AN INVESTIGATION INTO THE CAUSES OF STEADY STATE
ELECTRICAL POTENTIAL DIFFERENCES OCCURRING
NATURALLY ON THE SURFACE OF THE EARTH
by
S c o t t Eston Hii.lse
A T h e s i s S u b m it te d t o t h e F a c u l t y o f t h e
DEPARTMENT OF GEOSCIENCES
In P a r t i a l
F u l f i l l m e n t o f t h e R e q u i re m e n t s
For t h e Degree o f ;
MASTER OF SCIENCE
In t h e G r a d u a t e C o l l e g e
THE UNIVERSITY OF ARIZONA
19 7 8
STATEMENT BY AUTHOR
T h i s t h e s i s has been s u b m i t t e d in p a r t i a l f u l f i l l m e n t o f r e ­
q u i r e m e n t s f o r an advanc ed d e g r e e a t The U n i v e r s i t y o f A r iz o n a and is
d e p o s i t e d in t h e U n i v e r s i t y L i b r a r y t o be made a v a i l a b l e t o b o r r o w e r s
un der r u l e s o f t h e L i b r a r y .
B r i e f q u o t a t i o n s from t h i s t h e s i s a r e a l l o w a b l e w i t h o u t s p e c i a l
p e r m i s s i o n , p r o v i d e d t h a t a c c u r a t e acknowledgment o f s o u r c e i s made.
R e q u e s t s f o r p e r m i s s i o n f o r e x t e n d e d q u o t a t i o n from o r r e p r o d u c t i o n o f
t h i s m a n u s c r i p t in whole o r in p a r t may be g r a n t e d by t h e head o f t h e
major d e p a r t m e n t o r t h e Dean o f t h e G r a d u a t e C o l l e g e when in h i s j u d g ­
ment t h e pr o p o s e d use o f t h e m a t e r i a l is in t h e i n t e r e s t s o f s c h o l a r ­
ship.
In a l l o t h e r i n s t a n c e s , however, p e r m i s s i o n must be o b t a i n e d
from t h e a u t h o r .
SIGNED:
APPROVAL BY THESIS DIRECTOR
T h i s t h e s i s has been ap p r o v e d on t h e d a t e shown below:
Z- ^
JOHN S. SUMNER
P r o f e s s o r o f G e o s c ie n c e s
7
AmjI
7
Date
ll
ACKNOWLEDGMENTS
Dr. John S. S um ne r' s p a t i e n t and u n d e r s t a n d i n g d i r e c t i o n s as
t h e s i s a d v i s o r and h i s w i l l i n g n e s s t o s h a r e h i s f a m i l i a r i t y w i t h t h e
geophysical
lite r a tu r e are greatly appreciated.
The com pu ter t i m e
r e q u i r e d f o r t e s t s on t h e program SPMODL (Appendix C) we re p r o v i d e d
by t h e Dep artm ent o f G e o s c i e n c e s , c o u r t e s y o f Dr. John S. Sumner.
Dr.
Mi s a c N a b ig h i a n and Dr. Kenneth L. Zonge, members o f t h e t h e s i s com­
m i t t e e , we re alwa ys r ea d y t o h e l p s o l v e t h e v a r i o u s p r o b le m s t h a t
developed during th e w r i ti n g of t h i s t h e s i s .
t i o n s , and t h e d e t a i l e d
T h e i r comments, s u g g e s ­
inform ation they provided, p a r t i c u l a r l y
ma tio n p e r t a i n i n g t o t h e measurement and a n a l y t i c a l
infor­
t e c h n i q u e s used in
t h i s t h e s i s , were i n v a l u a b l e .
The i n i t i a l
i n t r o d u c t i o n t o t h e c o n c e p t o f SP and r e l e v a n t
l i t e r a t u r e were p r o v i d e d by Dr. C h a r l e s M. S w i f t , J r . ,
form erly with
\
Kennecott E x p lo ra tio n ,
In c.
Dr. S w i f t ' s e a r l y en co u r a g e m e n t and p e r s o n a l
r e s p o n s e s t o many q u e s t i o n s r e s u l t e d
in an e a r l y c o n t a c t w i t h t h e co n ­
c e p t s o f t h e therm ody nam ic s o f i r r e v e r s i b l e p r o c e s s e s .
Sam G. S a r g i s , a p e r s o n whom I w i l l always r e g a r d as i n s p i r a ­
t i o n a l , a l e r t e d me t o t h e i d i o s y n c r a s i e s o f f i e l d SP m e a s u r e m e n t s .
provided the f i n a n c i a l
s u p p o r t and p e r s o n a l
Sam
i n t e r e s t t h a t e n a b l e d me t o
c o m p i l e t h e c o m p r e h e n s i v e b i b l i o g r a p h y o f l i t e r a t u r e p e r t a i n i n g t o SP
c o n t a i n e d in Appendix D o f t h i s s t u d y .
Sam r e s u l t e d
in many e x p e r i e n c e s
The o p p o r t u n i t y t o work w i t h
I w ill never f o r g e t .
ili
One such
iv
e x p e r i e n c e made me v e r y aw are o f t h e d a n g e r s i n h e r e n t
e l e c t r i c a l t e c h n i q u e s ; f o r ex am p le ,
in t h e a c t i v e
IP.
Thr o ug ho ut t h e w r i t i n g . o f t h i s t h e s i s my c o l l e a g u e s a t Gulf
R es ea rc h and Development Company and t h r o u g h o u t Gul f Oil C o r p o r a t i o n
were g e n e r o u s w i t h t h e i r
w i t h t o n g u e - i n - c h e e k as
note, D r .E .
i d e a s and comments, many o f which we re t a k e n
I am c e r t a i n t h e y were i n t e n d e d .
On a s e r i o u s
B. D a v i e s , D i r e c t o r , G e o p h y s ic a l A n a l y s i s D i v i s i o n ,
Mr. T. K. F u l t o n , A p p l i c a t i o n s S e c t i o n D i r e c t o r , and Mr. Leonard S t e e l e ,
D i s t r i c t G e o p h y s i c i s t , were e x t r e m e l y g e n e r o u s and u n d e r s t a n d i n g .
Their
p r o v i s i o n o f p e r s o n a l ti m e o f f from my a s s i g n e d d u t i e s t o p e r m i t
c o m p l e t i o n o f t h i s t h e s i s as w e ll a s t h e i r u n d e r s t a n d i n g o f t h e change
in my h o r i z o n s f o l l o w i n g i t s c o m p l e t i o n w i l l always be a p p r e c i a t e d .
J o , my w i f e , and V i c t o r i a , my d a u g h t e r , w i l l a p p r e c i a t e t h e
f a c t o f t h e c o m p l e t i o n o f t h i s t h e s i s more t h a n any o t h e r s .
They made
c o n t i n u o u s c o n t r i b u t i o n s and s a c r i f i c e s d u r i n g sometimes d i f f i c u l t
periods.
The windows opened by J o ' s h u n d r e d s o f pag es o f sometimes
humorous F r e n c h and S p a n is h t r a n s l a t i o n s p r o v i d e d c o n s i d e r a b l e i n s i g h t
t h a t o t h e r w i s e would n o t have been a v a i l a b l e .
and V i c t o r i a ' s p a t i e n c e and u n d e r s t a n d i n g .
I am g r a t e f u l
f o r Jo
I somehow s u s p e c t t h a t
it
i s now my t u r n t o "weed t h e g a r d e n " .
S p e c i a l t h a n k s a r e g iv e n t o my many f r i e n d s a t Zonge E n g i n e e r ­
ing and R es ea r c h O r g a n i z a t i o n .
T h e i r t o l e r a n c e , s u g g e s t i o n s and g e n ­
e r o u s c o n t r i b u t i o n s o f work s p a c e and t i m e f o r c o n s t r u c t i o n and l a t e r ,
m o d i f i c a t i o n o f t h e i n s t r u m e n t used f o r t h e s e measu re men ts a r e a p p r e ­
ciated.
V
T h e r e a r e always many p e o p l e , c o l l e a g u e s , c h a n c e a c q u a i n t a n c e s
and o t h e r s whose i d e a s , e x p e r i e n c e and i n t r o d u c t i o n s t o o t h e r s en h an c e
a study.
All o f t h e s e , o f whom t h e r e w er e many, a r e remembered.
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS. . . . . . .
ABSTRACT .
1.
2.
.............................................................. v i l l
............................
,x
.....................................................................................
INTRODUCTION
REVIEW OF PREVIOUS WORK. . ..................................
.
.
1
.
.
H i s t o r i c a l Developments . . . . . . .
. .. . . . .
. . , .
Summary o f S p e c i f i c SP Mechanisms .
. . . . .
E l e c t r o c h e m i c a l Mechanisms. .
.....................................
Redox Charge T r a n s f e r . . .. .. . .
. . .
. . . .
Galvanic C urrent Generation .
. .
.
D i f f u s i o n C u r r e n t s . ............................
......................... .
E l e c t r o k i n e t i c Mechanisms . . . . . . .
E l e c t r i c C u r r e n t - G e n e r a t i n g Mechanisms
R e l a t e d t o Thermal Energy . . . . . . . . . . . . .
The Reduced Forms o f t h e P h en om e no lo g ic a l
E q u a t i o n s D e s c r i b i n g Energy T r a n s f e r ...........................................
N o is e E n c o u n t e r e d d u r i n g SP M eas ur em en ts. . . . . . . . .
3.
DEVELOPMENT OF THE SELF-POTENTIAL MODEL. .
. . . . . . . . . .
AN APPLICATION OF THE PROGRAM SPMODL TO SIMULATE
FLOWS OF ELECTROCHEMICAL ORIGIN.
I np u t D a t a .......................
G e o l o g i c a l , G e o p h y s ic a l and
Geographical Info rm atio n . . . . . .
E l e c t r i c P o t e n t i a l S o u r ce I n f o r m a t i o n
Data A c q u i s i t i o n and E r r o r P a r a m e t e r s . .
R e s u l t s O b t a i n e d Using t h e Program SPMODL
5.
EVALUATION . . . . . . . .
APPENDIX A:
................... .......................
NOTATION. . . . .
•:
.
.
VI
28
31
35
39
G e o l o g i c S t r u c t u r e o f t h e SP Model..........................................
Thermodynamic P r o p e r t i e s o f t h e SP Model. . . . . . . . .
The A n a l y t i c a l SP Model . . . , .......................
4.
7
11
12
13
16
19
22
40
45
50
...................
70
71
. . . . . . . .
.................................
. .
..................
. . .
. . . . .
71
76
78
80
. . . . . . .
84
. . . . . . .
.
88
.. .
VI
I
TABLE OF CONTENTS— C o n ti nu ed
Page
APPENDIX B:
MATHEMATICAL BASIS FOR THE PHENOMENOLOGICAL
EQUATIONS DESCRIBING IRREVERSIBLE THERMO­
DYNAMIC PROCESSES.
........................ ....
.
91
APPENDIX C:
COMPUTER PROGRAM SPMODL........................................... ...................
99
APPENDIX D:
COMPREHENSIVE LIST OF LITERATURE
PERTAINING TO SP MEASUREMENTS. . . . . . . . .
REFERENCES
. .
125
208
LIST OF ILLUSTRATIONS
Figure
1.
2.
Page
D e v i a t i o n s o f v a r i o u s e l e c t r o d e p o t e n t i a l s from '
th e ir resp ectiv e standard electro d e p o te n tia ls
a s a f u n c t i o n o f t e m p e r a t u r e . ; .............. . .
.............................
Redox c h a r g e t r a n s f e r mechanism o f s u l f i d e
s e l f - p o t e n t i a l s ................................. ................... ....
6
14
3".
Changes in s e l f - p o t e n t i a l a t g e o l o g i c c o n t a c t s
4.
C o n f i g u r a t i o n o f t h e d i f f u s e l a y e r o f c a t i o n s and
t h e f i x e d l a y e r o f a n i o n s on t h e p o s i t i v e l y
c h a r g e d r o ck m a t r i x . . . . . . . . . . . . . . . . . . .
25
5.
S e l f - p o t e n t i a l o v e r an a r t e s i a n s p r i n g ........................
27
6.
V a ria tio n s of th e spontaneous e l e c t r i c p o t e n t i a l
and t e m p e r a t u r e in a c o n t a i n e r o f powered
. p y r i t e and in a s l a b o f r ock c o n t a i n i n g
m a s s i v e s u l f i d e s as a f u n c t i o n o f d i s t a n c e
from t h e h e a t s o u r c e .......................
29
7.
The c o n c e p t u a l m o d e l ................................................
9.
C e n t r a l e l e m e n t o f t h e r e s i s t a n c e n et w o r k
s u p e r imposed on t h e g e o l o g i c model . .
11.
.. .
. .
I l l u s t r a t i o n o f t h e c o n t i n u i t y o f a fl o w and i t s
p o t e n t i a l and t h e d i s c o n t i n u i t y o f i t s g r a d i e n t
a t a phase boundary.
..........................................
8.
10.
. .
23
.
42
44
......................................
52
C e n t r a l e l e m e n t o f t h e r e s i s t a n c e net wo rk w i t h
c l o s e d lo o ps s u p e r imposed on t h e g e o l o g i c m o d e l ........................
54
Expanded r e s i s t a n c e ne t w o r k s u p e r im p o s e d on t h e
g e o l o g i c model . . . . . . . . . . . . . . . . .
...................
55
..................... . .
60
12.
Flow o f t h e program SPMODL
13.
Data p r o c e s s i n g p a r a m e t e r s use d in t h e ne tw or k a n a l y s i s .
14.
Expanded r e s i s t i v i t y g r i d used t o form t h e r e s i s t a n c e
network.
v? i I
.
62
.
63
ix
LI ST OF 1LLUSTRATIONS— C o n ti n ue d
Figure
15.
Page
R e s i s t a n c e n e t w o r k used f o r t h e ne t w o r k a n a l y s i s
.......................
of s e lf-p o te n tia l. . . . . . . .
64
16.
A c l o s e d loop in t h e r e s i s t a n c e n e t w o r k .
65
17.
R e s i s t a n c e v a l u e s f o r t h e loop s s i m u l a t i n g
the a i r - e a r t h in te r f a c e .
.........................................................
66
18.
Ob served and modeled s e l f - p o t e n t i a l d a t a . . . . . . . . .
67
19.
P l o t o f t h e modeled (1) and o b s e r v e d s e l f p o t e n t i a l d a t a (2)
...................................... ....
20.
21.
22.
23.
24.
. . . . . . . . .
.
68
G e o lo g i c c r o s s s e c t i o n b e n e a t h t h e modeled
se lf-p o te n tia l line. . . . .
. . . . . . . . . . . . . .
72
Expanded r e s i s t i v i t y g r i d s u p e r im p o s e d on
the geologic cross sec tio n . . . . . . .
73
.......................
Maximum a v a i l a b l e p o t e n t i a l d i f f e r e n c e s f o r
various conducting m in e ra ls . .
.......................
77
Lin e c o n f i g u r a t i o n used f o r s e l f - p o t e n t i a l
measu re men ts in t h e s u r v e y a r e a . . . . . . . . . . . . .
79
The r e l a t i o n s h i p between t h e modeled and o b s e r v e d
s e l f - p o t e n t i a l d a t a and t h e g e o l o g y . . . . . . . . . . .
82
ABSTRACT
S elf-potential
is a m a n i f e s t a t i o n o f c r o s s - c o u p l i n g between
e n e r g y t r a n s p o r t mechanisms in t h e e a r t h i n c l u d i n g h e a t f l o w , f l u i d
flow,
ion d i f f u s i o n and o t h e r s .
The r e t i c u l a r s t r u c t u r e o f t h e e a r t h
and t h e f u n c t i o n a l s i m i l a r i t y between membranes c i r c u m s c r i b i n g t h e
r e t I d e s and e l e c t r i c r e s i s t o r s
in d ic a te the a p p l i c a b i l i t y of e l e c t r i c
ne tw or k a n a l y s i s t o SP m o d e l i n g . . An a n a l y t i c a l model
is d e v e l o p e d
t h a t t a k e s a d v a n t a g e o f t h e n o n s l n g u l a r , p o s i t 1v e - d e f i n i t e , banded and
sy m m e tri c c h a r a c t e r i s t i c s , o f t h e r e s ?s t a n c e c o e f f i c i e n t m a t r i x and u s e s
C h o l e s k y ' s method
The model
fo r m atrix decom position.
was t e s t e d u s i n g SP d a t a measured in an a r e a where
g e o l o g i c and g e o p h y s i c a l d a t a we re a v a i l a b l e f o r c o n t r o l .
included a source
1nput d a t a
m a t r i x * o b s e r v e d SP d a t a and a r e s I s t i v i t y
Outp ut was a 1i n e p r i n t e r p l o t and a l i s t i n g o f t h e
modeled nodal e l e c t r i c p o t e n t i a l s .
array.
o b s e r v e d and
Redox c h a r g e t r a n s f e r m o d i f ie d
by n e a r - s u r f a c e o x i d a t i o n o f m e t a l l i c m i n e r a l i z a t i o n was t h e o n l y a p p a r ­
e n t a c t i v e e n e r g y t r a n s f e r mechanism g e n e r a t i n g SP.
spatial
The a m p l i t u d e ,
f r e q u e n c y and t h e r e g i o n a l g r a d i e n t o f t h e modeled d a t a c o r r e ­
l a t e d w e ll w i t h o b s e r v e d d a t a .
A dditional
s t u d i e s and co m pu ter s o f t w a r e d e v e l o p m e n t a r e
recommended t h a t w i l l expand t h e a p p l i c a t i o n o f e l e c t r i c ne tw or k ana l y ­
s i s t o mo d e lin g g e n e r a l i z e d e n e r g y t r a n s f e r
in t h e e a r t h .
A d e t a i l e d l i s t o f r e f e r e n c e s p e r t a i n i n g t o SP i s i n c l u d e d .
■
. : ■ ■ ■
■
x -
•
CHAPTER 1
INTRODUCTION
Energy t r a n s f e r between two l o c a t i o n s w i t h i n t h e e a r t h h a v i n g
different
levels of p o te n tia l
i n t e r r e l a t e d flo w p r o c e s s e s .
i s a c c o m p l i s h e d t h r o u g h many d i s t i n c t bu t
P ri m a r y f lo w s o c c u r a s a d i r e c t r e s u l t o f
p h y s i c a l and ch em ica l d i s e q u i 1 I b r i a .
conditions
in t h e e a r t h .
These flo w s a r e c a u s e d by c h a n g i n g
A c t i v a t i o n o f s e c o n d a r y f lo w s depends on t h e
c r o s s - c o u p 1ing p r o p e r t i e s o f t h e m a t e r i a l s th r o u g h which t h e flows p a s s .
The u l t i m a t e s y s t e m is one in which no f lo w s e x i s t ; t h a t
rium s t a t e .
A consequence o f t h i s
is t h a t a l l
is th e e q u i l i b ­
fl o w s a r e t r a n s i t o r y and
t h e r e f o r e can o n l y be a p p r o x i m a t e d by c o n s t a n t , s t e a d y s t a t e c o n d i t i o n s
fo r s h o r t p erio d s o f time.
The p r e d o m i n a t e f lo w s a c t i v e in g e o p h y s i c a l p r o c e s s e s p e r t i n e n t
to t h i s study include;
1.
C u r r e n t s o f e l e c t r o n s , i o n s , and o t h e r
ch a r g e d m a t t e r .
2.
F l u i d f lo w in a p o r o u s medium.
3.
Flow o f un ch ar g e d m a t t e r .
4.
Heat f lo w fro m r e g i o n s o f g e o t h e r m a l a c t i v i t y .
None o f t h e s e f lo w s can t a k e p l a c e w i t h o u t s i m u l t a n e o u s l y c a u s i n g o r
m o d i fy in g a l l o t h e r f l o w s .
I n h e r e n t in t h i s s t a t e m e n t i s t h e f a c t t h a t
a l l s p e c i f i c e n e r g y f lo w mechanisms a c t t o modify one a n o t h e r t o m i n i ­
mize t h e t o t a l
e n e r g y f lo w .
The r e s u l t i n g flow c h an ge s a r e u n d e t e c t a b l e
i f t h e m a g n it u d e s o f t h e c r o s s - c o u p l i n g c o e f f i c i e n t s r e l a t e d t o t h e
p r o p e r t i e s me n tio n ed above a r e small compared t o t h e c o n d u c t i v i t y term s
fo r the primary flow s.
C o n s i d e r a t i o n o f one o r more fl o w s is e s s e n t i a l
physical
studies.
in most g e o ­
D i r e c t o b s e r v a t i o n o f a p a r t i c u l a r f lo w is g e n e r a l l y
much more d i f f i c u l t t h a n measurement o f a p a r a m e t e r d i r e c t l y r e l a t e d t o
th e flow.
Assuming t h e c r o s s - c o u p l i n g c o e f f i c i e n t s a r e o f s u f f i c i e n t
m a g ni tu d e i t
is p o s s i b l e t o me as ur e a p a r a m e t e r r e l a t e d t o a s e c o n d a r y
flow and back c a l c u l a t e t o d e t e r m i n e t h e e n e r g y a s s o c i a t e d w i t h t h e
primary flow.
The measu re men ts u s e d t o d e t e r m i n e t h e f lo w o f e n e r g y a r e g e n e r ­
a l l y measu re men ts o f r e l a t i v e a m p l i t u d e d i f f e r e n c e s made u s i n g a p r e d e ­
t e r m i n e d s a m p l in g g e o m e tr y .
A p o t e n t i a l energy g r a d i e n t is determined
d i r e c t l y from t h e d i f f e r e n c e m ea sur em ent s o r i n d i r e c t l y u s i n g c o n t o u r e d
maps o r p r o f i l e s .
The g r a d i e n t
i n d i c a t e s t h e d i r e c t i o n o f a fl o w .
An
a p p r o x i m a t e l o c a t i o n o f t h e s o u r c e can be d e t e r m i n e d i f a d e q u a t e d a t a
are av ailable.
Self-potential
potential
(SP) d i s t r i b u t i o n s d e v i a t i n g from t h e normal
g r a d i e n t on and in t h e e a r t h a r e a s s o c i a t e d w i t h v i r t u a l l y a l l
flow t y p e s .
A m a jo r impediment t o u n d e r s t a n d i n g SP i s t h e la c k o f mea­
surements of the c r o s s - c o u p lin g p r o p e r t i e s of e a r t h m a t e r i a l s . . A la rg e
number o f me asurements o f t h e s e c r o s s - c o u p l i n g p r o p e r t i e s a r e r e q u i r e d
i f a r e l a t i o n s h i p between o b s e r v e d SP and t h e e n e r g y d i f f e r e n c e s c a u s i n g
s p e c i f i c flo w s i s t o be e s t a b l i s h e d .
T h i s s t u d y c o n s i s t s o f two p a r t s .
general
The f o l l o w i n g c h a p t e r is a
re v ie w o f t h e l i t e r a t u r e r e l e v a n t t o SP.
S pecific reports of
SP measu re men ts t h a t i l l u s t r a t e p a r t i c u l a r t o p i c s c o n s i d e r e d in t h i s
s t u d y a r e m e nt io ne d in t h e t e x t .
A bibliography of a ll
the l i t e r a t u r e
rev ie we d d u r i n g t h i s s t u d y i s i n c l u d e d in Appendix D.
C h a p t e r 3 i n c l u d e s a summary o f t h e p h y s i c a l c h a r a c t e r i s t i c s
d e s i r a b l e f o r any SP model, t h e t h e o r e t i c a l c o n s i d e r a t i o n s r e l e v a n t t o
t h e model, and dev el op m en t o f an a n a l y t i c a l
t e c h n i q u e f o r SP m o d e li n g .
The g e o l o g i c model d e v e l o p e d in t h i s s t u d y is b ase d on models pr o po s ed
in t h e l i t e r a t u r e as w e l l as f i e l d o b s e r v a t i o n s .
t h e o r e t i c a l model
Background f o r t h e
is t a k e n from work by b i o p h y s i c i s t s c o n c e r n e d w i t h
i r r e v e r s i b l e p r o c e s s e s and th e rm o d y n a m i c s .
The a n a l y t i c a l model u s es
t h e ne t w o r k t h e o r y d e v e l o p e d by e l e c t r i c a l e n g i n e e r s f o r a n a l y s i s o f
electric circu its.
The n o t a t i o n used f o r t h e d e v e l o p m e n t o f t h e s e
concepts is exp lain ed
in Appendix A.
An example o f t h e a p p l i c a t i o n o f t h e model d e v e l o p e d in
C h a p t e r 3 t o a s p e c i f i c f i e l d p r o b le m i s d e s c r i b e d in C h a p t e r 4.
f i n a l c h a p t e r (5)
The
Is a summary o f t h e way in which t h e model can be
expanded t o t h e g e n e r a l c a s e i n v o l v i n g m u l t i p l e mechanisms and t h e
c ro ss-c o u p le d flows.
in c lu de d, in C h a p t e r 5.
Recommendations f o r a d d i t i o n a l
stu d ie s are
)
CHAPTER 2
REVIEW OF PREVIOUS WORK
Reports c o n ta in in g inform ation about s e l f - p o t e n t i a l
classified
1.
can be
in f i v e g e n e r a l c a t e g o r i e s :
Theoretical
s t u d i e s co n c e r n e d w i t h e l e c t r o c h e m i c a l
theory,
e q u i v a l e n t c i r c u i t s , and l a b o r a t o r y mode ls.
2.
Summaries o f f i e l d s t u d i e s
including c o n s id e ra tio n of the
relevant th eo ry .
3.
Raw d a t a .
4.
D i s c u s s i o n s o f i n s t r u m e n t a t i o n and measurement t e c h n i q u e s .
5.
P r e s e n t a t i o n s o f methods f o r d a t a i n t e r p r e t a t i o n .
T h e o r e t i c a l models g e n e r a l l y l i m i t c o n s i d e r a t i o n t o a s i n g l e s o u r c e
mechanism.
The mechanism i s b i a s e d .toward t h e i n t e r p r e t a t i o n t h e w r i t e r
w i s h e s t o f i t an a r c h e t y p e in t h e f i r s t c a t e g o r y and s p e c i f i c d a t a in
th e second.
Data have been p u b l i s h e d f o r s e v e r a l
h a s been no a t t e m p t a t i n t e r p r e t a t i o n .
c a s e s f o r which t h e r e
Th es e r e p o r t s a r e g e n e r a l l y
co n c e r n e d w i t h me asuremen ts in a r e a s whe re s i g n a l a m p l i t u d e s a r e on t h e
order of 1 to 2 v o l t s .
O th e r r e p o r t s o f raw d a t a a r e made f o r a r e a s
where t h e c u r r e n t t h e o r i e s c a n n o t e x p l a i n o b s e r v a t i o n s .
I n s t r u m e n t a t i o n use d f o r SP me asurements i s g e n e r a l l y s i m p l e .
The main c o n c e r n is s e n s i t i v i t y and t h e r e l a t e d
cific
instrum ents.
i n p u t impedance o f s p e ­
The l a t t e r , c o n c e r n is due t o t h e low c u r r e n t .
4
d e n s i t i e s a s s o c i a t e d w i t h SP.
A pr oblem t h a t has r e c e i v e d s c a n t con^
s i d e r a t ion is t h a t o f t h e b e s t t y p e o f e l e c t r o d e f o r e l e c t r i c p o t e n t i a l
measurements.
The Cu-CuSO^ n o n p o l a r i z a b l e e l e c t r o d e has g e n e r a l l y been
a c c e p t e d as t h e s t a n d a r d f o r SP m e a s u r e m e n t s .
Where low s i g n a l
a r e e x p e c t e d , a b e t t e r c h o i c e i s t h e 0.1 N calomel e l e c t r o d e
levels
(Fig.
1).
Measurement methods a r e d e s i g n e d t o f i t t h e r e q u i r e m e n t s o f a
p a r t i c u l a r survey.
The u s e o f a l o n g - w i r e t e c h n i q u e i s b e s t s u i t e d f o r
a r e a s where improvement in t h e s i g n a l - t o - n o i s e r a t i o
is re q u ire d .
This
t e c h n i q u e r e q u i r e s t h a t a r e f e r e n c e e l e c t r o d e be f i x e d a t a b a s e ; a l l
measu re men ts a r e made r e l a t i v e t o t h a t b a s e .
A g r a d i e n t te chnique using
a movable d i p o l e w i t h a r e l a t i v e l y s h o r t f i x e d l e n g t h i s more s u i t e d t o
a r e a s where l a r g e c h an ge s in s i g n a l a m p l i t u d e o c c u r o v e r s h o r t d i s t a n c e s .
The s i g n a l - t o - n o i s e r a t i o
is i n c r e a s e d / 2 f o r t h e long-w i r e t e c h n i q u e
as opposed t o t h e g r a d i e n t method (Thompson, 1976).
I n n o v a t i o n s a r e use d by v a r i o u s a u t h o r s t o a c c o u n t f o r g e o m e t r i c
deviations,
inh om og ene it y and a n i s o t r o p y , p o l a r i t y c h a n g e s , and t h e d i s ­
t r i b u t i o n o f m u l t i p l e s o u r c e s d u r i n g i n t e r p r e t a t i o n o f SP d a t a .
Model­
ing t e c h n i q u e s , w i t h a few e x c e p t i o n s , a r e l i m i t e d t o a n a l o g s y s t e m s ;
f o r ex am p le , t a n k m o d e ls .
T h i s c h a p t e r summarizes t h o s e i d e a s c o n s i d e r e d r e p r e s e n t a t i v e
o f t h e domi nant t r e n d s
in t h e u s e o f SP m e a s u r e m e n t s .
An o v e r v ie w o f
t h e h i s t o r i c a l d e ve lo p m en t is f o l l o w e d by a summary o f t h e t h e o r y
r e l a t i n g eac h o f t h e f lo w mechanisms t o SP.
The f i n a l
section
is a
d i s c u s s i o n o f e x t r a n e o u s e l e c t r i c n o i s e a f f e c t i n g SP m e a s u r e m e n t s .
20
10
0
O--------- O —"O—
-20
AE
(mV)
10
-40
1.0 N
0.1 N
Ag-AgN03
Calome1
1.0 N
Calome1
Saturated
Calomel
0.6 N
Cu-CuS0,
0
10
20
30
40
50
60
70
80
90
100
Te m pe ra tu re (°C)
F i g u r e 1.
D e v i a t i o n s o f v a r i o u s e l e c t r o d e p o t e n t i a l s from t h e i r r e s p e c t i v e s t a n d a r d
e l e c t r o d e p o t e n t i a l s as a f u n c t i o n o f t e m p e r a t u r e — Data from Robinson and
Harned ( 1 9 4 1 ) , Harned and Owen ( 1 9 4 3 ) , P o t t e r ( 19 56 ) , G re el y and o t h e r s ( I 9 6 0 ) ,
W i l l a r d , M e r r i t t and Dean ( 19 65 ) , and D h il l o n and Blokhra (1967)
H istorical
Developments
E x p e ri m e n t s by Hans C h r i s t i a n O e r s t e d in 1819 r e s u l t e d
in t h e
f i r s t t h e o r i e s r e l a t i n g e l e c t r i c i t y and magnetism (Ampere, 1823).
t h e o r i e s we re e s s e n t i a l
Th es e
t o t h e d e s i g n and c o n s t r u c t i o n o f a g a l v a n o m e t e r
w i t h which t o s e n s e e l e c t r i c c u r r e n t s .
R o be r t Were Fox (1830, 1835)
used t h e s e t h e o r i e s t o c o n s t r u c t an i n s t r u m e n t c a p a b l e o f d e t e c t i n g t h e
c u r r e n t f l o w i n g in a w i r e c o n n e c t i n g v e i n s o f m e t a l l i c s u l f i d e s
mines o f C o r n w a l l , U. K.
in t h e
T h i s was t h e f i r s t r e c o r d e d o b s e r v a t i o n o f SP.
Fox, u s i n g d a t a from h i s e a r l i e s t o b s e r v a t i o n s , r e a c h e d two s i g n i f i c a n t
conclusions:
1.
The e l e c t r i c , p o t e n t i a l d i f f e r e n c e s o r i g i n a t e from e l e c t r o ­
ch em ica l o r t h e r m o e l e c t r i c p r o c e s s e s .
2.
The e l e c t r i c c u r r e n t s ca u s e d by t h e p o t e n t i a l d i f f e r e n c e s
are stab le.
Bennet s ( 1 8 3 3 ) , Henwood ( 1 8 4 1 ) , and Reich ( 1 8 4 4 ) , made o b s e r v a ­
ti o n s s u b s t a n t i a t i n g Fox's measurements.
The most s i g n i f i c a n t c o n c l u ­
s i o n r e a c h e d d u r i n g t h i s e a r l y work was t h e r e c o g n i t i o n t h a t t h e e l e c ­
t r i c c u r r e n t s were e l e c t r o c h e m i c a l l y r e l a t e d t o s u b t e r r a n e o u s m i n e r a l
d e c o m p o s i t i o n and d e p o s i t i o n
(Ambronn, 19 28).
S v e s h n ik o v and Dobychin
( 1 9 5 6 ) , Urazayev ( 1 9 6 4 ) , S v es hn ik o v and K e d r i n s k i y (1 965; 1966), Dzhashi
( 1966) ,
S v e s h n ik o v ( 1 9 6 7 ) ,
11 i n , S v e s h n ik o v and S h t e r n ( 1 9 7 0 ) , and
Volkov (1974) c o n s i d e r e d t h i s s u b j e c t
Fox ( c i t e d
in K e l l y ,
in g r e a t e r d e t a i 1.
1934) and Reic h (1844)
recognized the
p o s s i b i 1 i t y o f u s i n g SP measu re men ts t o e x p l o r e a r e a s w h er e m i n e r a l i ­
z a t i o n was p r e v i o u s l y unknown.
Fox used t h e method un d e r g r o u n d t o
discover a vein co n tain in g s u i f i d e m in e ra liz a tio n .
Rei ch s u g g e s t e d
s u r f a c e measu re men ts a s a way t o d e t e c t m i n e r a l i z a t i o n
unknown g e o l o g y .
in a r e a s o f
D e s p i t e t h i s work i n t e r e s t in SP waned u n t i l
i8 6 0 ,
when Barus (1882) made f i e l d measu re men ts in s e v e r a l mines in t h e
V i r g i n i a C i t y and Eureka mi nin g d i s t r i c t s o f Nevada.
An i n n o v a t i o n i n t r o d u c e d as t h e r e s u l t o f B a r u s ' s s t u d y was t h e
nonpolarizable e le c tro d e .
T h i s t y p e o f e l e c t r o d e was n e c e s s a r y t o
r e d u c e t h e m a gn it u de o f e l e c t r i c , n o i s e in o r d e r t o p e r m i t measurement
o f s i g n a l s w i t h a m p l i t u d e s on t h e o r d e r o f 20 t o 30 mV.
the k in e tic s of nonpolarizable e le c tro d e s
i s i n c l u d e d in a p a p e r by
S ato and Mooney ( I 9 6 0 , p. 233) and a book by P o t t e r
Barus
A summary o f
(1956, p.
(1882, p. 343) c o n c l u d e d t h a t e l e c t r i c p o t e n t i a l
e n c e s a t g e o l o g i c c o n t a c t s a r e an i m p o r t a n t component o f SP.
121).
d iffer­
Th is
o b s e r v a t i o n led Barus t o s u g g e s t t h e need f o r d e t a i l e d s t u d i e s o f t h e
ele c tro c h e m istry of rocks,
A s t u d y made as a r e s u l t o f t h e s e recom­
m e n d a ti o n s was c o m p le te d by W el ls ( 1 9 1 4 ) .
While t h e s t u d i e s by Barus and W el ls were in p r o g r e s s , European
s c i e n t i s t s we re o b s e r v i n g t e l l u r i c c u r r e n t s e x h i b i t i n g t e m p o r a l v a r i a ­
t i o n s in a m p l i t u d e and d i r e c t i o n .
During o b s e r v a t i o n s
in B u l g a r i a
between 1893 and 1894, Bachmetjew ( 1896) o b s e r v e d e l e c t r i c p o t e n t i a l
d i f f e r e n c e s he b e l i e v e d were a s s o c i a t e d w i t h t h e f lo w o f w a t e r t h r o u g h
subsurface sands.
T h i s i n t e r p r e t a t i o n was ba se d on t h e e a r l i e r e l e c t r o -
k i n e t i c s t u d i e s by Quincke (i8 6 0 ) and H elm ho ltz ( 1 8 7 9 ) .
A significant
o b s e r v a t i o n by Bachmetjew (1902) w a s . t h e r e l a t i o n s h i p bet ween t h e
t e m p e r a t u r e a t t h e s u r f a c e o f t h e e a r t h and v a r i a t i o n s
e le c tr ic potential difference.
in t h e measured
D espite the e a r l i e r re c o g n itio n , the f i r s t recorded discovery
o f a p r e v i o u s l y unknown s u l f i d e o r e b o d y was n o t made u n t i l
d i s c o v e r y was made in N a u t e n e n , Sweden,
1907.
The
. < by an a s s i s t a n t t o Burg-
m a s t e r M ue ns te r o f K o n i g s b e r g , Norway" ( L u n d b e r g , 1SkB, p.
179).
W i desp re ad r e c o g n i t i o n t h a t SP measu re men ts a r e a u s e f u l t o o l
w i t h which t o d e t e c t s u l f i d e m i n e r a l i z a t i o n o c c u r r e d f o l l o w i n g d i s c l o ­
s u r e o f , "A p a t e n t e d method o f s y s t e m a t i c a l l y m e a s u r i n g and mapping SP
fo r locating orebodies"
( S c h l u m b e r g e r , 1913, p. 257)•
Simultaneous d is
c l o s u r e o f t h e r e s u l t s o f SP measu re men ts o v e r t h e S a i n Bel p y r i t e mine
Rhone, F r a n c e , f u r t h e r f o c u s e d t h e a t t e n t i o n o f t h e m i n e r a l
I n d u s t r y on
t h e u s e o f SP d a t a ( S c h 1u m b e r g e r , 1920).
Sherwin F. K e l l y , a s t u d e n t a t t h e School o f Mi nes , P a r i s ,
France, during P ro fe s so r Schlum berger's te n u re , brought the instrum enta
t i o n and t e c h n i q u e s p e r f e c t e d by t h e l a t t e r t o N or th America in
(K elly,
1934). T e s t measu re men ts u s i n g t h e S ch lu m b er g er method were
made o v e r known m i n e r a l i z a t i o n a t s e v e r a l
1.
1921
locations:
Copper d e s p o s i t s a t Ducktown, T e n n e s s e e ( K e l l y ,
1922a; Wi1s o n ,
1928; H e i l a n d , 1929).
2.
A n t h r a c i t e co a l beds n e a r W i l k e s - B a r r e , P e n n s y l v a n i a ( K e l l y ,
1922a; H e i l a n d ,
3*
1929).
