ds were call-

hrated usin" a ttelllholtz .y.t to obtaln a constant field

rrom the.e mea.ur ents. and Croa data provlded by Domtnion

Ob~ervatory ',taff, Il sensltlvlty of 102 1 ..... per volt w'" .. taken for the ftuxaates. Th. direction. of field lnr.a.e

were checked, and rked on the cbatt Drl ft and nohe

rerfor.ance of .11 chann.l. w.re found to b. ,ati.f.ctory

,.in chanaed le than " ov.r the (l,Id Oft.

-, ,

,- ""f'lII "1 '~~

.(~

"

,t, ,-,

',~ , -;1 ,

, l,

~.

. Th. Illekbuta ,n.tici chanatl. wer. ,lven ,

full fr.queney cal.brat!oft. b.for. ,nd aft'T th. trip., , but no thr ~tr.qu.ft~y ch.ck.. Th v.r. d d r.dun-

dant in that th y.t w in ln lir-conditloft.d roo

Th.' lOC&tl01\~ of ~h t.tion Ind th. dat of recordln Ir. lhotm b,low:

Fi.ld Station Dit '1968

2 Trenhol. 4 Jan -, 17 'JIn Lennoxvl11. 19 Jan 30 Jin

. Wlckha 0J16"JUft Golden alY . 17 Jun S Jul

JC1n".y 8 Jul 17 Jui Vlctorlavllle 20 J\ll -. 31 Jul

J

St. Bd.ond, 1 Au. 10 Aua 1

Wat,rloo 11 AUJ - 19 Au,

The locations of the Itltions Ire shown ta Ftlur. ~.1.

"

j

( ,

\ .

6%

,

. ,

.~

.~:" '< ,

~-...

/

1 If

..

"

~"ljt ~"~,,,, "'N .. ~.. ;; .' ,

(

'l,UT. 4.1 1968 '1.14 Sea,on: Nap .howin. th. locations of .tatlons

Th. fteld station n .... ar. encl0 d in reet.n,l... Th. n~.r. Ire h1ahway tout. d.silnatlons .

".

63

, ~

J

.j , "

"

r

,.li

, .

65

\ C Il APT E'R ,. F 1 V B

A~ALYSIS AND

1 NTERPRETATION

5.1 Jland Calcul.tions on Ma'getotelluric D.~a , ) ..

As ch~ck on the prop.r oper.tion of the field

equip..,~t. and to aaln an id,e. of ,nO'tot,ollur.ic proper-

th~s. rouah calculations were .ad&-' durina th'e field season. , .... /

Each day a ,e~rch was conducted for slnuloidal waveforms in , ,. the records. Correlation bet en telluric and anetie

co.ponents was atte.pted, and where possible apparent re5~

istiviti~s were calculated. Selected results-.appear as "

Fi~ur~s S.1.1 and S.I.2.

This techni~e 15 extre.elY rou,h, and 15 5~bject

to error. It 15 diffi~lt to distinauish betwe~n dis

turbance which i5 whole cycle ion,. and one which il one-

hal' cycle in len,th. See fi,ur S.l.l. The ratlo of

E,to Il 15 correct in either case. ClearlY. however .. the

period could be wron, by a ractor 01 two. ThUit the cor-\

rect position of the point .ay be Il 101 2 docade. avay fro.

whore lt is plotted, alon, a line .t .S deatees to the abs-

cit'!'I. This 15 lllu.tr',ted ln Pieure S.2.1 .

ACter the,fleld on. arapbs of ~he r.tlo

! -,

"

l'

, .

i'

\

.'. . ,

Pliures S.1.1 to S.1.2 \

Maanetotetturlcl: band calcul.tions ,

'II'

J \....

Onry tho point. are plott~d for which the .a,neties sinulold .~ceeded two a.mma~/ peak-to-peak in a.plitude. /

The . bbrevi.tto~s for'.tatlon-~ame5 arc:

66

.'

Lf.N ,for Lenno~vl11. , KIN for kinasey

S~'e pase.s xi il ~n-d xiv tr the other a~bt"cviation~.

. , , \

,

: '

....

.. , " .. '

~

'.

( -

.., ,

III' ' _

-o Cl.. 2

10

'. .. ,

..

