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Potential Drop Ratios in the Case of a Stratified Medium

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P O flW IA L DROP RATIOS I S THE CASK OP A STRATIFIED MEDIUM
toy John Baird
ProQuest Number: 10795910
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uest
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P.O. Box 1346
Ann Arbor, Ml 4 8 1 0 6 - 1346
n'tteotia antalttoa to Wm F&onltf m& tke lo&ri
0# ffm stoot :# f the Ooiorat© ao&toi o f Mi&oa In p artial.
of %hj& ro<pirom@nta foirtlio itf f to pottos’;#"
InginaeriBg*
Solfien, Colorado
May m , 1940'
o.
the author wishes to aelmowle&ge hi# JU^ehfSteess
to Dr* 0* A. la lls n t nnies* whose
ttf&l direction th is
w rit t i l lone* to #i#o wishes to express his. &ppraei&tl$n
te Mr* 1* B* Iswhins*. s fellow gmtomtm statent* for aau^r
helpfml suggeefcieas*
$AB3$ o f m m m *
Oenontl 0%maMorsfci©HS
I
&ppar&hii0
NM» XS
Expanding Electrode System immmmim*m*>imm** Ifil.
l# lis rto m titl/f»n& work
in fe r Oase *iMjfc!fi#§iMi******§i^^
to
3#
$&*$* in fe r' On## .*1* * ^ ^
44
■3^'^!3i'
m a m a im sw am ktxm
Hit# w r k ■was m t o r taken with ■'tit©' in te n t of
e$0©ititng "and eo rrectln g the published lite ra tu re
■tosting- with' the p o te n tia l drop r a tio method of sieo~t r l e a t ‘preepeetlng*- the problem h asb een lim ited' to a
of th e r mm$&m p o te n tia l ra tio d istriboblon in a
■Ofr a tif ie d meOiom*
■ ih ''|n ^ip ettin i''fer o il the fe a r major geophysical
methods? magnetic* g ra n ite tio n a l, eleo trica l* 'and seiamie
'h ate teen -e^erimented'' with"'©&ftosiwif'' a t ‘one tim e or
©tother* 'fh e 'to s t':tw o f ^ th e ;;^ o te named methods o ffe r the
"p o eeih ilitf'ef- 'eo n tro lliiii:'^ # -d ep th o f -penetration to© t o
■t t o . feet; t h a t th e ': field s' th a t ■a r e ' measured.a re a r t i f i c i a l l y
ereatedt""Beeanee'ef' 'th is ' control o f the depth o f penetra­
tion* :tb r to p c h r'fe v''f l ^
imperianc
h o rito n e 'iiif t o studied, a 'p o s s ih llitr. wiiioh' Ie te ry limit*ed:'-ln the s p p lie a tlo n o f the magnetic an t g ra v ita tio n a l
■methete* ■fh© above refereneea' to the ■© leeirieal methods ’
to not inelnd© the s e lf-p o te n tia l method, a method which ;,:
is not applieabl#' to th e ' sta&y of the p ro b lem & isen ssed '
' Bi*irti_liftk~jriTL-' -'
nere*.
■ "■"In' the application of th e ' e le c tr ic a l methods'
■elttor 'Ofie'Of' tw otypes of'energy may fee studied? namely#
■the-'potential' d i s t r i t o t i t o '- w the electro^magnefIc fie ld '
iistrlb m tto n 'to©" to ■th© grtont' currents#' "Hiero: -are sev eral
fa c to rs t t l t o ' h are'"limited "'the a p p l ie s tim o f 'the ©lee* '
t r i c a l methods In o il prospecting*. Hie ch ief fa c to r i s the
"in- 'tto e le c tric a l' methods as in most other geo*'
■ g b t» l^ l'''^ th o te f:' te e formation©' etodleit m et" have a teielc*
■
te ^ ir
-p i -d etectt m* fte'Seismt-e t o f loot ion" method i© an exception
to ' th is ■m ie stoee the" r e f tooting- eharsehO rlstles o f a: "
"tetm ttost""ifir’la rg e ly todepeodejif' of" i t e thiolmees"* "
"■- '"Of mit"'tlie"foeiiOie'^oi©ati?ioai-^thoto-:te#wn at:; •
■'teto time^'^the^'mrfaee p o te n tia l methois o ffe r, i t seems, "
the g re a te st p o s s ib ility in prospecting for oil* te e
r e # ie tlv ity f'--f o t m t l a l ‘" 'irop"''i^tio>'mi- ''Otfeer' a llie d methods ■
'fa il" to te ir'iro a p * t o advantage of ■these'm ihods o te r other
eieotrtcal"m ethoi;S"lies in te e f a c t t t e t 't e # ' to p th o f "pen©*'
t r a t le n may ■%r'"'itortosod"l^:" ^ieortosteg te#'' frechency* I f
mmy one Of' tee" tednetive; meteodswer© oaed and the froto*
•-ereywer© rednoes#'""the:onrront' ©brengte^toinoed -in te e "•
■subsurface bodies would he greatly reduced, t e n t teereas- ■
to g te e d l f f i m l i f o f ' th ie r detection* ;
-'te'ito t^ aso ' te"tee-"'depth of'-'psnetratloii'm st*
'■neeessariiy ''te 'a o o o ^ ^ ie t'O y : mn' tocfias© t o te e /p re c is io n
■■of' te e
m aso f m»ntm"I f "formtieu©' o f t e o thick*
n ets "Of tee ©©"found' to' nature are to he detected a t any
"'tet"'teo shallew etedeptes*
• - - to'''has-'heen''''potetet'':'ont"to a rtiO le s dealing with
- the surface' p o te n tia l methods, the sheilding' o f e le o tr le & l"
“ f ie ld s b y e lth e r conductors or in su lato rs near' te e surface,,
■"teton" greatly' iia its " ftee"''poss'ihilitl#S' 'of "other o io o tr io a l';
methods i s completely In effectiv e in th is method*
ta itb e rg ^ to an artielepublish© & in I f i f das* erihea a tore# electrode •arrangement in which two of to#
tore#
electrodes ere se t a t a fixed distance
ap art and- the th ir d electrode is'mowed u n til a toleaee Is.
ehtmlnei* the r a tio of the electrode distances i s then
formed* Any itoomogsaeliy in the ground w ill be re fle c te d
In a change in the r a tio as c o h e re # -to the r a tio fo r
heim&geitoua ground*, th is appears' 'to be toe i orerm*mer ©# ■,
the p o te n tia l drop r a tio me'toed*
A* ®v Btge^* as e a rly as -!#$$■ need the potential-:
•drop r a tio method in tte d e s ia in -an. attempt to- secure an
electrode arrangement which would give curves m m e a sily ■in terp retab le than those given by toe tenner^fislr*Ioon^f
four electrode arrangement and other sim ilar electrode
arrangements*
p o te n tia l drop r a tio method requires m
oeaneebtou to toe primary -source o f power and a t to e same
time permits toe. aeasnrements of. email differences In.
apparent r e s ls tlv itl# e with' great precision* 'ioenigsberger^,
and tosohlag^ were, also instrum ental to toe e a rly develop*
meat of to la method *
to toe application o f toe p o te n tia l drop r a tio
method toe
requirements are comparatively'
modest.* toe- 'necessary tostm m ents are re la tiv e ly atmpi#*-'
'the power supply need: not- be large and i t m w ell as toe'
other necessary apparatus i s readily portable- an t e a sily
s e t up ant operated *
* i l l . numbers re fe r t© references, a t toe end of toe paper*
wmnm
th e p o te n tia l drop r a ti# method i s one of several
possible method# o f investigating, to© surface p o ten tial#
p reto isd 'by ** primary f ie ld In -order i# d etect anygemeity e ith e r horizontal or v e rtic a l, in to e area to
,
which toe metood i s -applied*
la th is method toe too power ©Xeebrodes are
spaded a t a larg e 41stomee In oomparlsen with toe lengthe f toe- trav erse t o t o rum* fhto-to- dene 00 th a t -toe f ie ld
around i t o to e etro d e .near, which toe Tiaeasmrements are to ' to
mad# -1#' eesemt ia lly O lrctilar In a homogenous medium.