Nick el d e p o s i t s a t t h e Frood mine a t Sudb ury , O n t a r i o ,
Canada ( K e l l y ,
1922a, 1924; Wi1s o n , 1928; Leonardon and K e l l y ,
1928; , H e i l a n d , . 192 9) .
4.
Nick el d e p o s i t s a t t h e F a l c o n b r i d g e mine a t S u d b u r y , O n t a r i o
Canada
(K elly,
1922a, 1922b; Mason, 1929).
10
5.
Copper and go ld d e p o s i t s a t t h e Horne c l a i m s , Noranda Mines
L t d . , Quebec, Canada ( K e l l y ,
1959b).
6.
Ruby mi ne, O n t a r i o , Canada (He?1a n d , 1929)•
7.
Hovey mi ne, Red L a k e , O n t a r i o , Canada ( K e l l y ,
1934; 1959b).
A common f a c t o r in t h e s e c a s e s was t h e h i g h c o n d u c t i v i t y o f t h e m i n e r a l ­
iz ed z o n e s o v e r which t h e t e s t s we re made.
A d d i t i o n a l t e s t s we re co m p le te d f o r t h e U. S.. G e o l o g i c a l Survey
d u r i n g t h e 1 9 3 0 ' s (Lee ,
1939)•
Th es e t e s t s were i n t e r p r e t e d t o i n d i c a t e
t h a t e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP a n o m a l i e s a r e t h e r e s u l t o f
electrochem ical
reactions
involving p y r i t e .
Lee c o n c l u d e d from t h e s e
t e s t s t h a t m e t a l l i c m i n e r a l s o t h e r th a n p y r i t e co u l d n o t be d e t e c t e d
u s i n g SP m e a s u r e m e n t s .
The u s e o f SP measurements in t h e U ni te d S t a t e s
v i r t u a l l y stopped fo llow ing p u b li c a ti o n o f th e se I n te r p r e t e d r e s u l t s .
Whether t h i s
r e p o r t o r t h e o u t b r e a k o f World War II had more i n f l u e n c e
on t h i s devel op men t i s d i f f i c u l t t o d e t e r m i n e .
The s i m p l i c i t y o f SP measu re men ts and t h e low c o s t o f s u r v e y s
made t h e method a t t r a c t i v e f o r m i n e r a l e x p l o r a t i o n in t h e d e v e l o p i n g
nations.
S i n c e 1940, most r e p o r t s p e r t a i n i n g t o SP measu re men ts have
been summaries o f f i e l d m e a su r e m e n t s.
Some s i g n i f i c a n t d ev el op m en ts
s i n c e 1950 i n c l u d e d e t a i l e d a n a l y s i s o f t h e SP c u r v e s o b s e r v e d on w el l
l o g s , a d e t a i l e d s t u d y o f t h e e l e c t r o c h e m i c a l mechanism o f s u l f i d e s e l f ­
potential
( S a t o and Mooney, 19 60) , and c o n s i d e r a t i o n o f c o u p l i n g between
d i f f e r e n t SP mechanisms ( N o u r b e h e c h t ,
1963 ).
11
Summary o f S p e c i f i c SP Mechanisms
Th re e e l e m e n t s a r e n e c e s s a r y f o r an i n t e r p r e t a t i o n o f SP d a t a :
1.
The s o u r c e o f a s i g n a l must be u n d e r s t o o d .
2.
The e n e r g y t r a n s p o r t mechanisms must be r e c o g n i z e d .
3-
The way in which a r e c e i v e r d e t e c t s and f i l t e r s
the signal
must
be known i n c l u d i n g t h e dipoT e c o n f i g u r a t i o n , e l e c t r o n i c s and
d i s p l a y mode.
The t h i r d e l e m e n t i s a f u n c t i o n o f t h e d e s i g n s p e c i f i c a t i o n s o f t h e SPdetecting
i n s t r u m e n t , c a b l e , and t h e geom etry o f t h e gr ou nde d e l e c t r o d e s
used f o r a s e t . o f m e as ur e m en t s.
The i n s t r u m e n t c h a r a c t e r i s t i c s a r e g e n ­
e r a l l y known o r can be e x p e r i m e n t a l l y d e t e r m i n e d .
The c a b l e c o n n e c t i n g
t h e e l e c t r o d e s t o t h e i n s t r u m e n t w i t h which measu re men ts a r e made does
n o t c o n t r i b u t e s i g n i f i c a n t l y t o t h e n o i s e as long as t h e c a b l e is w el l
i n s u l a t e d , and p o s s i b l y s h i e l d e d .
signal
between
E l e c t r o d e n o i s e adds t o t h e o v e r a l l
as a r e s u l t o f t e m p e r a t u r e o r i o n i c c o n c e n t r a t i o n d i f f e r e n c e s
the e l e c t r o l y t e s
in t h e e l e c t r o d e s
(Fig.
1).
■Electrode-
g e n e r a t e d n o i s e can be minimized i f t h e e r r o r t o l e r a n c e i s s p e c i f i e d
b efo re s e l e c t i n g equipment.
The n a t u r a l e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP and t h e k i n e t ­
i c s o f t h e e n e r g y s y s t e m th r o u g h which t h e s e c u r r e n t s p a s s a r e p o o r l y
understood.
The c o n c e p t u a l model most g e n e r a l l y use d i s a n a t u r a l
" b a t t e r y " which c a u s e s a c u r r e n t t o fl o w .
The o n l y f l o w s r e c o g n i z e d in
t h i s model a r e i o n i c and e l e c t r o n i c w i t h c u r r e n t s f l o w i n g t h r o u g h
s a t u r a t e d po ro us media in t h e f i r s t c a s e and a m e t a l l i c c o n d u c t o r in
t h e second.
T h i s l i m i t e d model does n o t a c c o u n t f o r t h e s e v e r a l o t h e r
mechanisms r e l a t e d t o SP.
12 .
This s e c t i o n
i s a summary o f t h e e l e c t r o c h e m i c a l , e l e c t r o k i -
n e t i c , and t h e r m o e l e c t r i c mechanisms a s s o c i a t e d w i t h SP.
ical
The mathemat­
r e l a t i o n s h i p s d e s c r i b i n g ea c h o f t h e fl o w s a s s o c i a t e d w i t h t h e s e
mechanisms a r e d i s c u s s e d
in te rm s o f t h e i r common e l e m e n t s .
A brief
summary Of e x t r a n e o u s e l e c t r i c n o i s e a s i t a f f e c t s SP me asurements
c o m p le te s t h i s s e c t i o n .
E1e c t rochem? ca t Meehan 1sms
SP a n o m a l i e s o f n a t u r a l e l e c t r o c h e m i c a l o r i g i n a r e t h e r e s u l t o f
variations
in t h e c h e m i s t r y and c o n d u c t i v i t y o f s u b s u r f a c e m a t e r i a l s .
Four c r i t e r i a must be s a t i s f i e d f o r any e l e c t r o c h e m i c a l mechanism t o be
active,
1.
The a c t i v e s u b s t a n c e s in t h e s y s t e m must be c a p a b l e o f d i s association
2.
into ions.
The s y st em must be c a p a b l e o f s u p p o r t i n g o x i d a t i o n and
reduction re a c tio n s.
C u r r e n t f lo w w i l l be maximized i f
o x i d a t i o n and r e d u c t i o n r e a c t i o n s a r e I s o l a t e d from each
other.
3.
C o n v e r s io n o f chem ica l e n e r g y t o o t h e r forms o f e n e r g y must
be p o s s i b l e , b u t c h an g e s in t h e t o t a l c h e m i s t r y o f t h e s yst em
a re not a c t u a l l y nece ssary .
4.
A l i q u i d j u n c t i o n must be p r e s e n t t o p e r m i t d i r e c t
ion t r a n s ­
p o r t between r e g i o n s o f o x i d a t i o n and r e d u c t i o n .
The u l t i m a t e s t a t e o f any s y st em s u p p o r t i n g e l e c t r o c h e m i c a l
reactions
is one in which a l l o p p o s i n g c h a n g e s in t h e sy ste m o c c u r a t t h e same
rate.
I f t h e e l e c t r i c c u r r e n t s a r e t o be c o n s t a n t , t h e s ys t em must
13
be op en ; t h a t
i s , one in which t h e components a r e f r e e t o ex ch an ge
m a t t e r and e n e r g y w i t h a s u p p o r t i n g e n v i r o n m e n t .
Several g e o lo g ic environments s a t i s f y i n g th e s e c r i t e r i a a re
known t o be r e l a t e d t o SP:
1.
One in which two o r more e l e c t r o l y t e s w i t h d i f f e r e n t o x i d a t i o n
p o t e n t i a l s a r e p h y s i c a l l y s e p a r a t e d by a l i q u i d j u n c t i o n b u t
e l e c t r o n i c a l l y c o n n e c t e d by a zo n e o f m e t a l l i c m i n e r a l i z a t i o n .
2.
A s y s t e m in which a s t r a t i f i e d ,
is
3.
p o l y m e t a l l i c m i n e r a l i z e d mass
immersed in a homogeneous e l e c t r o l y t e .
An e n v i r o n m e n t in which a l i q u i d j u n c t i o n o c c u r s
a t geologic
c o n t a c t s between e a r t h m a t e r i a l s h av in g d i f f e r e n t p h y s i c a l and
c h em ic a l p r o p e r t i e s .
O th er e n v i r o n m e n t s have been examined t o d e t e r m i n e w h e t h e r t h e y can
support electrochem ical processes capable of generating e l e c t r i c
currents.
S a t o and Mooney (I960) have d i s c u s s e d and l i s t e d
objections
t o most o t h e r p r o p o s e d me chanisms.
Redox Charge T r a n s f e r .
their
The f i r s t g e o l o g i c e n v i r o n m e n t i n v o l v e s
a m e t a l l i c c o n d u c t o r immersed p e r p e n d i c u l a r t o t h e s t r a t i f i c a t i o n o f
e le c tro ly tic solutions.
T h i s has been d i s c u s s e d p e r i o d i c a l l y s i n c e
Se h lu m be r g er p u b l i s h e d s u r v e y r e s u l t s f o r t h e S a i n Bel p y r i t e mine
(Leonardon and Kelly., 1928; P o l . d i n i , 1938a; among o t h e r s ) .
An e x t e n ­
s i v e e f f o r t t o e s t a b l i s h a t h e o r e t i c a l model and t o q u a n t i f y t h e SP
a n o m a l i e s t h a t r e s u l t from t h i s mechanism was r e p o r t e d by S a t o and
Mooney (I960)
(Fig. 2 ) .
by Mason ( 1 9 4 9 ) , G a r r e l s
T h i s model was based Oh p h y s i c a l measurements
( 1 9 5 4 ) , Germanov and o t h e r s
( 1 9 5 9 ) , H olland
o x id e
h o s t rock
F i g u r e 2.
conductive
mi n e r a 1i z a t ion
□
o x i d e zone
unconsolidated
s ed im en ts
Redox c h a r g e t r a n s f e r mechanism o f s u l f i d e s e l f - p o t e n t i a l s - - A f t e r
S a to and Mooney ( i9 6 0 )
N e a r - s u r f a c e o x i d a t i o n t a k e s p l a c e on ly to t h e e x t e n t e l e c t r o n s a r e
r e q u i r e d to co m p le te r e d u c t i o n o f n e a r - s u r f a c e o x i d i z i n g a g e n t s
15
( 1 9 5 9 ) , Be ck in g , Kaplan and Moore ( i 9 6 0 ) , and S a t o ( 1 960 a,
t h e Eh and pH o f s o l u t i o n s
E lectric currents
1960b) o f
in and aro und s u l f i d e m i n e r a l i z a t i o n .
in t h e redox c h a r g e t r a n s f e r s y s t e m flow as
t h e r e s u l t o f o x i d a t i o n r e a c t i o n s a t t h e anode and r e d u c t i o n r e a c t i o n s
a t the cathode.
The a n o d i c and c a t h o d i c h a l f - c e l l
w r itt e n using P o u rb a ix 's
(19^9) n o t a t i o n .
aA + cH^O = bB + pH
Cathode
reac tio n s are
E1e c t r o l y t e
E lectrolyte
The redox p o t e n t i a l
+ ne"
Anode
fo r th e n e a r - s u r f a c e environment is regu­
l a t e d by r e d u c t i o n o f n e a r - s u r f a c e o x i d i z i n g a g e n t s .
tial
The redox p o t e n ­
a t d e p t h is c o n t r o l l e d by o x i d a t i o n o f t h e r e d u c i n g a g e n t s .
Nernst equatio n
is used t o c a l c u l a t e t h e p o t e n t i a l
The
d i f f e r e n c e between
t h e two h a l f - c e l 1s .
II
E. =
RT
.
_E0 + r T 3 ,n
T h i s e q u a t i o n can be s i m p l i f i e d
P
Ta T
-
RT , .
_Eo + r 7 b ,n
P'
T bT
( 1)
i f t h e r e f e r e n c e is t h e hydrogen s c a l e
(S at o and Mooney, I9 60, p. 2 3 1 ) .
Eh = Eh
o
— pH + {p- ( - a In [A] + b In [ B])
F n
Fn
(2 )
The m i n e r a l i z e d body a c t s s o l e l y as. an e l e c t r o n i c c o n n e c t i o n
between t h e two i o n i c s o l u t i o n s and is u n a f f e c t e d by t h e h a l f - c e l l
tions.
reac­
T h i s c o n d i t i o n i s v a l i d a s long as t h e i o n i c s o l u t i o n s a r e
ideal; th at
is,
t h e e f f e c t i v e c o n c e n t r a t i o n s o f t h e me ta l
in t h e s o l v e n t s a r e l e s s t h a n 10
-6
( S a t o and Mooney, 1960, p. 2 3 2 ) .
S e v e r a l f a c t o r s a l t e r t h e r ed ox mechanism.
c o n s i d e r e d t h e g o s s a n p r o bl em .
ions d i s s o l v e d
F o r m at io n o f o x i d e s
Poldini
(1938b)
i n d i c a t e s t h e number
of e le c tro n s necessary fo r n e a r-su rfa c e reduction of o x id izin g agents
is i n s u f f i c i e n t .
required.
To c o m p l e t e t h e r e d u c t i o n a d d i t i o n a l e l e c t r o n s a r e
When n e c e s s a r y t h e e l e c t r o n s a r e made a v a i l a b l e t h r o u g h
o x i d a t i o n o f neai—s u r f a c e m a t e r i a l .
T h i s i n d i c a t e s a lo w e r i n g o f t h e
n e a r - s u r f a c e Eh, c o n s e q u e n t l y t h e r ed ox p o t e n t i a l o f t h e s y s t e m .
tional
reductions
liquid ju nction
Ad di­
in e l e c t r o n e x c h a ng e o c c u r a t t h e c a t h o d e i f t h e
is p o o r l y d e v e l o p e d o r i f m i n e r a l i z a t i o n
is d i s s e m i n a t e d
ra th e r than continuous.
Galvanic Current G en eratio n .
O x i d a t i o n and ch e m ic a l d i s p e r s i o n
o f m e t a l s a r e two t y p e s o f a l t e r a t i o n t h a t common1y o c c u r w i t h m e t a l l i c
m ineralization.
Th ese p r o c e s s e s a r e r e l a t e d t o t h e Eh and pH e n v i r o n -
ments in which t h e m i n e r a l i z a t i o n o c c u r s
o t h e r s , I9 60; S a t o ,
( H an s h ul d,
1966).
(G arrels,
1954; Becking and
19 6 0 a , 1960b) and t h e m o b i l i t y o f t h e meta 1 ions
The d e s t r u c t i o n o f me ta l s u l f i d e s t h r o u g h o x i d a t i o n ,
t h e t r a n s f e r o f me tal
i o n s , and t h e r e s u l t i n g g e n e r a t i o n o f an e l e c t r i c
c u r r e n t a r e a n a l o g o u s t o t h e p r o c e s s e s o c c u r r i n g in a commercial o r
laboratory galvanic c e l l .
The d i f f e r e n c e between t h e n a t u r a l c e l l and
i t s man-made c o u n t e r p a r t is t h e r e l a t i v e I o n i c m o b i l i t i e s .
Ion
17
m o b i l i t y i s a f u n c t i o n o f t o r t u o s i t y and d e g r e e o f s a t u r a t i o n .
Most
commercial and l a b o r a t o r y g a l v a n i c c e l l s c o n t a i n a f l u i d e l e c t r o l y t e in
which ion m o b i l i t y i s optimum.
In a n a t u r a l g a l v a n i c c e l l
p o r t is t h r o u g h a p o r o u s s o l i d c o n t a i n i n g
in terstitial
ionic t r a n s ­
electrolytes.
Two n a t u r a l , p h y s i c a l e n v i r o n m e n t s a r e a b l e t o s u p p o r t g a l v a n i c
reactio n s:
1.
E l e c t r o n i c a l l y c o n n e c t e d , s t r a t i f i e d , m e t a l l i c masses in. a
r e l a t i v e l y homogeneous e l e c t r o l y t e .
2.
A homogeneous m e t a l l i c mass c o n n e c t i n g two e l e c t r o l y t e s w i t h
d i f f e r e n t r ed o x p o t e n t i a l s .
A n e c e s s a r y c o n d i t i o n f o r eac h o f t h e s e i s t h e o c c u r r e n c e o f o x i d i z i n g
r e a c t i o n s a t t h e anode a t d e p t h .
aro u nd m e t a l l i c s u l f i d e s
The common o c c u r r e n c e o f li m O n i t e
in t h e o x i d i z i n g en v i r o n m e n t a t d e p t h p r o v i d e s
ample e v i d e n c e t h a t such r e a c t i o n s t a k e p l a c e .
must o c c u r n e a r - s u r f a c e .
The r e d u c i n g r e a c t i o n s
T h i s c o n f i g u r a t i o n o f o x i d i z i n g and r e d u c i n g
r e a c t i o n s i s r e q u i r e d t o m i n im i ze t h e p o t e n t i a l o v e r t h e c o n d u c t o r .
S c h lu m b e r g e r (1920) r e c o g n i z e d t h i s mechanism w h i l e i n t e r p r e t i n g
SP d a t a from t h e S a in Bel p y r i t e mine.
and K e d r i n s k l y (1965,
Fold i n i
(1938 a) and Sv es h ni k ov
1966) c o n s i d e r e d s e v e r a l p o s s i b l e h a l f - c a l l
reac­
t i o n s t h a t can p r o d u c e e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP and t h e
quan tity of m aterial
currents.
that
would be a l t e r e d t o s u p p o r t t h e e l e c t r i c
P o l d i n i ' s work was r e p e a t e d by Yungul
(19^5) who showed t h a t
15 kg o f p y r i t e must be c o n v e r t e d t o l i m O n i t e t o s u s t a i n a c u r r e n t o f
one ampere f o r one y e a r i n an e l e c t r o l y t i c c o n d u c t o r and a m e t a l l i c
c o n d u c t o r eac h h a v i n g a r e s i s t i v i t y o f one ohm.
using th e se param eters
is one v o l t .
The p o t e n t i a l
generated
Th es e v a l u e s a r e n o t r e a l i s t i c ,
18
b u t t h e y do s e r v e t o i l l u s t r a t e t h a t t h e d e s t r u c t i o n o f a m i n e r a l i z e d
body d u r i n g g a l v a n i c p r o c e s s e s
is n o t s i g n i f i c a n t o v e r s h o r t time
periods.
The n e t r e a c t i o n can be r e p r e s e n t e d u s i n g t h e sum o f two h a l f cel 1 r e a c t i o n s .
aA + ne~ = bB
-
(cC + ne" - dB)
aA + dD =
The s e n s e o f t h i s r e a c t i o n
is s p o n t a n e o u s t o t h e r i g h t i f t h e e l e c t r o d e
p o te n tia l of the f i r s t h a l f - c e l l
second.
The p o t e n t i a l
cC + bB
reaction
is higher than t h a t of the
d i f f e r e n c e t h a t can d e v e l o p in a g a l v a n i c c e l l
is c a l c u la t e d using the Nernst e q u a tio n .
Two s e t s o f h a l f - c e l l
attention
in t h e l i t e r a t u r e .
1923; P o l d i n i , 1938a,
the p y rite -g a le n a
cell
r e a c t i o n s have r e c e i v e d c o n s i d e r a b l e
Th es e a r e t h e s p h a l e r i t e - p y r i t e
1938b, 1939b; H e i l a n d ,
(Poldini,
1938a,
1940; U r a z a y e v ,
1938b, 1939b) r e a c t i o n s .
(Kelly,
1970) and
The h a l f ­
r e a c t i o n s and t h e c a l c u l a t e d e l e c t r o d e p o t e n t i a l s a r e shown below.
FeS + 2 e “ = =
Fe
+ S"
-
1. 0 0 V
- (ZnS + 2e~ =
Zn
+ S~~
-
1. 4 4 V)
FeS + Zn =
Fe
+ ZnS
+ 0.44 V
PbS + 2e~ =
Pd
+ S ~
-
Fe
. + S~~
- 1. 0 0)
+
+ 0.02 V
- (FeS +
PbS +
2e~ =
Fe -== FeS
Pb
. S p h alerite stable
0.98
P yrite stab le
The p y r i t e e l e c t r o d e is d e s t r o y e d when s p h a l e r i t e
r e s u l t i n g e l e c t r o d e p o t e n t i a l o f 0 . 4 4 V.
is p r e s e n t w i t h a
SP a n o m a l i e s a r e seldom a s s o ­
c i a t e d w i t h s p h a l e r i t e even tho ug h t h e maximum SP anomaly e x p e c t e d a t
t h e s u r f a c e i s 0 . 2 2 V.
The l a c k o f SP in t h i s c a s e i s p r o b a b l y a f u n c ­
t i o n o f t h e d e s t r u c t i o n o f t h e p y r i t e e l e c t r o d e and t h e poor conducti v i t y of sp h a le rite .
present.
The g a l e n a e l e c t r o d e i s d e s t r o y e d
i f p y r i t e is
The e l e c t r o d e p o t e n t i a l o f t h e r e s u l t i n g r e a c t i o n s
The m a g n it u d e o f t h i s p o t e n t i a l
is 0 . 2 0 V.
and t h e i n s u l a t e d h a b i t a t in which
g a l e n a commonly o c c u r s a c c o u n t f o r t h e a b s e n c e o f SP a n o m a l i e s o v e r
pyrite-galena m ineralization.
t h e g a l v a n i c mechanism can r e s u l t in p o l a r i z a t i o n o f t h e s y st e m
in such a way t h a t c u r r e n t f lo w i s s t o p p e d .
t h e r e s u l t o f many d i f f e r e n t ch em ica l
D e p o l a r i z a t i o n is p r o b a b l y
r e a c t i o n s . . S t r o n g o x i d i z i n g and
reducing agen ts a r e n e c e ssary i f p o l a r i z a t i o n
i s t o be p r e v e n t e d .
Th es e
a r e s u p p l i e d d i r e c t l y by t h e h o s t r o c k s o r t r a n s p o r t e d by ground w a t e r .
D i f f u s i o n C u r r e n t s . G e o l o g i c c o n t a c t s a c t as I on s e l e c t i v e mem­
b r a n e s i f two r o c k t y p e s in c o n t a c t c o n t a i n e l e c t r o l y t e s w i t h d i s t i n c t l y
d i f f e r e n t p h y s i c a l and ch em ica l p r o p e r t i e s
Kunori and I s h i i ,
1961).
(Polak,
1957; S h a p i r o ,
1958;
I f t h e Eh and pH a r e c o n s t a n t and an i o n i c .
c o n c e n tr a ti o n d i f f e r e n c e e x i s t s a c ro s s a c o n t a c t , d i f f u s i o n occurs as
t h e r e s u l t o f random ion m o t io n .
The g r e a t e r m o b i l i t y o f t h e s m a l l e r
a n i o n s e n h a n c e s t h e i r a b i l i t y t o p a s s t h r o u g h t h e c o n t a c t in t h e d i r e c ­
tion of decreasing concentration
(McConnell, 1954; Mi r o s c h n i che nko ,
1963; W i l l a r d , M e r r i t t and Dean, 1965).
The d i f f e r e n c e in t h e d i f f u s i o n
r a t e s between a n i o n s and c a t i o n s r e s u l t s
in an e l e c t r i c p o t e n t i a l
d i f f e r e n c e i f a c he m ic a l p o t e n t i a l g r a d i e n t e x i s t s a c r o s s t h e c o n t a c t
( N o u r b e h e c h t,
1963).
S e v e r a l f a c t o r s a f f e c t t h e r a t e a t which io ns d i f f u s e a c r o s s a
c o n t a c t u n d e r t h e i n f l u e n c e o f c o n c e n t r a t i o n d i f f e r e n c e s and chemical
potential gradients.
The c o m p o s i t i o n and i o n i c c o n c e n t r a t io ns o f t h e
e l e c t r o l y t e s on o p p o s i t e s i d e s o f t h e c o n t a c t d e t e r m i n e t h e che m ica l
potential
g r a d i e n t , which a c t s a s t h e f o r c e d r i v i n g t h e i o n i c c u r r e n t s .
The e l e c t r o l y t e c o m p o s i t i o n i s r e l a t e d t o m a t r i x m i n e r a l i z a t i o n and t h e
c i r c u l a t i o n of pore f l u i d s .
Rock m a t r i c e s a r e d e t e r m i n e d by m i n e r a l o g y ,
c r y s t a l l o g r a p h y , g r a i n s i z e , s h a p e , and p a c k i n g d e n s i t y .
d e t e r m i n e s p o r o s i t y and t o r t u o s i t y .
The m a t r i x
P o r o s i t y d e t e r m i n e s t h e maximum
s i z e o f io n s a b l e t o p a s s th r o u g h a m a t r i x .
T o r t u o s i t y i s a mea sure o f
t h e mean f r e e p a t h a c r o s s which any ion must t r a v e l .
The q u a n t i t y and
d i s t r i b u t i o n o f ions in an e l e c t r o l y t e a l o n g a c o n t a c t a r e a f u n c t i o n
o f the degree o f mixing.
An i m p o r t a n t c o n s i d e r a t i o n
is th e c o n c e n tr a ti o n of d i f f e r e n t
io n ic , s p e c i e s and t h e i r r e l a t i v e r a t e s o f d i f f u s i o n w i t h r e s p e c t t o
th e ir overall
I n f l u e n c e on t h e ch em ic a l p o t e n t i a l
to the co n c e n tra tio n s of the various
chem ica l
ionic species
gradient.
Related
is th e e f f e c t of
r e a c t i o n s bet ween t h e v a r i o u s s p e c i e s on t h e d i f f u s i o n r a t e .
Is o la tio n of the e l e c t r i c p o te n tia l d if f e r e n c e a s s o c ia te d with
Ion d i f f u s i o n c u r r e n t s from t h a t due t o o t h e r e l e c t r o c h e m i c a l p r o c e s s e s
is
i m p o s s i b l e in t h e f i e l d .
the exception of s p h a l e r i t e
Some m i n e r a l s , f o r exam ple s u l f i d e s w i t h
(G. B. Sveshni kov, c i t e d
in Ura za y ev ,
1 97 0) , do n o t b u i l d up l a r g e c o n c e n t r a t i o n d i f f e r e n c e s .
that
This i n d i c a t e s
in t h e a b s e n c e o f e v i d e n c e t o t h e c o n t r a r y d i f f u s i o n does not
21
a f f e c t t h e r e d o x c h a r g e t r a n s f e r mechanism, which has been shown by
S a t o and Mooney (1960) t o be t h e p r i m a r y e l e c t r o c h e m i c a l mechanism f o r
e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h c o p p e r and i r o n s u l f i d e s .
The p r i n c i p a l
ion s e l e c t i v e membranes in t h e e a r t h a r e t h o s e
made up o f c l a y m i n e r a l s .
The c l a y c o n t e n t o f r o c k s has a s i g n i f i c a n t
e f f e c t on t h e e l e c t r o c h e m i c a l p o t e n t i a l as has been d e m o n s t r a t e d d u r i n g
SP l o g g i n g in s e d i m e n t a r y r o c k s
1954; W y l l i e ,
adsorbing
Telford
1955).
(Winsauer and o t h e r s , 1952; McConnell,
Clay m i n e r a l s l i m i t e l e c t r o c h e m i c a l a c t i v i t y by
io n s , thus reducing e f f e c t i v e
ionic m o b ility .
(1965) have shown t h a t a h o r i z o n t a l
Becker and
l a y e r o f c l a y between t h e
s u r f a c e a l o n g which m ea sur em ent s a r e made and t h e c e n t e r o f e l e c t r o ­
chemic al a c t i v i t y can e f f e c t i v e l y s h o r t - c i r c u i t
ion c u r r e n t f lo w as a
r e s u l t o f ion a d s o r p t i o n and mask e l e c t r o c h e m i c a l a c t i v i t y below t h e
layer.
The e l e c t r i c p o t e n t i a l d i f f e r e n c e between two e l e c t r o l y t e s due
t o t h e c h em ic a l p o t e n t i a l
d i f f e r e n c e a c r o s s a c o n t a c t can be c a l c u l a t e d
u s i n g a m o d i f i e d form o f t h e N e r n s t e q u a t i o n .
Em
=I
t
p a
-
I f ]
i a
"
i d
I" -[fj-
(3)
S e v e r a l r e p o r t s o f e l e c t r i c p o t e n t i a l s on t h e e a r t h ' s s u r f a c e
a t t r i b u t e d t o ion d i f f u s i o n a c r o s s g e o l o g i c c o n t a c t s have been made.
T he s e a r e in a d d i t i o n t o t h e l a r g e amount o f r e s e a r c h r e p o r t e d by
scien tists
potential
in t h e p e t r o l e u m i n d u s t r y .
Hunkel
(1928a,
1928b) r e p o r t e d
g r a d i e n t s a c r o s s g e o l o g i c c o n t a c t s on t h e o r d e r o f 0 . 2 t o
2 2
0 . 3 raV/m a g a i n s t backgro und n o i s e l e s s t h a n a t e n t h t h i s m a g n it u d e .
B r a n t (1948)
r e p o r t e d r e s u l t s from measu re men ts a t R h y o l i t e , N eva da,
where anomalous e l e c t r i c p o t e n t i a l g r a d i e n t s o c c u r r e d whe re s e d i m e n t s
we re t h i n n e s t above c r y s t a l l i n e ro ck s in s e d i m e n t - f i l l e d v a l l e y s .
N ou r be he ch t (1963) c a l c u l a t e d t h e maximum m a g n it u d e o f a s u r f a c e SP
anomaly e x p e c t e d from i o n i c d i f f u s i o n a c r o s s a l i q u i d j u n c t i o n t o be
100 mV.
An i n t e r e s t i n g o b s e r v a t i o n from t h e s e d a t a is t h e p o s i t i o n
o f t h e i n f l e c t i o n p o i n t on t h e c u r v e d e s c r i b i n g t h e e l e c t r i c p o t e n t i a l
d iffe re n c e d i r e c t l y over a v e r ti c a l
contact
( F i g . 3)•
E1e c t r o k i n e t i c Meehan ? sms
E l e c t r i c c u r r e n t s a r e g e n e r a t e d by t h e f lo w o f an e l e c t r o l y t e
as t h e r e s u l t o f a p r e s s u r e d i f f e r e n c e a c r o s s an i o n - s e l e c t i v e membrane
or a c a p illa r y m atrix.
The e l e c t r i c p o t e n t i a l
w ith th e se c u rre n ts a re stream ing p o t e n t i a l s .
differences associated
The s t r e a m i n g p o t e n t i a l
i s one o f f o u r r e c o g n i z e d e l e c t r o k i n e t i c phenomena i n v o l v i n g t h e
me ch an ic al d i s p l a c e m e n t o f one p h a s e ; r e l a t i v e t o a n o t h e r , one o f which
must be l i q u i d .
detail
The o t h e r e l e c t r o k i n e t i c phenomena, d i s c u s s e d in
by H o rw it z ( 1 9 3 9 ) ,
sedim entation p o t e n t i a l s .
i n c l u d e e l e c t r o o s m o s i s , e l e c t r o p h o r e s i s , and
The l a s t t h r e e e l e c t r o k i n e t i c phenomena have
no s i g n i f i c a n t e f f e c t on SP and c o n s e q u e n t l y a r e n o t c o n s i d e r e d any
further.
In most ro ck s t h e s u r f a c e c h a r g e is p o s i t i v e .
The a n i o n s in
t h e e l e c t r o l y t e f i l l i n g t h e p o r e s in t h e m a t r i x a r e a d s o r b e d by t h e
s o l i d m i n e r a l s u r f a c e ( f i x e d l a y e r ) as a r e s u l t o f t h e c h a r g e d i f f e r ­
e n ce ( H a l l e n b e r g ,
19 71).
T hes e a n i o n s a r e e f f e c t i v e l y
immobile.
20
10
0
F i g u r e 3•
Changes in s e l f - p o t e n t i a l a t g e o l o g i c c o n t a c t s — Data from Hunkel
(1928a)
N3
VJ
24
C a t i o n s a r e In t u r n a t t r a c t e d t o t h e c h a r g e d l a y e r c o v e r i n g t h e s o l i d
surface.
The weak e l e c t r i c p o t e n t i a l
1izing the o u te r
(diffuse)
d i f f e r e n c e a t t r a c t i n g and s t a b N
lay er of c a t io n s to th e anions covering the
s o l i d s u r f a c e is t h e z e t a p o t e n t i a l
(C)
(Fig. 4 ),
!f an e l e c t r o l y t e
flow s th r o u g h t h e p o r e m a t r i x , some o f t h e l o o s e l y bound c a t i o n s from
t h e o u t e r l a y e r a r e c a r r i e d w i t h t h e flo w r e s u l t i n g
transfer
in t h e d i r e c t i o n Of t h e f lo w .
in a n e t c h a r g e
At i o n - s e l e c t i v e membranes
t h e l e s s m o b i le io ns a r e t r a p p e d w h i l e t h o s e t h a t p a s s t h r o u g h t h e
membrane c a r r y a n e t c h a r g e ,
Kozary (1948) and H a l l e n b e r g
( 1 9 7 T) used
t h e method o f H elm ho ltz t o show t h a t t h e s t r e a m i n g p o t e n t i a l can
be c a l c u l a t e d u s i n g t h e e q u a t i o n :
<«
MacDougal1 (1936) , Horwitz (1939) and Kozary (1948) t r i e d t o
determine the e l e c t r i c p o te n tia l
sions of the c a p i l l a r i e s ,
d i f f e r e n c e in te rm s o f p h y s i c a l dimen­
f lo w v e l o c i t i e s , and s a l t c o n c e n t r a t i o n s .
The o n l y p a r a m e t e r t h a t a p p e a r e d t o be d i r e c t l y r e l a t e d t o t h e e l e c t r i c
p o t e n t i a l was t h e s a l t c o n c e n t r a t i o n s
in t h e e l e c t r o l y t e s .
The s t r e a m ­
ing p o t e n t i a l was found t o be i n d e p e n d e n t o f p o r e ge o m et ry u n t i l t h e
pore rad iu s approached ionic r a d ii
Nourbehecht,
in
1963).
concentrations
difference.
( j . Th. G. O ver bec k, c i t e d
Kozary r e p o r t e d t h e s t r e a m i n g p o t e n t i a l f o r s a l t
_ jk
in e x c e s s o f 6 X 10
iH is i n d e p e n d e n t o f t h e p r e s s u r e
Below t h i s c o n c e n t r a t i o n s t r e a m i n g p o t e n t i a l s
increase
w i t h i n c r e a s i n g s a l t c o n c e n t r a t i o n s u nd er i s o b a r i c c o n d i t i o n s .
25
Figure 4
Q
- Cations
O
- Anions
C o n f i g u r a t i o n o f t h e d i f f u s e l a y e r o f c a t i o n s and th e
f i x e d l a y e r o f a n i o n s on t h e p o s i t i v e l y c h a r g e d rock
m a t r i x — A f t e r Winsauer and Mc Cardel1 (1953)
The d i f f u s e l a y e r is no t a w ell d e f i n e d s h e e t - l i k e
l a y e r , r a t h e r i t i s a l a y e r in which t h e a n i o n s a r e
concentrated.
2 6
T h i s ch ang e may be r e l a t e d t o c o m p re s s i o n o f t h e d o u b l e l a y e r o f ions
in such a way a s t o r e d u c e t h e i r s e p a r a t i o n and s t r e n g t h e n t h e mutual
i o n i c bonds. The z e t a p o t e n t i a l can be d e t e r m i n e d u s i n g t h e e q u a t i o n
( H o r w i tz ,
1939):
S -
'
(5)
S e v e r a l f a c t o r s w i l l modify t h e m a g n it u d e o f t h e s t r e a m i n g
potential
by a l t e r i n g t h e s y s t e m ' s c h e m i s t r y .
C a t i o n s and a n i o n s may
combine t o form i n s o l u b l e p r e c i p i t a t e s , c o a t t h e sol id m a t r i x , o r b l o c k
the pores.
Ions u n r e l a t e d t o t h e s o l i d m a t r i x may be a b s o r b e d .
p r e s e n c e o f c l a y and c a r b o n a t e s
The
in some b a s i c s o l u t i o n s w i l l a f f e c t t h e
m a g n it u d e and in some c a s e s t h e p o l a r i t y o f t h e c u r r e n t s a s s o c i a t e d
w ith stream ing p o t e n t i a l s
(Dahknov,
1962).
K e ll y (1959 a, p. 57) r e p o r t e d t h a t " r e g i o n s o f s t e e p l y d i p p i n g ,
t h i n l y bedded f o r m a t i o n s , p a r t i c u l a r l y s h a l e s and s h a l y s a n d s t o n e s ,
show a pr on oun ced and i r r e g u l a r i n c r e a s e in p o s i t i v e p o t e n t i a l s d u r i n g
the dry s e a s o n ."
Ot her o b s e r v e r s have r e p o r t e d s t r e a m i n g p o t e n t i a l s
on t h e o r d e r o f 10-20 mV due t o i r r e g u l a r e v a p o r a t i o n o f s u r f a c e m o i s ­
ture
( P o l d i n i , 1 9 3 9 a ).
Ambronn ( 1 9 2 8 ) , P o l d i n i
( 1 9 3 9 a ) , Rao (1953)
and C ag ni ar d (1956) have r e p o r t e d SP a n o m a l i e s a s s o c i a t e d w i t h s t r e a m ­
ing p o t e n t i a l s w i t h m a g n i t u d e s o f 30 t o 300 mV and pe ak g r a d i e n t s o f
25 mV/m.
Rao ( 1 9 5 3 ) , O g i l ' v y
(1956) and Lang (1971) have r e l a t e d s u b ­
s u r f a c e f lo w o f w a t e r in f l a t a r e a s t o s t r e a m i n g p o t e n t i a l s
( F i g . 5) •
A r e c e n t u s e o f s u r f a c e SP m ea sur em ent s t o d e t e c t f l o w i n g
e l e c t r o l y t e s has been f o r t h e e v a l u a t i o n o f e a r t h - f i l l e d dams and
A lluvium
Limestone
Tuffaceous
Volcanics
Fractures
100 -
80 -
60VO-
■m
| 20-\
0- 20-
F l u i d Flow
L i nes
ii
i
i i n
i i i i i i i
i
i
i
i
i
i
i
i
5U 3 2 1 2 3 4 5 6 7 8 910 12 M 16 18 20 22 2U 26 fK
4* + -K + + 4- + +
+ + + + + -»- + + -t + +
+ + + + + + - + + + J- + +
F i g u r e 5.