-.

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~

67

HANO AN~LYSIS 'LEN E Ev/tH p,AIR

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~:r'1~' ~'' ,'-" 1 ,r'

6.

,

HA~:D ANALYSIS

KIN ) o - Er~9 PAIR

o o

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r,

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Fi. ure S. 2 l,

Uan'd an.lysls': 0 IHa,r shows ho., pO'$lble ~rrorJ occur ln plcklna ,iriusolds f~r. h.nd:analyll~

, ...

.' ..

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HALF CYCLE

. .

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& ; ti' 44 ". ',' '",''' 1 i , ,

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Fllure 6). 2. Z

-",n4 analy.is: The re.u1t, wh.n plottin,. of an error in plc~in& tbe plitud.' and pertod of ~ slnusoid

"

"

'.fil

" , , ,

. J)\_ ..

, .

"

" "i~:.'"'74lf~., , , .' "

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71 , " ;

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LINOTH VT Lo02 -CORRECT POSITION ~

--.. ,,-.. "'PLOTTID POIITION

Jo .. 1 " " "C~""ICT PO,.'TION!'

P ERIOO' (LOO SCAl.E l

-,

. ~ Fllure S.Z.Jf

. .~

71

\

"

J'

.. ' f. - -

~ ~'t,. 't' . '1'-

... '"

'. b" D

,-'

.;." ,

het'l'.eh the' v.rticil .I,netB! flohl a. MOM,lured It fiold

~tRtlon. _nd It 8lackburn, pntarlo w.,o plotted. ualna

tult,,1 rh:ked .'lnulalda a. data. The .rror. Lnh.rent h~r . wcr~ dot~ll.d ln th. lait paraa!Mph. ft " .. pl(\" .. :urvt1

i' ft J1 pC' ft r" Il'' 1:' il" r. 5.:\.

t cJ t' .. " 1 t ah 1.. w 1 V. (0 r

FlKUrl' 5.4 ahow. th. moan rAtlt)! of tho v,'rth-"l

f\(\I\I,,_ wher .. they have h~on arrunaod ovrr porto,", hUlhl

Whll'4t tht' 11noll (rrolll Waterloo to Vh:turlllvt 110 and

1 rom St. I!,llnond to l.ennoxvlllo) .H" l1l'tthl'r IItrutKht flor l'xlHtly urll'ntl'd .aaneth. north-south ,.nd C:HlIt-W,"t, tllv

'''Ion ur thl' "t.tion. lnto Inlch tlnc1t l . \.'onvonhnt. 1 t

wlll ho nntl'd that the ttel.two~t Ilna", LC'. W"torloo

Vidorllvlllr, run. ,approlfll.atel'y plrl110t to th," "t'rlk4.' - . Th.'.oat _trlldn; ('Mturl' nf th" ~ .. urv.,,,

71

,~ -thfl wlIy thet t,ho lonl-jlorlQ4 n.tlo? url' cnhunoHI lat Tron~

ho 1 m. Thl" wpuld 'Ullollt tHe rro .. onc~ of "n lnhomo"ono-

Ity at tl~pth tander thh .tatlon. 1 r on" llluumc~ that th .. -

upp~r Iny~r r~11,tlvi~ie!l .r~ much the Aime at "Il ,tatlupK

Il hlll IH',umpt ton .. Id_lttedly - und thllt tha .ktn Jdpth .", . ~"ch ~~ tu mako 1 400.econd p,rlod oqutvalent to n dopth

f ~O "" or l'u, thon .uch enh.nrom.ent would lupport Fitz-

lHatrie"'1 Utell . that thore . .1. In uptiEr lH the IIun-tle. , .

Pl,ur. 5.5 .h~wJ co.pari.on of phalo rol.tion~

shlp!I of the vOl'tt4;al co.poncmt oC the ".notic r'cld at

'.

, .

~:, ...

14

"and .n.1y'!Il: . k.Uu 0' th ."lltud,. of th. Vttrt h'''' \oaponent ot' th ... a,nl'th: field VArl.tlun~ h.hf."n Wh,.,h , QuCtb.c.. and fUackbur'l. Onral'lo v~" l'~ r t (;,1

, 't('C' P"Il"" JeUl and, ~lv ftH "t'rtnitlu'1II pt thl' ~y.bo 1" .