the a iatrlh titio ii of toe p o te n tia l f ie ld Is- tom ato
igated by-means of am arrangement of three secondary else* ■
trodes placed on. a radiusfrom . toe' power ©le s t rod© near;to ieh toe measurement:# a re t o to made., fh© -potential
differences between toe eenter electrode ami toe electrode
m e ith e r side are- measured ami m ratio ' of. toe- p o te n tia l
difference between to# -two more- distant- o r leading ©lee*
iredes and toe two nearer or lagging eleeirod©# i s formed* :
'toy 'Itoom o^nelty to toe .area i s detected by a e&togo .of' :
to la ratio- from th a t given with toe same arrangement in
homogenous ground*
Wm apparatus used to measure to# p o te n tia l
drop r a tio is discussed t o the. sect toft e n title d apparatus *
-there are several possible ©Xeetro&e arrangements which,
w ill also be discussed to a separate teoitom # f th is
paper*
§
'%&&
4 me&m# ## $*$$$* tmm
m Wm
fm nM tlm #f He m&imm pmmMrnX. m&ie$8#
M i | t t mm mm :mmm■ty f * W*
&#
$« t*
4H§ &» f t HfcttfiKI# §:*’ f * t®g§^#. f *
$*%«$$ i&g f *
$*
I*.# f *
i e I 0# eni I#,
,411
mmMfcwtMmm mm,f: #f mamm§
tmaei m Wm'mmm$%%m. #f 6Ip&m»%mwmto
w f :l i
®%mm mm #f t » mW>®$t** th# mWm$, mt
Wrnmt w t aH tiir i* pru^aiif tte
if
W
the #a» $4$#
«M # « r ie feftitawpeA to a ftgMM* iU M £*©& tb*
ptffcmti&l ^tmmw
m &®m %f $*• Btafan#aai»#
't$ P '-tte %m .3*96* # # « Wb&' f t l i w i t i i inw a^a
gitea H# ?&$&* ## ita
a t a #4a t« ta # £*£» Ha
psroi*
,
go
. m
V = — ( — +2-l?‘ ------------zn<r \ r
%r, \/r*-t-(zmhP )
)
vftmm It i s a constant whose vain© |# g lt m by tho follow*
lag ©onatian*
<7; + ? l
Ib the afeowi equations, h Is the tttteteese of the top
layer* <77 is the conductivity of the top layer, 02 Is the
oogtastlrity of the eaeonfi layer* 0~ Is the apparsat ooa*
ttatetlvity, soft X is the current introdueed at the power
.:#!tetro d es *.
I n making the p o te n tia l -drop r a tio calculations ,.
from- this- formula th e f o ie iitia i is
a t the
.three .points -at -which bh# secondary e l H t r e is ii.a r e ,located#tb s d ifferen ce a# potentials. Between H a bm leading ami. . t
H a H a lagging e le c tro d e s, i# totem and Ifet r a tio la
fe.rmsd*
-.Figure 1 l i i graph o f .b b e-p etH tisI drop ratio -■
p l a t t e d ;against H a -distance -from the power electrode
divided by the thickness of the tap -layer* these curves '
teve mat* H s W i bmm:e®rmaba$ f a r the normal peten*
t i a l drop* Figure f shew©-.a graph of the same w f t s '- v
f a r d iffe re n t conductivity r a t lea which hrnm hem reduced
..far the martaal pebsmtliil .drop * th is reduction .is aeeomp*
-liisfeed i f m ultiplying H e values obtained by-a fa c to r
'.MjLSL*- # H e re r i s the distance of .He- cen ter secondary
r
-#- 0'
•
electrode frem H e power;, electrode- near ■which H e measure*
monte.- are-being/taken, and. e i s H e electrode spaaing, of
the secondary electrodes* t h i s reduction fa c to r holds, only
fo r the case in which the aeeomdary electrode spacing i s
held cornstamb* i f a curve Is taken over a normal home*.
genous in fin ite medium and i t i s reduced by H i t factor#
H e p o te n tia l drop r a tio w ill be sepal to unitv fo r sxnf
distance- from the-power electrode- *
4 comparison of fig u res I and 2 shows the defl*
mite advantage obtained in. spreading out the curves %
I
s
i
ii
9
reducing toe p o te n tia l drops fo r the normal ground p o te n ti­
a l drop*
A study of the carves to w n to figure too reveals
esvsfssl to to to s tls g facts# A ll to® curves for total* it i s
g re a te r than sero and to ss then plus m s 11# above to©
u n ity r a tio line* A ll of to# curves fo r to ieh 9 to Mm
t e n eero «afl g reater to ss minus one f o il below to® u n ity
line* to© p o te n tia l drop r a tio f o r to c a } p m i eoisolaes
with toe u n ity lino# I t to m m from toss® to rso s te a t to®
masinwn shift© fre e a point o f to# ana one-half times to®
depth fo r too ««®o toea k i s
to pins one to a point
o f about to rso tia s s too depth of to® top- toyor shea & i s
equal to minus one# A glancs a t to e fo rsa la shoos to o t toe
p o te n tia l drop r a tio curves become asy sp tetie to a u n ity
rati© Jin© «e too Alston©* fto® to# poesr electrode i©
iner&ased.
f t e t e has bsen considerable confusion rsg sraiag
toe in te rp re ta tio n # f toe too la y e r e u rv e s,.Possibly to la
o rig in ated fro® to® following statetsent by tendberg m&
Zuehlag^'® t
* to s distance to to# posh (of to©- p o te n tia l drop
r a tio two la y e r curve) la a function of to e thielmees o f
to® top lay er and m y he use# to determine tit® depth to
toe bottom layer# to® numerical. value, however* of to#
r a ti o ’thiehnese o f to# top lay er over toe filatanea to'
too rati© peak* 1# not a constant h a t varies with d if­
fe re n t r e s is ti v iti e s o f toe top two layers# la figures $
an i 6 i t has been assmmei as 0*66* & m in e th a t represents
a f a i r p ra c tic a l average* Creator acemracf may he Obtained
by basing the in te rp re ta tio n s mpen the- th e o re tic a l r a tio
emrves* which m f he competes fa r different, two lay er eon*
iitieas**1'
the figmres § ani # referred to in the above
fie ta tlo n are essentiallir.'im plicates eMcept that, one M Imvertei* In several other Instances i t has been assmmei
th a t the cnrves fo r the condition o f a gooa oon&moter
m nierlylag a poor eoniuetor is merely the same as the
mmm for- the ten ilb iea. of a gooi eontecter oirep lying
a poor eon&metor, fo r the . same ratio* except th a t i t Is.