S e l f - p o t e n t i a l o v e r an a r t e s i a n s p r i n g
From Og i 1 1vy (1956)
2 8
other s tru c tu re s
and O g i l ' v y ,
(1972,
( O g i l ' v y , Ayed and B o g o s l o v s k y , 196$; Bogos lovs ky
1970a,
1970b,
1973a,
1973b).
Bogo slovs ky and O g i l ' v y
1977) and B o g o s lo v s k y , O g i l ' v y and S t r a k h o v a
(1977) have a l s o
measured t h e SP c a u s e d by s t r e a m i n g p o t e n t i a l s a l o n g f a u l t s and in
a r e a s whe re l a n d s l i d e s were in p r o g r e s s .
E l e c t r i c C u r r e n t - G e n e r a t i n g Mechanisms
R e l a t e d t o Therma1 Energy
Yama shita (1961) has e x p e r i m e n t a l l y shown t h a t t h e r e i s a
d e f i n i t e r e l a t i o n s h i p between t h e e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP
and h e a t - f l o w .
experim ents.
Two s e t s o f m ea sur em ent s were m a d e . d u r i n g Yamashi t a ' s
A r o c k s l a b c o n t a i n i n g m a s s i v e p y r i t e and c o p p e r s u l f i d e s
and a c o n t a i n e r o f p u l v e r i z e d p y r i t e were h e a t e d .
e le c tric potential
The t e m p e r a t u r e and
d i f f e r e n c e s were me asured a t s p e c i f i e d d i s t a n c e s
from t h e h e a t s o u r c e in t h e s l a b and in t h e c o n t a i n e r o f p y r i t e .
The
r e s u l t s o f t h e s e e x p e r i m e n t s i n d i c a t e d a flo w o f e l e c t r i c c u r r e n t in
th e d i r e c t i o n of in c re a s in g te m p e ra tu re (Fig. 6).
F i e l d o b s e r v a t i o n s in a r e a s o f v o l c a n i c a c t i v i t y
1976) a t Long V a l l e y , C a l i f o r n i a
(Zablocki,
(Anderson and J o h n s o n , 1973, 1974,
I 9 7 6 ) , a c r o s s t h e Mud Volcano a r e a , Y e l l o w s t o n e N a t i o n a l P a r k , Wyoming
(Zohdy, Anderson and M u f f l e r ,
(Combs and W i l t ,
1973),
in t h e im p e r i a l V a l l e y , C a l i f o r n i a
19 76) , a t t h e Stea mbo at S p r i n g s t h e rm a l a r e a , Nevada
(White, Thompson, and S a n d b e rg ,
1 9 64 ),
in t h e o f f s h o r e C a l i f o r n i a a r e a
(Corwin, 197 3) , o v e r t h e Agua Blanca f a u l t ,
1972) ,
cited
in t h e Hawaiian I s l a n d s
in Ambronn,
1928, p.
(Furumoto,
Baja, C a l if o r n i a
19 76),
in J a p a n
(Sandstra,
( J . M iln e ,
149; O n o d e r a , 19 74) , and in I t a l y
(Rapolla,
55
(mV)
50
35
30
25
V
T em pe ra ture in p ow de re d pyrite
O
T e m p e ra tu re in massive su lfid es
< 7 ----- P o te n tia l in pow dered pyrite
20
P o ten tia l in m a ssiv e s u lfid e s
15
Electric
Temperature
(°C)
40
Potential
D ifference
45
10
5
0
2
8
12
4
D i s t a n c e (cm)
F i g u r e 6.
V a r i a t i o n s o f t h e s p o n ta n e o u s e l e c t r i c p o t e n t i a l and t e m p e r a t u r e in a c o n t a i n e r o f
powered p y r i t e and in a s l a b o f rock c o n t a i n i n g ma ss iv e s u l f i d e s as a f u n c t i o n o f
d i s t a n c e from t h e h e a t s o u r c e - - From Yamashita (1961 )
M
VO
30
1974) p r o v i d e f u r t h e r e v i d e n c e o f t h e r e l a t i o n s h i p between SP and h e a t
flow.
The m a g n i t u d e s o f t h e measured SP v a l u e s v a r i e d from 40-50 mV
(Zohdy and o t h e r s , 1973) t o 0 . 9 V (Anderson and J o h n s o n , 1974).
A d d i t i o n a l e v i d e n c e s u p p o r t i n g a r e l a t i o n s h i p between SP and
h e a t f lo w i s t h e p o s i t i v e n a t u r e o f t h e b a s e l i n e s h i f t w i t h d e p t h
o b s e r v e d on SP l o g s .
Becker and T e l f o r d
w h i l e l o g g i n g SP in d r i l l
(1965) o b s e r v e d t h i s s h i f t
holes near s u l f i d e m i n e r a liz a tio n .
Part of
t h i s s h i f t was a t t r i b u t e d t o t h e t e m p e r a t u r e d i f f e r e n c e between t h e
r e f e r e n c e and s e n s i n g e l e c t r o d e s .
Copper-copper s u l f a t e e l e c t r o d e s
were used f o r t h e s e m e a s u r e m e n t s .
The th e rm a l g r a d i e n t o b s e r v e d in
the d r i l l
h o l e s was + 3 ° C / 1 000 f t .
Yamashita (1961)
reversed.
(Fig. 6 ) ,
it
Comparing t h e s e d a t a w i t h t h o s e o f
is n o t a b l e t h a t t h e c u r r e n t f lo w is
P i r s o n and Wong (1972) f a v o r t h e ide a o f t e m p e r a t u r e d i f f e r ­
e n c e s a t t h e e l e c t r o d e s as an e x p l a n a t i o n t h a t can a c c o u n t f o r p a r t
of the b a s e lin e s h i f t .
T h e r m o e l e c t r i c i t y c a n n o t a c c o u n t f o r t h e m a g n it u d e o f t h e
o b s e r v e d SP a n o m a l i e s in a r e a s o f g e o t h e r m a l a c t i v i t y ,
potential
in g e o t h e r m a l a r e a s
however.
S elf-
in e x c e s s o f 100 mV u n d o u b t e d l y i n c l u d e s
a c o n v e c t i v e e l e c t r o k ? n e t i c , o r an e l e c t r o c h e m i c a l component as has
been s u g g e s t e d by S a n d s t r a
(1 9 7 2 ) , Corwin (1973)> and Anderson and
Joh nso n ( 1 9 7 6 ) . . .
T h e r m o e l e c t r i c i t y as i t c o n t r i b u t e s t o e l e c t r i c s i g n a l s mea­
s u r e d in g e o p h y s i c s has been v i r t u a l l y
p. 8 2 ) c o n s i d e r e d r e g i o n a l
ignored.
N o u r b e h e c h t (1963,
t h e r m o e l e c t r i c i t y due t o t h e th e rm al g r a ­
d i e n t c a u s e d by t h e t e m p e r a t u r e d i f f e r e n c e between t h e s u r f a c e and
31
base of th e e a r t h ' s c r u s t .
He c o n c l u d e d an e l e c t r i c p o t e n t i a l g r a d i e n t
o f 2 o r 3 mV/km can be g e n e r a t e d by h e a t f l o w i n g t h r o u g h t h e c r u s t .
No
o t h e r i n v e s t i g a t o r s have c o n s i d e r e d t h e r m o e l e c t r i c i t y a s i t a p p l i e s t o
geophysics
in any g r e a t d e t a i l .
S e v e r a l f a c t s c o n c e r n i n g t h e r m o e l e c t r i c i t y and t h e e f f e c t o f
t e m p e r a t u r e on c u r r e n t s g e n e r a t e d by o t h e r SP mechanisms a r e c e r t a i n :
1.
AM e l e c t r i c p o t e n t i a l s , w h e th e r o f e l e c t r o c h e m i c a l o r
e l e c tr o k i n e tic o r ig in , are temperature s e n s itiv e .
2.
S e p a r a t i o n o f t h e t h e r m a l e n e r g y t r a n s f e r r e d by t h e motion
o f m a t t e r t h r o u g h a p or o us medium from h e a t f lo w t h r o u g h t h e
s o lid m atrix is d i f f i c u l t ,
i f n o t i m p o s s i b l e , w i t h o u t imposing
u n n a t u r a l c o n s t r a i n t s on t h e s y s t e m in which measu re men ts a r e
made
3.
The a d d i t i o n o f h e a t t o an open s y s t e m i n e v i t a b l y cha ng e s t h e
ch em istry o f th e system.
The Reduced Forms o f t h e Ph en om e no lo g ic a l
E q u a t i o n s D e s c r i b i n g Energy T r a n s f e r
AM p r i m a r y f l o w s a s s o c i a t e d w i t h SP can be d e s c r i b e d in te rm s
o f a general energy t r a n s f e r e q u a tio n .
The m a g n it u d e and d i r e c t i o n o f
t h e e n e r g y f lo w (J) from any p o i n t Is t h e v e c t o r sum o f a l l
t h e flo w s
occurring at th a t point.
-
T = 2 7.
i
1
(7)
The maximum amount o f e n e r g y (E) f l o w i n g th r o u g h an a r e a
(A^) p e r u n i t
o f ti m e is
J
The symbol, n,
=
(8)
is t h e u n i t v e c t o r i n d i c a t i n g t h a t t h e maximum flow is
normal t o t h e s u r f a c e t h r o u g h which t h e flow p a s s e s .
The l e v e l o f e n e r g y in t h e flo w i s p r o p o r t i o n a l
to the product
o f t h e e n e r g y d i f f e r e n c e between two p o i n t s t h r o u g h which t h e flow
p a s s e s s e p a r a t e d by t h e o b s e r v a t i o n p o i n t and t h e c r o s s - s e c t i o n a l a r e a
o f t h e flow d i v i d e d by t h e d i s t a n c e
constant of p ro p o rtio n a lity
( r ) between t h e two p o i n t s .
is the c o e f f i c i e n t o f c o n d u c t i v i t y
The
(l_) .
E = L (X2 - X,)
(9)
Reducing t h e c r o s s - s e c t i o n a l a r e a o f t h e flow so t h a t an a p p r o x i m a t i o n
of a lin e a r ,
homogeneous,
i s o t r o p i c medium is v a l i d , e q u a t i o n
(9) can
be r e w r i t t e n .
AE = 1 im L
AA—*0
S u b s titu tin g equation
(10)
into equation
AX AAX
Ar
( 8 ) , t h e r a t e o f change o f
e n e r g y is r e p r e s e n t e d as a f u n c t i o n o f p o s i t i o n .
Mn)
33
The g r a d i e n t o f a s c a l a r f u n c t i o n such as e n e r g y is d e f i n e d as ha vi ng
a m a g ni tu de eq u al t o t h e g r e a t e s t s p a t i a l
r a t e o f cha n ge o f t h a t f u n c ­
t i o n in t h e d i r e c t i o n o f t h e maximum c h an g e .
spatial
The m a g n it u d e o f t h e
r a t e o f change o f t h e e n e r g y flow is AX/Ar.
the g r a d ie n t
flo w p a s s e s .
is t h a t o f t h e normal t o t h e s u r f a c e
Since the d i r e c t i o n of a l l
e n e rg y , the g r a d ie n t
is n eg ativ e.
The d i r e c t i o n o f
(n) th r o u g h which t h e
flow s is t h a t o f d e c r e a s i n g
Equation
(11) can be r e w r i t t e n
using the g r a d ie n t n o ta tio n .
T
= -
L VX
(12)
C o n s i d e r i n g t h e many p o s s i b l e modes o f e n e r g y flow ( i ) , t h e
g e n e r a l e n e r g y t r a n s f e r e q u a t i o n can be w r i t t e n by s u b s t i t u t i n g e q u a ­
tion
(12)
into equation
(7).
n
J = - I
M
For t h e c o n d i t i o n s
L. VX.
1
1
in which s i n g l e fl o w s a r e a c t i v e ,
(13)
the general energy
t r a n s f e r e q u a t i o n t a k e s t h e reduce d forms shown below.
D a r c y ' s law
P ick 's
law
F o u rie r's
=
J
law
- kVP
(14)
= - DVC
(15)
J q = XVT/j
( 16)
m
34
Ohms’ law
Each o f t h e s e e q u a t i o n s
= -aVV
(17)
is d e s c r i b e d as p h e no m en o lo g ic al
to account fo r
t h e e x p e r i m e n t a l l y d e r i v e d c o n d u c t i v i t y te rm s u n iq u e t o t h e p a r t i c u l a r
flow and t h e m a t e r i a l
th r o u g h which t h e flow p a s s e s .
E l e c t r i c charge t r a n s f e r
modes o f c o n d u c t i o n .
lyte f i l l i n g
I o n i c c h a r g e t r a n s f e r t a k e s p l a c e in t h e e l e c t r o ­
in terstitial
making up most r o c k s .
m inerals.
in t h e e a r t h depends on two d i s t i n c t
p o r e s p a c e s in t h e s e m i c o n d u c t i n g s i l i c a t e s
E lectron charge t r a n s f e r occurs
in t h e m e t a l l i c
The i n a b i l i t y t o s e p a r a t e t h e chem ica l and e l e c t r i c compo­
n e n t s o f t h e e l e c t r i c c u r r e n t makes i t n e c e s s a r y t o c o n s i d e r th e t o t a l
electrochem ical p o te n tia l
1939; Guggenheim c i t e d
as d e f i n e d
in e q u a t i o n
(18)
(MacDouga11,
in K a t c h a 1sky and C u r r a n , 1965).
“
= Zy. + Z.FVX
i 1
1
(18)
The p r e c e d i n g d i s c u s s i o n o f t h e flow s r e c o g n i z e d t o be r e l a t e d
t o SP i n d i c a t e s a d e f i n i t e c o u p l i n g between t h e s e flo w s and th e flow
o f an e l e c t r i c c u r r e n t .
T h i s and t h e s i m i l a r i t y o f t h e form o f t h e
e q u a t i o n s d e s c r i b i n g t h e flow s a l s o s u g g e s t s t h e p o s s i b i l i t y o f u n i ­
v e r s a l c o u p l i n g between a l l
L e n z ' s law r e l a t i n g
flows.
An a n a l o g y can be drawn between
inductive e l e c t r i c c u rren ts
in c o n d u c t o r s t o
ch ang es in m a g n e t i c f i e l d s and t h e c o u p l i n g o f f l o w s .
The c o u p l i n g o f
f lows i s r e c o g n i z e d by b i o p h y s i c i s t s and s o l i d - s t a t e p h y s i c i s t s as t h e
natural
r e a c t i o n o f a s y s t e m t o any a p p l i e d f o r c e .
o f t h e s i g n i f i c a n c e o f co u p l e d flow s t o g e o p h y s i c a l
Sim ilar recognition
i n v e s t i g a t i o n s has
35
been l i m i t e d t o i n v e s t i g a t i o n o f t h e i n d u c e d - p o l a r i z a t i o n phenomena
by M a r s h a ll and Madden (1959)> SP by No u rb eh ec ht
and Madden ( n . d . ) , and w e l l
sedim entary rocks ( S p ie g le r ,
(1963) and No u rb eh ech t
lo g g i n g use d t o e v a l u a t e p r o p e r t i e s o f
1958; McKelvey, Milne and Trump, n . d . ) - .
N o is e E n c o u n t e r e d d u r i n g SP Measurements.
The most e l u s i v e component o f a l l
p o r t i o n c a u s e d by e x t r a n e o u s a c t i v i t y .
is n o i s e .
s ig n a l s is the u n d e s ir a b le
The unwanted p a r t o f t h e s i g n a l
R e c o g n i t i o n o f n o i s e i s ah a r t t h a t depen ds on u n d e r s t a n d i n g
the d esired s ig n a l,
t h e p h y s i c a l p r o p e r t i e s o f t h e e a r t h , and t h e
c h a r a c t e r i s t i c s o f t h e i n s t r u m e n t s w i t h which m ea sur em ent s a r e made.
The amount o f n o i s e t h a t must be removed dep en ds on t h e maximum s l g n a l to - n o i s e r a t i o t h a t w ill not i n t e r f e r e w ith data i n t e r p r e t a t i o n .
The n a t u r a l l y o c c u r r i n g SP s i g n a l
is o n l y one component o f t h e
s p e c t r u m o f e l e c t r o m a g n e t i c s i g n a l s d e t e c t a b l e on t h e e a r t h ' s s u r f a c e .
S i n c e SP i s d e f i n e d a s a c o n s t a n t e l e c t r i c p o t e n t i a l ,
removal o f e l e c ­
t r i c n o i s e w i t h p e r i o d s l e s s t h a n t h e o b s e r v a t i o n p e r i o d d u r i n g which
m ea surements a r e made a t a s i n g l e s t a t i o n
f i l t e r designed in to th e in stru m en t.
is a f u n c t i o n o f t h e lo w - p as s
A t t e n u a t i o n o f dc n o i s e d u r i n g
SP m ea sur em ent s i s c u r r e n t l y i m p o s s i b l e .
Tem porarily vary in g e l e c t r i c
p o t e n t i a l g r a d i e n t s r a n g i n g from 0 . 5 mV/m/10 min have been o b s e r v e d
( S t o p p e l , 1929; P o r s t e n d o r f e r ,
Hoogervorst,
1975).
1961; R y s s ,
1964; P a r a s n i s ,
E l e c t r o n i c f i l t e r s a r e n ot an e f f i c i e n t way o f
removing t h i s kind o f l o w - f r e q u e n c y e l e c t r i c n o i s e .
of elim in atin g
1970; and
A p r a c t i c a l way
l o n g - p e r i o d v a r i a t i o n s suc h as t h o s e m e n ti o ne d above i s
t o r e c o r d t h e v a r i a t i o n s d u r i n g t h e p e r i o d o f a s u r v e y and s u b s t r a c t
them from t h e o b s e r v e d d a t a in t h e same, way d r i f t c o r r e c t i o n s a r e made
on o t h e r p o t e n t i a l d a t a .
Changes in c u r r e n t d e n s i t y as a r e s u l t o f t o p o g r a p h i c v a r i a t i o n s
a r e a more d i s c r e t e form o f n o i s e . t h a t must be e v a l u a t e d
and H oec her ,
1925; Hurd, 1944; Tuman,
1951).
(Koenigsberger
These e l e c t r i c v a r i a t i o n s
g e n e r a l l y conform t o mean t o p o g r a p h y and c o n s e q u e n t l y a r e e a s i l y r e c o g ­
nized.
O f te n t o p o g r a p h y is r e l a t e d t o s t r u c t u r e ; t h e r e f o r e , t o p o g r a p h i c
c o r r e c t i o n s s h o u l d al w ay s be use d j u d i c i o u s l y .
B i o e l e c t r i c n o i s e i s an e a s i l y a v o i d e d pr ob lem i f c a r e is t a k e n
t o make measu re men ts below p l a n t r o o t p e n e t r a t i o n .
Where t h i s p r e c a u ­
t i o n i s no t p o s s i b l e , n o i s e l e v e l s may be on t h e o r d e r o f 50 t o 70 mV
(L u nd eg a rd h , 1942; S c o t t ,
1962).
Wind can c a u s e a t i m e - v a r y i n g e l e c t r i c p o t e n t i a l
if the w ire connecting sensing e le c tro d e s
suspension.
to develop
is a l l o w e d t o move due t o
The e l e c t r i c p o t e n t i a l s d e v e l o p e d a r e a f u n c t i o n o f t h e
l e n g t h o f t h e exp o se d c a t e n a r y and t h e wind v e l o c i t y .
Magn itud es o f
w i n d - g e n e r a t e d " s w i n g i n g w i r e " p o t e n t i a l s have been o b s e r v e d as high
as 10-15 mV.
Regi ona l e l e c t r i c p o t e n t i a l g r a d i e n t s e x i s t a c r o s s t h e e a r t h ' s
surface.
N o u r b eh ec h t (1963) c a l c u l a t e d t h e g r a d i e n t due t o t e m p e r a t u r e
d i f f e r e n c e s between t h e s u r f a c e o f t h e e a r t h and b a s e o f t h e c r u s t t o
be 2 o r 3 mV/km.
A n o th e r p a r a m e t e r a s s o c i a t e d w i t h t h e r e g i o n a l g r a ­
d i e n t i s t h e chang e in t h e e a r t h ' s
r e s i s t i v i t y due t o c h a n g e s in compo­
s i t i o n corresponding to regional geology.
E lim ination of the regional
g r a d i e n t s e n c o u n t e r e d d u r i n g e l e c t r i c a l me asurements has been d i s c u s s e d
by F r o h l i c h
( 1 9 71 ) .
37
Man-made n o i s e t a k e s two f o r m s .
I n d u s t r i a l n o i s e is g e n e r a t e d
by p i p e l i n e c a t h o d i c p r o t e c t i o n s y s t e m s , e a r t h r e t u r n s o f t e n used in
mine t r a c t ion and o t h e r i n d u s t r i a l
lines.
s y s t e m s , e l e c t r i c f e n c e s , and power
Removal o f i n d u s t r i a l : n o i s e is a c c o m p l i s h e d by r e c o r d i n g and
s u b t r a c t i n g t h e n o i s e from o b s e r v e d s i g n a l s .
is a l s o c u l t u r a l l y d e riv e d .
The second form o f n o i s e
B ur ie d m e t a l , mine s l a g , o r any o t h e r
m a t e r i a l t h a t can p a r t i c i p a t e
sig n ifican t e le c tric signals.
in e l e c t r o c h e m i c a l p r o c e s s e s w i l l g e n e r a t e
C o n t a c t between m o i s t e n e d e a r t h and t h e
b r a s s h a n d l e on an e l e c t r o d e used d u r i n g an SP s u r v e y f o r t h i s t h e s i s
ca us ed an e l e c t r i c p o t e n t i a l d i f f e r e n c e o f + 50 mV t o d e v e l o p .
A n o th e r form o f n o i s e i s
measurement p r o c e s s .
instrum ent n o ise g e n era ted during the
E l e c t r o d e n o i s e r e s u l t s from t h e c o n t a c t impedance
between t h e e a r t h and e l e c t r o d e , d i f f e r e n c e s
in m o i s t u r e c o n t e n t o f t h e
e a r t h a t two e l e c t r o d e c o n t a c t s , c o n c e n t r a t i o n d i f f e r e n c e s
electrolytes
electrode.
in t h e
in eac h e l e c t r o d e , and t e m p e r a t u r e d i f f e r e n c e s a t each
The pr obl em o f c o n t a c t impedance can be overcome by u s i n g
a h i g h - i n p u t impedance i n s t r u m e n t f o r t h e m e a s u r e m e n t s .
Burr (I960)
r e p o r t e d e l e c t r i c p o t e n t i a l d i f f e r e n c e s due t o m o i s t u r e c o n t e n t d i f f e r ­
e n c e s a t two e l e c t r o d e s a s hi g h as. 100 mV.
A tem perature d if fe re n c e
o f 20°C between two Cu-CuSO^ e l e c t r o d e s can c a u s e a 25 mV
p o t e n t i a l d i f f e r e n c e t o d e v e l o p (Becker and T e l f o r d ,
electric
1965, p.
182).
Changes in t h e e l e c t r o l y t e c o n c e n t r a t i o n s o f two e l e c t r o d e s w i t h i n t h e
t e m p e r a t u r e r an g e e n c o u n t e r e d d u r i n g normal s u r v e y s a p p a r e n t l y do
not cause e l e c t r i c p o t e n t i a l d i f f e r e n c e s
saturation
level of the s a l t
in e x c e s s o f 10 mV i f a n e a r -
is m a i n t a i n e d .
The e f f e c t o f s a l t
38
c o n c e n t r a t i o n on t h e e l e c t r o d e has n o t been c o n s i d e r e d
t h e Cu-CuSO^ e l e c t r o d e s , however.
in d e t a i l
In c o n c l u s i o n t h e o n l y way t o
m i ni m i ze t h e e f f e c t o f n o i s e on SP d a t a is t o r e c o g n i z e p o t e n t i a l
s o u r c e s and t o a t t e m p t t o r e d u c e t h e i r i m p a c t . .
for
CHAPTER 3
DEVELOPMENT OF THE SELF-POTENTIAL MODEL
Any model d e s i g n e d t o s i m u l a t e n a t u r a l l y o c c u r r i n g p r o c e s s e s in
the e a r t h should s a t i s f y t h r e e c r i t e r i a :
1.
The p r i n c i p l e s upon which t h e model
is p r e d i c a t e d must
be
m a t h e m a t i c a l l y and p h y s i c a l l y s o u n d .
2.
The model must be c o m p u t a b l e .
3.
The model s h o u l d be a p p l i c a b l e t o as many
g e o lo g ic environments
as p o s s ib le .
The t h e o r y o f t h e thermodynamics o f i r r e v e r s i b l e p r o c e s s e s
(TIP) o r i g i ­
n a l l y d e v e l o p e d by b i o p h y s i c i s t s t o model e n e r g y - d i s s i p a t i v e ,
b r a n e f lo w phenomena is used f o r t h e m o d e l .
intramem­
Since the in tr o d u c tio n of
t h e b a s i c p r i n c i p l e s upon which t h e t h e o r y o f TIP i s b a s e d , t h e t h e o r y
has been a d a p t e d t o most p h y s i c a l s c i e n c e d i s c i p l i n e s
in which k i n e t i c
processes occur.
A c o m p u t a t i o n a l method r e a d i l y a d a p t a b l e t o any model i n v o l v i n g
fl o w s th r o u g h d i s c r e t e a r e a s eg me nt s (volume s eg me nt s in t h r e e dimen­
sions)
is t h e n et w o r k a n a l y s i s used by e l e c t r i c a l
engineers.
The mem­
b r a n e s t h r o u g h which f lo w s p a s s and a c r o s s which c h a n g e s in t h e p h y s i c a l
p r o p e r t i e s occur a r e re p re s e n te d as branch r e s i s t o r s .
tential
The e l e c t r i c po­
d i f f e r e n c e used t o d e t e r m i n e t h e e l e c t r i c p o t e n t i a l s i m u l a t i n g
t h e e n e r g y l e v e l a t a node in t h e n e t w o r k can be c a l c u l a t e d t o p r o v i d e
v a l u e s f o r c o m pa ri s o n w i t h o b s e r v e d f i e l d d a t a t o d e t e r m i n e t h e a c c e p t ­
a b i l i t y o f an i n t e r p r e t a t i o n .
39
.
40
The s e l f - p o t e n t i a l model d e v e l o p e d in t h i s c h a p t e r i s a p p l i c a b l e
t o any g e o l o g i c e n v i r o n m e n t in which t w o - d i m e n s i o n a l a n a l y s i s p r o v i d e s a
good a p p r o x i m a t i o n o f t h e p a r a m e t e r s t o be modeled.
The e f f e c t s o f t h e
t h i r d di m en s io n g e n e r a l l y can be i g n o r e d i f t h e t h i r d d im en s io n is much
g r e a t e r th a n t h e o t h e r two.
G e o l o g i c S t r u c t u r e o f t h e SP Model
N a t u r a l l y o c c u r r i n g c h e m i c a l , t h e r m a l , and h y d r a u l i c g r a d i e n t s
in t h e e a r t h c a u s e s p o n t a n e o u s d e ve lo pm en t o f e n e r g y t r a n s p o r t phenomena
in f l o w s . . The d i r e c t i o n o f e n e r g y t r a n s p o r t i s al w ay s t h a t o f d e c r e a s ­
ing e n e r g y .
The e x i s t e n c e o f e l e c t r i c c u r r e n t s r e l a t e d t o t h e s e flo w s
in d ic a te s t h a t the energy t r a n s f e r pro cesses
in t h e e a r t h a r e d i s s i p a ­
tive.
The e l e c t r i c p o t e n t i a l d i f f e r e n c e s a s s o c i a t e d w i t h t h e s e c u r r e n t s
are re la tiv e ly constant.
The s y s t e m must be open t o m a i n t a i n t h e s e c u r ­
r e n t s ; t h a t i s , c a p a b l e o f e x c h a n g i n g e n e r g y and m a t t e r w i t h t h e s u r ­
ro u n d in g e n v i r o n m e n t w i t h o u t c a u s i n g i n t e r n a l c h an ge s in t h e s y s t e m ' s
entropy.
The a p p a r e n t c o n s t a n c y o f e l e c t r i c c u r r e n t s
s y s t e m has r e a c h e d a n e a r s t e a d y s t a t e
im plies t h a t the
in which s t a t e p a r a m e t e r s do n o t
change a p p r e c i a b l y .
Energy g r a d i e n t s d e v e l o p w i t h i n t h e e a r t h a c r o s s t h e b o u n d a r i e s
where t h e p h y s i c a l and chem ica l p r o p e r t i e s o f e a r t h m a t e r i a l s ch a n g e .
These b o u n d a r i e s a r e membranes o r zon es o f d i s c o n t i n u o u s t r a n s i t i o n
between two d i f f e r e n t e n v i r o n m e n t s .
C o n d i t i o n s on e i t h e r s i d e o f t h e
membrane o f t e n a p p r o a c h r e l a t i v e p h y s i c a l and chem ica l h e t e r o g e n e i t y
and i s o t r o p y .
The p o t e n t i a l
membranes.
th is
i s c o n t i n u o u s a c r o s s a membrane o r a s y s t e m o f
is r e f l e c t e d
in t h e ch an g e o f c o e f f i c i e n t s d e s c r i b i n g
t h e a b i l i t y o f a p a r t i c u l a r f l o w t o p a s s t h r o u g h a s p e c i f i c membrane.
The r e s u l t o f t h i s
is t h a t
if the to ta l
p o t e n t i a l energy d i f f e r e n c e is
t o remain c o n s t a n t a c r o s s t h e s y s t e m , t h e t o t a l e n e r g y f lo w a c r o s s a
boundary must remain c o n s t a n t .
A chang e in t h e mode o f e n e r g y t r a n s ­
p o r t must Occur a t a membrane f o r t h i s t o be t r u e .
This im plies t h a t a
component o f t h e p r i m a r y flow must d e v e l o p p a r a l l e l
t o t h e membrane on
t h e s i d e o p p o s i t e t h e d i r e c t i o n o f flo w ( F i g . 7 ) .
The p r e s e n c e o f a membrane i m p l i e s d i s c o n t i n u i t y
which Is m a n i f e s t in t h e p o t e n t i a l e n e r g y g r a d i e n t .
in t h e s y s t e m ,
An i m p l i c i t assump­
t i o n made in c o n j u n c t i o n w i t h t h e h y p o t h e s i s o f d i s c o n t i n u i t y
is t h e
n e c e s s i t y o f c r o s s - c o u p l i n g between e n e r g y t r a n s p o r t mechanisms i f t h e
p o t e n t i a l e n e r g y a c r o s s t h e s y s t e m i s t o remain c o n s t a n t
(Nourbehecht,
1963; K a t c h a l s k y and C u r r a n , 1965).
The s y s t e m t o be modeled as i t has been d e s c r i b e d above i s one
that
is open t o t h e ex cha nge o f e n e r g y and m a t t e r w i t h i t s s u r r o u n d i n g s
and in which t h e e n e r g y t r a n s f e r mechanisms a r e d i s s i p a t i v e .
o c c u r r i n g w ith in th e system a r e i r r e v e r s i b l e .
Processes
A technique of physical
a n a l y s i s a p p l i c a b l e t o t h i s pr obl em i s t h e the rmodynamics o f i r r e v e r s i ­
ble processes.
Kedem and K a t c h a l s k y
(1963) have shown t h a t by u s in g
t h e t h e o r y o f TIP t h e o v e r a l l s t r u c t u r e o f i n d i v i d u a l e l e m e n t s in t h e
model can be i g n o r e d .
The s t r u c t u r a l
i n f o r m a t i o n i s i m p l i c i t in t h e
c o n d u c t i v i t y c o e f f i c i e n t s and t h e way in which t h e p o t e n t i a l
g r a d i e n t s a t eac h membrane a r e d e s c r i b e d .
en er g y
W W W wwwwww
F i g u r e 7-
w
w
w
w
w
I l l u s t r a t i o n o f t h e c o n t i n u i t y o f a flow and i t s p o t e n t i a l and t h e d i s c o n t i n u i t y
o f i t s g r a d i e n t a t a ph as e boundary - - A f t e r K a tc h a ls k y and Curran ( 1%5)
43
O th er c o n s i d e r a t i o n s a r e n e c e s s a r y i f a t w o - d i m e n s i o n a l model
is
t o be used t o a c c u r a t e l y d e s c r i b e e n e r g y f lo w s o c c u r r i n g in t h e e a r t h .
The d i m e n s i o n s o f t h e membranes a r e e s s e n t i a l p a r t s o f t h e model b e c a u s e
th e se a f f e c t the energy g r a d i e n t s .
The c o n s t r a i n t i m p l i e d by t h e two-
d i m e n s i o n a l n a t u r e o f t h e model has been m e n t i o n e d .
An i m p o r t a n t p r o b ­
lem t h a t re m a in s t o be s o l v e d i s t h e e f f e c t o f t h e b o u n d a r i e s on t h e
analytical solution.
The model as i t
is c o n c e i v e d f o r t h i s s t u d y i s shown in F i g u r e
8. T h i s model c o n s i s t s o f a f i n i t e number o f r e t i c u l e s s e p a r a t e d by
membranes.
T h e r e i s no t h e o r e t i c a l
can be c o n s i d e r e d .
l i m i t t o t h e number o f e l e m e n t s t h a t
C o m p u t a ti o n a l f a c i l i t i e s a r e t h e o n l y f a c t o r l i m i t ­
ing t h e s i z e o f t h e m o d e l.
The r e q u i r e m e n t t h a t t h e s y s t e m be open and t h a t t h e r e must be
a f r e e ex ch a n ge o f e n e r g y and m a t t e r w i t h t h e s u r r o u n d i n g s s u g g e s t s t h a t
the l e f t ,
r i g h t , and b ot to m e l e m e n t s o f t h e ne tw or k s h o u l d be I n f i n i t e
in e x t e n t .
In t h e c o m p u t a t i o n a l model t h e d i m e n s i o n s o f t h e netwo rk a r e
extended to sim u la te t h i s .
The amount o f t h e e x t e n s i o n
is a fu n c tio n of
t h e s i m u l a t e d p h y s i c a l and ch em ic a l p r o p e r t i e s o f t h e m a t e r i a l a l o n g t h e
b o u n d a r i e s and t h e m a g n it u d e o f t h e g r a d i e n t s a c r o s s t h e membranes imme­
d ia te ly adjacent to the boundaries.
The a i r - e a r t h
i n t e r f a c e p r e s e n t s a u ni q ue pr o b le m .
The r e s i s ­
t a n c e t o i o n i c and e l e c t r o n c u r r e n t f l o w s a t t h i s bo un da ry Is l a r g e b u t
fin ite.
The a t m o s p h e r i c e l e c t r i c p o t e n t i a l
100 V/m ( B r a n t , 1948, p. 5 7 0 ) .
The e l e c t r i c c u r r e n t d e n s i t y a s s o c i a t e d
with t h i s e l e c t r i c p o te n tia l g ra d ie n t
(Zonge, 1977) .
g rad ie n t is approxim ately
,
i s on t h e o r d e r o f 4 X 10
The r e s u l t i n g r e s i s t i v i t y
-12
. A/m
2
i s on t h e o r d e r o f 10 ' ^ fi-m,
44
Unconsolidated
sed iments
Weathered
r oc ks
Host rock
F i g u r e 8.
t i
Meta 111c
m i n e r a l i z a t ion
Peripheral
a lte ra tio n m ineralization
The c o n c e p t u a l model
45
a v a l u e t h a t f l u c t u a t e s as a f u n c t i o n o r a i r p o l l u t i o n , h u m i d i t y , w in d ,
and cl o u d c o v e r .
The e r r o r i n t r o d u c e d by t h e s e f l u c t u a t i o n s
is i n s i g ­
n i f i c a n t i f t h e r e l a t i v e m a g n it u d e s o f t h e a t o m o s p h e r i c and e a r t h r e s i s ­
t i v i t i e s are considered.
earth
The r e s i s t a n c e t o o t h e r f lo w s a c r o s s t h e a i r -
i n t e r f a c e a r e p r o b a b l y on t h e same r e l a t i v e o r d e r o f m a gn itu de a s
that for e l e c tr i c cu rren ts.
The o t h e r f lo w s can t h e r e f o r e be t r e a t e d
in a s i m i l a r way.
An a d e q u a t e e n e r g y s o u r c e i s t h e f i n a l p h y s i c a l
t h i s model.
requirement fo r
The s t r e n g t h o f t h i s s o u r c e must be c o m p a t i b l e w i t h t h a t
e x p e c t e d from n a t u r a l phenomena.
This i n d i c a te s t h a t th e i n i t i a l
steps .
in t h e m o de li n g p r o c e s s a r e t o i d e n t i f y t h e p r i m a r y f l o w ( s ) and t o c a l ­
c u l a t e a f i r s t - o r d e r a p p r o x i m a t i o n o f t h e m ag n it u d e o f t h e e x p e c t e d
signal using equ ations
(1-4).
Thefmodyhamic P r o p e r t i e s o f t h e SP Model
S elf-potential
is t h e r e s u l t o f n a t u r a l , i r r e v e r s i b l e , g e o l o g i c
p r o c e s s e s o c c u r r i n g s p o n t a n e o u s l y in o p e n , n o n e q u i l i b r i u m sy st em s In t h e
earth.
The c o n s t a n t e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP a r e g e n e r a t e d
by c o n s e r v a t i v e , s o u r c e - i n d e p e n d e n t , q u a s I s t a t i c p r o c e s s e s .
The com­
p l e x i t y o f SP mechanisms and o t h e r g e o p h y s i c a l phenomena i n v o l v i n g t r a n s ­
p o r t p r o c e s s e s makes i t e x p e d i e n t t o d e s c r i b e such phenomena in te r m s o f
k i n e t i c e q u a t i o n s bas ed on e m p i r i c a l m o d e ls .
The c l a s s i c a l d e s c r i p t i o n
o f t h e laws o f the rmodynamics i s u s e f u l f o r d e t e r m i n I n g t h e l o c a t i o n o f
flo w s and d i r e c t i o n
in which t h e y p r o c e e d b u t p r o v i d e s l i t t l e a d d i t i o n a l
i n f o r m a t i o n c o n c e r n i n g t h e n a t u r e o f c h an g e s o c c u r r i n g in t h e e a r t h .
46
A formal d e s c r i p t i o n o f k i n e t i c p r o c e s s e s ,
c ific kinetic or s ta tis tic a l
m o d e ls ,
independent o f spe­
i s p o s s i b l e by u s i n g t h e t h e o r y o f
t h e the rmodynamics o f i r r e v e r s i b l e p r o c e s s e s .