. \

, ..

...

:

g' m ", \

" -1

, ;

.,.

,,' \i a, ...

N' ~ Ir .... 111 0 ~ '. 9 'Q u ! .= - c z

. 0 -. ,

..

,.

1

c

--II ~o ou, ,-

c

l

, - 8

- 2

- -

1 '-

15

,'J

..

. , , .

/ .. '\

, ~--',- -,..

t"-.. \

Ft JI li rt' S. 4

"and IIn.ly"lf': AiAr Ilraph of the ratio of th" rlltudt'1t n( th" v.rth:-al lo.ponent of U,' ..... 'n.' h' n.ld variation. betw n fi."t .. tat (tn" Mnd 'Uackburn

Th~ ratio. are aver_a.cS ov.r fl.r1pd tt.nthi.

Th. top IrO'l1' ar.' ror .t.t lOnl alona th. m"an,~.lc northlouth Hn the, both>. ttour

/

th "t-wnt ,Ilne. Not. th".lml'.r ty,. " itncl th. enh.nc.d lonl-rer1o-.! ratlo fit Tr.nholtlt,

Tht' ,.hhrev'lttonl for 8tatlon na",,,,. IIr(*: S'fU f (). r St. Il d lIOn d )fIC for Wlc;:khl'" l'Rl! for. Tr.nhol .. (;01. for Gold.n '.y '1 I.l!N (or t.ennoJlvlll. WAT for WAterloo UN (or ltnttA'y VIC (or Vlctor1.~IJl~

, -

':. ,/

77 ...

! . J

t C r-

... W

- -" c

...

r . .. -.id! =:=. c si .. . -tif' - t

:11 --0'" ... .... C

. ~.~ ':::1 ... '.1.: . , ~N E ta , ... c.~ u , ..

0 >

0 ." 9 ft O' "! ~ .. . iii . .. - - - -'. '1 O.&.."Z Ot, ... MY" t

If' . .. '

\ \

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fi'

, .

1

"

,

.... ~) . 1. , , -

--

Pl.urt S. S

r

"a.4 iAa~)'.lt: -. -Ph c:o..,.rl.on. bet en the v ... tlcal cOllPon'J\~ of the upetlc fleld varlation. at flt1d . Ut~Oft. Incl af. Blackburn

, f-'

:

"

.,

.

f

1'*":"":' , , ;

, 'l ,

l -

.., i'\ ... , ,i ...

0

- /' ..,

~ W et -

i ' 0

t

0 -"" * 'w ...

~

/ - '

( ,

(JI

(,) .... S u w' z

- ; -, ... W > ~ ...J 1

8. W"\t' -Ct ; , ... 1

l't,........ ~

l'

'i

$" : ,11 ' 'w:. } .. r ........ ~-- ---, "

, ..

.,

and "out of phal'e" are u.ed loolely, ilnce the analysh . /

15 very rough. The hour .ark. on the charts wete used for

synch ron i tat' i on. Where the phase shift 15 in the Tapge

~ 45 deg ree!li ____ the te r. JI in phase u il used" "Ou t P f phase"

.ean, 180 t 4S degrees. Where the phase lies outside

these ll.its, no point was ~ltted, It will be noted that

at period~ gre.ter than 1000 seconds, (and in aost C85e5.

from considerably ,horter perlods), the co.ponent~ are in

ph8~e, Thi5 i5 hot ,\arprislngJ at long periods, field

distur~nce5 have larae borilontal waveJengths.

Blackburn to the Most distant flel,d station i, approxt ... t,ely

one-eight~ of .'w8velength. and ~uch a wavelength of 3000

k~ i, not unreasonable at 5uch periods.

At periods ,horter than 30 seconds. coaparison of

pha~e5 hec~mes difficult, ln thi, ranae, a period .. ea5ufes

less thsn 0.5 Clft on the,chart; it Is difficult to decide . , ,~hich peak5 ~n a pair of traces cprreJpon~r Phase co~arisons

at periods up to 100 second, were lenerally not atte.pted.

In Figure 5.S, the stations are arranled in pairs,

cho5en on the basis of 51_tlarity of their phase reversais, , ft.,

Thole pairs showina the least reversais appear at the top.