inirerbei *
th re e ’lay er Case
fhe feraaiae fo r-th e ealem latier of the p o te n tia l
in the three layer ease become censM ereblf more compli*
esbel* I f * as i n th is ease# I t Is i@st.rei to calcu late the
p o te n tia l a t a point on. a 'r a i l s ! lin e eirtenitng from th e ''
power electron©» ani i f th is point i s on the surface of the
‘gremmi* Bnmmells formulas fo r the three layer ease reinee
to th e following f crania i-
/* . X
(-L - + z y f
f*
h 0-/?)/(jr7C ' '
z/r<r * r
^ ( K f V M 2- ir*;-i-(zhxt 2m h f
+
'
( i- k ^ k lT o - K 1) * ^ - » > * ]
/ A* +(2fh, + 2mh)3'
/
Z*'3' V- ( 6 h* + z m h p
■where tfe# ■'vsim# ■o f ' hg Is given by the following tw m im t'
A
=
0 1 + qj
i s the conductivity of the th ird layer* h 'Is th# thieie*
ness of the second layer;* 'and the other terms have the same
meaning as in the two layer
I f la the
mm *
above th ree layer formula the- value of
kg is s e t efu al ' to. sere*, that, is* I f the conductivity of
the seoomt layer is egnai' to th a t ,of the third, layer*.;then"
a l l ,ef the term s'under the summation sign except the' f i r s t
reduce to sere, and the remaining portion o f the formula is'";'
the .formula for. the two; lay er case*
from the above "formula i t can be seen th a t the'"
calcu latio n s fo r the throe-'layer case are long and ■arduous
u n le s s .;on# has available a d if fe re n tia l -analyser such as
used by W# f* Wetsei and B* ?.*.. Melurry3^.- .glue# no such;
machine is available her#
a
^few representative curves, were
calculated using an adding type calcu latin g machine*
-gin most cases the calculations were carried out
s u ffic ie n tly f a r to give an assured three fig u re
m $& m f
In.. the p o te n tia l ra tio # formed* I t is In terestin g t# '#b*;
serve in th is connection th a t i t i s ■only necessary -to'
carry -the s e rie s a n tfte ie n tlf far' so th a t the maximum dif*
fcreme# between 'the seme terms In the p o te n tia l se rie s a t
two successive f o is ts lo less than fiv e In the fourth
s ig n ific a n t figure in the. p o te n tia l iifferemc##*'.It- may
seen from the calculatiohs.;:included In- th is paper th a t as
tisiesiee
-pmm: eieetreie l w&mmm the mm*--
lo r # f t # f » nec#gssry to- «lm fstti H it mrnmmnw increases
Xmfemeeiiem
three Sat$«* mpcm It'lt-
t&te&eett&g to i# t# that i f the ooo&mtivitSM art t#
il& i tie graiattot i t in tu t ilr tc titi* i* #♦*
$*$** tail#!1* geiti*. tie ttvcd. will its mil m mm #ii#
i f tii* u l t f ratio Ilac* m& will, to $ » extent wmtWbl#
He two layer m u # If.* m the ether isessd* the troiu#b* ■
tvity i f the ■itcomd layer dots not fa ll between the
ctetoctivltitt of the other two l*yas»6* tie curve- w ill
im m tm p#al#* mm mbm® m& mm above the unity rmii# ’
it
foiw itoi drop m %it
-my to earrioi
m t to fitte r #t*t o f %m wo?#* tte t to* o-ltter Of w ist:-:
itr o o t roaiittg i^ tM n rn tt-' or I f -w teg to * f t w of te iig e
ofiw piito'* lo ti too* of direei roaiiag pototi&toI imito
imo&te te w it e Mm&mm&mg® t o t tfetf a * o it o r .Mm®*
tw to m t to n o t o r t o o t o f to w os* afp m o to tto tM m t iif
tw tr to $ m #it wtMMuqr t o t o i t t o it tetttu^rfore*
nrt pfw ttoai to w a a to o t rto to g to trw u ete to >totoai#
too te to tto t imp ratio* *to tetia# tfpo of
tea t o tew toa# t o t it it teih om? to optfsto tod
draw# o r m
to * i # to draw ro rr l l t t l # o&rropi a t te te tt# * . •
fa otter «r#a it# oow iiiottf i t Mgte M mMmg mmtm®
pa&mt t o l tM m rw M ta t o o i t o tto te io i to o rta* to o t t o
otootrto t toto w ill not te ootooiy opaot i f tte prommm,
of too atoooi&rf O&tetwtfto* to a ll of to# omperlMato
wmtt ion# to ooooaottoii w ito to t# paper m m t o r t of ’t e i i i # ;
mmm&Mum* mm nto#«
Ite r # a r t t o w i i f f o t w t t f p t t of to l f tp arrang#*
tooto 'toito te w tom w # i am#tor w t o o t o l f at ottt -ilno
o# l e t t e r to w iring p o te n tia l ins# r a tio '»atoT O *ott«''
9to$# » f to o ls t o f t o i m too teatotetaoo* o a f w itf * m t
t& totito type totigae* f te otoptoit of t o w to
m m iff# tetoa#*- Figaro s tow# t o otoirtoai- aiw n g o sm t ’'
of t o # typo of teiiao* toto .too of te to p to ooir w it*
to i# fo r d iro o t o m rm t' o r mwy tow- tmmsmay mttowtoWto®
ovtatoot *atoroi»iitt#v%tet to#- teawr#*oti- to o t o f t e w .
m
s h i f t Is n eg lig ib le *
M •figure 3, A# 8#. a r t € ax*# electrodes connect^
log the bridge to the gronrt*. M m
a irsriabi# resistance;* Mie «■
f t e r t re sisto r* 8* is
.art I is a tsuil
Indicator of' soma sorb*
.figure, $*: Healst&nee. Bridge fo r
P o ten tial Prop Katie Measurements*
Is th is esse the p o te n tial -trap r a tio is equal :
Mk - V c^ =
V&~ Yb
7 ? , '- * "
R
i
T
_
(ft+ 7 ? i)Z '
( R + R a ,) Z
$&#!»#■ V is the p o te n tia l a t .the point indicated % the
subscript# X a r t I* are the currents in' .the too arms o f ; ■'
the bridge# a r t i a r t t* are the re s ie ta rte s o f the ax*m
of the bridge as shorn* E | a r t 8^ are equal to H pine the
re s is ta n t# '# f .electrode 4# K * a r t 8* plus the rs s is ts s o #
of. electrode B,
4 t balance -the currents 1 art, ! 1 o re equal a r t
the aboire express Ion reduces to s
~
_ /? f ^
I t is. seen from -this formula -that .the electrode
re sista n c e a ffe c ts the. rain# of the- ratio* t h i s e ffe c t
b# md# neg lig ib le by making the resistan ce of the .arm# ■
stiffle ie ttily high so th a t the resistan ce of the electrodes
is small in comparison* I f th is is dene the- electrode
resistan c e terms become n egligible and the formula fo r th e
p o te n tia l drop r a tio becomes;
Vb -V c = R '
V„-V b
r
fh ls method ha# the advantage over the- method of
elim inating the electrode resistan c e suggested by Euseblsg
and described below*since only
-one s e t of readings Is
required while in the a lte rn a te method two se ts are neoee*
sary*
'the e ffe c t of electrode resistan c e m f be oompv
la te ly elim inated -in the following manner.* .If-8 i s bne:
fixed resistan ce and it1 is the resistan ce which i s varied
in order to obtain a balance* then i f the value of i is
changed to a new vain# H0 and then another balance is
obtained*, the v ariab le resistan c e w ill take on a new ■■
value 1^* the potential-drop .ratio- w ill then, be equal.-to/
both o f the following e fu atieo tf
Vb -V s = f y + R *
V//-V8
/?*->/?*.
VB~^c _ R '-tR j,
^ ~ K
b
R -t-K o .
By elimimating the el©strode resistan ce from the
above equations we- obtain an equation* given below* inf.--'
which the electrode- resistan ce is absent from the -p o te n tia l
16
oxpmmian.