The n o t a t i o n o f TIP makes
i t p o s s i b l e t o s p e c i f y a s e t o f e x t e r n a l and i n t e r n a l p a r a m e t e r s
variables)
to d e s c r ib e energy t r a n s f e r
in a s y s t e m .
(state
The f u n c t i o n s com­
p l e t e l y d e t e r m i n e d from t h e s t a t e v a r i a b l e s a r e t h e s t a t e f u n c t i o n s .
External p aram eters a r e th o s e t h a t a f f e c t th e e n t i r e system.
These i n c l u d e t h e volume arid mass o f t h e s y s t e m , t h e t y p e o f m a t e r i a l
p r e s e n t , e x t e r n a l p r e s s u r e on t h e bo un da ry o f t h e s y s t e m , and e l e c t r o ­
magnetic f i e l d s
in flu e n c in g the system.
The l a s t i n c l u d e s t h e i n t e r n a l
and e x t e r n a l c h a r g e d e n s i t y and d i s t r i b u t i o n .
describe a ll
The i n t e r n a l p a r a m e t e r s
l o c a l and t e m p o r a r y p r o p e r t i e s o f t h e s y s t e m .
These have
d e f i n i t e v a l u e s a t e a c h p o i n t in t h e s y s t e m , which a r e i n d e p e n d e n t o f
the sy ste m 's s i z e .
Systems g e n e r a t i n g e l e c t r i c c u r r e n t s r e l a t e d t o SP a r e a b l e t o
exist
in q u a s i s t a t i c s t a t e s as long a s a d j u s t m e n t s t o t h e v a l u e s o f
i n t e r n a l p a r a m e t e r s o c c u r s i m u l t a n e o u s l y w i t h and a r e e q u a l t o ch ang es
in e x t e r n a l p a r a m e t e r s .
The q u a s i s t a t i c s t a t e s r e s e m b l e t h e e q u i l i b r i u m
s t a t e s o f t h e i r r e s p e c t i v e s y st e m s i f t h e r a t e a t which e x t e r n a l param­
e t e r s chang e is slow enough t h a t an a p p r o x i m a t i o n o f t i m e i n v a r i a n c e i s
possible.
D e v i a t i o n s o f t h e s e s y s t e m s from e q u i l i b r i u m a r e e v i n c e d by
entropy production r e l a t e d to g e n e ra tio n of th e e l e c t r i c c u rre n ts a sso ­
c i a t e d w i t h SP.
E n t r o p y , which is a me asu re o f t h e c a p a c i t y o f a s y s t e m t o
chang e s p o n t a n e o u s l y ,
is t h e q u a n t i t y used t o d e s c r i b e t h e f r e e e n e r g y
47
c o n t e n t o f a s y s t e m in which I r r e v e r s i b l e p r o c e s s e s o c c u r .
All n a t u r a l ,
s p o n t a n e o u s p r o c e s s e s must i n v o l v e p o s i t i v e d e f i n i t e e n t r o p y p r o d u c t i o n ;
t h a t i s , t h e f r e e e n e r g y in n a t u r a l s y s t e m s must alwa ys be a t a minimum.
Local e n t r o p y in a s y s t e m i s d e s c r i b e d
param eters.
in te r m s o f i n t e r n a l
The c o n s t a n c y o f t h e p r i m a r y f lo w s a s s o c i a t e d w i t h SP i n d i ­
c a t e t h a t l o c a l e n t r o p y p r o d u c t i o n must be z e r o .
T h i s in t u r n i n d i c a t e s
t h a t e n t r o p y p r o d u c t i o n a t any p o i n t in a s y s t e m must be matched by an
eq u iv alen t reduction of entropy a t th a t p o in t.
The r e d u c t i o n o f e n t r o p y
a t a p o in t provides the b a s is fo r the c ro s s -c o u p lin g of flo w s .
E q u i l i b r i u m i s t h e f i n a l s t a t e o f a s y s t e m in which a l l flo w s
c e a s e and e n t r o p y i s ma ximized.
The i n t e r n a l p a r a m e t e r s a r e e x a c t l y
d e t e r m i n e d by t h e e x t e r n a l p a r a m e t e r s a t e q u i l i b r i u m .
The s i m i l a r i t y
between q u a s i s t a t i c s t a t e s and e q u i l i b r i u m s t a t e s w i t h i n t h e e a r t h p e r - .
m i t s u s e o f t h e t h e o r y o f TIP f o r a n a l y s i s Of flow p r o c e s s e s g e n e r a t i n g
e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP.
When an e n e r g y im p u ls e o f any kin d i s i n t r o d u c e d I n t o a s y st e m
a s h i f t from t h e q u a s i s t a t i c s t a t e r e s u l t s .
A nalysis using the theory
o f TIP becomes l e s s a c c u r a t e t h e f u r t h e r a s y s t e m s h i f t s from t h e e q u i ­
librium s t a t e .
statistic al
I t i s o f t e n n e c e s s a r y t o r e v e r t t o s p e c i f i c k i n e t i c and
models f o r c a s e s where e n e r g y imp uls es a r e t o be a n a l y z e d .
T h i s is t r u e f o r i n d u c e d - p o l a r i z a t i o n , e l e c t r o m a g n e t i c , and some
r e s i s t i v i t y measurements.
The g e n e r a l t h e o r y o f TIP has been c o n s i d e r e d
d e Groot (1952, 19 61) , Harmon and Honig ( 1 9 6 7 ) , M i l l e r
in d e t a i l by
(195 6a,
1956b,
I 9 6 0 ) , On sager and Fuoss (1932) among o t h e r s . ; D e t a i l e d a n a l y s i s
of
48
t r a n s p o r t p r o c e s s e s a c r o s s membranes is a r e c e n t a d a p t a t i o n o f t h i s
theory.
The s i m i l a r i t y between t h e c o n c e p t o f a membrane, and t h e p h y s ­
i c a l and ch em ica l d i s c o n t i n u i t i e s
existing naturally
in t h e e a r t h i n d i ­
c a t e s t h e u t i l i t y o f t h i s h y b r i d thermodynamic t e c h n i q u e .
others
( n .d .), Spiegler
MeKeIvey and
(1958) , Duncan ( 1 9 6 2 ) , Kedem and K a t c h a l s k y
( 1963) , and K a t c h a l s k y and Cu rr an (1965) have s p e c i f i c a l l y c o n s i d e r e d
TIP as t h e t h e o r y p e r t a i n s t o t r a n s p o r t p r o c e s s e s a c r o s s membranes.
The p u r p o s e o f a thermodynamic d e s c r i p t i o n o f f lo w s o c c u r r i n g
in t h e e a r t h i s t o d e t e r m i n e t h e t o t a l e n e r g y t r a n s f e r
in te rm s o f t h e
c o n j u g a t e f lo w s and f o r c e s and t h e c o n d u c t i v i t y c o e f f i c i e n t s .
c o n d i t i o n s must be s a t i s f i e d
Four
i f a thermodynamic a p p r o a c h i s t o . b e v a l i d
(Harmon and H o e n i g , 1967, p. 2 0 ) .
1.
The f l o w , J . , must be a ti m e d e r i v a t i v e o f a thermodynamic
variable.
2.
S = ET
- 77
i 1
1
(19)
3.
T
'
(2 0 )
4.
L . . - L..
U
J 1
= E L .. T
i
'J J
(21)
The r e q u i r e m e n t s t h a t t h e s y s t e m must be q u a s i s t a t i c and t h a t t h e r e be
no i n t e r n a l s o u r c e s were m e n tio n ed p r e v i o u s l y .
Using t h e laws o f c o n s e r v a t i o n
and t h e f i r s t and seco nd laws
of
mass, e n e r g y , and momentum
o f th erm od yna mi cs
expressedas e q u a l i t i e s
t h e v a l i d i t y o f t h e f i r s t t h r e e c o n d i t i o n s l i s t e d ab ov e is shown in
Appendix B.
Onsager (1931a,
1931b) u s ed a s t a t i s t i c a l
approach to
hs
prove th e v a l i d i t y o f th e f o u r th c o n d i t i o n .
s i d e r e d in d e t a i l
Equations
O n s a g e r 1s p r o o f was co n­
by C a s i m i r (1945) and Coleman and T r u e s d e l 1 ( I 9 6 0 ) .
(19) and (20) p r o v i d e a c o n v e n i e n t way t o r e l a t e t h e
e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP t o t h e t o t a l f r e e e n e r g y in any
s y s t e m in t h e e a r t h .
An a l t e r n a t e s t a t e m e n t o f E q u a t i o n (20)
is t h a t
any f lo w o c c u r r i n g in a s y s t e m i s a l t e r e d by a l l o t h e r flo w s so as t o
m i ni m i ze t h e a v a i l a b l e f r e e e n e r g y and maximize e n t r o p y .
nological c o e f f i c ie n t s
t i v i t y term s.
(L.j)
The phenome­
f o r which i = j a r e t h e o r d i n a r y condu c­
Those c o e f f i c i e n t s f o r which i ^ j d e s c r i b e t h e c r o s s -
c o u p l i n g bet ween a c t i v e f lo w p r o c e s s e s .
Use o f t h e s e c o n c e p t s depen ds on t h e d e v el o pm en t o f t e c h n i q u e s
w i t h which t o me as ur e t h e c r o s s - c o u p l i n g c o e f f i c i e n t s and a c t i v e g r a d i ­
ents, preferably in -s itu .
Techniques f o r measuring s p e c i f i c p o t e n t i a l
e n e r g y g r a d i e n t s v a r y , d e p e n d i n g on t h e p h y s i c a l p a r a m e t e r s a s s o c i a t e d
w ith each.
Techniques e x i s t f o r measuring d i f f e r e n c e s
in p a r a m e t e r s
t h a t c a u s e f lo w s suc h as p r e s s u r e , e l e c t r i c p o t e n t i a l , t e m p e r a t u r e , and
ion c o n c e n t r a t i o n s .
This inform ation
is used t o a p p r o x i m a t e t h e
respective gradients;
Measurement o f p he no m e n o lo g ic a l c o e f f i c i e n t s
i s more d i f f i c u l t .
Two measurement t e c h n i q u e s a r e n e c e s s a r y f o r b i n a r y s y s t e m s .
The f i r s t
t e c h n i q u e is t o s t o p one f lo w and me as ur e t h e r a t i o o f t h e r e s u l t i n g
gradients.
The second t e c h n i q u e i s t o s h o r t c i r c u i t on e g r a d i e n t and
me asure t h e r a t i o o f t h e r e s u l t i n g f l o w s .
all
f lo w s and g r a d i e n t s
These s t e p s a r e r e p e a t e d f o r
in t e r n a r y s y s t e m s , q u a t e r n a r y s y s t e m s , e t c .
The f a c t t h a t t h e i n d i v i d u a l e l e m e n t s c a n n o t be e n e r g y s o u r c e s o r s i n k s
50
ensures the p o s iti v e condition of a l l c o e f f i c i e n t s .
e x p r e s s e d in e q u a t i o n
(22)
This f a c t is
(de G r o o t , 1952).
L ..L .. - L ..L .. > 0
ii
ij
jj
(22)
J i -
Few me asurements o f t h e c r o s s - c o u p l i n g p r o p e r t i e s o f ro ck s have
been made.
Sakuma ( 1 9 5 2 ) , Noritomi
s h t e y n (1959,
( 1 9 5 3 ) , Kobranova ( 1 9 5 7 ) , V e n d e l 1-
19 6 0 a , 19 6 0b ), Heath ( 1 9 6 3 ) , W o r t h i n g t o n (1973) and
S t o e s s e l 1 and Manor (1975) have c o n s i d e r e d t h e d I f f u s i o n - a d s o r p t i o n
a c t i v i t i e s o f r o c k s a s a f u n c t i o n o f c h e m i s t r y and m i n e r a l o g y .
( 1 9 5 7 ) , S h a p i r o ( 1 9 5 8 ) , and Kunori and I s h i i
properties
(1961)
P o la k
recognized these
in te rm s o f t h e s i m i l a r i t y between e a r t h m a t e r i a l s and i o n -
s e l e c t i v e membranes.
The u n i q u e n e s s o f ea c h p h e n o m e n o lo g ic a l c o e f f i c i e n t t o a s p e ­
c i f i c combination of g ra d ie n ts
in a p a r t i c u l a r g e o l o g i c e n v i ro n m e n t
makes many me asurements n e c e s s a r y i f the rmodynamics i s t o be u s e f u l f o r
m o d e li n g .
A d e s c r i p t i o n o f t h e way in which t h e c o e f f i c i e n t s a r e t o be
used f o r m od e li n g f o l l o w s .
The A n a l y t i c a l SP Model
Two f e a t u r e s o f t h e SP model d e s c r i b e d p r e v i o u s l y in t h i s c h a p ­
ter
i n d i c a t e t h e p o s s i b l e a p p l i c a b i l i t y o f t h e ne t w o r k a n a l y s i s used by
electrical
e n g i n e e r s a s a method o f m o de li ng t h e f l o w s and c r o s s - c o u p l e d
e l e c t r i c c u r r e n t s a s s o c i a t e d w i t h SP.
These a r e t h e r e t i f o r m a p p e a r a n c e
o f t h e SP model shown in F i g u r e 8 and t h e f u n c t i o n a l
resemblance of the
membranes c i r c u m s c r i b i n g t h e r e t i c u l e s t o r e s i s t o r s used in e l e c t r i c
circuits.
The us e o f an i n t e r c o n n e c t e d c o m b i n a t i o n o f e l e c t r i c
51
components t o s i m u l a t e f lo w s and e n e r g y s o u r c e s p e r m i t s bo th a n a l o g and
a n a l y t i c a l a n a l y s i s o f t h e model.
The n e t w o rk used t o model SP is s im ­
p l i f i e d by r e c o g n i z i n g t h a t e l e c t r i c c u r r e n t s a r e c o n s t a n t , c o n s e q u e n t l y
all
impedance e l e m e n t s a r e r e s i s t i v e .
C a p a c i t i v e and i n d u c t i v e e l e m e n t s
do n o t a f f e c t t h e a n a l y s i s .
Network a n a l y s i s has been used w i t h c o n s i d e r a b l e s u c c e s s by
e l e c t r i c a l en gineers to analyze th e response of e l e c t r i c c i r c u i t s to
varied
inputs.
The e a r l i e s t r e p o r t e d us e o f t h i s t e c h n i q u e f o r g e o p h y s ­
i c a l a n a l y s i s was by S c h e r b a t s k o y and N e u f e ld
im pu lse r e s p o n s e o f a s e is m o g r a p h s
(1937 ) , who modeled t h e
Schop per (1966) and Rink and Schopper
(1968) used n e t w o r k a n a l y s i s t o model t h e f o r m a t i o n f a c t o r , p e r m e a b i l i t y ,
and p o r o s i t y o f r o c k s .
model t h e e a r t h ' s
G reenfield
(1965) a d a p t e d n e t w o r k a n a l y s i s t o
response to magnetic m i c r o p u ls a ti o n s .
S w i f t ( 1967) , Pel t o n , R i j o and S w i f t
(1976,
More r e c e n t l y ,
1977) and Hohmann. (1977)
r e p o r t e d t h e i r us e o f ne t w o r k a n a l y s i s f o r IP and r e s i s t i v i t y m o d e li n g .
The n et w or k used t o r e p r e s e n t t h e c e n t r a l e l e m e n t o f t h e p r o ­
posed model shown in F i g u r e 8 i s shown in F i g u r e 9.
The nodes in t h e
ne tw or k a r e p o i n t s a t which two o r more r e s i s t o r s a r e c o n n e c t e d .
Th es e
r e p r e s e n t h e t e r o g e n e o u s and i s o t r o p i c a r e a s bounded by membranes.
individual
The
r e s i s t o r s s i m u l a t e t h e membranes th r o u g h w h ic h t h e flo w s p a s s
and a c r o s s which p h y s i c a l and c he m ic a l p r o p e r t i e s c h a n g e .
Edge e f f e c t s a r e a s i g n i f i c a n t s o u r c e o f e r r o r
c a l mo de lin g t e c h n i q u e s ; net wo rk a n a l y s i s
in a l l g e o p h y s i ­
i s no e x c e p t i o n .
Several
a d d i t i o n s t o t h e ne t w o r k a r e r e q u i r e d t o mi ni m iz e a l t e r a t i o n s t o
e l e c t r i c c u r r e n t f lo w p a t t e r n s
in t h e model.
i n t r o d u c e d by a b r u p t d i s c o n t i n u i t i e s
The f i r s t s t e p i s t o c l o s e a l l
the e x i s t i n g
loops.
52
■ m
rn m
F i g u r e 9.
s
C e n t r a l el e m e n t o f t h e r e s i s t a n c e n et w o r k
s u p er im p o se d on t h e g e o l o g i c model
53
T h i s i s a c c o m p l i s h e d by a d d i n g a r e s i s t o r t o c l o s e ea c h l o o p .
r e s i s t a n c e v a l u e a s s i g n e d t o eac h added r e s i s t o r
diately adjacent, parallel
resistors
resistor.
The
is t h a t o f t h e imme*
The ne tw or k w i t h t h e added
is shown in F i g u r e 10.
The edge e f f e c t s a t t h e l e f t and r i g h t ends o f t h e n et w o rk a r e
compensated f o r by u s i n g t h e c o n c e p t o f an open s y s t e m ; t h a t i s , t h e
e l e m e n t s must be a b l e t o f r e e l y exc h a ng e m a t t e r and e n e r g y w i t h t h e
s u r r o u n d i n g s w i t h o u t a l t e r i n g t h e i n t e r n a l p r o p e r t i e s o f t h e sy st em .
T h i s i s s i m u l a t e d by l a t e r a l e n l a r g e m e n t o f t h e n e t w o r k .
The number
o f e l e m e n t s added t o ea c h row i s a f u n c t i o n o f t h e e l e c t r i c p o t e n t i a l
g r a d i e n t s and t h e r e s i s t a n c e s o f t h e e l e m e n t s a d j a c e n t t o t h e e d g e s .
The r e s i s t a n c e v a l u e s a s s i g n e d t o t h e added r e s i s t o r s a r e t h o s e o f t h e
last parallel
resistor
in t h e same row o f t h e c e n t r a l e l e m e n t s .
c o r r e c t i o n f o r edge e f f e c t s a t t h e bo tt om o f t h e model
The
i s made by u s i n g
t h e same p r i n c i p l e and t e c h n i q u e s used f o r t h e l e f t and r i g h t e d g e s .
The u n i q u e c o n d i t i o n s a t t h e a i r - e a r t h
i n t e r f a c e a r e simulated
by a d d i n g a r e s i s t o r t o eac h column a t t h e modeled s u r f a c e .
loop a t t h e to p o f t h e model
is closed w ith a h o riz o n ta l
The v a l u e a s s i g n e d t o eac h o f t h e new r e s i s t o r s
was p r e v i o u s l y d e t e r m i n e d .
Each open
resistor.
13
is 2 . 5 X 10
fi-m as
The e x t r e m e d i f f e r e n c e in t h e o r d e r o f
m a g n it u d e between t h i s v a l u e and normal e a r t h r e s i s t i v i t i e s
(10-10
k°
fi-m)
i n d i c a t e s t h a t t h e e r r o r i n t r o d u c e d by u s i n g a s i n g l e row o f loops a t
t h e s u r f a c e i s l e s s th a n t h e l e a s t s i g n i f i c a n t d i g i t
and can t h e r e f o r e be i g n o r e d .
in t h e c o m p u t a t i o n s
The n e t w o r k used f o r t h e c o m p u t a t i o n s
w i t h o u t s o u r c e s is shown in F i g u r e 11.
54
C'uK
F i g u r e 10.
C e n t r a l e l e m e n t o f t h e r e s i s t a n c e ne t w o r k w i t h c l o s e d
loops su p er im p o se d on t h e g e o l o g i c model
Vo £\
F i g u r e 11.
Expanded r e s i s t a n c e network s up eri m po sed on t h e g e o l o g i c model
Any c o n f i g u r a t i o n o f s o u r c e s i s p o s s i b l e u s i n g n e t w o r k a n a l y s i s .
The o n l y l i m i t a t i o n
is t h a t t h e l o c a t i o n , o r i e n t a t i o n and m a gn it u de o f
t h e s o u r c e ( s ) be known.
Once t h e n et w or k p a r a m e t e r s have been s p e c i f i e d , a n a l y s i s can
p r o c e e d u s i n g e i t h e r o f two t e c h n i q u e s .
p h y s i c a l measu re men ts made.
Analog s y s t e m s can be b u i l t and
Analog s y s t e m s a r e u n d e p e n d a b le and cumber­
some b e c a u s e o f t h e l a r g e number o f components t h a t must be i n c o r p o ­
rated.
D i g i t a l co m p u te r s and n u m e ri c a l a p p r o x i m a t i o n t e c h n i q u e s make i t
p o s s i b l e t o a n a l y z e l a r g e n et w or k s e f f i c i e n t l y .
used f o r t h i s s t u d y .
analysis
A more d e t a i l e d d i s c u s s i o n o f n u m e r i c a l net wor k
i s c o n t a i n e d in Network A n a l y s i s by Van V a lk e n b e r g
Network a n a l y s i s
1.
The l a t t e r t e c h n i q u e i s
Ohm's law.
(1955).
is bas ed on f i v e p r o p o s i t i o n s .
The p o t e n t i a l d r op a c r o s s a r e s i s t o r
i s equal t o
t h e p r o d u c t o f t h e c u r r e n t in amperes f l o w i n g in a c i r c u i t and
t h e r e s i s t a n c e in ohms.
2.
K i r c h o f f ' s laws.
a.
The t o t a l p o t e n t i a l drop aro un d a c l o s e d loop o f a net wor k
Is z e r o .
b.
The t o t a l c u r r e n t a t any j u n c t i o n o r node o f a netwo rk Is
zero.
3.
T h e v i n i n ' s th e o re m .
From K i r c h o f f ' s laws any n et w o rk can be
t r a n s f o r m e d i n t o an e q u i v a l e n t v o l t a g e s o u r c e f o r which t h e
internal
impedance i s z e r o in s e r i e s w i t h an e q u i v a l e n t r e s i s ­
ta n c e , or a c u rre n t source w ith i n f i n i t e
internal
in p a r a l l e l w i t h an e q u i v a l e n t r e s i s t a n c e .
impedance
57
4.
The p r i n c i p l e o f s u p e r p o s i t i o n .
Any e f f e c t t h a t
is th e r e s u l t
o f s e v e r a l d i f f e r e n t s o u r c e s can be c a l c u l a t e d a s t h e sum o f
t h e e f f e c t s due t o eac h i n d i v i d u a l s o u r c e a c t i n g a l o n e .
The p u r p o s e o f a p p l y i n g n e t w o r k a n a l y s i s as a g e o p h y s i c a l mode lin g
t e c h n i q u e i s t o a n a l y z e t h e r e s p o n s e o f e a r t h s y s t e m s t o an i n p u t .
The
i n p u t s i g n a l used f o r SP mo de lin g i s t h e s i m u l a t e d s o u r c e mechanism.
A f i r s t - o r d e r approxim ation o f the so urce s t r e n g t h is p o s s i b le using
equations
(1) t h r o u g h ( 4 ) .
s o u r c e s t h e model
By i n c o r p o r a t i n g t h e r e s i s t a n c e net wo rk and
i s used t o d e t e r m i n e t h e q u a l i t y o f a h y p o t h e t i c a l
i n t e r p r e t a t i o n as compared w i t h t h e o b s e r v e d d a t a and i f n e c e s s a r y t o
.
improve i t .
The f i r s t s t e p in c a l c u l a t i n g t h e n et w or k r e s p o n s e i s t o d e t e r ­
mine t h e e l e c t r i c c u r r e n t s f l o w i n g in t h e c l o s e d lo op s o f t h e n e t w o r k .
T h i s i s accompl is h e d by a p p l y i n g Ki r c h o . f f 1s laws t o s e t up n s i m u l t a n ­
eous e q u a t i o n s and s o l v i n g f o r t h e unknown loop c u r r e n t s .
An e f f i c i e n t
t e c h n i q u e o f a n a l y z i n g a s y st em o f l i n e a r nonhomogenous e q u a t i o n s
is
through th e use o f m a tr ix a l g e b r a .
A p p ly in g Ohm's law, i t
is p o s s i b le to r e p r e s e n t th e e q u iv a le n t
r e s i s t a n c e o f t h e n e t w o rk in te r m s o f a v o l t a g e s o u r c e .
the c o e f f ic ie n t m atrix,
||
R ||
it
By i n v e r t i n g
is p o s s i b l e t o s o l v e d i r e c t l y f o r
t h e s o l u t i o n v e c t o r c o n t a i n i n g t h e loop c u r r e n t s .
Ill
II = II v II
II R | | - '
(23)
58
The s o l u t i o n o f e q u a t i o n
(23)
is g r e a t l y s i m p l i f i e d by r e c o g ­
nizing th a t:
1.
The m a t r i x | |
R | | i s alwa ys p o s i t i v e - d e f i n i t e .
2.
The m a t r i x | |
R ||
is n o n s i n g u l a r b e c a u s e t h e r e can be no z e r o
v a l u e s on t h e main d i a g o n a l .
3.
The m a t r i x
||
R [[is
sy m m e tr ic i f a p r o p e r c h o i c e o f c o e f f i ­
c i e n t i n d i c e s i s made.
By d e s i g n a t i n g t h a t t h e d i a g o n a l e l e m e n t s a r e e qu al t o t h e p o s i t i v e
sum o f t h e m a g n it u d e o f t h e r e s i s t a n c e s aro u nd ea c h lo o p , t h e p o s i t i v e d e f in ite c h a r a c te r is tic of
th e magnitudes o f th e
t h e c o e f f i c i e n t m a t r i x is e n s u r e d .
Because
b r a n c h r e s i s t o r s a r e al wa ys g r e a t e r t h a n z e r o ;
t h e d i a g o n a l c o e f f i c i e n t s a r e p o s i t i v e , t h e m a t r i x i s n o n s i n g u l a r , and
th e decomposition of | |
R ||
is unique.
M a t r i x symmetry i s a s s u r e d by d e s i g n a t i n g a r e g u l a r p a t t e r n o f
indexing th e in d iv id u a l c lo se d loops.
A c h o i c e o f numbering in t h e
d i r e c t i o n o f f e w e s t loop s m i n im i z e s t h e band widt h o f [ j R | [.
The
m a t r i x ba n dw id th (M) i s d e f i n e d as t h e number o f t h e c o d i a g o n a l beyond
which a l l
codiagonals c o n ta in only zero c o e f f i c i e n t s .
I f a s y st em o f r e c t a n g u l a r loop e l e m e n t s i s used t h e r e w i l l
n e v e r be more t h a n two n o n z e r o c o d i a g o n a l s .
The a d v a n t a g e o f t h i s f e a ­
t u r e i n h e r e n t w i t h r e c t a n g u l a r loop e l e m e n t s is t h a t
i t can s i g n i f i ­
c a n t l y r e d u c e t h e co m pu ter s t o r a g e r e q u i r e d f o r t h e c o e f f i c i e n t m a t r i x .
The c o e f f i c i e n t s a l o n g t h e c o d i a g o n a l s a r e t h e n e g a t i v e r e s i s t a n c e
v a l u e s o f t h e r e s i s t o r s common t o two l o o p s .
The p o s i t i v e - d e f i n i t e ,
s y m m e t r i c , n o n s i n g u l a r , banded propel—
t i e s o f t h e n et w o rk c o e f f i c i e n t m a t r i x can be used t o s i g n i f i c a n t l y
r e d u c e t h e number o f c o m p u t a t i o n s r e q u i r e d f o r t h e d e c o m p o s i t i o n o f
||
R
II
( L.
Fox
, 19 54).
Chole sky ( c i t e d
in B e n o i t ,
1924) showed t h a t
m a tric e s with th e se p r o p e r t i e s a re e q u iv a le n t to th e product of a r e a l ,
nonsingular, t r i a n g u la r m atrix ||
L ||
and i t s t r a n s p o s e
I I R I I = II L II
||
||.
II LT II
(24)
In t h e c a s e f o r a banded m a t r i x t h e r e a r e (N /2) (M +l ) (M+2) m u l t i p l i c a ­
t i o n s and N s q u a r e r o o t s
in v o l v e d in t h e d e c o m p o s i t i o n i f N is t h e o r d e r
of the c o e f f i c i e n t m atrix | |
R ||
( M a r ti n and W i l k i n s o n ,
1965).
The s o l u t i o n o f t h e e q u a t i o n
(25)
i s d e t e r m i n e d in two s t e p s ,
II L II
II Y | | -
||
V ||
( 26 )
and
II LT | |
II I
(27)
II = II Y II
Program SPMODL used f o r t h e c o m p u t a t i o n o f t h e s o l u t i o n v e c t o r
c o n t a i n i n g t h e i m a g in a r y loop c u r r e n t s a l o n g w i t h a c o d i n g form on which
t h e i n p u t d a t a f o r m a t s a r e summarized i s i n c l u d e d in Appendix C.
s k e l e t o n f lo w c h a r t summarizing t h e program s t e p s
A
i s shown in F i g u r e 12.
60
DIMENSION
&
ZERO ARRAYS
DATA
PR O C E S SIN G
PARAMETERS
NODAL
RESISTIV ITY
ARRAY
SET UP
R E S IS T A N C E NETWORK
IN BAND STORAGE
, MODE
SOURCE
LOCATION
O R IEN TA TIO N
MAGNITUDE
T
CHBDET
DETERMINE TRANSPOSE
OF THE LOWER
TRIA N GLE MATRIX
CHBDSL
SOLVE FOR
LOOP CURRENTS
OBSERVED
DATA
APPLY DC S H I F T
TO THE
OBSERVED DATA
L IST
RESULTS OF
CALCULATIONS
E
PLOTXY
D ISPLA Y
L IN E P R IN T E R
PLOTS
F i g u r e 12.
Flow o f t h e program SPMODL
61
The i n i t t i a l o p e r a t i o n s
in t h e program s e t up t h e c o e f f i c i e n t
m a t r i x in band s t o r a g e mode and d e f i n e t h e e n e r g y s o u r c e s
17)•
The second s e t o f o p e r a t i o n s r e s u l t s
solution vector.
w ritten
( F i g s . 13“
in t h e c o m p u t a t i o n o f t h e
An a l g o r i t h m t h a t u s e s t h e Chole sky m e th o d , o r i g i n a l l y
in ALGOL-60 by M a r t i n and W i l k i n s o n (1965) and M a r t i n , P e t e r s
and W i lk in s o n (1965) was t r a n s l a t e d
i n t o FORTRAN IV f o r t h i s a n a l y s i s .
The prog ram c o n s i s t s o f two s u b r o u t i n e s , CHOBANDDET and CHOBANDSOL.
From e q u a t i o n
||
l_T | |
(24) t h e lower t r i a n g l e m a t r i x | |
a r e d e t e r m i n e d in CHOBANDET.
in CHOBANDSOL u s i n g e q u a t i o n s
the fin al operations
L ||
and i t s t r a n s p o s e
The s o l u t i o n v e c t o r
i s computed
(26) and ( 2 7 ) .
in t h e program c o n d i t i o n t h e o b s e r v e d d a t a
by a p p l y i n g a dc s h i f t , o u t p u t t h e computed d a t a and p l o t t h e o b s e r v e d
and modeled d a t a
( F i g s . 18^ 19).
The dc s h i f t
is c a l c u l a t e d by d e t e r ­
mining t h e a v e r a g e dc l e v e l a l o n g t h e f l a n k s o f t h e modeled c u r v e and
ad d i n g t h a t q u a n t i t y t o t h e o b s e r v e d d a t a .
The a d j u s t m e n t o f t h e
o b s e r v e d d a t a as oppos ed t o a d j u s t m e n t o f t h e modeled d a t a i s j u s t i f i e d
by t h e a r b i t r a r y b a s e r e l a t i v e t o which t h e f i e l d o b s e r v a t i o n s a r e
made.
The modeled d a t a a r e c a l c u l a t e d r e l a t i v e t o an a b s o l u t e b a s e .
The program SPMODL has been w r i t t e n t o be a s g e n e r a l as p o s s i ­
b le to permit a r b i t r a r y
in p u ts, e ith e r a r t i f i c i a l or n a tu r a l.
The
program i s c u r r e n t l y f o r m a t t e d t o d i s p l a y t h e p o t e n t i a l a t eac h node
a l o n g t h e modeled s u r f a c e .
Minor c h a n g e s in f o r m a t a r e p o s s i b l e t h a t
would p e r m i t t h e d i s p l a y o f p o t e n t i a l s a t any s p e c i f i e d no des in t h e
network.
SPMODL can a l s o be used t o model
IP and r e s i s t i v i t y d a t a
62
THE NUMBER OF ROHS IN THE INPUT RESISTIVITY ARRAY HAS BEEN EXPANDED FROM
6 TO 9 .
THE NUMBER OF COLUMNS IN THE INPUT RESISTIVITY ARRAY HAS BEEN EXPANDED FROM 17 TO 2 5 .
4 COLUMNS HAVE BEEN ADDED TO THE LEFT AND RIGHT MARGINS OF THE ARRAY.
3 ROHS HAVE BEEN ADDED, ONE TO THE TOP OF THE MODEL TO ACCOUNT FOR THE AIR-EARTH INTERFACE,
THE RBMA±NDER TO THE BASE OF THE MODEL.
13 SET(S) OF DATA HITH
8 SOURCES HAVE BEEN INPUT.
5
THE ORDER OF THE COEFFICIENT MATRIX I S
192.
THE BANDHIDTH OF THE COEFFICIENT MATRIX I S
9
INPUT SOURCE VOLTAGES
LOOP
COEFFICIENT
RON
INDEX
COLUMN
INDEX
106
114
2
2
2
2
3
3
5
10
122
130
107
131
101
109
F i g u r e 13.
5
11
12
13
10
13
9
10
ORIENTATION
OF THE SOURCE
2
2
2
2
2
2
2
2
SOURCE
POTENTIAL
-0 .1 4 0
-0 .1 4 0
-0 .1 4 0
-0 .1 4 0
0 .580
0 . 580
-0 .1 5 0
-0 .1 5 0
Data p r o c e s s i n g p a r a m e t e r s used in t h e n e t w o r k a n a l y s i s
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
200.
200. 200.
200.
200.
200.
*>
200.
200.
200.
200.
200.
200.
200.
194.
194.
19 4 . 2 0 2 .
255.
308. 292.
276.
307.
338.
213.
88.
63 .
37 .
186.
186.
186.
186. 216. 246. 28 7 . 3 28.
368.
408.
264.
10 2.
86.
51.
196.
196.
196.
196.
196. 206.
199.
19 9.
199.
19 9 .
199.
197.
1 9 8 . 19 8 .
1 9 8.
198.
198.
198.
198.
198.
198.
19 8.
198.
0.
200.
20 0 . 2 0 0 .
194.
194.
186.
0.
0.
0.
0.
200. 2 0 0 . 200.
200.
200.
200. 200.
200. 200.
83.
130.
125.
120.
110.
110.
11 0.
110.
110.
90.
130.
125.
120.
115.
111,.
111.
1 11.
111.
111.
81. 127. 173.
140.
1 08.
1 20 .
1 09.
110.
110.
110.
110. .110.
182. 260.
180.
136.
130.
123.
1 16.
110.
110.
110.
110.
110.
314. 333. 352. 270.
187.
162.
145.
134.
125.
118.
1 18.
118.
118.
118.
145.
1 34 .
125.
118.
118.
118.
118.
118.
145.
134.
125.
1 18.
118.
118.
118.
118.
326.
414.
267.
120.
101.
19 5.
250.
302.
294.
286.
1 95 .
104.
19 5 .
218.
240.
259.
277. 296.
19 8.
195.
218.
240.
259.
277.
296. 314. 333. 352. 270.
rCO
0.
222. 238.
162.
198.
198.
195.
218.
240.
259.
277.
296. 314. 333. 352. 270.
187.
162.
F i g u r e 14.
0.
0-
UD
OD
0.
0.
Expanded r e s i s t i v i t y g r i d used t o form t h e r e s i s t a n c e net work
0.
0.
0.
0.
64
0.
0
.
0.
0
.
0. 0.
0
.
0
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0.
0
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
0.
.
0
b.
.
0
0..
.
0
.
20 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 . 2 0 0 .
197.
197.
19 4 .
190.
19 9 .
199.
199.
198.
198.
191.
198.
198. 198.
198.
198.
190. 209.
198.
198.
198. 198,
F i g u r e 15.
251.
298.
211.
239.
263.
198.
310.
322.
198.
358.
327.
229. 250.
391. 338.
301.
277.
192.
158.
195.
218.
250.
240.
197. 207. 229.
296.
57.
69.
84.
64.
71.
89.
132.
143.
219.
265.
311.
314. 333. 352. 270.
187.
277. 296. 319. 333. 352. 270.
268. 267. 305.
187.
324. 343. 311. 229.
119.
123.
123.
120.
122.
127.
138.
154.
162.
145.
139.
195.
159.
134.
140.
111.
111.
110.
113.
121.
155.
155.
110. 110. 110.
111.
111.
111. 111.
125.
122.
110.
118.
118.
118.
118.
110.
111.
111.
111.
111.
118.
118.
118.
118.
118.
118.
118.
118.
114.
118.
118.
118.
110.
110.
114.
118.
118.
118.
110.
110.
114. 114.
118.
118.
122.
110.
110.
114.
122.
125.
130.
110.
155.
110. 110. 110. 110. 110.
113.
130.
155.
113. 111. 111. 1 1 1 . 1 1 1 .
112.
140. 130.
155.
115.
118.
120.
129.
159. 14 0 .
162.
175.
117.
133.
149.
175.
128.
160.
124. 114. 1 1 5 .
138.
175.
163.
126. 123. 118.
135.
158.
184.
229.
107.
157.
177.
165.
107. 128.
110.
132.
221. 220.
267.
393.
194.
192.
60.
9 1 . 104. 150.
103.
324.
87.
50.
268. 287- 305. 324. 343. 311. 229.
259.
250.
305.
102.
150.
76.
94-
111.
286. 291. 255.
268. 287.
158.
183.
37 0 . 3 4 1 . 194.
195. 218. 290. 2 59. 277.
229.
276. 151.
398. 3 88. 336.
196. 207. 245. 28 1 .
197. 2 07.
198.
269. 207. 194. 132. 119.
196.« 2 2 3 . 2 7 6 . 2 9 8 . 2 9 0 . 2 4 1 .
197. 20 7 .
196.
254.
284. 292. 323.
201. 219. 230. 282.
199.
198.
198.
282. 300.
238.
198. 2 02. 2 0 9 . 244. 3 1 4 . 354.
198.
198.
246.
201. 231. 267. 308.
191.
199.
199.
198.
198.
19 6 . 1 9 8 .
191.
199.
199.
198.
190.
228. 254.
198. 229.
196. 196.