It is noteworthy that there f5 correlation between .tations

of 1 ike (a) orienta~l'tl to the strike of the ano.ary, and

(b) distane 'f.ro. the centre of the ano.aly . ... --

\ )

, .11" \_,""i:"""q-'""""::"'I.--~-----~. ~- ~ ~ ~- - ~ -- ,

\

)

'" The perlod ranle of principal interest (because J

rt

of the aifferences between Itationl) 15 100 to 1000 sec-

ond!. Figure 5.6 1. a bar Iraph of thi. ranle. ln plot-

tina. a reRion of in~pha.e and out-~r-pha5e va~ con~idered , '

to extend rrOM half-vay betveen poInts of different pha~e

sense to half-vay between the next pair. For exallple. at

St. Edaond. the in-~h.le segMent h up to ,113 seconds. th h

point beinR half-vay between the in-phase potnt at 109

second!', and the out~.Ph e point at 116 'econd .

It 15 reasonable to think that there Is 8 phase

reversaI between St. Ed.ond and Victoriaville because they

are onlJifferent sides of Logan's Lin~'J

~

More Interpretat ion of. this ar.ph vi l}' be pas-

Il

5ible when .ore 15 knovn about phase reversal5 fro. a theor '\ etital viewpoint. Perhaps the next ~a5k i5 to nor~.lize

'. the results to a hypotbetical constant-pha,e ba5e 5tat)on.

Thi~ ~ay be possible by statistical averaaina of the eight

Rlots. and by re.oval of th!s aver'le.

.f

-.J S.2 COMEuter AnalYlis of Ma,netotellurie Da~a

for -eaeh station. one .a.ple of each record

wa , dia 1 t il e d . A Do.lnlon Observatory

(Wiekens and Kollar (1967) wal .odl(led to peTait sa*p1ing

every O. S ... At the usual record!n, speed of 0.5 \nehel

pel" .inute. thi ay dil.lttziftl tnt.rval of 2.36

, , '-~r ~ :...dl ........... """'- ........... ~_""fo ... ,._

~'.

..

..

. , 1\

.. '

"l, '''~\'.

" ~

\'

Uand .naly.l.:

Ph.s~ coaparilon. bet en the vertical cOMponent. of the 'a,netic field virlatlons at the field s~atlon nd at Blackburn.

Note the Iroupina with - t,. and dl,! tance fro ~entred It Trenhol .

detai 15 .

.. " .

, 1 respect to orleritaUod--the arlvlty Ino ly See th. text (or

" " ~ .. 1.. ".

l"

'~

, ' f' r~~s;\~ . " .' .

~ ,

~

as ) \ 1

( ; -i 1 Il = ... ~'E .: t-a e w " Co) Ir

~ i ; Il ; i lJ 4 ... C ... ~ - If,. , .... 5 d 1 ~

, r , ... t .. t f Ge .. * + , 1 + + + t lAI \. t + + ~ + + t

'8 'z wQ. + + " CI) C&I. 1 * .. + %0 * + Q.a .' + i ~ .. t -* * " 8 *. 0 0 + 1 * i 0 + 0 0 .. 0 * c.-+ .! 0 0 ... .. + 1 0 .. + + -+ 0 +

! i 1 0 + + 8 1; * + + 0 i III * 0 . + .. i + .. .f\ 0 + 0 *

.. , 1 .. 1 + + + * " + + * .. + + + *

+ + ~ + + + + :i

" , ;' ~" 1

Q j F E g III ~., - i' -i 1 .:.1 te SI! Ir ft ....... Il t-li > .: , , '\ '. '.

"" ~~ .. . ,. ,,..

.-....: ~'L . i''- -b..,. ( . IbiJ-,-~", ~\ ~_.:i'f ' _ l:t,

,'l ... 1..l. J,-

, .