Vb-Vc. - jR - R f
V/j ~
R ~~fte
jfcto mf to# umm
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this top# of hriif#5hat to# aifasitag# .tout to#"
mmmmptem&m* a# wnto$hm$$* w to aittf tlimtfIf if
hti#r
Ito in a to i ■to til# ' #&$# tm lts.
f to t o i r t g*$eto 1 if f # of hri% # Is to# totter*
t i f # ■hptig#* to' t o i l ■totogt fw to b l# toteito#### ar#
m od to aifto # with to# resistan c es to # ri# r I# haloo##'
to# tot #f .to### #tisp#ii#hi ato if 'iiiirtl totato to#W’?
n to to g if. 4 #t»pl#t# a sse rip tio n of t o i l h r tii# ia giiren
h r S* I tt ir a ^ * to a l l # f to# #xperi%#ftt&l work a fr#«p#n#r # f
to to tr #?#!## per second was ms#i to to# lah o rato rr an#
#f#i## p#r second to to# f ie ld ♦ 4 t itoto i&#
frnqmmtmu to# reactance of to# g p tw i ia r# ff lew ami#"
therefor#* to# to###- t o l f t o f to# p o te n tia l with r#.gp#it.
t# to# mmmmt to mmit% .la to# f to to wort to e re to#
ipaetoggi . a r t iafg# to la phase s h if t
't o
to t' large ene&gh
to he tr#tol###to to to ta to to g a halafit#* to to# tto h ^ p # r .i» a ti# h#w#?#r* to# phas# s h if t to- anffieienfclf
large a# that- to erier. to tohato mm rnmmmM te lto a e I t
ssaei h# eesipw taiei*
4 te rto # type e a p a c tif triig s- waa meed to wiMm§
-to# t&isk
to e ith e r ®m mm
to a l l ana## toe mintonm reeiahtoe*
10##000
.toms ana to# « to lw « capacity '
mm I M # r# firai* the fo liw to g oalom latioai show th a t to#
capacity term m y b# neglected when forcing to# p o te n tia l
drop Patio since to# capacity term only changes to# f i f t h
place- In to# ratio # dine# the variable resistance- w e t to
to# bridge m s 'a' tor## d ia l ieead# re sista n c e , neglecttog
to# capacity to well' within to#- lim it o f scouracy of •toe
bridge* "toe f i r s t d ia l of to# variable resistan c e decade
to d steps o f 10Q*CK}$ to$#» to# memi d ia l steps of 10,00#
tom * and to# la s t d ia l step# of 1,000 toms, 4 fourth dial,
to# added in an a t t e s t to increase to# accuracy of to#
m asu rem ats t o t certain ' other fa c to rs
In
to #
arrangemeiit
were- of th ird order- accuracy so th a t to# ad d itio n of a
fourth d ia l did not increase to# over a i l accuracy of toe
Measuremnts*
W&- to# followiug aitampl# to# p o te n tia l drop ra tio
Is calcu lated both considering ami neglecting toe eapse*
itlv#- reactance* In th is case to# resistan ce i s s e t . #<gual
to 100,000 to m in. both arm# 'of the bridge*- to# capacity
Is sot efu al H I microfarad* toes# conditions are as urn*
favorable as m f which occurred In to# experimental -work*
to#- p o te n tia l drop r a tio is given by to# formula t
Yb -V c =• K - z h c - /*<?, *<*=> —
n
)40,000
=
/ 0 0 , o a o - j S 'S C S
---------------- ---- ^ ---------/<£7<9, COG
r r / g?£?/ - f
m
-fegieettog toe e a p sc itlre reactance »
Yb ~ Yo _ _/?_ _ Jt0OO
V/?~~ Vb
^
from to# shot?#- oalew letieii I t la seen th a t to#
patio la actu ally ©«$ual to 1*0014 toil© i f toe capacitive
pea# tone# is- neglected to e approximate r a tio I s found to
t e e^uat to 1*00* Stooe to© lim it o f accuracy of the
%pldg# is to th© th ird sig n ific a n t figure*, th a t i s » to
toe aooffit' decimal piae# to the ratio# the eapso.it it©
roootmoo may he neglected to- o i l tsatc eseswsaasxits to lto
wore made*
Hi# phase correction does* however, a s s is t to
oeoortog a tolsue© since the component of current thru
the n u ll in d icato r duo to the unbalance to phase Is
eliminated.*
to toe. laboratory m ts o llla to p and power asp*
I l f to r m# used as $ source of power fo r the tank* e&peri*
-mania* to' toe f ie ld work a twenty* fiv e oyel© gasoline
driven generator was used as a sours# of primary power*.
to to# la b o rsto rf measurements an output meter
was use# to connection with a tore# stage am plifier as
a m 11 in d icatin g instrument* to to# fto'M work .a two
.stag# am plifier and m. sensitive- lig h t type gatoa?to»ter
was used as a n u ll indicator*
21
.mM&mm Mmmmmm
So f a r in a l l of the calculation# ana discussion
o f the experimental worh a constant electrode spacing has
been assumed* While th is type -of spaaing i s easy to us©,
i t has the disadvamiag© th a t as the iiahane© from the power
© Ifetroie i s inereasei. sssA the mmm®& p o te n tia l -curve
b e s e t s « i* i nearly, f la t* the p o te n tia l d if f e r eases which
Mist he measured to th e ferming of the p o te n tia l ;$r©p ra tio
besom© smaller* fhey no t only beeomeamaller hat they also
be-tom© more nearly ©qual* f h i t has the © fleet o f reducing
the'accuracy of the experimental and:fie ld measurements
fo r the q u a n titie s measured approach the s e n s itiv ity o f ■"
the instrument as a lim its
I f instead of maintaining the electrode spacing
eongtaith we Increase. the spacing of the sear eh prohef
as the distant© from the power ©I©©trod© i s inorea.soi*
the- ahov© mentioned disadvantage is somewhat reduced*
th is is te e m as the expahdlng eleetrode arrangement-* I f
Is 'customary to mate the r a tio of te e electrode s p a c i n g "
divided by the d istan ce from the power -eieebroi© to 'the"
center prohe a oonstant* Si# distance to e ith e r outside
;p roh# from the center probe Is then kept equal f o r a n y
§ 1 « location of the .tenter prohe h u t changes--' as fhe
location. o f the oontor prob# is ©hanged* ft*© .re#hi.t -isth a t as the m in e o f the p o te n tia l a t the probes is de­
creased* the distanc© between the probes i s increased abd*
m
tberefefe# the p o te n tia l M iimmm- decreases a t # .slower
rat© than In the ease of a constant electrode spacing
a r r a n s a m e n t# .
la the wwfa m dertaheo m th© oxpra&il&g electrode
arrangement in connection with th is paper, a rati© of the
e le o tro ie mmM$ to the distance to the center probe o f
on© to three was used sxotosireiy*
fhen Ic is ©faai t# aero, th a t is' when the ©on&ue■tiiritios of" the two top la sers are ©<p*al» the p o te n tia l
iro p r a tio assumes a constant Tain© as shown by the follow­
ing calculations* the' meaning of the terms is made c le a r ' '
b y . the sfeeteh which.shows the expanding electrode arrange**
m e a t*
ti—------ T- CL-
A
/
d
/
r,
VD.R. = ~ it --------1—
w here / / = anc{r3= ~^/
ct
fs
%
P.P.R.=
J-C
r*-. = -L ~ c
*
^
t f
,_ _ 3
P .D .R . = J_
*
L
£_ = _4_
*•
euryes fo r the expanding ©leetroa© arrange­
ment haw# been reduced so .that the curt© fo r homogenous
greuni has the same u n ity -ralu® as in the constant
• '€MI
electrode' spacing arrangement * £kis la dens so that, the
©apves given by .the two d iffe re n t methods may be more
©a#Uy compared*
IS the distance from the- tower electrode la
.