198.
199.
197. 201.
186.186.
196.
198.
197.
194.194.
186.
191.
196.
198.
194.
1 9 0 . '1 9 0 .
186.
191.
197.
118.
118.
R e s i s t a n c e n et w or k used f o r t h e n et wo rk a n a l y s i s o f s e l f ­
potential
An e n l a r g e m e n t o f t h e c i r c l e d p o r t i o n o f t h e r e s i s t a n c e
net wo rk i l l u s t r a t i n g t h e way in which t h e c l o s e d r e s i s t a n c e
loo p s a r e r e p r e s e n t e d in t h i s di a gr a m i s shown in F i g u r e 16.
The a c t u a l r e s i s t a n c e v a l u e s used t o s i m u l a t e t h e ai r - e a r t h
i n t e r f a c e i n d i c a t e d by t h e z e r o v a l u e s a t t h e to p o f t h e
di a g ra m a r e g iv e n in F i g u r e 17.
|
65
Node
F i g u r e 16.
A c l o s e d loop in t h e r e s i s t a n c e n e t w o r k
0.250E + 14
0.250E+14
0 .250E -H 4
0 . 250E+ 14
0 .250E + 14
0o 2 5 0 E + 14
0 .2 5 0 B -M 4
0 .2 5 0 E + 1 4
0.250E-H 4
0»250E*14
0«250E*M4
0.250 E * 1 4
0« 25GE+14
0 ..2 50E +14
0.250E *14
O'. 250E+14
0 .2 5 0 E + 1 4
0.250E-H 4
0.250E + 14
0 .2 5 0 E + 1 4
0.250E + 14
0 . 250E,fr 14
0 . 250E'4-14
0 e 2 5 0B * 14
0 .2 5 0 B - H 4
0 . 2 5 0 E * 14
0o2 50E -H 4
0.250E+14
0 . 2 5 0 E *14
0 . 250E-9-14
0. 250E+14
0 . 2 5 0 E + 14
0.250E + 14
0 . 2 5 0 E + 14
0.250E+ 14
0 . 2 5 0 E + 14
0.250E *14
0 . 2 5 GB'!'14
0..2 50E +14
0 .2 5 0 E + 1 4
0 . 250E+14
0,250E4-14
0.2 5 0 E * 1 4
0.2 5 0 E -H 4
0o250E*14
0.250E+14
0 . 250E+14
0.250E > 14
0.000E*00
0 . 2 5 0 E + 14
F i g u r e 17-
R esistance values fo r the
loo p s s i m u l a t i n g t h e a i r earth interface
67
POTENTIAL DATA
SET
NODE
1.0 0
2.0 0
3 .0 0
4.0 0
5 .0 0
6.0 0
7 .0 0
8 .0 0
9.00
1 0.00
11.00
12.00
13.00
14.00
15 .0 0
16 . 00
1 7 .0 0
18.00
1 9 .0 0
20.00
21.0 0
2 2 . 00
2 3 .0 0
24.00
2 5.00
F i g u r e 18.
3
OBSEBVED
POTENTIAL
208.
208.
208.
208.
208.
208.
208.
205.
202.
200.
19 5.
197.
191.
162.
15 3 .
187.
189.
182.
185.
185.
185.
185.
185.
185.
185.
CALCULATED
POTENTIAL
202.
202.
202.
202.
201.
201.
200.
199.
19 6 .
192.
18 4 .
16 9.
147.
140.
173.
15 5.
186.
167.
173.
180.
184.
187.
189.
1 90.
190.
Observed and modeled s e l f - p o t e n t i a l d a t a
68
BOOZLZO (1) 1 1 0 OBSEBTZO SP (2 )
PLOT POSSES 3
SC I L I PICT OPS . . X • 0 . 3 0 0
T • 1 .4 0 0
210.
209.
207.
206.
204.
203.
202.
200.
199.
197.
196.
195.
193.
192.
190.
169.
188.
186.
185.
183.
182.
181.
179.
178.
176.
175.
174.
172.
17 1 .
16 9 .
168.
16 7 .
165.
164.
162.
161.
160.
158.
157.
155.
15 4 .
153.
151.
150.
148.
147.
146.
144.
143.
141.
140.
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
to
10
10
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10
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2
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2
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2
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I
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i
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I
I
I
I
%
I
I
1
1
I
I
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I
Z
I
I
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I
I
I
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1
2
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1
2
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2
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2
2
1
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2
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2
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I
1
3 .0 0
6 .0 0
9 .0 0
1 2 .0 0
1 5 .0 0
1 8 .0 0
2 1 .0 0
2 4 .0 0
2 7 .0 0
DISTIMCZ IP OMITS OP OIPOLZ SP1CIPC
gure 19.
P l o t o f t h e modeled (1) and o b s e r v e d s e l f - p o t e n t i a l
d a t a (2)
3 0 .0 0
w i t h any t w o - d i m e n s i o n a l e l e c t r o d e c o n f i g u r a t i o n .
O th e r o p t i o n s cu
r e n t l y n o t implemented in t h e program i n c l u d e :
1.
An i t e r a t i v e summation o f e l e c t r i c c u r r e n t s g e n e r a t e d by
d i f f e r e n t c r o s s - c o u p l e d s o u r c e mechanisms.
2.
A least-sq u are cu rv e-fittin g , routine
for internal auto­
c o m pa ri s o n o f t h e o b s e r v e d d a t a w i t h t h e modeled d a t a and
an i t e r a t i v e t e c h n i q u e f o r imp ro vin g t h e modeled s o l u t i o n .
CHAPTER 4
AN APPLICATION OF THE PROGRAM SPMODL TO SIMULATE
FLOWS OF ELECTROCHEMICAL ORIGIN
The s e l f - p o t e n t i a l model d e v e l o p e d in t h e p r e v i o u s c h a p t e r can
be used t o model e l e c t r i c p o t e n t i a l d i f f e r e n c e s r e l a t e d t o e n e r g y flow s
o c c u r r i n g in v i r t u a l l y any e n v i r o n m e n t .
The f a c t o r s
lim itin g successful
a p p l i c a t i o n o f n et w o r k a n a l y s i s t o m o de lin g e l e c t r i c p o t e n t i a l d i f f e r ­
e n c e s r e l a t e d t o e n e r g y fl o w s i n c l u d e :
1.
R e c o g n i t i o n o f a c t i v e flo w p r o c e s s e s .
2.
U n d e r s t a n d i n g e n e r g y d i s s i p a t i o n as a r e s u l t o f c r o s s c o u p l i n g between f l o w s .
3.
Knowledge o f g e o l o g y in a r e a s f o r which f lo w p r o c e s s e s a r e
t o be modeled.
4.
Measurements o f t h e p h y s i c a l p r o p e r t i e s o f t h e r o c k s t h a t a r e
u n iq u e t o s p e c i f i c f lo w p r o c e s s e s .
The program SPMODL was t e s t e d u s i n g SP d a t a from an a r e a in
which e n e r g y d i s s i p a t i o n o c c u r r e d a s t h e r e s u l t o f a s i n g l e flow
mechanism.
The re do x c h a r g e t r a n s f e r mechanism p r o p o s e d by S a to and
Mooney (I9 60 ) a l t e r e d , by n e a r - s u r f a c e o x i d a t i o n was t o be t h e o n l y
a c t i v e mechanism.
Good g e o l o g i c a l and g e o p h y s i c a l c o n t r o l
o f s u r f a c e g e o l o g i c mapping, g e o l o g i c lo g s f o r d r i l l
r o c k p r o p e r t y m e a s u r e m e n t s , f o r ex am p le ,
h o l e s and in s i t u
induced p o l a r i z a t i o n and
r e s i s t i v i t y d a t a , was a v a i l a b l e f o r t h e t e s t a r e a .
70
in t h e form
A c o m p l e t e u n d e r s t a n d i n g o f t h e c r o s s - c o u p 1ing between flo w s was
not n ec e ssary fo r t h i s p a r t i c u l a r case because a l l
f lo w s o t h e r than t h o s e
o f e l e c t r o c h e m i c a l o r i g i n we re assumed t o be n u l l .
The r e s i s t i v i t y g r i d
in p u t t o t h e program SPMODL t o form t h e r e s i s t a n c e n e t w o r k i s a c t u a l l y a
f u n c t i o n o f t h e combined e f f e c t i v e m o b i l i t i e s o f ions and e l e c t r o n s mov­
ing in t h e s y s t e m un de r t h e i n f l u e n c e o f e l e c t r o c h e m i c a l p o t e n t i a l g r a ­
d i e n t s and a l l o t h e r g r a d i e n t s .
A ll r e s i s t i v i t y me asu re me nt s made u s i n g
p re s e n t technology a r e cum ulative energy d i s s i p a t i o n f u n c tio n s th a t
in­
c l u d e l o s s e s due t o t h e p u r e r e s i s t a n c e o f e a r t h m a t e r i a l s t o t h e f l o w
o f e l e c t r i c c u r r e n t s a s w e ll a s l o s s e s due t o f lo w s ind uced by c r o s s
coupling.
R ef in em en t o f t h i s s p e c i f i c c a s e t o p e r m i t s e p a r a t i o n o f
t h e e n e r g y d i s s i p a t i o n due t o t r u e ohmic l o s s e s from t h e v a r i o u s
o t h e r components o f t h e t o t a l e n e r g y d i s s i p a t i o n w i l l be p o s s i b l e when
additional
r o c k p r o p e r t y measu re men ts a r e a v a i l a b l e .
In p u t Data
G e o l o g i c a l , G e o p h y s ic a l and G e o g r a p h i c a l
Information
P r i o r t o m o de li ng t h e SP d a t a , g e o l o g i c lo gs and s u r f a c e g eo ­
l o g i c mapping were used t o c o n s t r u c t a g e o l o g i c c r o s s s e c t i o n b e n e a t h
t h e l i n e a l o n g w hi ch SP m ea sur em ent s had been made ( F i g . 2 0 ) .
An e x ­
panded g r i d o f a p p a r e n t e l e c t r i c r e s i s t i v i t y d a t a mea sur ed a l o n g t h e
same l i n e was s u p e ri m p o s e d on t h e c r o s s s e c t i o n t o c h e c k f o r c o n s i s t e n c y
between t h e two ( F i g . 2 1 ) .
I f a good c o r r e l a t i o n between t h e g e o l o g i c
and g e o p h y s i c a l d a t a was o b t a i n e d , t h e r e s i s t i v i t y d a t a were used as an
i n p u t t o t h e program SPMODL.
o o
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Cr e t a c e o u s
and e a r l y
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volcanics
G e o lo g i c c r o s s s e c t i o n b e n e a t h t h e modeled s e l f - p o t e n t i a l
line
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Expanded r e s i s t i v i t y g r i d su perim posed on t h e g e o l o g i c c r o s s s e c t i o n
V)
The a s s u m p t i o n o f a s i n g l e a c t i v e s o u r c e mechanism f o r t h e s u r ­
vey a r e a is j u s t i f i e d by t h e d e p t h o f t h e zone o f w a t e r s a t u r a t i o n and
the apparent absence of s i g n i f i c a n t heat sources.
t h e s e might have been a c t i v e and n o t r e c o g n i z e d .
t a b l e v a r i e d b u t was g e n e r a l l y
Mechanisms o t h e r t h a n
Depth t o t h e w a t e r
in e x c e s s o f 500 f e e t .
Under n a t u r a l
c o n d i t i o n s a t t h a t d e p t h s t r e a m i n g p o t e n t i a l s would n o t be d e t e c t a b l e a t
the su rface.
Most o f t h e s u r f a c e in t h e a r e a o f t h e l i n e t o be modeled
was c o v e r e d by L a t e C r e t a c e o u s and e a r l y T e r t i a r y , t h i n l y bedd ed, a n d e s i t i c flows.
T h e i r a p h a n i t i c t e x t u r e i n d i c a t e d t h a t t h e y had c o o l e d
q u i c k l y and t h e r e f o r e c o u l d n o t now be a s i g n i f i c a n t h e a t s o u r c e .
m i d d le T e r t i a r y r h y o l i t e and l a t i t e d i k e s and s i l l s
were g e n e r a l l y l e s s t h a n 300 f e e t t h i c k .
The
in t h e s u r v e y a r e a
These a l s o showed e v i d e n c e o f
r a p i d c o o l i n g and t h e r e f o r e c o u l d no l o n g e r be a s i g n i f i c a n t h e a t s o u r c e .
No e x p l i c i t
i n f o r m a t i o n was a v a i l a b l e c o n c e r n i n g t h e a g e and c o n s e q u e n t l y
t h e c o o l i n g h i s t o r y o f t h e i n t r u s i v e q u a r t z m o n z o n it e b e n e a t h t h e T e r t i ­
a r y and C r e t a c e o u s v o l c a n i c s and p y r o c l a s t i c c o n g l o m e r a t e a t t h e w e s t
end o f t h e . t e s t
relationships
line.
C h r o n o l o g i c a l c o r r e l a t i o n s o f o b s e r v e d 1i t h o l o g i c
i n d i c a t e an age o f 50 t o 70 m.y. f o r t h e q u a r t z m o n z o n i t e .
Because no h e a t f lo w measu re men ts w er e a v a i l a b l e and no o t h e r in f o r m a ­
t i o n was c o n t r a r y , an a s s u m p t i o n was made t h a t t h e r m o e l e c t r i c e f f e c t s
wer e i n s i g n i f i c a n t .
Two f a c t s s u p p o r t t h i s c o n c l u s i o n .
The q u a r t z mon­
zon i t e i s a t a d e p t h in e x c e s s o f a t h o u s a n d f e e t and t h e w a t e r t a b l e
o c c u r s above t h e i n t r u s i o n .
The e l e c t r o c h e m i c a l p o t e n t i a l
ponents.
includes several
i n s e p a r a b l e com­
D iffusion p o t e n t i a l s probably occur acro ss th e c o n ta c ts
between t h e a n d e s i t e s and c o n g l o m e r a t e s , b u t t h e s e p o t e n t i a l s a r e p a r t
75
o f t h e t o t a l e l e c t r o c h e m i c a l p o t e n t i a l and c a n n o t be s e p a r a t e d from
the e l e c t r i c p o te n tia l
red ox c h a r g e t r a n s f e r .
r e l a t e d t o e l e c t r i c c u r r e n t s r e s u l t i n g from
No a t t e m p t has been made in t h i s s t u d y t o j u s ­
t i f y t h i s a s s u m p t i o n . . The m a g n it u d e o f t h e e l e c t r i c p o t e n t i a l d i f f e r - ?
e n c e s due t o ion d i f f u s i o n a r e p r o b a b l y s m a l l e r t h a n t h e t o t a l e l e c t r i c
p o ten tial.
Because no way e x i s t s t o s e p a r a t e t h e d i f f u s i o n p o t e n t i a l
from t h e t o t a l , e l e c t r o c h e m i c a l p o t e n t i a l o t h e r t h a n m o d e l i n g , s e p a r a ­
t i o n becomes a moot q u e s t i o n .
The s e l e c t i o n o f a l i n e o f SP d a t a t o be modeled was p a r t l y
ba s ed on t o p o g r a p h y .
r a i n was f l a t .
The i d e a l
l i n e would be one a l o n g which t h e t e r ­
The s e l e c t e d l i n e , which was on a t y p i c a l s o u t h w e s t e r n
U.S. p e d i m e n t , had a g r a d u a l d e c r e a s e in e l e v a t i o n o f 200 f e e t from
e a s t to w est.
S l i g h t u n d u l a t i o n s in t h e t e r r a i n n o t e x c e e d i n g 20 f e e t :
were c a u s e d by a r r o y o s c r o s s i n g t h e l i n e in an. i r r e g u l a r f a s h i o n .
p o s s i b l e no measu re men ts were made in t h e a r r o y o s .
Where
T h i s p r e c a u t i o n was
t a k e n t o a v o i d sudden chan ge s in t h e Cu-CuSO^ e l e c t r o d e c o n t a c t r e s i s ­
t a n c e , which was o b s e r v e d t o a f f e c t t h e measu re men ts q u a n t i t a t i v e l y .
The measu re men ts we re made more th a n a month a f t e r t h e l a s t
d e te c ta b le p r e c i p ita tio n to ensure a c o n s is te n t, n e a r-s u rfa c e e le c tro d e
contact re sista n c e .
Near-surface v aria tio n s
in s o i l m o i s t u r e a f t e r a
r a i n an d .sn ow s t o r m c a u s e d e a r l y t e r m i n a t i o n o f th e . measu re men ts b e c a u s e
irregular s h ifts
was p o o r .
in SP o c c u r r e d a l o n g d i f f e r e n t l i n e s and r e p e a t a b i l i t y
S e v e r a l o f t h e i r r e g u l a r s h i f t s o b s e r v e d d u r i n g me asurements
made a f t e r t h e s t o r m we re in t h e v i c i n i t y o f m i n e r a l i z e d f l o a t expos ed
on t h e s u r f a c e .
76
E l e c t r i c P o t e n t i a l So ur ce I n f o r m a t i o n
The most common c o n d u c t i v e m i n e r a l i z a t i o n o b s e r v e d in t h e d r i l l
h o l e s n e a r t h e s u r v e y a r e a was p y r i t e .
O th e r m e t a l l i c m i n e r a l i z a t i o n
i n c l u d e d c h a l c o p y r i t e , g a l e n a , s p h a l e r i t e and t e t r a h e d r i t e .
The minimum
Eh in t h e d e p t h e n v i ro n m e n t was - 0 . 1 4 mV b as ed on t h i s m i n e r a l assem­
b l a g e and S at o and Mooney's ( i 9 6 0) d a t a .
The maximum Eh in t h e n e a r -
s u r f a c e e n v i ro n m e n t was + 0 . 5 8 mV. ( F i g . 2 2 ) .
E l e c t r o c h e m i c a l s o u r c e s ha v i n g a p o t e n t i a l o f + 0 . 5 8 mV were
p l a c e d a l o n g t h e c o n t a c t s between t h e p y r i t i c c o n d u c t o r and h o s t r o c k s
in t h e n e a r - s u r f a c e e n v i r o n m e n t .
were p l a c e d a t t h e c o n t a c t s
S o u r c e s w i t h a p o t e n t i a l o f - 0 . 1 4 mV
In t h e d e p t h e n v i r o n m e n t .
No i n t e r n a l
s o u r c e s were p l a c e d in t h e c o n d u c t o r b e c a u s e charge, t r a n s f e r o c c u r s
o n l y a t t h e i n t e r f a c e between e l e c t r o l y t i c s o l u t i o n and t h e e l e c t r o n i c
conductor.
A s o u r c e - f r e e a r e a was s p e c i f i e d between t h e n e a r - s u r f a c e
zone o f r e d u c t i o n and t h e zone o f o x i d a t i o n a t d e p t h t o s i m u l a t e a
zone o f t r a n s i t i o n .
S u r f a c e g e o l o g i c mapping i n d i c a t e d an o x i d i z e d ,
a t t h e s u r f a c e Over t h e m e t a l l i c m i n e r a l i z a t i o n .
oxidation
leached capping
Be ca use n e a r - s u r f a c e
in what was o t h e r w i s e a zone o f r e d u c t i o n i n d i c a t e d t h a t t h e
m e t a l l i c m i n e r a l i z a t i o n was n o t immune t o p a r t i c i p a t i o n
in r edo x r e a c ­
t i o n s , n e a r - s u r f a c e p s e u d o - s o u r c e s we re added t o d e c r e a s e n e a r - s u r f a c e
r ed ox p o t e n t i a l s .
The d e t e r m i n a t i o n o f t h e p o t e n t i a l s o f t h e n e a r -
s u r f a c e s o u r c e s was e m p i r i c a l l y made by a d j u s t i n g t h e p o t e n t i a l s t o
a c h i e v e a good c o r r e l a t i o n w i t h t h e o b s e r v e d d a t a .
77
(V o lt)
a
E
Graphite
P y rite
Eh
Chalcocite
G alena
-.2
-4
F i g u r e 22.
Maximum a v a i l a b l e p o t e n t i a l d i f f e r ­
ences fo r v ario u s conducting m inerals
- - From S at o and Mooney (1960)
Data A c q u i s i t i d h and E r r o r P a r a m e t e r s
P r i o r t o making t h e SP m ea sur em ent s used f o r c o m p ar is o n w i t h
t h e modeled d a t a t h e o n l y a v a i l a b l e
IP -resistivity
lines.
i n f o r m a t i o n was t h e l o c a t i o n o f t h e
No g e o l o g i c o r g e o p h y s i c a l d a t a we re a v a i l a b l e .
The g e n e r a l c o n f i g u r a t i o n o f t h e l i n e s a l o n g which SP me asurements w er e
made was d e s i g n e d so t h a t t h e SP l i n e s would be col l i n e a r w i t h as many
o f t h e 1P - r e s i s t i v i t y
l i n e s as p o s s i b l e .
S e l f - p o t e n t i a l measurements
were made a l o n g n o r t h - s o u t h l i n e s w i t h a l i n e s p a c i n g o f 150 m and a
S t a t i o n s p a c i n g o f 30 m.
E a s t - w e s t t i e . l i n e s w i t h t h e same s t a t i o n
s p a c i n g were l o c a t e d a t 600 m i n t e r v a l s .
The i n i t i a l
s t e p in s e t t i n g up t h e s u r v e y p r o c e d u r e was t o
e s t a b l i s h a p r i m a r y b a s e r e l a t i v e t o which a l l me asurements were
adjusted.
Measurements we re made u s i n g a m o d i f i e d long-wi r e t e c h n i q u e .
An e i g h t e e n g a g e , t e f l o n - c o a t e d , s t r a n d e d c o p p e r c a b l e was used t o
connect a s t a t i o n a r y e l e c t r o d e w ith th e roving e l e c t r o d e .
had
a
l e n g t h o f 600-m.
At eac h s t a t i o n a r y e l e c t r o d e s e t - u p , f o u r
s e t s o f measu re men ts were made f o r t h e 600-m i n t e r v a l s
e a s t and w e s t s e t s ) .
intervals
The c a b l e
(north, south,
Two s e t s o f me asurements were made f o r t h e 150 m
( n o r t h and s o u t h s e t s ) .
All 600-m i n t e r v a l
stationary
e l e c t r o d e s e t - u p s were co m p le te d p r i o r t o making t h e measurements a t
t h e 150rm s e t - u p s
to t i e a l l
(Fig. 23).
By u s i n g t h i s t e c h n i q u e i t was p o s s i b l e
th e s t a t i o n a r y e l e c tr o d e s e t-u p s to the primary base.
Care
was t a k e n t o make c e r t a i n t h a t , a l l measu re men ts we re made w i t h d i f f e r e n t
"pot" holes fo r a l l
s t a t i o n s along o v erla p p in g li n e segments.
T h i s was
done t o a v o i d i r r e g u l a r s a l t c o n c e n t r a t i o n b u i l d u p a t t h e e l e c t r o d e -
79
i
1
1
1
1
1
1
1
1
1
1
1 I
1
1
1
r |
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1
1
1
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- 4 ------------------
k
i
A
J l
III
i \
r * j - p
i
i
i
i
i
i
.u
T 1
1
1
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r
1
L
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! ! y
; J
----------------- L l
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Ai \
i i ^
1
1
1
i i i
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- 4 ----------------o. L t — i ,i
-----)----1r > -4-^— 4— ^
>
i
i
i
i
i
■ i
ri
>
!
o
-
Stationary electro d e
•
-
P ri m a r y b as e
— -
!
'
►
w
r
600m 1 ine
150m 1in e
F i g u r e 23.
Line c o n f i g u r a t i o n used f o r s e l f - p o t e n t i a l
me asuremen ts in t h e s u r v e y a r e a
80
earth contacts.
Where t h i s p r e c a u t i o n was n o t o b s e r v e d e r r a t i c mea­
s u r e m e n t s we re r e c o r d e d .
The i n s t r u m e n t used f o r t h e s e measu re men ts was c o n s t r u c t e d
from a m o d i f i e d d e s i g n f o r t h e Model 5 SF m e te r m a n u f a c t u r e d by Zonge
E n g i n e e r i n g and R e s e a r c h O r g a n i z a t i o n , Tuc so n.
The i n p u t s i g n a l
is
p a s s e d t h r o u g h t h r e e s t a g e s , a 10 X f i x e d - g a i n a m p l i f i e r in s e r i e s
w i t h a l o w - p a s s f i l t e r f o l l o w e d by a v a r i a b l e - g a i n a m p l i f i e r w i t h
d ec a d e g a i n s t e p s .
I n s t r u m e n t s e n s i t i v i t y was 100 pV.
impedance o f t h e f i r s t a m p l i f i e r s t a g e was 10
]k
fi.
The in p u t
The h igh Inp ut
impedance was n e c e s s a r y t o m i n im i z e i n t e r n a l power d i s s i p a t i o n w i t h
consequent a r t i f i c i a l
c h an ge s In t h e o b s e r v e d s i g n a l .
Two c o r r e c t i o n s were a p p l i e d t o t h e measured d a t a .
A separate
b u l k b a s e c o r r e c t i o n was made f o r ea c h s t a t i o n a r y e l e c t r o d e s e t - u p t o
account for d if f e r e n c e s
in t h e p o t e n t i a l a t t h e r e f e r e n c e e l e c t r o d e s
r e l a t i v e to the c e n tra l
base.
the d iffe re n c e s
. T h is c o r r e c t i o n was made by d e t e r m i n i n g
in p o t e n t i a l between t h e b a s e and e a c h s t a t i o n a r y e l e c ­
t r o d e and removing t h e d i f f e r e n c e from a l l measu re men ts made r e l a t i v e
t o ea c h s t a t i o n a r y e l e c t r o d e .
A d r i f t c o r r e c t i o n was a l s o a p p l i e d t o
t h e d a t a t o a c c o u n t f o r te m p o r a l v a r i a t i o n s .
m aintain a r ig id schedule of t i e s a t
An a t t e m p t was made t o
l e a s t e v e r y two h o u r s .
Closed loop
t i e s a v e r a g e d 1 .8 mV and l i n e r e p e a t a b i l i t y was 3*3 mV ± 2 . 2 mV.
R e s u l t s O b ta i n e d Using t h e Program SPMODL
As w i t h a l l
t y p e s o f p o t e n t i a l d a t a an i n f i n i t e number o f s o u r c e
solutions are possible.
S e l f - p o t e n t i a l d a t a a r e no e x c e p t i o n .
Judi­
c i o u s u s e o f s u p p l e m e n t a r y g e o l o gy and g e o p h y s i c s r e d u c e s t h e number o f
probable s o lu t i o n s c o n s id e r a b ly , enhancing the f i n a l
All a v a i l a b l e
interpretation.
I n f o r m a t i o n has been used f o r t h e i n t e r p r e t a t i o n o f t h e
o b s e r v e d SP d a t a
shown in F i g u r e 24.
o b s e r v e d SP d a t a
and t h a t computed u s i n g program SPMODL a r e e n c o u r ­
aging.
obvious o f th e s e s i m i l a r i t i e s
The most
The s i m i l a r i t i e s between t h e
include:
1.
The c l o s e c o i n c i d e n c e o f t h e 50-6 0 mV t r o u g h s .
2.
S i m i l a r c h an ge s in the. r e g i o n a l
g r a d i e n t a t t h e e a s t and
w e s t ends o f t h e p r o f 11e .
3.
S im ilar frequency c o n te n t.
The l o c a t i o n o f t h e 5 0 - 6 0 mV t r o u g h i s c o r r e l a t a b l e w i t h t h e
a r e a o f c o n d u c t i n g m i n e r a l i z a t i o n bounded on t h e e a s t by a n e a r ­
vertical fau lt
(F ig. 24).
T h e r e does n o t a p p e a r t o be a d i s t i n c t
w e s t e r n boun dary t o t h e m i n e r a l i z a t i o n ,
r a t h e r a g r a d a t i o n a l change
from m a s s i v e t o d i s s e m i n a t e d m i n e r a l i z a t i o n w i t h a c o r r e s p o n d i n g ch an g e
in r e s i s t i v i t y .
The r e g i o n a l g r a d i e n t s
in t h e o b s e r v e d and c a l c u l a t e d
d a t a c o n f i r m t h i s ch ang e in m i n e r a l i z a t i o n .
The s p a t i a l
frequency
c o n t e n t o f t h e d a t a i s d i r e c t l y c o r r e l a t a b l e w i t h l o c a l cha n ge s in
resistiv ity .
An example o f t h i s
i s t h e 30-40-mV
t h e w e s t f l a n k o f t h e SO-GO-mV t r o u g h t h a t
resistiv ity
array
o s c i l l a t i o n along
is r e l a t e d t o t h e 37-^-m
in t h e s e co nd row and t w e l f t h column o f t h e r e s i s t i v i t y
(Fig. 2 1 ).
Two o b s e r v a t i o n s a r e a d i r e c t r e s u l t o f t h e m o de li n g p r o c e s s .
The s o u r c e s t r e n g t h s a p p e a r t o c o r r e l a t e w i t h t h o s e e x p e c t e d f o r a
p y r i t e e l e c t r o d e immersed in a s t r a t i f i e d e l e c t r o l y t e in which o x i d a ­
t i o n o f r e d u c t a n t s o c c u r s a t d e p t h and r e d u c t i o n o f o x i d a n t s o c c u r s
200
c
CD
4-»
0
O.
1
150
O modeled SP d a t a
• o b s e r v e d SP d a t a
100
o o
=c n:
cr> vn
o o
3= 3:
jr- VO
o
3:
M
r
Rhyoli t e d i k e
F i g u r e 24.
—r—\
Poss i b l e V< i» Laramide
quartz
sulfide
monzon i t e
intrusion
O
3:
—
m
WWW
%
La te C r e t a c e o u s
and e a r l y
Tert iarv
v o l c a n i cs
Pyroclast i c
The r e l a t i o n s h i p between t h e modeled and o b s e r v e d s e l f - p o t e n t i a l d a t a and
t h e g e ol og y
oo
N)
.83
in t h e n e a r - s u r f a c e e n v i r o n m e n t .
The s o u r c e s used t o a c c o u n t f o r t h e
l e s s th a n maximum n e a r - s u r f a c e r e d o x p o t e n t i a l
that resu lts
in o x i d a ­
t i o n o f t h e e l e c t r o d e a r e on t h e same o r d e r o f m a g n it u d e a s t h e re d o x
potential
in t h e d e p t h e n v i r o n m e n t .
The red ox p o t e n t i a l a t d e p t h may
w e ll be an i m p o r t a n t f a c t o r l i m i t i n g n e a r - s u r f a c e o x i d a t i o n o f t h e
electrode.
More c o n s i d e r a t i o n , i n c l u d i n g f i e l d m ea sur em ent s and
geoc he mi ca l s t u d i e s , a r e n e c e s s a r y b e f o r e t h i s can be pr ov ed o r d i s ­
proved.
The i n t e r p r e t a t i o n r e s u l t i n g from t h e s e d a t a i s t h a t a f l o o r e d
zone o f m a s s i v e p y r i t e m i n e r a l i z a t i o n o c c u r s d i r e c t l y b e n e a t h t h e t r o u g h
on t h e SP c u r v e s .
The i n t e r p r e t a t i o n t h a t t h e s o u r c e s t r e n g t h i n d i c a t e s
p y r i t e m i n e r a l i z a t i o n does n o t r e d u c e t h e p r o b a b i l i t y t h a t o t h e r m e t a l ­
lic su lfid e s are present.
in d r i l l
O th er m e t a l l i c s u l f i d e s have been o b s e r v e d
h o l e s a d j a c e n t t o t h e 50 -6 0 mV SP t r o u g h and a r e t h e r e f o r e
probably p r e s e n t w ith th e p y r i t e .
P y r i t e s im p l y c o n t r o l s t h e maximum
po ssib le p o te n tia l d iffe re n c e d e te c ta b le a t the su rface.
As w i t h a l l
i n t e r p r e t a t i o n s of geophysical d ata th e source of
an anomaly i s n e v e r known f o r c e r t a i n u n t i l
a drill
hole.
inform ation.
Even d r i l l
i t has been p e n e t r a t e d by
h o l e s sometimes f a i l
to provide the necessary
.
CHAPTER 5
EVALUATION
Energy t r a n s f e r
libria.
In t h e e a r t h o c c u r s t o r e d u c e n a t u r a l d l s e q u i -
The mechanisms o f e n e r g y t r a n s f e r
in c lu d in g h e a t flow, f l u i d
flo w and t h e f lo w o f c h a r g e d and n e u t r a l m a t t e r a r e i n t e r r e l a t e d by
cross-coupling.
S p e c i f i c e n e r g y t r a n s f e r mechanisms c a n n o t o c c u r w i t h ­
o u t i n d u c i n g o r m o d i f y i n g a l l o t h e r f lo w p r o c e s s e s .
The c o m p l e t e m a th e­
m a t i c a l d e s c r i p t i o n o f e n e r g y t r a n s f e r must t h e r e f o r e c o n s i d e r a l l
a c t iv e flows.
The the rmodynamics o f i r r e v e r s i b l e p r o c e s s e s p r o v i d e s a
convenient n o ta tio n f o r th e d e s c r i p t i o n of q u a s i - s t a t i c . , energy t r a n s f e r
mechanisms.
S elf-potential
i s one n a t u r a l m a n i f e s t a t i o n o f t h e s e
q u a s i - s t a t i c f lo w p r o c e s s e s o c c u r r i n g in t h e e a r t h .
.
The r e t i c u l a r s t r u c t u r e o f t h e e a r t h and t h e s i m i l a r i t y between
t h e p r o p e r t i e s o f n a t u r a l membranes s e p a r a t i n g t h e r e t i c l e s and r e s i s ­
t o r s used in e l e c t r i c c i r c u i t s a r e i n d i c a t i o n s o f t h e p o s s i b l e a p p l i c a ­
b i l i t y o f e l e c t r i c n e t w o r k a n a l y s i s f o r mo de lin g f lo w mechanisms
r e l a t e d t o SP.
An a d v a n t a g e o f e l e c t r i c net wo rk a n a l y s i s
is the r e l a ­
t i v e s i m p l i c i t y o f a p p l i c a b l e mathematical te c h n iq u e s .
An a n a l y t i c a l
SP model t h a t u s e s e l e c t r i c n e t w o r k a n a l y s i s has
been d e v e l o p e d in a n t i c i p a t i o n o f d e t a i l e d measu re men ts o f t h e the rm o ­
dynamic p r o p e r t i e s o f e a r t h m a t e r i a l s .
The model r e q u i r e s
inform ation
p e r t a i n i n g t o e n e r g y s o u r c e s , t r a n s p o r t mechanisms and t h e r e s p e c t i v e
p h e no m en ol og ic al c o e f f i c i e n t s ,
S e p a r a t e s o u r c e and c o e f f i c i e n t m a t r i c e s
84
85
a r e r e q u i r e d f o r ea c h a c t i v e f lo w mechanism.
The t o t a l
energy t r a n s ­
p o r t e d a c r o s s a s y s t e m i s modeled a s t h e sum o f t h e e n e r g y t r a n s p o r t e d
by t h e p r i m a r y mechanisms and t h e e n e r g y d i s s i p a t e d o r added as t h e
r e s u l t o f c r o s s - c o u p l i n g between f l o w s .
A computer pr o gr am , SPMODL, was w r i t t e n t o c a l c u l a t e t h e e l e c ­
t r i c p o t e n t i a l a t t h e nodes in t h e ne t w o r k t h a t s i m u l a t e h e t e r o g e n e o u s ,
i s o t r o p i c r e g i o n s in t h e e a r t h .
The program was t e s t e d u s i n g SP d a t a
from an a r e a where good g e o l o g i c a l and g e o p h y s i c a l d a t a were a v a i l a b l e
fo r e v a lu a tio n of the f in a l
results.
The t e s t was made as su m in g t h a t
t h e o n l y a c t i v e mechanism was r ed ox c h a r g e t r a n s f e r a l t e r e d by n e a r surface oxidation.
C ro s s c o u p l i n g between f l o w s was n o t c o n s i d e r e d .
The r e s u l t s o f t h e mo de lin g i n d i c a t e d e l e c t r o c h e m i c a l p r o c e s s e s
o c c u r r i n g in a n e a r - s u r f a c e zone o f r e d u c t i o n , e l e c t r o n i c a l l y c o n n e c t e d
w i t h t h o s e o c c u r r i n g in a zone o f o x i d a t i o n a t d e p t h by a p y r i t e e l e c ­
t r o d e t h a t has u n d er go ne o x i d a t i o n a t t h e s u r f a c e , can p r o d u c e e l e c t r i c
potential
d i f f e r e n c e s on t h e o r d e r o f t h o s e t h a t we re m e a s u r e d .
The
c l o s e c o r r e l a t i o n bet ween t h e r e g i o n a l g r a d i e n t , a m p l i t u d e and s p a t i a l
f r e q u e n c y o f e v e n t s on t h e c u r v e s f o r t h e o b s e r v e d and modeled d a t a
shown
in
F i g u r e 24 adds c r e d a n c e t o t h i s
interp retatio n .
One s u c c e s s f u l a p p l i c a t i o n o f a mode ling t e c h n i q u e does not
pr ov e i t s e f f e c t i v e n e s s , however.
P e rfe c tio n of t h i s technique re q u ire s
a c o n s i d e r a b l e amount o f a d d i t i o n a l d a t a a c q u i s i t i o n and computer s o f t ­
ware d e v e l o p m e n t .
Two g e n e r a l c a t e g o r i e s o f recom men dat ions a r e made
f o r c o n t i n u e d a n a l y s i s o f t h e r e l a t i o n s h i p between f l o w p r o c e s s e s and
S .
86
1.
Recommendations f o r r e f i n e m e n t o f t h e model d e v e l o p e d in
t h i s study.
2.
Measurements and c o m p i l a t i o n o f d a t a n e c e s s a r y f o r t h e
expanded a p p l i c a t i o n o f t h i s model.
Several
r e f i n e m e n t s a r e p o s s i b l e t h a t would Improve t h e u t i l i t y o f t h e
program SPMODL.
A d d i t i o n o f an o p t i o n t h a t would p e r m i t c o m p u t a t i o n and
d i s p l a y Of e l e c t r i c p o t e n t i a l s a t any node o r a l o n g any d e s i g n a t e d
s u r f a c e would p e r m i t u s e o f t h i s model t o a n a l y z e downhole e l e c t r i c
measurements.
A sec o nd d e s i r a b l e o p t i o n
is a c u r v e - f i t t i n g r o u t i n e
t h a t would u s e a c o n v e r g e n c e t e c h n i q u e t o improve t h e f i n a l s o l u t i o n .
Improvement would be a c c o m p l i s h e d
by c h a n g i n g t h e s o u r c e s t r e n g t h s ,
s o u r c e l o c a t i o n s o r c o e f f i c i e n t m a t r i x u n t i l a good c o r r e l a t i o n
between o b s e r v e d and c a l c u l a t e d d a t a Is o b t a i n e d .