"

; --

,~. 1

11 seconds in rea1 tl.e. The aple records wer. chosen for

!1.ultancou5 larle on-scale deflecQ;ons on ail ciaht co.-

~oncnt tracc!, ~nd aIl elaht wcrc dilitized. 1800 point-,

val~es were reQorded on punch cards fro. each trace. Care

wa! taken to ensure allanaent in tiMe a.ang the traces,

Tho ~a.p}es vere. 1 hour 10.8 seconds in lenath. and thelr

~tartlng tl~s we(e:

Station Ti .. (UT) Date ~1 Trenholm 1700 12 Jan

., l.enno,xvllie 03S4 JO J~n

Wickham ClS22 10 Jun

Golden Bay 2252 25 Jun n

Kinlsey 2126 10 Jul .., '", f " 1

Victoriaville 0300 26 .luI

St. Edaond 1048 6 Aug

Waterloo 04:\0 16 Aug

A progra. wa, written to util1ze the Control Data

3100 coaputer and Calco.p S63 pIotter in check!na the dig-

itizing. When the coaputer-produced point plot! were ov-'\. ~aid on the origlnal traces, points in error could be

noticed. The dia1tizer failed to ptm'ch point-value, Cro.

ti .. to ti ... added extra onel, and aultiply-punched col-

uans. A praara. wal wrltten.~.Cilitate corr~ction of

these errors. Dependin, on the holes aultlply-punched,

.uItipunchlnl .ilht or .laht not be detected by thls tech-, ,

.. ,

.. ,

"

r '"'F.:"ryl'.' H

4.

, , ,

w , ;:;.. ..."., ...,.." '" , -~ --- ~- 7 1

Xt xt .}" 0.8 xt

and th. rocolourln, the for~

1

",

J'h cre x t 1" the t - th po t n t 1 n the , (\ r 1 e14. wh 15 t hl' h th fr~quenlY. and 6t 1. the I pltna Interval. Thr rllw

~pe~tral oJtlmate. were .moothed by h.MMlni. ';

Cro!'.-covarl.ncel, ~rol!l-spertra. cohcrcl\(c. and

tran~rer (unctlon. were coaputed hetwcrn /Ill ~lmultanoou~

Iy rc,ord~d pairs of .erle .

. 1-

The' thlrd Job .tep co.puted apparent re,lttlvlty.

ratio of the vertical coaponenta of the maanctiL fleld he

tween the field Itatlon. and Blackhurn, and (-ratio. 1

r Il t i 0, ~ de fin ed bye 1 n e r et a l ( l 969) 11 the r Il t 1 0 0 f

thr vertlcal co.ponent of the .. ,net1c field to the square .,

root o"f.,the "u. of the Iqulre. of the horilontll (-omponenU.

The!. nuahe-rs were plotted on an HAt 3500 nat.plotter.

The prolra. included a routine to el1alnate point' wherc

the data wa~ ~~low the noil. lev.1 of the record in, and dia"

The reslt. appelr a. F1lur.s S~7.1 to 5.7.16.

Only 1 few of thc.e curve. have been drawn with

reference.to cohet.ne they are Pllur., S.8.1 to S.I.l .

rt will be I n that ln the ce , cho.en It rendo., the

LJ6J'

..

.'

~._!I!I;""'IIJ!74-----""'" .""" _ .. *_,""'4_"';;_---..............,,........--.,~ .. , ~--, - , . 'c '. ,;, -'1' 1 .-

6

Pliure. 5.7.1 to S.7.16

, <

,

'" ( ~,

'v

MI.netotel1urlc.: dl.l~ll co.put!r Inaly!ts As de.tribed in th. text. power spectral analysi. w~ used t vith detrendln. and pre-whitenln. (with a flctor of 0.8). The atihrevtations are:

TR8 for Trenhol.

"

__ ..J

WIC for Wickha" LaN for Lennoxvl11e GOL for Golden .ay k 1 N (or Ki n,ley VIC for Victorilvl11e STe for St. Bd.ond WAT for Waterloo

\ PREW 0.8 Mean. that the serie. wer, prewhlten.d.

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Pl.ures 5.8.1 to 5.8.3

Malnetotelluricl: di,ltal co.puter analy.is

A selection of plots for whicll the coher.nce hal been includ6d. The code' 1.:

Nuaeral Coherence raille 0 .0 - 1 1 1 - 2 2 2 ~ 3 3 .3 .. .4 4 .4 - S S 5 - .6 6 .6 .. 7 1 1 .8 8 .8 ,9 9 .9 ,- 1.0

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