tnoreaaed when a eonatant electrode spacing la need the
y sllie-ef the potential, drop r a tio reaches a peat atfrom mm and one^half to two times the depth of the top
layer. la most M i9 « . .a fte r I t has passed i t f peah the
r a tio decreases rap id ly approaching a u n it? value m an
«t
asymptote* th i s ©an read ily be seen by m m thing the
constant electrode spacing ©mrvea included In th is paper#
3&. fee case o f - the ©spending ©lectroi©,'arrange^
meat# however* the mmimm rain© is reached a t a distance
considerably fa rth e r from the power electrode and a f te r
the peak has been passed the rain© o f the r a tio drops le ss
rap id ly than in the m m ■o f the constant spacing electrode
system# Becanse o f th is difference the e ffe c t of the
ta sk sides and o f the d is ta n t 'power electrode in the
experimental worh i s .greater in the expanding'system#:f b is necessitated sp ecial mm* in m%M$. the tank mmtmrn
meats as explained in th a t section- of th is paper*
fb t
.graph «£mmhi a grot# of mm*»
r e tic a l carves calculated fo r varioms values o f eo n tectiv ity
co n trast between the- two- layers using the expanding ©lee*
trod© system# I t i s in te re stin g to note how- very sim ilar'
the m m m given by the two d iffe re n t systems are in th e ir
general A a ra o to ris tic s * fh© gra|hs following th is group
o f 't e o r o t i o a l curves
fo r the constant and
e:spandiit|| electrode arrangements p lo tted on the ©am©
seal# fo r d ire c t comparison# Gurves for-, the ©©me .value
of' k are p lo tted on the- ©.©me sheet fo r 'the ■two d iffe re n t
-electrode systems*
A oet^srison o f the curve© fo r the two d iffe re n t
.tle o fro i# arrangement© ©hows th a t fee expanding electrode
arrangement field© curt#© which peak a t a g reater distance
fp#® the power electrode end th a t the magnitude # f the
-■
peak in the
p o te n tia l drop ra tio of the ©standing electrode-
epfOhi#®#hi
curve© i© also greater# th e
curve© calculated
■for the constant ©pacing electrode arrangement do# however*
■give a m m
d e fin ite peak* fhi© i t larg ely due to the fa c t
th a t th e ir value decrease© more rapidly a f te r the peak h a t
been' pasted*
i discussion of th e expanding electro d e tank
■curves .is given in the ■section On tank work#
a
comparison
o f the th e o re tic a l and tank curves i s also-:,given in th is ‘
©ection-i
25
26
aidant
27
lifttx iiifa i* w m wwm
■'In
m k Im
«m
Wmi
ma»
in
is m w #
«a * wMU M d *
i f tt n fs$ i$
**■'--i*.mrlPit^Hi'-i Y
i—
nfV -s,j|fe._*.•■*»«. nfclin■*A
v$&*$ .§
j)$£3^HSN
$•&
& 1$€..-MiN
Sllll- wB15vS£
JhPUm i&if' I k.-U
a.s-iA
-
&&0% X0ffc||
two « o t one**half fe e t wifis oy two te s t deep was used. She
electrodes
mm
mounted on a beam which eatanSeft lengtfa-
wise Sam the center a t the tank, fha three secondary
electrod es w t mounted In such a may that they could ba
moved together as a u n it» fhe d istan t power electrode n $
ts ttM . too centim eters from the end o f tls® tank* Sha othsr
power ©leebrofis was mounted near the ether end o f the tank '
a t * distance o f 38 cant ta sters ftp®# the and. fhe distance
from th is electrode to the out of' too tank ant. to eith er
a lto o f the tank was the samea a ll measurements were fflads
within, a distance o f 40 centim eters o f 'this electrod e,
between fcfeia and the other power electrod e, She two power
electrod es wore* placed 158 centim eters apart*
She ©leetneflos were an arranged that the depth .'
to which they were i&aerted in to the top layer could be
varied, Sfaie depth
m s kept
epprozimately e<|ual to M
m illim eters a t a ll tim es. I t i s e sse n tia l that a ll of the
electrod es with the exception o f th® d istan t power else-*
trade he kept near 'the surface of the'top layer In order
that the conditions o f the theory w ill be reasonably w ell
reproduced.
Measurements war® wade In order to determine
lahether tils#
o f the tank walla weal# hare W&. ,-:
.a p p e a la b le 'a ffa fI -mpm the p o te n tia l drop r a tio meaamre#
meats * In order to #o th is the tank was f il le # with water
a a i th e p o te n tia l drop rati© mrm mm measure#* fh© eeedm#*
ti v i t y of the water was then m rie # by the ad# i t ion of
salt*. Other .#ifte.s # t the p o te n tial to o t pat la were then
meaanre# fo r d iffe re n t © ondnetlrities* in a l l , f i r e enrres
were 'taken fo r d iffe re n t ■o o n in o tiritie e of the water .in
the tank* these f i r e ■enrres a i l Peeked w ell w ithin the
lim its of the experimental aoemraey., showing th a t th e a lia
walls of the tank were f a r enough away, m th a t -they #i#
not. appreciably d is to r t .the- fie!#. in the region. In which
the measnremerbs were made * th a t there' was some s lig h t
d is to rtio n o f the primary fie ld , is evident from-- the
following considerations *
4 curve of the p o te n tia l drop r a tio p lo tte d
against dlatanoe from the power electro # # .is shown in
the following graph together wi^h the th e o re tic a l ’curve
■f o r a homogenous medium* I t is seen th a t there -is a s lig h t
iiserepaney between th e two aarvao* th is is due to several
factors* the most important on# is th e presence o f "the
tank, side
m
U i # 4 minor fa c to r as shown by the graph.,. I s
.$*# .presenoe. o f 'th e d is ta n t electro##,.
la. making such tank, measurements the water in the
tan k shorn!# b# t t i r r e # an# the measurements taken a t :
soon as possible* I f th is Is not done the water In-the
tank w ill, la y e r #ne.t o ,iempetaiure* th a t i s , the'warm-
3
a
Eli
m
a
rtTWTHT
■sSdsstp:
water w ill r ise be the surface and mm be lt« talk er fcet^p- :
©yatwre lb s conauotivity w ill b© greater* I f the water 1b
net stirred a v ertica l anisotropic eoHaitton w ill e x ist and
the waaurem nts w ill m t r®prmmn% a uniform layer eond ib its*
In waiting the tank measurements coaeiderRble
a iffic u lty was eneouBterofi In attempts to repeat the
measurements a t the same paint* St Is believed that th is
is principally Sue to sweetie and changing electrode
resistan ces. Many curves were secured Which wore of no
woo Ana to the fact that th© leading and lagging secondary electrodes had d ifferen t resistan ces. th is condition
aay bo minimised by feeing careful in th® cleaning of the
electrod es, keeping th eir spacing exactly uniform, and
keeping th© depth to which they penetrate the surface
layer « is ©aw for a l l o f the secondary eisefero&es*
©specially the leading and lagging electrod es, As la
mentioned In th© Siacuaeion of the apparatus i t to poe-'
aiblo to elim inate th is factor eosp letely by obtaining
two balances with d ifferen t values of resistan ce, in the '
bridge arms* «hcn the conductivity of the solution is
increased, th© importance o f th is factor is reduced* th is
Is because of-th e foot that the electrode resistance
bsaow© lower .and* therefore, wore nearly n egligib le in
relation to the resistance o f the arms of th© bridge
which are in a ll cases in excess of 'Was hundred thousand
m
toe conductivities of the various layers were ■
measured by means of a four electrode Wenner*0ish*Heoaey
aiu^gemenb*- toe electrodes were plated s i a distance of
two centimeters apart and mm insula ted for their full
length with the exception of.their tips* toe- electrodes
were made in this, way so that it would he possible to.