The computer s t o r a g e
r e q u i r e m e n t s can be re d u c e d by t a k i n g a d v a n t a g e o f t h e f a c t t h a t o n l y
twd c o d i a g o n a l s a r e n o n - z e r o .
This p e rm its s t o r a g e o f th e c o e f f i c i e n t
m a t r i x in an N X 3 a r r a y f o r a l l
networks using r e c t a n g u l a r elements
re g a r d l e s s o f th e s i z e of th e network.
The p r e s e n t s t o r a g e r e q u i r e ­
ments f o r t h e c o e f f i c i e n t m a t r i x a r e N X M; N i s t h e o r d e r and M t h e
b a n dw id th o f t h e c o e f f i c i e n t m a t r i x .
I t is a l s o p o s s i b le to introduce
a g e o m e t r i c c o r r e c t i o n t h a t would p e r m i t d i r e c t
input o f ap parent
r e s i s t i v i t i e s t o t h e ne t w o r k r a t h e r t h a n t r u e r e s i s t i v i t i e s .
A final
improvement c o n t i n g e n t on t h e r ec om me nd at ion s in t h e se co n d c a t e g o r y
i s i m p l e m e n t a t i o n o f t h e o p t i o n f o r a n a l y s i s o f m u l t i p l e f lo w s u s i n g
t h e program SPMODL.
T h i s o p t i o n would p e r m i t u se o f a s i n g l e p a s s t o
an aly ze a complete s e t o f d a t a .
87
B e f o r e t h e program SPMODL can be expanded f o r c o n s i d e r a t i o n o f
m u l t i p l e p r i m a r y and c r o s s - c o u p l e d f lo w s a c o n s i d e r a b l e q u a n t i t y o f
thermodynamic d a t a Is n e c e s s a r y .
The i n i t i a l
p r i o r i t y must be on a
thorough co m p ila tio n o f a v a i l a b l e inform ation p e r t a i n i n g to th e primary
and c r o s s - c o u p l e d e n e r g y t r a n s f e r c o e f f i c i e n t s .
When n e c e s s a r y , s u p p l e ­
m e n ta r y me asuremen ts o f t h e s e p a r a m e t e r s must be made w i t h some s p e c i f i c
me asuremen ts r e q u i r i n g t h e i n n o v a t i o n o f new i n s t r u m e n t a t i o n and mea­
suring te ch n iq u es.
t h e i m p l i c i t r e l a t i o n s h i p between p r i m a r y m e t a l l i c m i n e r a l i z a ­
t i o n and s e c o n d a r y e n r i c h m e n t o f m i n e r a l i z e d z o n e s , and SP i n d i c a t e s
t h e need f o r s u p p l e m e n t a r y s t u d i e s p e r t a i n i n g t o e l e c t r o c h e m i c a l p r o ­
cesses.
The economic s i g n i f i c a n c e o f t h i s r e l a t i o n s h i p
consideration
indicates th is
is o f p r i m a r y i m p o r t a n c e . A c o n s i d e r a b l e number o f i n v e s ­
t i g a t o r s have a p p r o a c h e d t h i s s u b j e c t
in te r m s o f t h e g eo che mi ca l
e n v i ro n m e n t in which m e t a l l i c m i n e r a l i z a t i o n o c c u r s .
Additional s tu d ie s
a r e r e q u i r e d t h a t would s u p p le m e n t S a t o and Mooney's (I9 60)
research
and would p e r m i t e x t e n s i o n o f t h i s model t o a d d i t i o n a l m i n e r a l s p e c i e s .
The p r e c i s i o n o f any m od e li n g p r o c e s s i s l i m i t e d by t h e q u a l i t y
of the inform ation a v a i l a b l e fo r the com putations.
no e x c e p t i o n ,
T h i s m o d e l , which i s
is designed to s im u la te energy t r a n s f e r
flo w mechanism.
i n i t i a t e d by any
A l a r g e number o f t e s t s a r e n e c e s s a r y b e f o r e t h i s
model can be c o n s i d e r e d r e l i a b l e .
The a l g o r i t h m use d in t h e program
SPMODL c a r r i e s o u t a s p e c i f i c s e q u e n c e o f n u m e r i c a l and l o g i c a l o p e r a ­
tions.
The i n p u t d a t a upon which t h e s e o p e r a t i o n s a r e c a r r i e d o u t w i l l
determine the f in a l
results.
Therefore,
it
is i m p e r a t i v e t h a t t h e
a c t i v e k i n e t i c p r o c e s s e s be c o m p l e t e l y u n d e r s t o o d .
APPENDIX A
NOTATION
The f o l l o w i n g symbols a r e used in t h i s t h e s i s :
a
Gram
formula weight
of substance A
b
Gram
formula weight
of substance B
c
Gram
formula weight
of substance C
e~
Charge o f an
k
C o e ffic ie n t of f l u i d tr a n s m is s i b ? 1ity
m
Gram fo r m u l a w e i g h t o f a s u b s t a n c e
n ,n 1
Number o f e l e c t r o n s t r a n f e r r e d d u r i n g e l e c t r o d e r e a c t i o n s
n
Normal u n i t v e c t o r
pH
The n e g a t i v e l o g a r i t h m o f hydrogen ion
r
D i s t a n c e s e p a r a t i n g any two p o i n t s
t
Time
Ax
Cross s e c t i o n a l a r e a
[A]
Ionic a c t i v i t y o f su b sta n c e A
[B]
Ionic a c t i v i t y of substance B
D
C oefficient of diffu sio n
E
Amount o f e n e r g y c o n t a i n e d a t a p o i n t in a f l o w
Eq ,
Standard e l e c t r o d e p o t e n t i a l
electron
■
E.
.
Nernst p o t e n t i a l
■
i
activity
-
d i f f e r e n c e between two h a l f - c e l I s .
88
Eh
Eho ’
T o t a l e l e c t r o c h e m i c a l p o t e n t i a l d i f f e r e n c e measu red
on t h e hydrogen s c a l e
Eho '
S t a n d a r d e l e c t r o d e p o t e n t i a l measured on t h e hydrogen s c a l e
Eq
E lectro k in etic potential
Em
P o t e n t i a l d i f f e r e n c e ca u s e d by ion d i f f u s i o n
F
Faraday's c o n stan t
la
N et.anion m o bility
Ic
Net c a t i o n m o b i l i t y
ill I
S o l u t i o n v e c t o r c o n t a i n i n g t h e im a g in a r y loop c u r r e n t s
7
G e n e r a l i z e d t o t a l e n e r g y flo w
Ji
( 2 3 ,0 6 0 c a l . / V )
. Component fl o w s o f t h e t o t a l e n e r g y fl o w
Flow o f mass
F l u i d flo w
E lectric current
Heat fl o w
L
Generalized c o n d u c tiv ity c o e f f i c i e n t .
When s u b s c r i p t e d
L i s t h e normal c o n d u c t i v e f o r i=j and c r o s s c o u p l i n g
co efficien t for i ^ j .
M
C o e f f i c i e n t m a t r i x ban d w id th
M
Mol a !
N
Order o f t h e c o e f f i c i e n t m a t r i x
P, P 1
E le c to ly tic solution pressure
R
U n i v e r s a l gas c o n s t a n t
||R ||
C o effic ien t m atrix
S
Entropy
||V ||
Sou rce m a t r i x
SP
S elf-potential
( 0 .0 8 2 f - a t m / m o l e - ° K )
90
I
A bsolute tem perature
X
T o t a l e n e r g y a t a p o i n t in a s y st e m
X
Thermodynamic " f o r c e s " g e n e r a t i n g flo w s
Z.
V al e n c e o f t h e i t h component
S
Mean e l e c t r i c a l
£
D ie le c tric constants of e l e c tr o l y te s
5
Zeta p o t e n t i a l
X
C o e f f i c i e n t o f thermal c o n d u c t i v i t y
y
E lectrolyte viscosity
y
Chemical p o t e n t i a l o f t h e i t h component o f a s y s t e m
y
Electrochemical p o te n tia l
p
E le c tric r e s i s t i v i t y of e l e c tr o l y te s
a
C oefficient of e l e c tr i c conductivity
9
Charge d e n s i t y
AE
D i f f e r e n c e o f t h e e n e r g y l e v e l s between two p o i n t s
VP
P r e s s u r e d i f f e r e n c e between two p o i n t s .
VX
G eneralized energy g r a d ie n t
th ick n ess o f the ionic d o u b le -la y e r
in r o ck s
in a s y st e m
in r o c k s
APPENDIX B
MATHEMATICAL BASIS FOR THE PHENOMENOLOGICAL
EQUATIONS DESCRIBING IRREVERSIBLE
THERMODYNAMIC PROCESSES
Four c o n d i t i o n s o u t l i n e d
in C h a p t e r 3 must be s a t i s f i e d f o r t h e
a p p l i c a t i o n o f t h e therm od yna mi cs o f i r r e v e r s i b l e p r o c e s s e s t o be v a l i d .
1.
All f l o w s , J . , must be t i m e d e r i v a t i v e s o f thermodynamic
variables.
2*
3 7 = ? Xi ° 7 i
I
(19)
3.
J. = E
'
U
(20)
k.
L . . “ Lj j
L . . X.
U
J
The e n e r g y d e n s i t y
first
(21)
(U^) o f a k i n e t i c sy ste m i s d e s c r i b e d by t h e
law o f therm ody nam ic s a s t h e sum o f t h e i n t e r n a l e n e r g y d e n s i t y
(U) and t h e work (W) t a k i n g p l a c e in a s y s t e m .
dlfj. = dU + dW
The f i r s t
law e x p r e s s e d a s e q u a t i o n
(B-l)
(B-l)
is s i g n i f i c a n t b e c a u s e i t
predicts th at:
1.
Energy can be c o n v e r t e d from one form t o a n o t h e r .
2.
Energy c a n n o t be o b t a i n e d from any mechanism n o t p r o v i d e d
w i t h an a d e q u a t e s o u r c e .
The second law o f thermo dyn amic s e x p r e s s e d a s an i n t e g r a l e q u a ­
tion
in d icates the d ire c tio n
in which s p o n t a n e o u s , n a t u r a l
processes
w i 11 p r o c e e d .
(dW)T < 0
E q u a t i o n (B-2)
(B-2)
I n d i c a t e s t h a t u nd er i s o t h e r m a l c o n d i t i o n s t h e work
r e q u i r e d t o r e s t o r e a n a t u r a l s y st em t o i t s . i n i t i a l
t h a n any p o s s i b l e g a i n in e n e r g y .
state
is g r e a t e r
If a p o t e n t i a l e n e r g y d i f f e r e n c e
(AX) e x i s t s , e n e r g y o r m a t t e r i s t r a n s p o r t e d and p o s i t i v e work i s
obtained.
(dW)
=
1
Equation
„
Z AX.
i=1
1 1
f.
(B-3)
( B - 3 ) d e s c r i b e s t h e work done in t r a n s p o r t i n g e n e r g y o r m a t t e r
from one p o i n t
a t which
t h e r e is
a unique p o te n ti a l energy level
second p o i n t w i t h
a n in d e p e n d e n t
dynamic v a r i a b l e s
( £ . ) a r e d e p e n d e n t on e x t e r n a l p a r a m e t e r s , f o r exam­
p l e volume and mass.
level of p o te n tia l energy.
to a
The thermo
These v a r i a b l e s d e s c r i b e t h e s p e c i f i c en e r g y
t r a n s f e r p r o p e r t i e s o f t h e medium t h r o u g h which e n e r g y o r m a t t e r i s
transported.
By s u b s t i t u t i n g e q u a t i o n
(B-3)
i n t o ( B -l) and e x p r e s s i n g t h e
e n e r g y d e n s i t y o f t h e k i n e t i c s y s t e m in t h e P f a f f i a n fo r m , K a t c h a l s k y
93
and Curran (1965) have shown t h a t t h e e n e r g y d e n s i t y e q u a t i o n f o r a
r e v e r s i b l e p r o c e s s is. e x a c t .
dlL = dU +
AX. I .
E
E
i =:
•
(B-4)
'
T h e r e f o r e , t h e e n e r g y d e n s i t y e q u a t i o n can be i n t e g r a t e d u s i n g an i n t e ­
grating fa c to r
(l/T ).
The r e s u l t
Expanding e q u a t i o n
is th e entropy equation
dS
(B-5)
(B~3)
i n t o i t s c o m p o n e n t s , work is d e s c r i b e d
as a f u n c t i o n o f i n t e r n a l and e x t e r n a l p a r a m e t e r s .
dW - PdV -
S u b s titu tin g equations
n
E p.dn.
i= v 1 1
-
(B-5) and (B-6)
n
E
i=i
Z .e F ^d n. - qd<p
1
1
into equation
(B-6)
(B -1), th e G ibb's
equatio n is o b ta in e d .
TdS = dU
This eq u a tio n
n
+ PdV = E
i=i
p.
n
dn. = EZ.eF<f>dn.
- qd(J>
1 1 i=i
1 1
is i m p o r t a n t b e c a u s e i t a c c o u n t s f o r a l l
(B-7)
c h an ge s in t h e
e x t e r n a l p r o p e r t i e s o f t h e s y s t e m in te r m s o f e x t e r n a l p a r a m e t e r s and
e x p r e s s e s t h e c h an ge s in t h e i n t e r n a l e n e r g y as f u n c t i o n s o f i n t e r n a l
p a r a m e t e r s ; f o r ex am p le , p r e s s u r e and i o n i c c o n c e n t r a t i o n s .
the G ibb's equation fo r t h i s a n a l y s i s
The u s e o f
is j u s t i f i e d by t h e a s s u m p t i o n
t h a t l o c a l c o n d i t i o n s o f i s o b a r i c and i s o t h e r m a l e q u i l i b r i u m e x i s t
(Harmon and Honig, 1967 ).
i f n is t h e ou tw ar d normal t o a boundary e l e m e n t w i t h s u r f a c e
a r e a A a c r o s s which a n e t t r a n s f e r o f e n e r g y (J^) t a k e s p l a c e , t h e
total
inward f l u x o f e n e r g y t r a n s p o r t e d a c r o s s t h e b ou nd ary is
9E
9t
V
dV
transported
(B-8)
J £ '• n dA
A p pl y in g t h e th e o re m o f G auss, t h e r i g h t s i d e o f e q u a t i o n
(B-8) can be
transform ed.
J E • n dA =
(B-9)
J E dV
The e n e rg y d e n s i t y d e r i v e d e n t i r e l y from t h e i n t e r n a l p a r a m e t e r s o f t h e
s y s t e m i s found u s i n g an i n t e g r a l s i m i l a r t o t h e l e f t s i d e o f e q u a t i o n
(B-8).
*9E'
[ 9 tJ
( B - 10)
dV
internal
The t o t a l e n e r g y t r a n s f e r r e d a s t h e r e s u l t o f a f lo w i s t h e sum o f
equations
(B-9) and ( B - 1 0 ) , and
dE dV =
dt
3E
9t
dV
internal
V • J £ dV
(B -ll)
95
For e q u a t i o n
(B - 11) t o be t r u e , t h e i n t e g r a n d s must a l s o be e q u a l . .
E q u a t i o n (B-12) can be s i m p l i f i e d by s p e c i f y i n g t h a t no l o c a l
internal
s o u r c e s a r e a c t i v e in t h e s y s t e m , t h e n
H
=> V • J£
(B-13)
The same s t e p s can be used t o d e t e r m i n e t h e r a t e a t which
c h a r g e d and u nc ha rg e d p a r t i c l e s , h e a t , e l e c t r i c c u r r e n t , o r f l u i d
flo w a c r o s s a b o u n d a r y .
H
= - V ° Jj.
E lectric current
(B-14)
j£ .i
dt
=- y «j
Mass f lo w
(B-15)
4r
at
= “ V ° J.
Q
Heat f lo w
(B-16)
—
dt
= - V ° J
F l u i d flow
( B - 17)
m
q
S u b s titu tin g equations
(B-14) t h r o u g h ( B - l ? )
i n t o ( B - 7 ) , an
e q u a t i o n o f t h e form r e q u i r e d t o s a t i s f y t h e f i r s t c o n d i t i o n
dS _
1
dt
" T
V * J_ - q V * J t - P V ° J
Q.
^
q
+ Z ■ Z.eFV ° J .
•
i
mi
is d e r i v e d .
By u s i n g t h e i d e n t i t y
V • (AB) = A V “ B + B V ° A
equation
( B - 18) can be r e w r i t t e n a s t h e sum o f t h e e x t e r n a l o r r e v e r s ­
ible c o n trib u tio n s
and t h e i n t e r n a l o r i r r e v e r s i b l e components
dS;
to the t o t a l entropy production
dt
dS
dt
dS,
dt
(de G r o o t,
1952).
dSj
dt
(B-19)
where
dSe
= - V
dt
dt
n
E- Z . e F4>Jm
1= 1
1
T Ja." f JI + T Jq
rv
= J. ° V
T
Q
r >
- J - ° V 3L ■+ J
1
q
° V
S
T i=t
S u b s t i t u t i n g X f o r t h e g r a d i e n t te rm s in e q u a t i o n
V
T
y . dn.
'
(B-20)
(B-21)
'
(B -2 1) , t h e second
c o n d itio n is s a t i s f i e d .
m
if'
= }
Xi ° J i + . Z Ai Yi (Q)
j= l
i= l
w here
XQ " V IT
Thermal g r a d i e n t
( 19)
97
Xx = - V
Charge d i s t r i b u t i o n
P ress ure g ra d ie n t
xq =
It
Chemical e l e c t r i c p o t e n t i a l
gradient
Chemical a f f i n i t y
Ai * “ i
The o c c u r r e n c e o f v e c t o r and s c a l a r f lo w te r m s in t h e same e q u a t i o n is
p e r m i t t e d by t h e C u r r i e th e o re m which s t a t e s t h a t v e c t o r and s c a l a r
" f o r c e s '1 cannot in t e r a c t .
forces
true
T herefore the c o e f f i c i e n t s fo r the s c a la r
in a v e c t o r f lo w e q u a t i o n must v a n i s h .
( F i t t s , 1962).
The c o n v e r s e i s a l s o
As a c o n s e q u e n c e o f t h i s th e or e m t h e g e n e r a l
v e c t o r f l o w e q u a t i o n can be w r i t t e n as i s shown in e q u a t i o n
_
J. =
'
m
_
E L . . X.
i,j U J
The s c a l a r flow e q u a t i o n is w r i t t e n
y. =
n
Z
iJ
Equations
L ,, A
U
(20a).
i , j = 1 ,m
(20a)
in a s i m i l a r way.
(20b)
i , j = 1 ,n
J
(20a) and (20b) show t h a t t h e t h i r d c o n d i t i o n i s s a t i s f i e d .
An i m p o r t a n t e x c e p t i o n t o t h e d i s t i n c t i o n between s c a l a r and
v e c t o r f lo w s i s t h e c o m b i n a t i o n o f t h e s e t o form t h e e l e c t r o c h e m i c a l
potential
(iue ) •
Guggenheim (1929) p o i n t e d o u t t h a t t h e work in v o l v e d
in ch a n g i n g t h e number o f moles o f an i o n i c s p e c i e s
(1) by dn.
is
composed o f two t e r m s , a ch em ica l p o t e n t i a l and an e l e c t r i c p o t e n t i a l .
98
T hes e two te rm s c a n n o t be p h y s i c a l l y s e p a r a t e d .
c o n s i d e r e d t o g e t h e r as shown in e q u a t i o n
p@ =
n
n
2
p.d . +
2
i = i
1 ni
;=i
ch em ica l
potential
Onsager ( c i t e d
T h e r e f o r e t h e y must be
(B-22).
Z.eF^dn.
1
1
(B-22)
electric
potential
in de G r o o t , 1952, p. 6) pr ov ed t h a t
v i d e d ap r o p e r c h o i c e o f f lo w s and f o r c e s
n o m e n o lo g ic a l c o e f f i c i e n t s
L.j
i s made
the m atrix of
. . pro­
p he ­
is symmetric, t h a t i s . . .
Li j = Lj
i
1-
and t h e r e f o r e
and
D e t a i l e d d i s c u s s i o n s o f O n s a g e r 1s r e c i p r o c a l
relation
f o r b oth vector
and s c a l a r f lo w s a r e i n c l u d e d in r e p o r t s by de G ro o t ( 1 9 5 2 ) , R a s t o g i ,
Singh and S r i v a s t a v a
( 1 9 6 9 ) , and Mi l l e r
( i 960) .
APPENDIX C
COMPUTER PROGRAM SPMODL
00001
DIMENSION BRBES ( 1 7 , 2 5 ) , RE S IS ( 9 , 2 5 ) ,B ( 1 9 2 , 2 ) ,X ( 1 9 2 , 2 ) , F ( 2 5 , 2 )
DIMENSION I T I T L ( 8 0 ) ,L T IT L (80) ,INAME (50)
00002
DOUBLE PRECISION A ( 1 9 2 , 9 ) , L ( 1 9 2 , 9 )
00003 z
INTEGER S R O t i , S C O L , FCOL, FRON, R
000 04
DATA B R R E S / 4 2 5 * 0 / , R E S I S / 2 2 5 * 0 / , A / 1 7 2 8 * 0 / , B / 3 8 4 * 0 / , 1 / 3 8 4 * 0 / , F / 5 0 * 0 /
000 05
DATA 1 / 1 7 2 8 * 0 /
000 06
00007
C
000 08
C SET THE VARIABLES TO PRINT THE TITLES ON THE PROFILE PLOTS. ■
C
00009
C
IT IT L THE PLOT LABEL.
000 10
,4 H
,4 H
,4H
, 4H
,4H
M,4H
00011
DATA ( I T I T L ( I ) , 1 = 1 , 20) /4 H
,4H
,4H
20DEL, 4HED (,4 H 1) A , 4 HND 0 , 4HBSER,4HVED ,4HSP (,4H 2)
00012
3 ,4H
,4H
,4H
,4H
000 13
/
00014
C
LTITL THE ABSCISSA LABEL.
00015
C
, 4H
,4 H
,4H
,4H
,4HDI,4H
DATA (LTITL ( I ) , I = 1 , 2 0 ) /4 H
00016
, 4H
2STAN, 4HCE I,4 H N 0N ,4H IT S , 4HOF D, 4 HIP O L ,4 HE S P , 4 HACIN, 4HG
000 17
3 ,4H
,4H
,4H
,4H
00018
/
000 19
G
C
INAME THE ORDINATE LABEL.
00020
DATA (INAME(l) , 1 = 1 , 5 0 ) /1 H , 1H ,1H ,1H ,1H ,1H ,1H ,1 H , 1H , 1 8 ,1H ,
00021
2 1 H , 1 H , 1 H , 1 H , 1 H ,1 H ,1H , 1 H ,1 H , 1 H M ,1 H I,1H L ,1H L ,1 H I,1H V ,T H O ,
00022
3 1 HL,1 H I , 1 HS, 1 H , 1 H ,1 H , 1H ,1H ,1 H ,1H ,1H ,1H , 1 H ,1H ,1H ,1H ,
00023
4 1 H , 1 H ,1H ,1H ,1H , 1 H ,1H /
00 0 2 4
C
00025
00026
C
*
*
*
*
*
*
*
*
*
*
*
*
00027
C
INSTRUCTIONS FOR DIMENSIONING
00028
C
C
00029
G
000 30
C
SUBSCRIPT VALUES
00031
C
00 0 3 2
DEFAULT
I=NROH*5
I=NROH+IVEXPN+1
00033
C
DEFAULT
J=2*NCOL
J=NC0L*2*IHEXPN
0 00 34
c
K =2*I-1
G
00035
0 00 36
L=2
C
N= ( 1 - 1 ) * ( J - 1 )
0003 7
C
LL=J
00 0 3 8
C
c
M1 = I
0003 9
c
0 0040
ARRAY DIMENSIONS
00041
c
c
00042
A
(N ,M 1)
c
00 043
B
(N,L)
00 0 4 4
c
BE RES
(K , J)
c
0 0045
F
(LL,L)
c
00046
L
(N ,H1)
00 0 4 7
c
RESIS
(I,J )
c
00048
X
(N,L)
0 00 4 9
c
c
00050
c
00051
*
*
*
*
*
*
*
*
*
*
*
'*
00052
c
c
00053
SP MODELING PROGRAM
00054
c
00055
c
000 56
c THIS ALGORITHM USES THE NETWORK ANALYSIS USED BY ELECTRICAL ENGINEERS
99
100
MAIN,
LNNT2Y. FOR
00057
000 58
00059
000 6.0.
00061
0006 2
00063
00064
00065
00066
00067
0006 8
00069
00070
00071
00 072
00073
00074
00075
00 076
00077
00078
00079
00080
00081
0008 2
00083
00084
00085
00086
00087
00088
00089
00090
00091
00 092
00093
00094
00095
00096
00097
00098
00099
00100
00101
00 102
00103
0010 4
00105
00106
00107 .
00108
00 109
001 10
001 11
001 12
C
c
c
c
c
C
c
c
c
c
c
c
c
C
c
c
c
c
c
c
c
c
c.
c
c
c
c
c
c
c
c
c
c
c
c
c
c
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
FORTRAN V. 5 ( 5 1 5 )
/KI
5- MAR- 78
11: 48
PAGE 1” 1
TO MODEL A SYSTEMS RESPONSE TO AN INPUT.
THE MODEL INPUT AND OUTPUT
PARAMETERS ARE LISTED BELOW.
THE SET OF EQUATIONS TO BE SOLVED ARE
WRITTEN USING OHM'S LAW AND KIRCHOFF'S LAWS.
THE FORM OF THE MATRIX
EQUATION I S :
(E )=(I)*(R )
THE IMAGINARY LOOP CURRENTS ARE SOLVED FOR USING THE CHOLESKY
ALGORITHM.
ONCE THE LOOP CURRENTS ARE KNOWN IT IS POSSIBLE TO
CALCULATE THE POTENTIAL AT EACH OF THE NODES IN THE NETWORK.
INPUT DATA
NCOL
THE NUMBER OF COLUMNS IN THE ARRAY OF NODAL R E SIST IV IT IE S.
THIS PARAMETER IS EXPANDED INTERNALLY TO NCOL+2*IHEXPNTHE EXPANSION I S NECESSARY TO ALLOW SPACE FOR INSERTION
OF ADDITIONS TO THE ARRAY TO MINIMIZE THE BOUNDARY EFFECTS
AT THE LEFT AND RIGHT MARGINS OF THE MODEL.
NROW
THE NUMBER OF ROWS IN THE ARRAY OF NODAL R E SIST IV IT IE S.
THIS PARAMETER IS EXPANDED INTERNALLY IN THE PROGRAM TO
NROW+IVEXPN+1. THIS EXPANSION I S NECESSARY TO ACCOUNT FOR
THE AIR-EARTH INTERFACE AT THE TOP OF THE MODEL, AND THE
BOUNDARY EFFECTS AT THE BOTTOM OF THE MODEL.
IHEXPN THE NUMBER OF NODAL COLUMNS TO BE ADDED TO THE INPUT ARRAY
TO MINIMIZE THE BOUNDARY EFFECTS AT THE EDGES OF THE MODEL.
IVEXPN THE NUMBER OF NODAL ROWS TO BE ADDED TO THE INPUT ARRAY
TO MINIMIZE BOUNDARY EFFECTS AT THE BASE OF THE MODEL, AND
ACCOUNT FOR THE. AIR-EARTH INTERFACE AT THE TOP.
ISOURCE THE NUMBER OF CURRENT SOURCES ACTIVE IN THE MODEL FOR A
. SPECIFIC MECHANISM.
ISET
THE NUMBER OF DISTINCT SETS OF SOURCE DATA TO BE MODELLED.
ISETM THE NUMBER OF MECHANISMS GENERATING ELECTRIC CURRENTS.
THIS PARAMETETER I S NOT CURRENTLY USED IN THE MODEL. I T I S
INCLUDED HOWEVER TO PERMIT FUTURE EXPANSIONS IN THE
MODEL TO ACCOUNT FOR EFFECTS FROM MULTIPLE SOURCE MECHANISMS
THE EXPANSION SIMPLY INVOLVES THE ADDITION OF A DO LOOP.
RESIS ( I / J) THE VALUES OF THE INPUT NODAL R E S IS T IV IT IE S .
THE
VALUES FOR THE SUBSCRIPTS ARE COMPUTED AS SHOWN ABOVE.
POT •
ELECTRIC -POTENTIAL DIFFERENCE OF THE CURRENT SOURCE..
IXCORD THE NUMBER OF THE COLUMN IN WHICH THE CURRENT SOURCE
OCCURS.
IYCORD THE NUMBER OF THE ROW IN WHICH OR BELOW WHICH THE CURRENT
MAIN.
LNNY2Y.FOR
FORTRAN 7 . 5 ( 5 1 5 )
/KI
5 - HAR- 7 8
11:48
PAGE 1 - 2
00113
G
SOURCE OCCURS.
001 14
C
001 15
C
LOCATP THE ORIENTATION OF THE CURRENT SOURCE.
A" 1 INDICATES THAT
C
00116
THE CURRENT SOURCE IS HORIZONTAL.
THE CURRENT SOURCE I S
00117
C
VERTICAL I F THE VALUE OF THIS PARAMETER IS 2.
ANY OTHER
00118
C
.'
VALUE FOR. THIS PARAMETER WILL RESULT IN AN ERROR,;
00119
c
THE CURRENT SOURCE I S ALWAYS CONSIDERED TO BE AT' THE NODE'
00120
c
IN THE UPPER LEFT HAND CORNER OF A PARTICULAR LOOP.
00121
c
c
F (L L ,L ) THIS I S THE COMPUTED NODAL POTENTIAL USING THIS MODEL
00122
00123
c FOR L=1, AND THE OBSERVED SP DATA FOR L=2.
INDEXES OF L.
00124
c
0012 5
c
00126
c
*
*
*
*
*
* .
*
*
*
*
*
*
00127
c
00128
c
c
OUTPUT
00129
00130
c
00131
c
DATA PROCESSING PARAMETERS
c
00132
00 133
c
c
RESISTIVITY GRID
00134
00135
c
GRID OF RESISTANCE LOOPS
00136
c
c
0 0137
LIST OF RESISTANCE VALUES FOR THE AIR-EARTH INTERFACE
c
00138
00139
c
c
MATRIX PARAMETERS
00140
00141
c
00142
c
SOURCE INPUT DATA LIST
c
0 0143
00144
SURFACE POTENTIAL DATA BY NODES
c
00 145
c
c
SP PLOT (S)
00146
0 0147
c
*
*
*
*
*
*
*
# .
*
*
*
• *
00148
c
00149
c
00150
c IN IT IA L IZE VARIABLES
00151
c
INPUT THE NUMBER OF THE INPUT DEVICE USED IN THE MODELLING..
00152
c
INPUT=20
0 0153
00154
c
OUTPUT THE NUMBER OF THE OUTPUT DEVICE.
0 015 5
c
OUTPUT=6
00156
c
0 0157
IPAGE
A COUNTING PARAMETER USED TO COUNT PAGES OF OUTPUT.
00158
c
0 0159
IPAGE=1
00160
c
RESAE THE RESISTIVITY AT THE AIR—EARTH INTERFACE.
c
00161
00162
, .RESAE=2.5E+13
00163 . C.
0 0 1 6 4 . - c- READ IN". DIMENSIONS OF THE NODAL RESISTIVITY ARRAY, THE EXPANSIONS TO
0 01 65
c CORRECT FOR EDGE EFFECTS, THE NUMBER OF SOURCES AND THE NUMBER OF DATA
00166
c SETS.
READ (INPUT, 1) NCOL ,NROW,.IHEXPN,IVEXPN,ISOURC ,IS E T
00167
1
FORMAT (6110)
00168
MAIN.
LNNY2I. FOE
FORTRAN V. 5 ( 5 1 5 )
/K I
5- MAR- 78
11:48
PAGE 1 - 3
00169
C
00170 C R IS USED IN THE SUBROUTINES FOR
THECHOLESKYDECOMPOSITION.
00171
R=1
00 1 7 2
C
00173
C CHECK TO DETERMINE I F THE AUTO-EXPANSION OPTION I S REQUIRED.0017 4 C
00 175
I F (IHEXPN. EQ. 0'J IHEXPN'■=NCCiL/2‘ ' '
0017 6
I F (IVEXPN.EQ.0) IVEXPN=4 00177
C
00 178
C RETAIN THE ROW AND COLUMN DIMENSIONS OF THE INPUT RESISTIVITY ARRAY.
00179
C
00 180
C
NCOLIN THE NUMBER OF COLUMNSIN THE INPUT
ARRAY.
00181
NGOLIN= NCOL
0018 2
C
00183
C
NROWIN THE NUMBER OF ROWS IN THEINPUT ARRAY.
0 01 84
NROWIN=NROW
00185
C
00186
C EXPAND THE ARRAY ACCORDING TO THE DESIRED OPTIONS.
001 87
C
00188
NCOL=NCOL+2*IHEXPN
001 89
NROW= NROW+ IVEX PN + 1
00190
C
00191
C DISPLAY THE DATA PROCESSING PARAMETERS.
0019 2
C
00193
PRINT 8 , IPAGE
0 01 94
8
FORMAT ( 1 H 1 , I 4 )
001 95
JVEXPN=IVEXPN+1
00196
PRINT 2 , NROWIN,NROW,NCOLIN,NCOL,IHEXPN,JVEXPN,ISET,ISOURC
00197
2
FORMAT ( 5 2 X , *DATA PROCESSING PARAMETERS1, / / , 2 2 X , • THE NUMBER OF ROWS
00 198
2 IN THE INPUT RESISTIVITY ARRAY HAS BEEN EXPANDED FROM', 1 4 , 1 X , 'T O '
00199
3 , 1 4 , ' . ' , / , 2 2 X , ' T H E NUMBER OF COLUMNS IN THE INPUT RESISTIVITY ARRA
00200 4 Y HAS BEEN EXPANDED FROM', 1 4 , I X , ' TO*, 1 4 , * . « , / , 2 2 X , I 1 , I X , ' COLUMNS H
00201
SAVE BEEN ADDED TO THE LEFT AND RIGHT MARGINS OF THE. ARRAY. ' , / , 2 2 X ,
00202
6 1 1 , 1 X, ' ROWS HAVE BEEN ADDED, ONE TO THE TOP OF THE MODEL TO ACCOUN
00203
7 T FOR THE AIR-EARTH INTERFACE, ' , / , 22X ,'T H E REMAINDER TO THE BASE O
00 204
8F THE MODEL.' , / , 2 2 X ,1 2 , 1 X, ' SET (S) OF DATA WITH', 1 4 , IX,'SOURCES HAV
0 02 05
9E BEEN I N P U T .')
00 206
C
00207
C
FCOL THE FINAL COLUMN OF THE INPUT NODAL ARRAY.
THIS PARAMETER
00208
C
I S COMPUTED INTERNALLY IN THEPROGRAM
AND CHANGES AS THE
00209
C
ARRAY IS
EXPANDED.
00210
C
00211 .
FCOL= NCOL-IHEXPN
00 212
C
00213
C
FROW THE FINAL ROW OF THE INPUT NODAL ARRAY.
THIS NUMBER I S
00 214
C
COMPUTED INTERNALLYWITHIN THEPROGRAM AND CHANGED
0 0215
C
INTERNALLY WITHIN THE PROGRAM ASTHE ARRAY OF NODAL
00 216
C
R E SIST IV IT IE S I S EXPANDED.
0 0217
C
002 18
FROW=NROW-IVEXPN
00219
C
00220
C
SCOL THE FIRST COLUMN OF THE INPUT ARRAY IN THE EXPANDED ARRAY '
00221
C
COMPUTED INTERNALLYWITHIN THEPROGRAM.
002 22
C
00223
SC0L=IREXPN+1
00 224
C
MAIN.
LNNY2Y.FOR
00225
00226
00227
00228
00229
002.30
00231
00232
00233
00234
00 235
00236
00237
00 238
00239
00240
00241
00242
00 243
00244
0024 5
00246
0024 7
00248
00249
00250
00251
00252
00253
00254
002 55
00256
00257
00258
00 259
00260
00261
00262
0 0263
00264
0 026 5
00266
002 67
00268
00269
00270
00271
00272
00273
00274
00275
00 276
00277
00278
00279
00280
C
C
C
SROH
F O R TRAN
V . 5(515)
/KI
5-MAR-78
11:48
PAGE 1 - 4
THE FIRST ROW OF THE INPUT ARRAY IN THE EXPANDED ARRAY
COMPUTED INTERNALLY WITHIN THE PROGRAM.
SROW=FROW+1
'
C
"READ
IN
THE
NODAL
RESISTIVITY
DATA
USING
FORMAT
8
F
1 0 .0 .
c
C
RE AD (INPUT , 21) ( (RESIS ( I , J) :,,J=SCqL, FCOL) , 1 = 2, FRO W)
FORMAT (8F 1 0 .0 )
21
C
c ADD NODAL RESISTIVITY DATA TO ACCOUNT FOR THE BOUNDARY EFFECTS AT THE
c LEFT AND RIGHT MARGINS.
c
DO 10 K=1 ,IHEXPN
DO 10 1 = 1 , FROM
RESIS ( I , K) = RE S IS ( I , S COL)
CONTINUE
10
c
c THE VALUE OF SCOL IS CHANGED TO THAT OF THE FIRST COLUMN AFTER THE
c INPUT NODAL ARRAY"
c
S COL= FCOL+1 *■
DO 20 K=SCOL, NCOL
DO 20 1 = 1 ,FROW
RESIS ( I ,K ) =RESIS (I,FCOL)
20
CONTINUE
C
c ADD NODAL RESISTIVITY DATA TO ACCOUNT FOR THE BOUNDARY EFFECTS
c AT THE BASE OF THE MODEL.
c
DO 30 I=SROW,NROW
DO 30 J = 1 , NCOL
RESIS ( I , J ) =RESIS (FROK, J)
30
CONTINUE
C
C CHECK TO MAKE CERTAIN THE DATA WAS READ IN AND EXPANDED PROPERLY..
C
3
4
IPAGE=IPAGE+1
PRINT 3 , IPAGE
F O R M A T ( 1 H 1 , I 4 , / / , 5 2 X , 1 EXPANDED RESISTIVITY ARRAY*, / / )
PRINT 4, ( (RESIS ( I , J) , J = 1 , NCOL) , 1 = 1 , NROW)
FORMAT( 1X, 2 5 F 5 . 0 / / )
C
c COMPUTE THE BRANCH RESISTOR VALUES
C
C THE SIZE OF THE ARRAY I S EXPANDED TO ACCOUNT FOR THE NECESSITY TO
C INDEX ROWS AND COLUMNS CONSISTING OF HORIZONTAL AND VERTICAL ELEMENTS.
C
FROW=2*NROW-1
FCOL=NCOL-1
c
1=2
IROW=FROW-2
DO 40 K=3,IROW, 2
DO 4.0 J= 1 , FCOL
I F ( J . EQ.FCOL) GO TO 41
MAIN.