push them thru the top layer tm order to measure the tin*
ductiwity of the second layer and. in the thro# layer- case
to push them late the third layer*'’
Using this, arrangement the resistivity of the
layer is given by the- -expression 4KVa/l* where f. is the
potential-differemoe between the two center electrodes:
In Veits* *&* is the electrode separation in centimeters,
I is the current flowing into the power electrode in
amperes* and the resistivity Is given in ohms per cubic
centimeter* this fermula applies -only In the case in
which the current' source is la the center of an infinite
medium* to order to emtosie h| and
it is -only neces**-asry.io 1mm the relative electrical resistivities of the
layers since these constants are ratios* toe power used
in the resistivity measurements was thirty cycle per see*
..end. alternating current* the current being measured by
means of a milliammeter and the potential, difference
being measured by means of a vacuum, tube voltmeter* 'toe
power was supplied by means of an oscillator and power-'
aapilfler as -in toe cate of toe other tanlc measurements*
toe resistivity of a few -samples was chested by
u s in g .a conductivity ceil# toe ■r e s u l t s .mmm& by .■th is ■
method Sheeted very closely with toe re s u lts obtained by
to# l#nher^§ith*l#oney arrangement* to ll# toe- method used
.|#..giib|##t:.to certain e rro rs , c h iefly to#- error,, in# to. to#
fa c t th a t to# layers are not in f in ite In v e rtic a l extent*
It. to. f e l t - to st. i t to s u ffic ie n tly accurate fo r toe. wm&t
-at hand* I r t o i s connection i t should,be pointed out th a t
toe curves are n e t v e ry .sen sitiv e to small changes in. to#
vmlne #£,&*
.
fta'iMsi mss
to to# two lay er case to# top layer' consisted of
a 'layer # f water toe conductivity o f which was varied by ; .
to# addition of .salt* .the second, lay er m s mad# up of a
medium fine, sand fo r toe condition of toe top lay er 'being-.;
a b e tte r conductor than to# second layer , to'- -to# case of .
'to# second layer being a .better eoafeobir it wm made ttp
of clay* in attempt' to- vary' -to# conductivity of to# sand
toon it was used at a second layer was made#, fbit was •
don© by to# addition of a solution Of s a l t water to
to# sand layer* fh ls proved to be- 'unsatisfactory# however,
because i t seemed impossible to secure a layer of uniform
eo& iactiV iif in th is manner *
the following .graph shows a group of experimental
too'layer tomb curves for constant electrode spacing and'"
various values of fc* Following tois graph are-a series of
graph# showing, a theoretical and experimental carves m
■ to# Mmm Sheet#, for; direct eompaPIsoa#. In a l l o t to#
'^grato# ■to# totontial-drop- ratio Is. plotted along on#.
axis and .x*.toe distant# to to# t#nt#r.a#ttoda^:#1#^.
trod#-.fro®'to# nearest’‘power electrode in terms of to#
depto* along, to# otoer* In; a ll css## x Is #em l to' r
:-Oivid#4 by -trtoer# r if'to # distant# to- to# center ole#*
tyoto and- h is to# depth of to© top layer* both -express- e l
■'.in -toe. same -mlts*.
to,torr#ttlng-toes# tank curves to toe.normal.
. ■POiential drop a# unify.*' to# experimental normal potential
- drop rati#- .curve-mm: maed, th is * therefore* approximately
'corrects, each,curve.'for toe effect of tot .distant p o w e r ■.
electrode and'to some, extent for to# proximitf '-of. toe tank
side- walls *
If i t is- desired the correction for toe tie tout '-,electrode may he -made In toe following m m accurate
. firmer* to#- potential due to to# distant power electrode
■'Is calculated'for to# points, at which a ll tor##-of'toe
secondarf electrodes -are located* to# potential die to
to# near power electrti# is Ikm tolsnlatod for any two" '
of toe three secondary, electrodes and by means of to#
'experlmentallf determined potential drop ratio toe p#*
teablal at toe third- point is then calculated* toe cor*
rested potential is toon formed by adding toe potentials '
due
- t o
to# too power -electrodes*, on# experimental* one
toeore-tlcal* with their proper signs* M toe theoretical
36
^
37
to© p o te n tia l i t la #a##ntial.| of
th a t ;to© '.©asa© number o f image#' btTm#©#*' th a t la* to# p#*-.toutiml s trie a rrnst bt/e& rried o a t-to to#'bo©# number Of: \.
..t##©#' f o r 'o i l points*
■it ©an be B#eo:'froa' to© abem diaeuaaloft' toeb
;tiit'>robl#©: of' otrreoiing, tb# 'ton* ©urte# to. to la
-mmm
Iw e lre # a laborous s e t of ealealations in /its e lf # fbe
©bjeobloa m f t o ”fal#©i' to u t toi# e e to e t of; o o rre e tto i
. tto
oiiroe#' is b»s©d';.#n to©or©bi#a! oaloaiatioB#
to il# to# re s t Of to© eurres ©re experimentally dot ermine
•to*' I t should W eag&ealtoi to o t to#' ©orroeiloa m et-b e ; v
.©toe- in e ith e r -to© p o te n tia l ito e lf or- la toe p o te n tia l
iiffe re n o e s and not' to toe- p o te n tia l drop ratio * In otoer ^
.word# e ith e r toe p o te n tial o r to© p o te n tia l different©#©
toe t# to© tve power ©leotrodes m$ be anperiffiposet to
obtain to# oorreot p o te n tia l a t a p o in t o r to# o erreet . .’■
potential'.diff© r© n#e:between too point#, t o t to# potential,
drop- r a tio # , ©an.neb :h# .snperiisi>os#et...to '.order to-.©©top© .
.to© oorreot rain# of toe- p o te n tia l.iro p r a tio a t ear g ltto
. looatlon of to# seooMary ©leotroi©#*
to# necessity #f mkkbng toe oorreetIon for.;to# ;
ii a ta n t power eleotrod© cotiXd be ©brlat#<t .#r a t .le a s t- '
niniwi#©i i f to# search eleotrodes were -pia##i along-'
t o t a r t o f a oirol© too©# ©enter
to#, lo ta ted-
a t to# d ista n t
power ©ieebmi# and i f to# d is ta n t power eleetro&e could be
h tp t at. a tlatan## o f about .to ir% -ti» # . to© iep to o f
•t o t layers. upon which the measurements m m being 'toi© *...
in to e experimental work undertaken In connection
w ith th is paper the dimemaione o f the' bank: were, such th a t
■toes# Id eal conditions could net he re a lis e d , w a r e s u lt
^all e f the curves which have- not been corrected mast be
eensldered somewhat approximate.
' '"fto above tis to s s lo h b f eo rreetio n s 'applies .
as,w ell l a to# ease of other electrode arrangements and
e t h e r !systems o f s tr a tif ic a tio n as to 'the two' layer case
using the constant spacing eleotroie' ai#amgeaeiit*.
to m f be seen from’toe. graphs* some o f the.
p o te n tial' drop ra tio ' cofires are o f f s e t e ith e r upward m :.-y
downward from toe corresponding th e o re tic a l ourre* fh is .■:;
Is probably1larg ely due to rm ria tlto s to "toe resistan ce
:
o f t h e ' leading and lagging of toe secondary electrodes*
;
I f toe leading electrode is s e t s lig h tly deeper than toe lagging electrode* I t s re s is ta n c e 'w ill be 1m m tod a t
a r e s u lt toe leading potential' difference w ill be g re a te r
than i t should h e to re la tio n to toe lagging potentialdiffepteo#.*'to'is w ill fiv e m p o te n tia l drop ratio- cuff#
which i s everywhere somewhat fa rth e r from to# normal
'curve than i t should to*
'.the fa c t to s t "toe t a i l s o f'to e experimental
m m m ■are lower than toe corresponding portion o f toe
th e o re tic a l curves is. t o some extent due to toe presence
e# to# side' w alls of toe tank* th a t "this e ffe c t i s ®m*
traneous -Ms b e e n 'd e fin ite ly established by reducing to to '
m
the thiei®mm<of;the..top/layer ;#*&
$■the electrode spacing:
la -the same retie* this mnmm' the tails-of. Ske'sxperie /
mental iitfw w to more nearly agree with the t a i l s of the
1$*eeP#tl#s.l curves*
’M tpli® the discrepancies wmkimM& the axperl*
mental eurirea cheek the th e o re tic a l curves very w elt In
'th e ir general character 1st la© * .
'fsspaailng lle e tro d e arrangement
feperlm eutal .turves were a lto meesurei fo r t h e ■.:-;
two lay er case with the expanding electrode mvmgmm* *
4 group o f these experimental curves p lo tted fo r d iffe re n t
values Of % i s shown i s the: following graph* the s e rie s .
o f graphs following th is one show experimental and the#**.
r e tlo a l curves- for d iffe re n t values''of k p lo tted on the
same, sheets so th a t they may he d ire c tly compared* In
a l l of the- experimental expanding electrode arrangement
eurres the value of the r a tio of the spaaing to- the ais*
tanee to the center electrode was made eoual- to one#
th ird #
la running .the experimental curves' fo r the ex**
pending electrode arrangement the thickness of the top
la y er had to ha reduced from te a to fiv e eenfimetera so
th a t the o f fe e t of the tank sid e w alls did not fompMtely:;
mask te e -effect due to s tra tiflo a tlo a * Before th is was
dime She e w e s secured displayed none -of -the c h e r a a tw "
I s ti e s of the- t h s w t i e a l 'curves* th is .greater .effect e#
th e tank.elie. walls i s in# to the .foil-owing three factors*
th e electrode ©pacing i s g reater in .the case of the
expending arrangement them in the ease of the eons t e a t
;>
e le c tro d e •spacing system when the. distance to the -center.,
.search electrode is g re a te r than three, times the depth # f
toe top layer*- Wxm toe center: electrode is out th is fa r
toe lead e le c tro d e .is fa rth e r fro® toe ,power- electrode
-than i t la m m ' toe center electrode of -toe •constant else*
trade, system, i s in. toe same.- relativ e-p ea i t ion* .t o t o e r
fa c to r: toito-.infInencas- to la 'Is the necessity of carrying
toe expanding curves fa rth e r from- the power electrode
than In the case o f toe constant spacing system*
41
i
m
IIB
ISSSaK
E
SiSj
\
-f-B± tr.
mm
■t+i
±t±
±n: itt
i±i:
I
::X
±
UTt'
iH!
"f"f"i—
f"
•ill:
HE±
:±
jffi
/
I f i s In te re stin g f# met# th a t i f t h e .eoniSnet*lirif ie a 's r e m arrange§ th a t the gra&atton in om taei* ;
tariff ■I# In-an# &£re«hie& as in meteors I *&&$
th e
<RW w ill sh sf a l l on ana s ite of the m i f f r a ti# lin e.'
M
w ill to some extent resemble the two la y e r ow#es* ■•■■
I f # hmmm&p the
f f l f f #f th e eeoeati Stayer &e@e ;
n # i;'f a ll between the e o n in o ti^ itie e ;ef the other two
■'la y e rs ' tte#' mx*m' w i l l ' haw two.-pesks* one' below an# one;
.abefe;the m i f f ' r a ti# ■line*': f ‘ ' the point a t whloh the hheoretleal ami e iip e i^ ;:'
isemfal eufrea peak agrees w ry well* th o n ^ there 'is some
ilsorepanof in the am plltnie o f the onrves .
m
mm
Work mm undertaken in the fie ld In an e ffo rt i#
apply;:the theoretical and bank work to f ie ld problems*
fhere are a number of conditions which a ris e In Ike f ie ld
work which a r e not present In the laboratory work where
lueoaststsiieloa may be- investigated and eliminated* flit
.r e s u lt of t h i s Is t b a t - n s e f t i 'f l t i a r e te lls if # much mere
•difficult le obtain* there. are,, however, a number' of ■
techniques' which m y be applied when making -field measure**
©enbs in order to lim it Hie a ffe c t of iaoonsisCanales and
lota! '
■variables*
Field measurements were undertaken in ©o*me.otlon
with th is work in m e f f o r t t# lo ta I t Hi#- water ta b le
elev atio n a t a point about Hire# miles e a st of 0©Msb*
the measurements wet# made near a well* Hit elevation of
the water ta b le being determined by dropping a measuring
tape in to th e well#.. M. .this manner the e le fa tlo n of Hie
water ta b le was found to be twelve fe e t below the surfae©
o f the ground a t th is -point*
in -this ease the conductivities of the ground above
and below the water ta b le a te not known* I t may be possible
Meat the co n trast in the conductivities I t not s u ffic ie n tly
g re a t to give d is tin c t curves*
In a l l o f the f ie ld work# fo r every location
of- the secondary electrodes, the primary power was applied
from both ends o f the secondary electrode base# In th is
ts f# as has been pointed out by f« 1* l i h l s t e d t ^ and
Others# near surface m o b ile s may be elim inated
large e&tent« Figure 5” Id a sketch shewing the
arrangement used In the f ie ld work*
300
N
SwS—A / -
figure ^ ,.
.Electrode Arrangement fo r Field Work
the fallowing graph shews the ■re s a lts mf mm of
th e f ie ld 'tests carried, eat .In m e ffo r t to locate the
water tab le elevation* I t 1# seen th a t th ere i s a d e fin ite peak in the curve indicating. a change ha e e n in e tiri% ata depth, of about eight fe e t I f the curve i s in terp reted
in the ■lig h t of the information gained .from fee tank
measurements# While the water ta il# i s a t # depth of
twelve fe e t as measured in the well# i t
he th a t the
ground is s u ffic ie n tly moist above th is point to cause a
gradual change in -the conductivity ant there, may be, there*
fo re , me sharp conductivity change# th is would te n t to make
s a tisfa c to ry curves much more d if f ic u lt to obtain*
: In the following .curves the dotted limes are the
resu lt, o f the surveys rum, in two directions* $be .solid
Mm# represents an average of th e two dotted' curves.* ih is
curve should then represent the bmm p o te n tia l drop r a tio
-free imm the effect# of .surface variation# in r e s is ti v ity
almost completely*
Other curves, were measured ±m th e same location
hot they m m In general-, no more s a tisfa c to ry than those
given 'ami in many eases fa ile d to show any in terp retah le
-result#’ a t -a ll#
In the fie ld ' work a bwerty^ftw© eyele gasoline
driven generator was used a# a primary source o f power*
th e ratio, measurements m m made with the a i t of a re**
sistanoe type .bridge, using a two singe am plifier m i a
sen sitiv e lig h t type galvanometer as a n u ll Indicating,
dovie#* fh e ..d e e tm ie s 'u a e t were copper clad s te e l stake#'
■about, th rt# * in artert. .of an Inch in diameter and two fe e t
long.* these were driven about ten, inches in to the ground*
lh© three secondary electrode# were kept a t a constant
four foot spacing t*i .relation b# one another 'and. moved
along the secondary e le o iro ie ha##* leadings o f the po**
te n b ia l drop ra tio were taken a t four foot intervals* fh©
mmm&mf e le c tro i# h a st was. f o r ^ e i i h t ,f##t long' as
shown in- 'the fig u re -giving the. electrode arrangement, and
Moated in a d ire c tio n perpendlouiar to ’t he p r im a l hast*
fhe generator m s near the d is ta n t primary eleetrod©*
ir r e g u la r itie s la the p o te n tia l d ro p 'fa il# carve
may he somewhat' smoothed out In s t i l l m additional'w ay*..