LNNY2Y.F0R
FORTRAN V . 5 ( 515)
/K I
5- MAR- 78
11:48
PAGE 1 - 5
00281
C
C
BRRES(K,L) THE CALCULATED VALUES OF THE BRANCH RESISTORS.
0028 2
002 83
C
THE VALUES OF THE SUBSCRIPTS ARE CALCULATED AS SHOWN ABOVE
C
00284
002 85
BRRES (K ,J) = ( E E S I S ( I , J ) + R E S I S ( I , J + 1 ) ) / 2
00 286
•. BRRES (K + 1> J ) = (RESIS ( I , J j +RESIS (1+1 , J ) ) / 2
00287
GO' TO 40
, :
: ;
41
00288
BRRES (K+1, NCOL) = (RESIS.(I , NCOL) +RESIS (1 + 1 ,NCOL) ) / 2
BRRES (K+1 , J) = (RESIS ( I , J) +RESIS ( I - H , J ) ) / 2
002 89
BRRES (K, J) = (RESIS ( I , J ) +RESIS ( I , J + 1) ) / 2
00290
00291
1=1+1
00292
40
CONTINUE
C
00 293
00294
C COMPUTE THE BRANCH RESISTORS FOR THE FINAL ROW.
C
00 295
DO 50 J = 1 , FCOL
00296
BRRES (FRO W, J) = (RESIS.(NROW t J) +RESIS (NROW,J+1) ) / 2
00297
00298
50
CONTINUE
00 299
C
00300
C DISPLAY THE RESISTIVITY GRID CONSISTING OF COLUMNAR LOOPS.
00301
C
00302
IPAGE=IPAGE+1
PRINT 5,IPAGE
00303
FORMAT ( 1 H 1 , I 4 , / / , 5 3 X , 1 GRID OF RESISTANCE LOOPS1, / / )
0 0304
5
DO 62 1 = 1 ,FROW, 2
0 0305
I F ( I . EQ.FROW) GO TO 61
00306
PRINT 6, (BRRES ( I , J ) ,J=1,FCO L)
00307
FORMAT ( 4 X , 2 4 F 5 . d / / )
00308 . 6
PRIN T22, (BRRES (1 + 1 , J ) ,J=1,NCOL)
003 09
00310
22
FORMAT ( I X , 2 5 F 5 . 0 / / )
62
CONTINUE
00311
61
PRINT 6 , (BRRES ( I , J ) , J = 1 , FCOL)
00312
C
0 0313
00314
C ADD BRANCH RESISTORS TO SIMULATE THE AIR EARTH INTERFACE.
0 0315
C
DO 60 J = 1 , FCOL
00316
BRRES (1., J ) =RESAE
00317
BRRES (2 , J) =RESAE
00318
I F ( J . EQ.FCOL) BRRES ( 2 , NCOL) =RESAE
00319
60
00320
CONTINUE
IPAGE=IPAGE+1
00321
PRINT 7 , IPAGE
00322
FORMAT(1H1 , 1 4 , / / , 48X,'RESISTANCE VALUES FOR THE LOOPS» , / , 4 6 X , *SIMU
7
00323
00324
2LATING THE AIR—EARTH INT E RFACE *,//)
PRINT 9 , ((BRRES ( I , J ) , 1 = 1 , 2 ) , J=1,NCOL)
00325
0032 6
9
FORMAT (60X,E1 0 . 3)
00327
C
C COMPUTE THE NUMBER OF LOOP COLUMNS.
00328
00329
C
C
00330
LCOL THE NUMBER OF COLUMNS OF LOOPS IN THE CALC.ULAT'ED NETWORK.
00331. . c
LCOL=FCOL
'
0 0 33 2
00333
c COMPUTE THE NUMBER OF LOOP ROWS.
c
LROW
THE
NUMBER
OF
ROWS
OF
LOOPS
IN
THE
RESULTING
NETWORK.
00334
003.35
LROW= NROW—1
00 336
c COMPUTE THE ORDER OF THE LOOP COEFFICIENT MATRIX.
MAIN.
LNNY2Y.F0R
00337
00338
00339
00340
00341
00342
00 343
003 4.4
003 45
003 46
00347
00348
00349
00350
00351
00352
00353
00354
00355
00356
00357
003 58
003 59
00360
00361
003 6 2
00 363
003 64
00365
00366
003 67
00368
0 03 69
00370
00371
00372
00373
00 374
00375
00 376
00377
00378
00 379
00380
00381
00 382
003 83
00384
00385
00 386
003 87
00388
00389
00390
00391
0 03 92
C
C
N
FORTRAN V . 5 ( 515)
/KI
5-MAR- 78
11:48
PAGE 1 - 6
THE ORDER OF THE LOOP COEFFICIENT MATRIX COMPUTED IN THE
PROGRAM.
N=LCOL*LROW
C COMPUTE THE NUMBER OF NONZERO CODIAGONALS BHTCH GIVES THE BAND WIDTH
C OF THE LOWER TRIANGLE MATRIX.
THE NARROWEST BANDWIDTH CORRESPONDS .
C TO THE NARROWEST DIMENSION OF THE NETWORK.
C
M '
THE NUMBER OF NON-ZERO CODIAGONALS IN THE COEFFICIENT MATRIX
M=LROW.
C
C DETERMINE WHETHER THE VERTICAL DIMENSION (NUMBER OF ROWS) EXCEEDS THE
C HORIZONTAL DIMENSION (NUMBER OF COLUMNS).
I F THIS I S THE CASE THE
C RUNSTREAM WILL ABORT AND AN ERROR MESSAGE WILL BE DISPLAYED.
C
I F (LCOL. LT. LROW) GO TO 70
C SET UP THE LOWER TRIANGLE MATRIX IN THE BAND STORAGE MODE..
THE
C DIMENSION OF THE ARRAY I S N X M+1.
C
C THE POSITIVE CURRENT DIRECTION I S ASSUMED TO BE COUNTERCLOCKWISE.
C
C THE DIAGONAL COEFFICIENTS ARE THE POSITIVE SUM OF THE BRANCH RESISTORS
C AROUND THE INDIVIDUAL LOOPS.
THE OFF DIAGONAL COEFFICIENTS ARE THE
C NEGATIVE BRANCH RESISTOR VALUES AROUND THE LOOPS.
IP.AGE=IPAGE+1
PRINT 8 , IPAGE
M=M+1
C PRINT THE ORDER OF THE MATRIX AND THE BANDWIDTH OF THE MATRIX.
PRINT11,N,M
11
FORMAT(1H0,«THE ORDER OF THE COEFFICIENT MATRIX I S * , 1 5 , * . < , / / ,
2 ' THE BANDWIDTH OF THE COEFFICIENT MATRIX I S 1, 1 4 , 1. ' )
K=1
C
C COMPUTE THE COEFFICIENTS FOR THE LOOPS IN THE F I R S T . COLUMN.
C
DO 80 1 = 1 , LROW
A(I,M )=BRRES(K,1)+BRRES(K +1 , 1 ) +BRRES(K+2, 1 ) +BRRES(K+1,2)
I F ( I . GT. 1) A ( I , M-1) =-BRRES (K, 1)
K=K+2
80
CONTINUE
I=LROW+1
DO 90 J=2,LCOL
K=1
C SET UP THE COEFFICIENT MATRIX.
THIS STEP COULD BE CHANGED TO GET RID
C OF THE SIX COLUMNS HAVING ZERO VALUES SO THAT IN ALL CASES THE SIZE
C OF THE COEFFICIENT MATRIX WILL BE N X 3 RATHER THAN N X M.
C THIS STEP WOULD NECESSITATE A CHANGE IN THE SUBROUTINES FOR THE
C CHOLESKY DECOMPOSITION.
C
C COMPUTE THE COEFFICIENTS FOR THE REMAINING LOOPS.
C
DO 90 LL=1,LROW .
A(I,M )=rBfiR ES(K ,J )+ BRRES(K +1,J)+BRRES(K+2,J)+BRRES(K +-1,J*1)
A ( I , 1) =-BRRES (K+1, J)
I F (LL.GT. 1) A ( I , M-1) =-BRRES (K, J )
K=K+2
1=1+1
90
CONTINUE
MAIN.
00393
00394
00395
0 0396
00397
00398
00399
00400
00401
0040 2
00403
00 404
00405
00 406
00407
0040 8
00409
00410
00411
00 412
00413
00 414
00415
00416
00 417
00 418
00419
00 4 20
00421
00422
00423
00 424
00425
00426
00427
0042 8
00429
00430
00431
0043 2
00433
0 0434
00435
00436
00437
0 043 8
00439
00440
00441
00442
004 43
004 44
00445
0044 6
00447
004 48
LNNY2Y.F0R
FORTRAN V . 5 ( 5 1 5 )
/KI
5- MAR- 78
11:48
PAGE 1 - 7
M= M-1
C
C
C
G
C
C
C
C
C
C
C
C
C
c
c
I F ANY OF THE MAIN DIAGONAL COEFFICIENTS ARE ZERO THE CHOLESKY
DECOMPOSITION HILL FAIL AND THE PROGRAM WILL ABORT FOLLOWING THE
SUBROUTINE CHBDET IN WHICH AN ERROR FLAG,. I ERROR I S SET.
READ- IN' THE SOURCE VOLTAGES AND THEIR NODAL COORDINATES.
THESE VALUES
ARE STORED IN AN NXR ARRAY.
A POSITIVE VOLTAGE INDICATES THE CURRENT
FLOW I S COUNTERCLOCKWISE.
B (N)
THE MATRIX OF SOURCE POTENTIALS.
BEGIN THE CHOLESKY DECOMPOSITION.
Ml
THE BANDWIDTH OF THE LOWER TRIANGLE MATRIX IN THE
COEFFICIENT MATRIX.
M1=M+1
c
A (N,M1) THE COEFFICIENT MATRIX IN BAND STORAGE MODE.
c
c
THE OUTPUT ARRAY
c THE SUBROUTINE CHBDET CALCULATES THE TRANSPOSE OF A.
THE SOLUTION VECTOR X,
c L, IS INPUT TO CHBDSL ALONG WITH THE ARRAY, B.
c I S OUTPUT.
c
CALL CHBDET(N,M1, M, A , L , D 1 , D2,TERROR)
c
I F IERROR=1 THE PROCESSING I S ABORTED.
. c CHECK THE ERROR FLAG.
c
I F (IERROR. EQ. 1) GO TO 71
c
c
c SET THE INPUT PARAMETERS FOR PLOTXY TO TAKE ADVANTAGE OF THE AUTO­
c SCALING OPTION.
MNMN=0
NN=LCOL+1
MM=2
XMINZ=1
XMAXZ=XMINZ
YMINZ=1
YMAXZ=YMINZ
c
DO 190 K=1,TSET
c
c INCREMENT THE GRAPH COUNT.
III=K
c
c
c CHECK TO SEE I F A NEW SET OF SOURCE DATA I S REQUIRED.
I F (K. GT. 1)
GO TO 91
c
GO TO 92
c
c READ IN THE NUMBER OF SOURCES IN THE NEW SET OF DATA.
91I
24
READ(INPUT,24) ISOURC
FORMAT (40X>I10)
IPAGE=IPAGE+1
MAIN.
00449
00450
00451
00452
004 53
00454
0045 5
00456
0045 7
0045 8
00459
00460
00461
00 462
00463
00464
00465
00466
00467
00 468
00469
00470
00471
00472
00473
004 74
00475
00476
00477
004 78
00479
00480
00481
00482
004 83
00484
00485
004 86
00487
004 88
00489
00490
00491
00492
00493
0049 4
00495
00496
00497
,0 0 4 9 8
• 0 0499
00500
00501
0 05 02
0 0 50 3
00 504
LNNY2Y.F0R
FORTRAN V . 5 ( 5 1 5 )
/K I
5-MAR-78
1 1 :4 8
PAGE 1 - 8
PRINT 8,IPAGE
PRINT 2,NROWINr NROW,NCOLIN,NCOL,IHEXPN,JVEXPN,ISET,ISOURC
C
C DISPLAY THE CURRENT SOURCE INFORMATION.
C
92
IPAGE=IPAGE+1
PRINT 12,IPAGE
12
FORMAT (1H1, 1 4 , / / / 5 4X, • INPUT SOURCE VOLTAGES• , / / , 2 3 X , ' L O O P S 1 7 X , 1RO.
■
• 2N' ,1 5X ,'CO LU M N *,11X ,'O RIE N T A T IO N ",12X ,«SO U RCE *,/,1 9X ,'CO E FF ICIEN T*
3 , 1 3 X , 'I N D E X 'f 1 5 X ,* IN D E X ',1 O X ,' OF THE SOURCE",10X»'POTENTIAL*, / / )
C
C
DO 100 J=1,ISOURC
READ(INPUT,2 3 ) POT#IXCORD,IYCORD,LOCATP
23
FORMAT ( F 1 0 . 5 , 3 1 1 0 )
IYC0RD=IYC0RD+1
C
C DETERMINE THE INDEX OF THE SOURCE.
C
C IXCORD I S THE NUMBER OF THE COLUMN IN WHICH THE CURRENT SOURCE OCCURS
C I F THE CURRENT SOURCE IS VERTICAL, ORTO THE RIGHT OF WHICH THE
C CURRENT SOURCEOCCURS I F THESOURCE I S HORIZONTAL.
C
C IYCORD I S THE NUMBER OF THE ROW IN WHICH THE CURRENT SOURCE OCCURS I F
C THE CURRENT SOURCE IS HORIZONTAL, ORBELOW WHICH THE CURRENT SOURCE
C OCCURSI F THE CURRENT SOURCE I S VERTICAL.
C
C LOCATP INDICATES THE ORIENTATION OF THE CURRENT SOURCE. LOCATP=1 FOR A
C HORIZONTAL CURRENT SOURCE.
LOCATP=2 FOR A VERTICAL CURRENT SOURCE.
C
1= (IXCORD + IHEXPN-T) *LROW + IYCORD
B ( I , 1) =POT
I F (LOCATP. EQ. 1) B (1 -1 , 1) =B ( 1 - 1 , 1 ) - POT
I F (LOCATP. EQ. 2) B (I-LROW, 1) =B (I-LROW, 1) -POT
PRINT 1 3 , I,IYCORD, IXCORD,LOCATP,B ( I , 1)
13
FORMAT( 1 2 6 , 3 1 2 0 , F2 2. 3)
100
CONTINUE
C
C CALL CHBDSL.
C
C
X (N,L) THE IMAGINARY LOOP CURRENT SOLUTION VECTOR..
CALL CHBDSL(N,M1,M,R,L,B,X)
C
C USING THE LOOP CURRENTS CONTAINED IN THE SOLUTION VECTOR X, THE
C POTENTIAL IS COMPUTED ALONG THE ROW OF NODES BELOW THE LOOPS SIMULATC ING THE AIR-EARTH INTERFACE.
THIS COMPUTATION I S CARRIED OUT IN
C THREE STEPS.
C
C
C STEP ONE
C
C BEGINNING WITH A NODE AT WHICH THE - POTENTIAL I S KNOWN, THE POTENTIAL "
C AT CONSECUTIVE NODES TOWARDS THE SURFACE I S CALCULATED BY DETERMINING
C THE POTENTIAL DROP ACROSS THE RESISTOR USING THE LOOP CURRENTS FROM
C THE TWO ADJACENT LOOPS.
SINCE THE CURRENT FLOW I S ASSUMED TO BE
C COUNTERCLOCKWISE IN THE LOOPS THE POTENTIAL "INCREASES" TOWARDS THE
MAIN.
LNNY2Y.F0R
FORTRAN V .5 ( 5 1 5 )
/K I
5- MAR-78
1 1 :4 8
PAGE 1 - 9
00505
00506
00507
00508
00509
00510
00511
00512
00513
00514
0051 5
00516
00517
00518
00519
00520
00521
00522
00523
00524
0 0525
00526
00527
00.52 8
00529
00530
00531
00532
00533
00534
0 0535
00536
00537
00538
00 539
00540
00541
00542
00543
00544
0054 5
00546
00547
00548
00549
00550
00551
00552
00553
.00554
005 55
00556
005 57
00558
00559
00560
C SURFACE.
THUS THE POTENTIAL DROPS ARE ADDED TO THE POTENTIAL AT EACH
C SUCCESSIVE NODE.
THE SIGN OF THE LOOP CURRENT CORRECTS FOR ANY INCONC SISTANCIES.
C
C
. Y
THE NODAL POTENTIAL.
THIS VARIABLE IS USED TO RETAIN THE
C
' POTENTIAL. AT THE LAST NODE THROUGHOUT CALCULATIONS.
Y-PO t '
•'
r
I
-: y c
c CALCULATE THE STARTING LOOP INDEX."
1 = (IXCORD+IHEXPN-1)*LROW+IYCORD
c
c CALCULATE THE COLUMN INDEX OF THE FIRST BRANCH RESISTOR ABOVE THE NODE
c AT WHICH THE POTENTIAL I S KNOWN.
J = I F I X ( (FLOAT (I) ) /FLOAT (LROW) ) +1
c
c CALCULATE THE ROW INDEX OF THE SAME BRANCH RESISTOR.
LL=2*IYCORD-2
c
c BEGIN COMPUTING NODAL POTENTIALS UNTIL THE POTENTIAL AT THE NODE IN
c THE THIRD ROW IN THE SAME COLUMN I S KNOWN.
c
DO 110 1 1 = 1 , LROW
c
c CHECK TO DETERMINE I F THE SOURCE IS ON THE SURFACE.
I F (LL. EQ. 2) GO TO 120
c SET THE LOOP INDEX.
1=1-1
c
I F THIS IS
c CHECK TO MAKE CERTAIN THE NODE I S BELOW THE SECOND ROW.
c NOT THE CASE, THE RUNSTREAM IS DISCONTINUED AND AN ERROR MESSAGE I S
c DISPLAYED.
I F ( L L . L E . 2) GO TO 130
c
c CALCULATE THE NODAL POTENTIAL.
c
Y=Y+X ( 1 , 1 ) *BRRES (LL, J) -X (I-LROW, 1) *BRRES (LL, J )
c
G RESET THE BRANCH RESISTOR LOOP INDEX.
LL=LL-2
c
c CHECK TO. SEE I F THE NODAL POTENTIAL AT THE NODE IN THE THIRD COLUMN
c HAS BEEN. DETERMINED.
I F (LL . EQ. 2) GO TO 120
c
110
CONTINUE
GO TO 130
C
C RETAIN THE LOOP INDEX.
120
I 1=1
C
G RETAIN .THE COLUMN INDEX.
JJ=J
■
C
C RETAIN THE POTENTIAL.
YY=Y
C STEP TWO
MAIN.
LNNY2Y.FOR
FORTRAN V . 5 ( 5 1 5 )
/K I
5-MAR -78
11 :4 8
PAGE 1 - 1 0
00561
C
00 562
F (J J , 1) = Y
00563
B ( J J , 1) = FLO AT ( J J )
/
0056 4
C
00565
C .CALCULATE THE POTENTIALS AT. THE NODES ALONG THE TOP OF THE LOOPS BELOW
00566
c THE.'ROW OF LOOPS SIMULATING- THE AIR?-EARTH INTERFACE.
IN STEP TWO
00567 • c THE POTENTIALS ARE CALCULATED AT NODES TO THERTGHT.
THE LOOP
c CURRENTS FOR THE TOP ROW ARE IGNORED AS. THEY ARE MANY ORDERS O F.'005 68
00569
c MAGNITUDE LESS THAN ALL'OTHER LOOP CURRENTS.
00570
c
00571
" F ( L L ,L ) THE NODAL POTENTIALS ALONG THE ROW BELOW THE AIR-EARTH
c
c
INTERFACE.
0057 2
00573
150
F (JJ + 1 ,1)=Y+X ( I I , 1) *BRRES ( 3 , J J )
'
00574
C
00575
C
0 0576
C
B (L L , L) THE HORIZONTAL SPREAD COORDINATE.
THIS VALUE I S OVER­
0 0577
C
WRITTEN ON THE SOURCE ARRAY WHICH I S NO LONGER REQUIRED.
005 78
B { J J + 1 , 1) =FLOAT ( J J + 1)
00579
C
00580
C DETERMINE I F THE POTENTIAL AT THE NODE IN THE FINAL COLUMN TO THE
00581
C RIGHT HAS BEEN DETERMINED.
I F ( J J . G E .L C O L ) GO TO 140
005 82
00583
C
0 058 4
C INCREMENT THE COLUMN INDEX.
005 85
J J —J j 1
00 586
C
005 87
C RETAIN THE NODAL POTENTIAL.
0 0 58 8
Y = F(JJ,1)
00589
G
00590
C INCREMENT THE ROW INDEX.
!I=II+LROW
00591
C
0 059 2
GO TO 150
00593
00 594
C STEP THREE
00595
c
c SET THE LOOP INDEX.
00 596
140
II=I-LROW
00597
00 598
c
00599
c SET THE COLUMN INDEX.
JJ= J-1
00600
00601
c
c SET THE INITIAL NODAL POTENTIAL.
0 06 0 2
006 03
Y=YY
006 04
c
00605
c CONTINUE NODAL POTENTIAL CALCULATIONS TO THE LEFT.
00606
G
006 07
C
00 608
C DETERMINE THE NODAL POTENTIAL.
00609
17 0
F ( J J , 1 ) = Y - X ( I I ,1 ) *BRRES(3, J J )
00610
C DETERMINE THE SPREAD COORDINATE; ...
00611
B (J J , 1) = FLO AT ( J J ) 00 6 1 2
C
00613
C CHECK TO SEE I F THE POTENTIAL AT THE FIRST NODE HAS BEEN CALCULATED.
00614
I F ( J J . L E . 1) GO TO 160
00615
C
00616
C SET THE NODAL POTENTIAL.
FORTRAN V . 5 { 5 1 5 )
/K I_
5-MAR-78
11:48
PAGE 1 - 1 1
MAIN.
LNNY2Y.F0R
00617
00618
0 0619
00620
00621
00622
00623
00624
00 625
00626
00627
00628
00629
00630
00631
00632
006 33
00634
006 35
00636
00 637
00638
00639
00640
0 0641
00642
00 643
00644
0064 5
006 46
00647
00 648
00649
00650
00651
0 0 65 2
00653
0 06 54
00655
00656
00657
006 58
00 659
006 60
00661
006 62
00663
00664
0066 5
00666
00667
00668
00 669
00670
00671
00672
Y = F (JJ,1)
C
C SET THE COLUMN INDEX.
JJ=JJ-1
C
C SET THE LOOP INDEX.
^
t
II=II-L RO W
C
GO TO 170
160
SCOL-IHEXPN+1
FCOL—NN-IHEXPN
C
C READ IN THE OBSERVED SP DATA.
AN OPTION TO BE ADDED I S DETERMINATION
C OF A LEAST SQUARES FIT TO THE CURVE DESCRIBING THE OBSERVED POTENTIAL.
C THE POTENTIALS AT POSITIONS CORRESPONDING TO THOSE NODES AT WHICH THE
C POTENTIALS HAVE BEEN CALCULATED USING THIS MODEL WILL BE COMPUTED FOR
C THE PLOTTING ROUTINE.
C
c
C SET SCALING FOR DC LEVEL DETERMINATION.
A7=0
DO 194 I F = 1 / SCOL
AV-AV+F ( I F / 1)
194
CONTINUE
DO 195 IF=FCOL,NN
AV=AV+F ( I F , 1 )
195
CONTINUE
FMIN= AV/FLOAT (2*IHEXPN+2)
I F (K.GT. 1) GO TO 192
READ (INPUT, 14) ( F ( I , 2 ) ,I= SC O L , FCOL)
FORMAT (8F10. 5)
14
DO 200 1 = 1 , NN
192
I F ( I . L I . SCOL) F ( 1 , 2 ) =F (SCOL, 2)
I F ( I . GT. FCOL) F ( 1 , 2 ) =F (FCOL,2) -FM IN *1 000 .
C
C SCALE FMIN FOR DISPLAY IN MILLIVOLTS.
F ( 1 , 2 ) =F ( 1 , 2 ) + FMIN* 1 0 0 0 .
C
C SCALE THE MODELED POTENTIAL FOR DISPLAY IN MILLIVOLTS.
F ( I , 1) =F ( I , 1) * 1 0 0 0 .
C
20 0
CONTINUE
C DISPLAY THE SP DATA. FOR EACH DATA SET.
IPAGE=TPAGE+1
PRINT 1 5 ,IP AG E,K
FORMAT(1H1,1 4 , //, 5 8 X , • P O T E N T I A L DATA* , / / , 6 1X , *SET« , 1 4 , / / , 3 3 X , 1NODE
15
2* ,24X ,* O BSE RV E D *,21X ,»CALCULATED' , / , 60X,'POTENTIAL *, 2 1 X , *POTENTIAL
3 ',//)
PRINT 16^ ((B ( 1 , 1 ) , F ( 1 , 2 ) , F ( 1 , 1 ) ) , 1 = 1 , NN)
FORMAT (F 3 ; 7 . .2 , ,F 2 9 . 0 ,F 3 0 .0 )
16
' CALL PLQTXY (N , R , MM, NN, MNMN , XMINZ , XMAXZ, YMINZ ,.YMAXZ, B, F., I l l v I T I T L , L ;
2TITL,INAME) .
C RESET THE POTENTIAL ARRAY TO ZERO I F MORE THAN ONE SET OF SOURCE DATA
C ARE TO BE EXAMINED.
DO 191 J=1,NN
F (J,1 )= 0
MAIN.
LNNY2Y.F0R
FORTRAN V. 5 ( 5 1 5 )
/K I
5- MAB-78
1 1;48
PAGE 1 - 1 2
00673
F ( J , 2 ) =F ( J , 2 ) - F M I N * 1 0 0 0 .
00674
191
CONTINUE
00675
C
0 0676 . C ZERO THE X AND B ARRAYS TO PREVENT OVERFLOW.
00677
DO 193. J= R,N
00678
B (J,R )= 0
00679 .
X (J, R ) - 0
00680
193
CONTINUE
00681
C
C
00.6 82
006 83
C RESET FMIN.
0068 4
FMIN=0
00685
190
CONTINUE
00 686
GO TO 180
00687
70
PRINT 17,IPAGE
0 06 88
17
FORMAT(1H1 , 1 4 , / / , 1 THE ROW INDEX I S GREATER THAN THE COLUMN INDEX.*
00689
2)
00690
GO TO 180
00691
71
PRINT 1 8 , IPAGE
0069 2
18
FORMAT( 1H1 , 1 4 , / / , • THE ERROR FLAG WAS SET DURING THE CHOLESKY DECOM
006 93
2POSITION INDICATING THE INPUT ARRAY I S NOT ALGORITHMICALLY */* POSIT
00694
3IVE DEFINITE.
CHECK TO MAKE CERTAIN THE DIMENSIONS OF A AND L ARE
006 95
4CORRECT *)
00696
GO TO 180
00697
130
PRINT 1 9 , IPAGE
00698
FORMAT(1H1,1 4 , / / , 'DURING CALCULATION OF NODAL POTENTIALS AN ERROR
19
00699
2 WAS MADE DURING INDEXING')
007 00
180
CONTINUE
00701
END
SUBPROGRAMS CALLED
IFIX .
CHBDET
FLOAT.
CHBDSL
PLOTXY
SCALARS AND ARRAYS [
* in
*LL
*YMAXZ
. S0035
. S 0033
. S0030
*YY
*NCOL
*XMAXZ
*IVEXPN
*IPAGE
. SOOOO
X
.5 0 0 1 3
*ISOURC
L
. S 0.02-6
1
.300,20
656
*LCOL
744
FCOL
. S0034
751
756
.5 0 0 3 2
763
★OUTPUT
1567
SROW
157 4
*D2
1601
★Ml
1606
RESTS•
• • SO0 0 5
2153
216 0
. A
1076.4 ‘ •SCOL
.5 0 0 1 6
10771
11575
R
11721
I T IT L
12.045
*1
.SO 025
20732
NO EXPLICIT DEFINITION 2
657
745
752
757
764
1570
1575
1602
1607
2154
2161
10765
11571
11576
11722
20 6 4 5
20733
BRRES
★IHEXPN
.50037
★N
★XMINZ
★JVEXPN
★IYCORD
.5 0 0 4 0
★M
.5 0 0 0 7
. 3.0004
• S0002
★LROW
.50015
LTITL
.50 0 1 0
★MNMN
.50024
3
660
746
753
760
765
1571
1576
1603
2150
215 5
10761
10766
1 1 57 2
11 577
12042
2064 6
20734
NOT REFERENCED ]
★AV
INAME
.50036
★NCOLIN
★K
★ISET
★FMIN
★Y
★IXCORD.
★D1
★ II
★POT
.50017
FROH
.50012
★NROWIN
F
★LOCATP
654
661
747
754
761
766
1572
1577
1604
2151
2156
10762
10767
11573
11717
12043
20647
20735
★NROW
*JJ
★IF
★INPUT
.50031
B
★TERROR
★RESAE
★MM
.50006
.5 0 0 0 3
. SQ001
★IRON
.50014
.50011
★YMINZ
.5 0 0 2 7
. 5 00 2 3
655
743
750
755
762
767
1573
1600
1605
2152
2157
10763
10770
11574
11720
12044
20731
20736
MAIN.
LNNY2Y. FOR
. 5 0022 20737
*NN
FOETEAN V . 5 ( 5 1 5 )
20 7 4 0
/K I
5-MAE-7 8
11 :4 8
.5 0 0 2 1 20741
TEMPORARIES
MAIN.
' [ NO ERRORS DETECTED ]
■
‘
^
■
PAGE 1 - 1 3
CHBDET
LNNY2Y. FOE
FOETEAN V. 5 ( 5 1 5 )
/K I
5-M AE-7 8
1 1:48
PAGE 1
00001
SUBROUTINE CHBDET(N,M1 , M ,A ,L ,D 1 , D2,IERROR)
0 000 2
DOUBLE PRECISION A (N,M1) ,L(N,M1)
00003
INTEGER P,Q„R
0 0 00 4
C THIS SUBROUTINE I S A FORTRAN TRANSLATION OF A PROGRAH ORIGINALLY
00005
C. WRITTEN IN ALGOL 6 0 ,
THE ORIGINAL ALGORITHM IS INCLUDED IN AN ARTICLE:
00 006 ' C
00007
C
MARTIN,R.S. AND'WILKINSON, J . H . , 1 9 6 5 , SYMMETRIC DECOMPOSITION OF
00008
C
POSITIVE DEFINITE BAND MATRICES: NUMERISCHE MATHEMATIK, V. 7 , P,
00009
C
355-361.
0 0010
C
00011
C
0 0 01 2
C THE TRANSLATION OF CHOBANDDET WAS WRITTEN BY SCOTT E. HULSE.
00013
C VERSION 3 MARCH, 1978
0 0 01 4
C
00015
C
* *** *
*****
*** **
0001 6
C
00017
C
COMPUTATIONAL TECHNIQUE
0001 8
C
00019
C THE LOWER HALF OF A POSITIVE DEFINITE SYMMETRIC BAND MATRICES, A, WITH
000 20
C M LINES ON EITHER SIDE OF THE DIAGONAL I S STORED AS AN NX(M+1) ARRAY
00021
C A ( I ,K ) ,1=1 (1) N, K=0 (1) 7 , A ( I , M) BEING THE DIAGONAL ELEMENTS.
THE CHO00022
C LESKY DECOMPOSITION A=LU, WHERE U I S THE TRANSPOSE OF L, I S PERFORMED
000 23
C AND L IS STORED IN L ( I , K) IN THE SAME FORM AS A.
THE RECIPROCALS OF
00024
C THE DIAGONAL ELEMENTS ARE STORED INSTEAD OF THE ELEMENTS THEMSELVES.
00 025
C A IS RETAINED SO THAT THE SOLUTION OBTAINED CAN SUBSEQUENTLY BE IM0002 6
C PROVED.
HOWEVER L AND A CAN BE IDENTIFIED IN THE CALL OF THE
0 0027
C PROCEDURE.
THE DETERMINANT,D1*2**D2, OF A I S ALSO COMPUTED.
THE
00028
C PROCEDURE WILL FAIL I F A, MODIFIED BY THE ROUNDING ERRORS, I S NOT
00 029
C POSITIVE DEFINITE.
00030
C
00031
C
VARIABLE LIST
00032
C
0 00 33
C
00034
C INPUT TO CHBDET
0 0 03 5
C
N
ORDER OF THE MATRIX A
00036
C
M
NUMBER OFNONZEROLINES ON EITHER SIDE OF THE DIAGONAL IN A
0 0037
C
A(N,M)ELEMENTS OF THE LOWERTRIANGULAR MATRIX OF THE
POSITIVE
00038
C
DEFINITE BAND MATRIX A.
THESE ELEMENTSARE STORED IN
AN
0003 9
C
NX(M+1), ARRAY SO THAT THE MAIN DIAGONAL I S THE LASTCOLUMN
00040
C
OF THE ARRAY OR A(N,M) FOR M MAXIMUM.
00041
C OUTPUT FROM CHBDET
00042
C
L(N,M)THE ELEMENTS OF THELOWER TRIANGLE OFTHE CHOLESKY
0 00 43
C
DESCRIPTION OF A.
L I S STOREDIN THE SAME
WAY AS A. L COULD
00044
C
BE OVERWRITTEN ON A.THIS WOULD NOT PERMIT THE
USE OF A TO
0 0 04 5
C
IMPROVE THE SOLUTION HOWEVER.
00046
C
D1
THE ELEMENTS OF DETERMINANT A DESCRIBED ABOVE
0004 7
C
D2
0004 8
C
0004 9
C
SUBPROGRAM CHOBANDDET
00050 -•
D1 = T
00051
.....
D2=0
00052
' IERROR=0
0 005 3
M=M+1
00054
1
FORMAT ( 4 1 1 0 , 2 F 1 0 . 2)
00 055
DO 10 1 = 1 , N
00056
I F ( I . GT. M) GO TO 150
114
CHBDET
00057
0005 8
00059
00060
00061
0Q0 62
00063
00064
00065
00066
00067
00068
00069
00070
00071
00072
00073
00074
0007 5
00076
00077
00078
00079
00080
00081
00 0 8 2
00083
00084
00085
0008 6
00087
00088
00089
00090
0 0091
0009 2
00093
00 094
00095
0009 6
LNNY2Y.F0JR
150
160
40
50
70
80
90
100
110
120
60
30
10
130
140
FORTRAN V. 5 ( 5 1 5 )
/K I
5-MAR-78
1 1:48
PAGE 1 -1
P=M-I+1
GO TO 160
P=1
R=I-M+P
DO 30 J=P,M
Q=M-J+P
Y =A (I,J)
DO 40 K = P,J
Y-Y-L ( I , K ) * L ( R , Q)
Q=Q+1
CONTINUE
I F (J.EQ.M)GO TO 50
GO TO 60
D1=D1*Y
I F (Y* EQ.0) GO TO 70
GO TO 80
D2=0
GO TO 130
I F (ABS (D1) . GT. 1 . 0 R . ABS (D1) . E Q . 1 )
GO TO 100
D 1= D 1 *0.062 5
D2=D2+4
GO TO 80
I F (ABS (D1) . L T . 0 .0 6 2 5 ) GO TO 110
GO TO 120
D1=D1*16
D2=D2-4
GO TO 100
I F (Y.LT.O) GO TO 130
L ( 1 / J ) = 1/SQRT ( Y)
GO TO 30
L (I,J)= Y * L (R ,H )
R—R+ 1
CONTINUE
CONTINUE
GO TO 140
IERROR=1
CONTINUE
H= M-1
END
SUBPROGRAMS CALLED
SQRT.
ABS.
SCALARS AND ARRAYS [
1
Q
6
*Y ■
*D1
13
20
R
.1 0 0 0 1 25
*N
P
A
.10004
*1
NO EXPLICIT DEFINITION - '*%" NOT REFERENCED ]
2
7
14
21
26
*K
3- .
to..
. • ; . s o 002 15
- 1 0 0 0 3 22
.1 0 0 0 0 27
.
*IERROR 4
11
-SO001 16
.1 0 0 0 2 23
*D2
5
.12
.SOOOO 17
L
24
CHBDET
LNNY2T,. FOB
FORTRAN V .5 (5 1 5 )
TEMPORARIES
„ A0016 33
CHBDET
[ NO ERRORS DETECTED ]
/K I
5 -H A B -7 8
1 1 :4 8
PAGE
CHBDSL
LNNY2Y.FOE
FORTRAN V . 5 ( 5 1 5 )
/K I
5-MAR-78
1 1 :4 8
PAGE 1
00001
SUBROUTINE CHBDSL ( N , f l l , H,R*Lr B,X)
INTEGER P , Q , R , S
00002
DIMENSION B (N,R) ,X (N,-R)
00003
0 00 0 4
DOUBLE PRECISION L(N,M1)
00005 - C THIS SUBROUTINE I S A FORTRAN TRANSLATION OF A. PROGRAM ORIGINALLY
THE ORIGINAL ALGORITHM IS INCLUDED IN AN ARTICLE:
0 0 0 0 6 : . c WRITTEN IN ALGOL 6 0 .
00007
C
00008
C
MARTIN,R.S. AND WILKINSON, J . H . , 1 9 6 5 , SYMMETRIC DECOMPOSITION OF
POSITIVE DEFINITE BAND MATRICES: NUMERISCHE MATHEMATIK, V. 7 , P.
C
00009
.
3
55-361.
C
00010
00011
C
c
0001 2
c THE TRANSLATION OF CHOBANDSOL WAS WRITTEN BY SCOTT E. HULSE.
00013
0001 4
c VERSION 3 MARCH, 1978
c
00015
*****
**** *
* ** **
c
000 16
c
00017
000 18
c
COMPUTATIONAL TECHNIQUE
c
00019
c
00020
00021
c THE EQUATION AX=B I S SOLVED WHERE A I S A POSITIVE DEFINITE BAND
■c MATRIX WITH M LINES ON EITHER SIDE OF THE DIAGONAL AND B IS AN NXR
00 022
c MATRIX WITH R RIGHTHAND SIDES.
THE PROCEDURE CHOBANDSOL MUST BE
00023
0 0024
c PROCEDED BY CHOBANDDET IN WHICH L I S PRODUCED IN L ( I , K ) , FROM A.
AX=B
THE MATRIX B I S RETAINED IN
c I S SOLVED IN TWO STEPS, LY=B AND UX=Y.
00025
000 26
c ORDER TO FACILITATE THE REFINEMENT OF X, BUT X I S OVERWRITTEN ON Y.
c HOWEVER, X AND B CAN BE IDENTIFIED IN THE CALL PRODEDURE.
00027
00 028
c
c
VARIABLE LIST
00029
00030
c
00031
c INPUT TO CHBDSL
c
N
ORDER OF THE MATRIX A
00 032
M
THE NUMBER OF NONZERO CODIAGONALS ON EITHER SIDE OF THE MAIN
00033
c
DIAGONAL
0 0034
c
R
THE NUMBER OF RIGHTHAND." SIDES FOR WHICH AX=B I S TO BE SOLVED
c
00035
L(N,M)THE ELEMENTS OF THE LOWER-TRIANGULAR MATRIX OF THE CHOLESKY
000 36
c
DECOMPOSITION OF A POSITIVE DEFINITE MATRIX A PRODUCED BY
e
00037
THE PROCEDURE CHOBANDDET.