this. method consist# o f moving the power electrode' and
51
f+4-
- f - tr H -
±ttj
tfc:i
St
-H-
allowing to© tore©
electrodes t® remain In to#';
pOSlttoiN ' fH®' e ffe c t Of dicing til®. meamrements to toi®
way I* t© Maintain to© same electrode resistan ce In a l l
ra tio s# tills may r e m i t in sh iftin g toe ©rCir© curve to
some ©nCont t o t each p oint #111 to affected In to®, m m
iianaer m i to appfOistiiiateiy to® same egim t# t t o carves
oHtmtoed to toto manner were » t o m m regular to m toes®
obtained to moving to® seoondary electrodes* However, toe
curves were s t i l l ineonsistamt m i eouM n e t to ; d e fin ite ly
oorp®latoi with toe geologic conditions *
to# danger to-mstog to is method of to if tto g :toe
power- e le e tro ie is tost- to® secondary electrodes may t o
moved over an area of ground Having a higher r e s is tiv ity
than toe anivNniadtog-areas# to is would proteo® a pmk or
otoer irre.g alarit|r to to© p o te n tia l drop ra tio curve which
would Have n® meaning. a*' f a r as to® a tra tifIc a tto n ®# to®'
greani is concerned* to is f ie ld t®6tai<p© Has h e m suggested Hr Mirentorg and Watson? m i- i t s advantages are
discussed In wore d etail. "Hr toem.
I t is f e lt' to a t lo cal anomalies near to® tofta®#
of to® ground are to e g r e a te s t soar©© of trotibl© to. making
toe- f ^ U - m m i m t i vhlto war® attempted, to to is ©on*
n o iti m i t is w ell to- point out th a t small irre g u la ritie s
to to® ground located near to® surface, unless they are
compensated, -for, are s u ffic ie n t to conceal any
posStoie e f f e c t th a t toe s tr a tif ic a tio n # f toe ground might
Have on to© surface d is trib u tio n of to® p o te n tia l s e t up by
to® primary electrode#-*
toil® a l l of- the re s u lts secured so. f a r to toe
f ie ld ere o f a ilse m ra g to g mature i t to- -net f e l t .tost
toe problem is Impossible o f .* sa tisfa c to ry solution#
Probably i f toe measurements were undertaken to am-area
to to l'to t o e 1eontrasi to eemitof itib to # o f 'toe upper.toe
b t p i i t o t o l ; bed# was greater' much more- sa tisfa c to ry re s u lts
would be obtatoed *
l t : to a. aottooe'-bf: re g re t t# toe « to # r- toat. it.
was topoasibl# to spend more time- to- working out a -.suit*
able f ie ld ■tetomi*p©* toe- sn to er believes th a t satis**
factory- f ie ld re s u lts
3*9
'be seeured by modify tog to# f ie l d
p ra c tic e as c a rp le t out here#
54
BIBLIOGRAPHY
I* Londberg, H. “Potsntialmetod f8r elektrisk malmletning,"
Jerakontorots Annalei*, Stoeldiolni, 1919, pp. 203-215.
t* Edge, At, B. and Laby* f « B, "The Principles and Practice
of Geophysical Pfospoettog#* Cambridge University
Press, 1031, pp. 50-54, 268-274.
3* Koenigaberger, J. "Zur Erraitelung auegedelhnter Sehiehten
versohledener teitfaeh igk elt,” Zeitsehrift fuer
Seophyslk, Vol. § (1930), pp. 71-78
4 . Xundberg, H. end Zusehlag, ®« "A Sew Development In
Electrical Prospecting,8 Geophysical Prospecting
V ol., A.I.M.E., 1038, pp, 47-62.
5.
Hummel, jr. N. "a Theoretical Study of Apparent Resis­
tiv ity la Surface Potential Ifethods,” Geophysical
Prospecting V ol., A»I*8»1»» 1932, pp. 392-422.
6. Weaver, 0. "Certain Applications of the Surface
f,
Potential Method,8 Geophysical Prospecting Vol.*
A.I.M.E., 1929, pp. 68-86.
Ihrunburg, $« 0, and Watson, R. £« ”Shthaaatieal Theory
of Electrical Plow to Stratified I3edia,” Geophysical
Prospecting V ol., A.I.B.1** 1088, pp. 423-442.
®« ' fag®, t . f * ”Interpretation of R esistivity »asurements,B
■ A.I.B.B* Tech, Paper 477, 1088,
f *. Roman, 1» ”How to Compute fables for Determining Elec­
trica l R esistivity of Underlying Beds and Their
App. to Geophysical Problems,8 U.S.Bur. of Bines
Tech. Paper 80S, 1931, 44 pp.
10. Peters, l>* # , end Bardeen, f » “Some Aspects of Elec­
trica l Prospecting In Locating Oil Structures,"
Physics Vol. 8, larch 1938, m* 103-128.
11. Stefan©s»o, 3# 3, “Stt* la measure do* reslstiv ites
apparenles far la method® de la afire eirealaire,”
Gerlands Beitrage Zur Angewandten Geophyaik, Band
5;, 1935-1935, W* 172-188*
IS* Sehlumbarger, c. and »* "Depth of Investigation
Attainable by Potential Jtethods of Electrical
Exploration and Electrical Studies of the Earth*©
Crust at Great Depths," Geophysical Prospecting
. . V ol., A.I.M.E., 1932, pp. 134-140.
13* SOS' reference 4 pages 54 and 53*.
14. Wetsel, ®. w. end fiteliirry, B. V. "A set of Curves to ,
Assist in the Interpretation of the Three Layer
R esistivity Problem,” Geophysics Vol. ®# Got.
1037, pp* 380-541.
IS* So© .reference 8 page 268.
IB* itttera, Z. "A Theoretical and Experimental Examination
of the Potential Drop Ratio Sfethod," Colo. Seh.
o f S&nes Quarterly, fan* 1937, pp. 189-221.
17. BeHand* C. A* "Advances in the Technique and Appli­
cation of R esistivity and Potential Drop Ratio
Sfethoda In Gil Prospecting," A.A.P.G. Ball*
Vol* I t , Dee. 1038, pp. 1850-133®.
18* Heiland, C. A. "A Demonstratlon of' the Geologic
P ossib ilities of the R esistivity rad Magnetic
Prospecting SSfetheda," Terr# ifeg. and Abases* Else.
Vol. 87* sept* 1932, PP* 343-350.
If* Evjen, 1* a, "Depth Factors and Resolving Power of
Electrical KSeasurementa," Geophysics, Vol. 3,
M»*«h 1936, pp. 78-95.
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