0 0038
c
B (N, R)THE MATRIX FORMED BY THE MATRIX OF RIGHT HAND SIDES.
c
00039
e OUTPUT FROM CHBDSL
00040
c
X (N, R) THE MATRIX FORMED BY THE SOLUTION VECTOR (S)
00041
c
000 42
SUBPROGRAM .CHOLBANDSOL
c
00043
00044
S=M
00045
M=M+1
00046
DO 10 J = 1 ,R
c BEGIN SOLUTION OF LY=B.
00047
00 048
DO 20 1 = 1 , N
I F ( I .G T . M) GO TO 30
00049
00050
P=M-I+1
go to 40
00051
30
P= 1
.00052
40
Q=I
00 053
00054
Y = B (I,J)
I F (P .G T .S ) GO TO 51
0 0055
00056
KK=S
CHBDSL
LNNY2Y.F0B
FORTRAN V - 5 ( 5 1 5 )
0 0057
00058
0 0059
00060
00061
00062
00 063
00064
0 0065
00066
00067
00068
0 0 0 69
00070
00071
00072
0007 3
00074
00 075
00076
00077
00078
00079
00080
00081
00082
0008 3
00084
0008 5
00086
DO 50 K=P,S
Q=Q-1
Y=Y-L (I,K K) *X(Q/.J)
KK=KK-1.
50
CONTINUE
51
X ( I , J ) = Y * L ( I ,M )
20
CONTINUE
c ;BEGIN SOLUTION OF UX=Y
II= N
DO 60 1 = 1 , N
NN=N—I I
I F (NN.GT. M) GO TO 7
P=M-N+II
GO TO 80
70
P= 1
80
Y = X ( I I , J)
Q -ii
I F (P. GT. S) GO TO 9
KK=S
DO 90 K=P,S
Q=Q+1
Y=Y-L (Q,KK) *X ( Q ,J )
KK=KK- 1
90
CONTINUE
91
X (II,J)= Y * L (II,M )
1 1 = 1 1 -1
CONTINUE
60
10
CONTINUE
M=M—1
END
/K I
5-M A E -7 8
11:48
SDBPROGRAMS CALLED
SCALARS AND ARRAYS [
1
Q
S
6
*KK
13
.S 0 0 0 1 20
25
R
L
32
*N
P
.50004
-SOOOO
.10005
.10001
NO EXPLICIT DEFINITION 2
7
14
21
26
33
TEMPORARIES
-A0016 37
CHBDSL
[ NO ERRORS DETECTED. ]
*K
*M1
.iSOOOS
X
.1 0 0 0 4
*1
3
10
15
22
27
34
NOT REFERENCED ]
E
*M
*11
.10007
.1 0 0 0 3
.10000
4
11
16
23
30
35
*Y
*J
.50002
.1 0 0 0 6
.1 0 0 0 2
*NN
PAGE 1 -
118
PLOTXY
LNNY2Y.FOR
FORTRAN V .5 ( 5 1 5 )
/K I
5-MAR-78
11:48
PAGE 1
SUBROUTINE PLOTXY(N,R, M , NN,MNMN,XMINZ, XMAXZ,YMINZ, Y M A X Z ,B ,F ,I II , I
00001
2T IT L , LTITL,INANE)
00002
C THIS PLOTTING ROUTINE I S AN ADAPTATION WITH MINOR CHANGES AND CORREC­
00003
00 004
C TIONS OF THE SUBROUTINE:
00005: C
0000 6,. ' c
SHELLY,E. LAURENCE AND WAIT., JOHN V , , 1 9 7 0 , SELF-SCALING LINE
00007
G
' PRINTER PLOTTING ROUTINE: UNIVERSITY OF ARIZONA, DEPARTMENT OF
ELECTRICAL ENGINEERING, ANALOG/HYBRID COMPUTER LABORATORY.
c
00008
00009
c
00010
c CORRECTIONS IN PLOTXY WERE MADE BY SCOTT E. HULSE.
c VERSION 3 MARCH, 1978
00011
c
000 12
c
00013
PLOT12.80
THIS X - Y PLOTTING ROUTINE SIMULTANEOUSLY PLOTS UP TO 3
000 14
c
PLOT 1290
FUNCTIONS OF AN INDEPENDENT VARIABLE
00015
c
PLOT1300
IT I S DIMENSIONED FOR UP TO 201 POINTS PER FUNCTION
00016
c
PLOT 1310
c
AUTO-SCALING I S PROVIDED, I F DESIRED
00017
PLOT 1320
X
ARRAY NAME OF INDEPENDENT VARIABLE
00018
G
PLOT1330
F
ARRAY NAME OF DEPENDENT VARIABLE (S) , F ( J , I )
c
00 019
PLOT 1340
J I S INDEX ON FUNCTION VALUES
00020
c
PLOT1350
I IS FUNCTION NUMBER
c
00021
PLOT136 0
c
MM
NUMBER OF DEPENDENT FUNCTIONS
00022
PLOT 1370
NN
NUMBER
OF POINTS PER FUNCTION
c
00023
c
MNMN
POINT SPACING
PLOT1380
00024
PLOT1390
'
0 AUTOMATICALLY SPACES FOR GOOD APPEARANCE
00 025
c
PLOT1400
1
PLOTS EVERY POINT
c
00026
PLOT1410
2
- PLOTS EVERY 2ND POINT,
ETC.
00027
c
XMINZ,XMAXZ LIMITS ON INDEP. VARIABLE, MAKE EQUAL FOR AUTO-SCALINPLOT1420
00028
c
YMINZ,YMAXZ LIMITS ON DEPENDENT VARIABLE(S) , EQUAL FOR AUTO-SCALIPLOT1430
c
00029
PLOT147 0
REAL LOWER
00030
- INTEGER R,.A
00031
DIMENSION I T I T L (80) ,LTITL (80) ,INAME(50)
00032
DIMENSION F (NN, MM) , LINE (101) ,X G (11 ) , 1 1 (9) , B (N,R)
00033
PLOT1450
MORE POINTS OR FUNCTIONS MAY BE ACCOMODATED BY
00034
c
PLOT 1460
c
RE-DIMENSIONING X AND F
0 003 5
PLOT 1490
DATA ( I I ( I ) , 1 = 1 , 9 ) / 1H1, 1H2, 1H3, 1 H4, 1H5., 1 H 6 ,1 H 7 ,1 H 8 ,1 H 9 /
00036
DATA MARK,MARKS/3H----- , 1H*/
00037
PLOT 1520
DATA I C B , I C 0 / 1 H , 1 H 0 /
000 38
PLOT1530
M=MM
0 0 039
PLOT1540
N=NN
000 40
PLOT1550
MN=MNMN
00041
PLOT1560
XMIN=.XMIN
Z
000 42
PLOT 1570
00043
XMAX=XMAXZ
PLOT 158.0
0004 4
FMIN=YMINZ
PLOT 1590
000 45
FMAX=YMAXZ
PLOT1600
00046
I F (MN) 3 0 0 0 , 3 0 0 0 , 5 0
PLOT1610
3000 MN=N/60
00 047
PLOT 1620
IF(MN.EQ.O)
MN= 1
00048
PLOT1630
I F (XMIN-XMAX) 5 1 , 5 2 , 5 1
50
00049
00050
52:
XMAX=B ( 1 , 1)
00051
XMIN= B (1 > 1)
PLOT.1 66 0
000 52
DO 3 K=1, N
I F (XMAX. LT. 3 (K, 1) ) XMAX=B (K, 1)
00053
1
I F (XMIN.GT.B (K, 1) ) XMIN=B(K, 1)
00054
2
PLOT 1690
000 55
3
CONTINUE
PLOT 1700
00056
XMIN1=XMIN
119
PLOTXY
00057
0 0058
00059
00060
0006T
00062
00063
00064
00065
00066
00067
00068
00069
00070
00071
00072
00073
0 0074
00075
0 0 07 6
00077
00078
0007 9
00080
00081
00 082
00083
00084
00085
00086
00087
00088
00089
00090
00091
00 092
00093
00094
00095
00096
0009 7
00098
00099
00100
00101
00 102
00103
00 104
00105
001 06
00 107 .
00108
00109
00110
00111
00112
LNNY2 Y. FOB
1000
1001
51
53
4
5
6
2000
2001
29
28
27
26
200
201
207
20,8
209
202
7
" FORTRAN V . 5 ( 5 1 5 )
/K I
5-MAR-78
11: 48
PAGE 1- 1
X11AX= RNDUP (XMAX, 1,XMA)
P10T 1710
PLOT1720
XDIF=XMAX-XMIN
. XMIN=XMAX-RNDUP(XDIF,1,XMI)
PLOT 1730
GO TO 1000
PLOT1740
I F ( (XHA/XMI) .GE. ( 1 0 0 . 0 ) )
I F (.(XMI/XMA) .G E. (.100.0) ) ...
GO TO 1001
PLOT 1750
PLOT1760
GO. TO .5:1 .
.
PLOT1770
X"MIN= 0 . 0 0 0 ' ■
PLOT 1780
XDIF= XMAX :
GO TO 51
PLOT 1790.
XMAX=0.000
PLOT1800
XDIF= ABS(XMIN1)
PLOT1820
XMIN=~RNDUP(XDIF, 1 ,XMI)
PLOT1830
IF(FMIN-FMAX)2 9 , 5 3 , 2 9
FMAX=F(1,1)
PLOT1840
PLOT1850
FM IN=F(1, 1)
PLOT1860
DO 6 K=1 , M
PLOT1870
DO 6 L=1,N
I F (FMAX.LT. F (L , K) ) " FMAX=F(L,K)
PLOT 1880
PLOT1890
I F (FMIN.GT.F (L,K) )
FMIN=F (L, K)
PLOT1900
CONTINUE
PLOT 1910
FMIN1=FMIN
FMAX= RNDUP (FMAX, 2 , FMA)
PLOT1930
FDIF=FMAX-FMIN
FMIN=FMAX-RNDUP (FDIF, 2 , FMI)
GO TO 2000
PLOT1950
I F ( (FMA/FMI) .G E . ( 1 0 0 .0 ) )
PLOT 1960
I F ( (FMI/FMA) . GE. (1 0 0 . 0) )
GO TO 2001
GO TO 29
PLOT197 0
PLOT1980
FM IN=0.000
PLOT 1990
FDIF=FMAX
PLOT2000
GO TO 29
FMAX=0 . 0 0 0
PLOT2010
FDIF= ABS (FMIN1)
FMIN=-RNDUP(FDIF, 2 , FMI)
I F ( (XMIN. GE..XMAX) . OR. (FMIN.. GE. FMAX)) GO TO 28
PLOT2040
PLOT2050
GO TO 26
PRINT 2 7 , XMIN, XMAX, FMIN, FMAX
PLOT2060
PLOT207 0
FORMAT (1 H I , 5 X , 4 1 HPLOT X-Y ROUTINE —
BAD DATA ERROR EXIT / / / /
$ / / / / / / / / 5 0 X,5 HXMIN = ,E20.8/50X,5HXMAX=
,E 2 0 .8 /5 0 X ,5 H F M IN =
, 2 2 0 . 8PLOT2080
PLOT2090
$/50X,5HFMAX=
,E 2 0 .8 )
PLOT2100
RETURN
XDIF-ABS (XMAX-XMIN)
PLOT2110
FDIF=ABS (FMAX-FMIN)
PLOT2120
PL 0T 2130
XSCALE=XDIF>0.01
PL 0 T 2 140
FSCALE=FDIF*0.02
ZERO=FDIF*0.0 00001
PLOT2150
PL0T2 160
I F (XMIN*XMAX) 2 0 0 , 2 0 0 , 2 0 1
PL0T2170
J= IR D O FF( 0 . 5 0 0 0 0 2 —XMIN/XSCALE)
PLOT2.180
GO TO 207
PL 0T 2190
J=101
PLOT2200
I F (FMIN*FMAX) 2 0 8 , 2 0 8 , 2 0 9
PLOT2210
J J = I F I X (. 999+FMAX/FSCALE)
PLOT2220
GO TO 202
PLOT2230
JJ=101
PRINT 7 , (IT IT L (I) , 1 = 1 , 2 0 )
FORMAT (1H1, 25X, 2 0 A4)
PRINT 9 , III,XSCALE,FSCALE,FMAX,MARKS,MARK,MARK, MARK,MARKS, MARK,
120
PLOTXY
00113
001 14
00115
0011 6
00117
00118
001 19
00120
00121
00122
0012 3
0 0 12 4
00125
00 126
00127
00128
00129
00130
00131
00132
0013 3
0013 4
00135
00136
00137
00138
00139
001 40
00141
0014 2
00143
00144
00145
0014 6
00147
00148
00149
00150
00151
00152
0015 3
00154
00155
00 156
001 57
00158
00159
LNNY2Y.FOR
9
302
203
204
205
30
31
91
89
92
90
98
100
102
103
104
8
FORTRAN 7 . 5 ( 5 1 5 )
5 -H A R -7 8
1 1 :4 8
PAGE 1 - 2
2HARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,MARK,MARK,MARKS, MARK,
3MARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,
4 MARK,MARK,MARKS, MARK,MARK,MARK, MARKS,MARK,MARK, MARK,MARKS
FORMAT(59X,'PLOT N U M B E R ', I 2 , / 4 6 X , ' SCALE FACTORS . . X = ' , F 6 . 3 , '
,2= ' , F6 . 3 , / / , 5X , FI 6 . 0 , 4X, 10 (A1,3A3) , A1)
DO 100 LIN E S= 1,5 0
"LOtiER=FMAX-FSCALE*FLOAT (LINES) ' •
UPPER=FMAX-FSCALE*FLOAT ( L I N E S - 1.)
IF ( L IN E S - J J ) 3 0 2 , 2 0 3 , 3 0 2
A=ICB
GO TO 204
A=IC0
DO 205 1 = 1 , 1 0 0
LINE ( I ) =A
CONTINUE
LINE ( J ) = I C 0
DO 90 K=1,M
DO 90 L=1 , N,MN
IF.(F ( L ,K ) —LOWER) 9 0 , 9 2 , 9 1
I F (F (L,K) -UPPER) 9 2 , 8 9 , 9 0
I F (LINES. EQ. 1) GO TO 92
GO TO 90
I= IR D O F F ( ( B ( L , 1 ) —XMIN)/XSCALE+0 . 5 0 0 0 0 2 )
I F ( I .E Q .O )
1=1
I F ( ( I .G T . 100.) .OR. ( I . L T . 0) )
1=101
LINE (I) =11 (K)
CONTINUE
I F (ABS (LOWER) . LE. ZERO)
LOWER=0. 0
FORMAT ( 1 2 X , A 1 , 2 X , F 6 . 0 , 3 X , 1 H I , 1 0 0 A 1 , 1 H I )
PRINT 9 8 , IN AME (LINES) , LOWER, (LINE (I) , 1 = 1 , 1 0 0 )
CONTINUE
PRINT 1 0 2 , MARKS,MARK,MARK, MARK, MARKS,MARK,MARK,MARK* MARKS,MARK,
2MARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,
3MARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,MARK,MARK,MARKS,MARK,
4 MARK,MARK,MARKS,MARK,MARK,MARK,MARKS
FORMAT(25X,10 (A1,3A3) ,A1)
ZERO=XDIF*0.00 0001
DO 103 1 = 1 ,1 1
XG (I) =XMIN+FLOAT (1 -1 ) *XSCALE*10.0
I F (ABS (XG (I) ) . LE. ZERO)
XG (I) = 0 . 0
CONTINUE
PRINT 1 0 4 , (XG ( I ) , 1 = 1 , 11)
FORMAT ( 1 9 X , 1 0 ( F 9 . 2 , 1 X ) , F 9 . 2 / / )
PRINT 8 , (LTITL.(I) , 1 = 1 , 2 0 )
FORMAT ( / , 3 5 X , 2 0 A 4 )
RETURN.
END
SUBPROGRAMS CALLED
IRDOFF
IF IX .
/K I
FLOAT.
RNDUP
ABS.
PLOT2300
PLOT2310
PLOT2320
PLOT2330
PLOT2340
PL0T2350
PLOT2360
PLOT2370
PL0T2380
PLOT2390
PLOT2400
PL 0T 2410
PLOT2420
PLOT 2430
PLOT2440
PLOT2450
PLOT2460
PLOT247 0
PLOT2 480
PLOT2490
PLOT2500
PLOT2510
PLOT2520
PLOT2550
PLOT2600
PLOT2610
PLOT2620
PLOT2630
PLOT2640
PLOT2650
PLOT267 0
121
PLOTXY
LNNY2Y. FOR
FORTRAN 7 . 5 ( 5 1 5 )
/K I
5-MAR-78
11:48
PAGE 1-3
SCALARS AND ARRAYS [ «*« NO EXPLICIT DEFINITION - »%» NOT REFERENCED ]
*111
*YMAXZ
*FDIF
*XMIN
*MN
* OPPER
.S 0 0 0 6
II
*FSCALE
R
ITITL
.10002
F
*NN
1
613
20
25
32
37
44
61
232
237
256
263
270
'
*MARK
*FM A
*N •
'B '
*MARKS
*J
.50005
A
LOWER
. S0012
.5 0 0 1 0
*YMINZ
*MNMN
2
7
14
21
26
33
40
55
62
233
240
257
264
TEMPORARIES
. A0016 3 77
PLOTXY
. Q0000 400
[ NO ERRORS DETECTED ]
INAME
*FMIN1.
*XMI
' *ZERO
*XMAXZ. .
*MM
. S000 4
.5 0 0 0 2
LINE
.10005
.10003
.10001
*XMA
3
10
15
22
27
34
41
56
63
234
241
260
265
*LINES
*IC0
*K
*FM I‘
*XMAX
.5 0 0 0 7
.50 0 0 3
.5 0 0 0 1
.50 0 1 3
.50011
XG
4
11
16
’ 23
30
35 '
42
57
230
235
242
261
*1
*XMIN1 266
'
*JJ
*ICB
*XMINZ
*FMIN
5
12
17
24
31
*XSCALE 36
*FMAX
43
. 5 0 0 0 0 60
LTITL 231
. 1 0 0 0 4 236
*L
255
.10000 262
*XDIF
267
122
RNDUP
LNNY2Y.FOR
00001
00 002
C
00003
C
00004
000 05 00006:
00007
10
00008
00009
20
00010 30
0001 1 1
00012
0 0013
00014
00 015
00016
00017
00018
00019
00020
00021
00022
00023
00024
00 025
00026
00027 .
00028
00029
00030
00031
2
3
4
7
8
9
100
'
FORTRAN V . 5 ( 5 1 5 )
/K I
5-HAR-78
1 1 :4 8
PAGE 1
FUNCTION RNDUP (A,N,Z)
FUNCTION WILL ROUND-UPFLOATING-POINT
NUMBER " " A " " TO" " N " "
SIGNIFICANT DIGITS, /RNDUP/ . GE. / A / , ALSORETURNS
POWEROF TEN
B=ABS (A)
IF (B .E Q .0 .0)
GO TO 100
IF(A /B )
1 0 ,2 0 ,2 0
S IG N = - 1 . 0 '
'
.•’"W--'.
GO TO 30
SIG N=1.0
'
0= 1 . 0
I F (Q-B) 3 , 4 , 2
0= 0 * . 1 0
GO TO 1
Q=Q*10.0
I F (Q-B) 3 , 4 , 4
B= B/Q
Z = Q /1 0 .0
J =1
DO 7 1 = 1 , N
J=J*10
CONTINUE
I=B*FLOAT (J)
B=B*FLOAT (J)
I F (B-FLOAT (I) ) 9 , 9 , 8
I F (SIGN.L T. 0) GO TO 9
1=1+1
RNDUP=SrGN*FLOAT(I)* 0/FLOAT(J)
RETURN
RNDUP=0. 0
RETURN
END
SUBPROGRAMS CALLED
FLOAT.
ABS.
SCALARS AND ARRAYS [
*SIGN
*RNDUP
1
6
*Z
*J
NO EXPLICIT DEFINITION 2
7
*Q
*A
NOT REFERENCED ]
3
10
*N
4
.S 0 0 0 0 11
.. AO003 15
. A0004 16
TEMPORARIES
. A001 6 13
RNDUP
. A0002 14
[ NO ERRORS DETECTED ]
*B
*1
5
12
PLOT2690
PLOT2700
PLOT2710
PLOT2720
PLOT2730
PLOT2740
PLOT2750
PLOT2760
PLOT277 0
PLOT2780
PLOT2790
PLOT2800
PLOT2810
PLOT2820
PLOT2830
PLOT2840
PLOT2850
PLOT2860
PLOT287 0
PLOT2880
PLOT2890
PLOT2900
P L 0T 2910
PLOT2920
PLOT2940
PLOT2950
PLOT2960
PLOT297 0
123
IEDOFF
LNNY2Y. FOR
00001
00002
C
00003
00004
000 05
00006
00007
00008
00009
00010
00011
00012
00013
00014
00015
10
20
30
100
FORTRAN V. 5 ( 5 1 5 )
/K I
5-MAR-78
11: 48
PAGE 1
FUNCTION IRDOFF(A)
THIS FUNCTION RETURNS THE INTEGER NEAREST TO A
B= AB5 (A)
IF (B .E Q .0 .0 )
GO TO 100
I F (A/B)
1 0 ,2 0 ,2 0
S IG N = -1.0
GO TO 30
SIGN=1 . 0
I =B
I F ( (B-FLOAT (I) ) . GE. (. 5000) ) 1=1+ 1
IRDOFF=IFIX(SIGN) *T
RETURN
IRDOFF=0
RETURN
END
PLOT299 0
PLOT3000
PLOT3010
PLOT3020
PLOT3030
PLOT3040
PLOT3050
PLOT3060
PLOT3070
PLOT3080
PLOTS090
PLOT 3 100
PL0T3110
PLOTS 120
SUBPROGRAMS CALLED
IFIX .
FLOAT.
ABS.
SCALARS AND ARRAYS [
*SIGN
1
NO EXPLICIT DEFINITION - »%» NOT REFERENCED ]
*IRDOFF 2
*B
3
TEMFORARIES
. A0016 6
IRDOFF
-A0002 7
[ NO ERRORS DETECTED ]
.A0003
10
*A
4
*1
5
PROGRAM SPMOOL
INPUT DATA COPtNO FORM
DATA PROCESSING
PARAMETERS
ounc
NPO
CARD FORMAT (7 1 1 0 )
R E S IS T IV IT Y GRID
,-CARO^ FORMAT J 8 F 10. q ) J „ l „ .
Number o f V iln e s » NCOL*HROW
j • i i
i i
i i i i • 3 .. _ _
SOURCE DATA
PO
CARD FORMAT ( F I 0 . 5 . J I I 0
ORSERVEO DATA
CARD FORMAT (C F IO . I )
Number o f V a lu e * • NCOl
CHANGES IN DATA
P
r o c e s s in g
parameters'
ounc
CARD FORMAT ( 4 0 X . I I 0 )
SOURCE DATA
CO
CARD FORMAT ( F I 0 . 5 . J I I 0 )
ISET SETS OF DATA PROCESSING
PARAMETER CARDS AMD SETS OF
SOURCE DATA CARDS ARE REQUIRED
AFTER THE FIRST SET OF CARDS
OMIV THE DATA PROCESSING
PARAMETERS AND SOURCE INFORMA­
TION ARE REQUIRED.
iU i
Figure
C -l.
Coding
form f o r
p r o g r a m SPMODL
.c -
APPENDIX D
COMPREHENSIVE LIST OF LITERATURE
PERTAINING TO SP MEASUREMENTS
Aba .ke lia, M. S. , Bukhnik as hvi 1 1, A. V. , Taragua., G. G. , K h v i t i a , G. P.
and D z h a s h i, G. G. , 1963, On t h e pro blem s o f u s i n g e l e c t r i c a l
s u r v e y i n g on t h e C h i a t u r a manganeze d e p o s i t ( i n G e o r g ic w i t h a
R u s s ia n a b s t r a c t ) : Akad. Nauk Gruz. SSR, I n s t . G e o f i z . , T r . ,
v. 21, p. 9 9 -1 2 0 .
Abramovich, L. I . , 1965, Use o f g e o p h y s i c a l methods in p r o s p e c t i n g and
e x p l o r i n g o r e d e p o s i t s in N o r t h e r n Kazak hs ta n ( i n R u s s i a n ) :
in G e o f i z i c h e s k i y a i s s l e d o v a n i y a v K a z a k h s t a n , Alma-Ata,
I z d a t e l ' s t v o K a z a k h s t a n , p. 158-168.
Ahmad, Mo id Uddin, 1960, A l a b o r a t o r y s t u d y o f s t r e a m i n g p o t e n t i a l :
MS t h e s i s , New Mexico I n s t i t u t e o f Mining and T e c h n o l o g y ,
Socorro.
Ahmad, Mo id Uddin, 1964, A l a b o r a t o r y s t u d y o f s t r e a m i n g p o t e n t i a l :
Geophys. P r o s p e c t . (The H agu e), v, 12, no. 1, p. 4 9- 6 4 .
A l b u l , S. P . , 1 9 6 9 , D e t e r m i n a t i o n o f metal c o n c e n t r a t i o n c h an ge s in
underground s tre a m s:
I n t . G e o l . R e v . , v. 11, no. 1, p. 1-7.
A l e s h i n , A. S . , B a u l i n , Yu. I . , B o g o s lo v s k y , V. A. and O g i l ' v y , A. A . ,
1969, G e o ph ys ic al o b s e r v a t i o n s o f v e r t i c a l d r a i n a g e o p e r a t i o n s
in t h e Arazdayan S te p p e ( i n R u s s i a n ) : G i d r o t e k h . M e l i o r a t . ,
no. 5, p. 82- 9 0 .
A l e v a , G. J . J . , I 9 6 0 , Geochemical and g e o p h y s i c a l e x p l o r a t i o n o f t h e
Nigadoo b a s e me tal d e p o s i t :
Ge ol. Mijnbouw, v. 3 9, no. 10,
p. 4 9 2 - 4 99 .
A l e x a n i a n , C. L . , 1932, T r a i t e p r a t i q u e de p r o s p e c t ion g e o p h y s i q u e a
1 ' u s a g e des g e o l o g u e s e t des i n g e n i e u r s des m i n e s : P a r i s and
L i e g e , L i b r a i r i e P o l y t e c h . Ch. B e r a n g e r , p. 2 0 5 - 2 1 2 .
Alp i n , L. M. and Schoenmann, S . , 1936, Some c a l c u l a t i o n s on s p o n t a n e o u s
p o l a r i z a t i o n in b o r e h o l e s ( i n R u s s i a n ) : N e f t . G e o f i z . B y u l l . ,
no. 3, p. 4 4 - 6 4 .
125
126
A l t h a u s , Voy E . , 1967, E l e c t r o k i n e t i c p o t e n t i a l s in s o u t h L o u i s i a n a
t e r t i a r y sedim ents:
Log A n a l y s t , v. 8, no. 1, p. 2 9 - 34 .
Ambronn, R i c h a r d , 1926, E l e k t r i s c h e E r d e r f o r s c h u n g s m e t h o d e n : in
Methoden d e r Angewandten G eo ph ys ik , Dresden and L e i p z i g ,
V e r l a g von Theodor S t e i n k o p f f , p. 105-123.
Ambronn, R i c h a r d , 1928, E a r t h c u r r e n t s :
in El ements o f Geoph ys ics
( t r a n s . M. C. Cobb);, New York, McGraw-Hill Book C o . , I n c . ,
p. 134-160.
A n d er s o n , L e n n a r t A . , I9 6 0 , E l e c t r i c a l p r o p e r t i e s o f s u l f i d e o r e s in
igne ou s and metam orp hic ro ck s n e a r E a s t Union, Maine: U. S.
G e o l . S u r v . , P r o f . P a p e r , no. 400-B, p. 125-128.
A n de rs o n, L e n n a r t A. and J o h n s o n , Gordon R. , 1973, The a p p l i c a t i o n o f
t h e s e l f - p o t e n t i a l method in t h e s e a r c h f o r g e o t h e r m a l en er g y
(abstract):
G e o p h y s i c s , v. 3 6 , no. 6, p. 1190.
A n de rs o n, L e n n a r t A. and J o h n s o n , Gordon R . , 1973, The a p p l i c a t i o n o f
t h e s e l f - p o t e n t i a l , method in t h e e x p l o r a t i o n f o r ge o th er m al
e n e r g y in Long V a l l e y , C a l i f o r n i a ( a b s t r a c t ) :
Am. Geophys.
Union T r a n s . , v. 54, no. 11, p. 1212,
A n d er s o n , L e n n a r t A. and J o h n s o n , Gordon R . , 1974, A s e l f - p o t e n t i a l
s u r v e y o f Long V a l l e y c a l d e r a , Mono Co unty, C a l i f o r n i a :
U, S.
Geol. S u r v . , Open F i l e R e p o r t , 2 p . , 3 d i a g r a m s .
A n de r s on , L e n n a r t A. and J o h n s o n , Gordon R . , 1976, A p p l i c a t i o n o f t h e
s e l f - p o t e n t i a l method t o g e o t h e r m a l e x p l o r a t i o n in Long V a l l e y ,
C alifornia:
J . Geophys. R e s . , v. 8 l , no. 8, p. 1527-1532.
A n p i l o g o v , A. P . , G a l a y a v i c h , A. Sh. and Masyukova, L. G . , 1962,
E f f e c t s o f v a r i o u s f a c t o r s on S. P. dia gr a m s ( i n R u s s i a n ) :
Razved. Promys. G e o f i z . » no. 43, p. 121-126.
A n s e l , E. A . , B a r t e l s , J . and G u t e n b e r g , B . , 1929, G e o p h y s i k a l i s c h e
A u f s c h 1ie s s u n g s m e t h o d e n (G e o p h y s ic a l e x p l o r a t i o n m e t h o d s ) :
in
Lehrbuck d e r Geophysik (ed . B. G u t e n b e r g ) , B e r l i n , G ebruder
B o r n t r a e g e r , p. 500- 61 4. .
A r l i c k , A. B . , 1945, E l e c t r i c a l p o t e n t i a l o f t h e e a r t h ' s s u r f a c e :
S c i . , v. 14, no. 6 , p. 151.
C urr.
A r n o l d , G . , 1937, F e h l e r q u e l l e n bei d e r Messung von E r d s tr o m en in Kurzen
L e i t u n g e n u n t e r s u c h t im T a u n u s - O b s e r v a to r iu r n ( S o u r c e o f e r r o r s
d u r i n g measurement o f n a t u r a l c u r r e n t s in s h o r t w i r e s ) :
G e r l a n d s B e i t r . G e o p h y s . , v. 49, p. 140-164.
127
A s t i e r , J e a n - L o u i s , 1971, Geophysique a p p l i q u e e a 1 1h y d r o g e o l o g i e :
P a r i s , Masson & Cie .
A t k i n s , E. R . , 1961, T e c h n i q u e s o f e l e c t r i c a l
J . P e t r o l . T e c h n o l . , v. 13, no. 2 , p .
log i n t e r p r e t a t i o n :
118-124.
A u z in , A. K . , 1962, The us e o f t h e s e l f - p o t e n t i a l method on v e i n d i s s e m i n a t e d copper-mplybdenum d e p o s i t s o f c e n t r a l Kazakhstan
(in Russian):
L e n i n g r a d U n i v . , Uch. Z a p . , Vop. G e o f i z . , no.
303, p. 2 34 -2 4 0.
A u z in , A. K . , 1963, The n a t u r a l e l e c t r i c a l f i e l d s in t h e o r e d e p o s i t s
o f C e n t r a l Ka za k hs ta n ( in R u s s i a n ) :
L e n i n g r a d U n i v . , Uch. Z a p . ,
Vop. G e o f i z . , no. 320, p. 100-121.
A u zi n , A. K. and L o g v i n e t s , M. N . , 1959, O b s e r v a t i o n s o f t h e n a t u r a l
e l e c t r i c a l f i e l d p o te n tia l w ith simultaneous w aterin g of the
holes f o r grounding (in R u ssian ):
L e n i n g r a d U n i v . , Uch. Z a p . ,
Vop. G e o f i z . , no. 2 7 8 , p. 160-163,Baag, Czang Go and Kim, Kyung S i k , 1962, The d e t a i l e d , r e p o r t o f mag­
n e t i c p r o s p e c t i n g and S. P. measurements a t Hwan Sun n i c k e l
mine ( i n Korean w i t h an E n g l i s h a b s t r a c t ) :
K orea, Geol. S u r v . ,
B u l l . , no. 5, p. 22 6 -2 3 4.
Baba, Kenzo and Suyuma, J u n j l , 1962, On t h e r e s u l t s o f e l e c t r i c a l
p r o s p e c t i n g by t h e p r o f I l i n g , method n e a r t h e Y o ts u g i mine a t
Ningyo P ass ( i n J a p a n e s e w i t h an E n g l i s h a b s t r a c t ) :
Jap .,
Geol. S u r v . , B u l l . , v. 13, no. 1, p. 17*28.
Bachmetjew, P o f i r i j , 18 9 6 , H a u p t r e s u l t a t e d e r U n te r s u c h u n g u b er d i e
A b h a n g i g k e i t d e r e l e k t r i s c h e n E r d s tr o m e von Niveau-Schwankungen
des Gr un dw as se rs in B u l g a r i a n (P r im a ry r e s u l t s
o f the in v e s t ig a ­
t i o n o f t h e d ep en de n ce o f e l e c t r i c c u r r e n t s on t h e l e v e l o f
ground w a t e r flow in B u l g a r i a ) :
N a c h r i c h t e n von d e r Ko nig l.
G e s e l l s c h a f t d e r W i s s e n s c h a f t e n und d e r Georg- A u g u s t s U n i v e r s i t a t zu G o t t i n g e n , p. 300*303.
Bachmetjew, P o r f i r i j , 1902, The e a r t h c u r r e n t q u e s t i o n :
Memo?res
Academie I m p e r i a l e des S c i e n c e s , S t . P e t e r s b u r g , Memoire 12,
s e r i e s V I I I , p. 1-55.
Bachmetjew, P o r f i r i j and P e n c e v , N . , 1894, Sur l e s c o u r a n t s e l e c t r i q u e s
p r o d u i t s p a r l e mouvement de 1 l eau a t r a v e r s des c o r p s p or eu x
(On t h e e l e c t r i c c u r r e n t s pr o d u c e d by t h e movement o f w a t e r
th r o u g h a po ro u s medium): J o u r n a l o f t h e R u s s i a n P h y s i c o Chemical S o c i e t y o f t h e Im p e r i a l U n i v e r s i t y o f S t . P e t e r s b u r g ,
v. 26 ( P h y s i c s ) , p. 225.-248.
128
Bachmetjew, P o r f i r i j and P en ce v, N . , 1895, Sur l e s c o u r a n t s e l e c t r i q u e s
p r o d u i t s p a r l e mouvement de 1 ' e a u a t r a v e r s des c o r p s po r eu x
(On t h e e l e c t r i c c u r r e n t s pr o d u c e d by t h e movement o f w a t e r
t h r o u g h a p or ous medium): J . P h y s . T h e o r . App1 . , v. k, p. 581.
Back, W i l l i a m and B a r n e s , Ivan , 1961, Equipment f o r f i e l d measurement
o f electrochem ical p o te n tia ls :
U. S. G e o l . S u r v . , P r o f . P a p e r ,
kzk- c , p. 3 6 6 -3 6 8 .
Back, W i l l i a m and B a r n e s , I va n, 1965, R e l a t i o n o f E l e c t r o c h e m i c a l
p o t e n t i a l s and Fe c o n t e n t t o g r o u n d w a te r flow p a t t e r n s : U. S.
G e o l . S u r v . , P r o f . P a p e r , A98- C , 16 p.
Bacon, L. 0.., 1948, For mat ion c l a y m i n e r a l s and e l e c t r i c l o g g i n g : Penn.
S t . C o l . , Min era l Ind. Exp. S t a t i o n B u l l . , no. 52, p. 53“ 75.
B a k s h t , F. B. and Gladkov, N. A . , 1968, F e a t u r e s o f t h e n a t u r a l e l e c ­
t r i c a l f i e l d s in t h e Gornyy A l t a y and S a l a i r ( i n R u s s i a n ) :
in
Vop. Rudn. G e o f i z . S i b i r . , S i b i r . Nauch. , I s s l e d . I n s t .
G e o l o g i i , G e o f i z . i M i n e r a l , J r . , no. 73, p. 5 2 - 6 1 .
B a l e v a , Z d i s l a v a , 1964, E x p e r i e n c e in t h e u se o f e l e c t r o c h e m i c a l l o g g i n g
o f o i l w e l l s in P o l a n d : P e t r o l . G e o l . , v . 8, no. 3, P • 182-184.
B a l t o s s e r , R. W. and Lawrence, H. W., 1970, A p p l i c a t i o n o f w e ll lo g g i n g
t e c h n i q u e s in m e t a l l i c m i n e r a l m i n i n g :
G e o p h y s i c s , v. 35, no. 1,
p. 143-152.
B a n n e r j e e , Buddhadeb, 1970, I n t e r p r e t a t i o n o f s e l f - p o t e n t i a l d a t a f o r .
v e r t i c a l and n e a r l y v e r t i c a l s h e e t s o f i n f i n i t e h o r i z o n t a l
e x t e n t i o n : Pur e A p p l . Geophys. , v. 82, p. 2 3 8 - 2 5 0 .
B a n n e r j e e , Buddhadeb, 1971, Q u a n t i t a t i v e i n t e r p r e t a t i o n o f s e l f p o t e n t i a l a n o m a l i e s o f some s p e c i f i c g e o m e t r i c b o d i e s : P ur e
Appl. Geophys. , v. 90 , p. 138-152.
B an w e ll , C. J . , 1970, G e o p hy s ic al t e c h n i q u e s in g e o t h e rm a l e x p l o r a t i o n :
U. N. Symp. Development U t i l i z a t i o n Geothermal Re s ou rc es
( P i s a ) , F i r s t G e o t h e r m i c s , s p e c . i s s . 2, v. 1, p. 32r
Barlow, W. H . , 1849, On t h e s p o n t a n e o u s e l e c t r i c a l c u r r e n t s o b s e r v e d
in t h e w i r e s o f t h e e l e c t r i c t e l e g r a p h :
P h ilo s. Trans. R . S o c .
London, v. 139, p. 6 1 - 7 2 .
B a r r o n , C. N. and Ha rden, G . , 1966, An i n t e r i m a c c o u n t o f s u b s u r f a c e
p r o s p e c t i n g n e a r H a i m a r a l 1 i F a l l s , Cuyuni R i v e r , B r i t i s h G u i a n a :
in C o n f e r e n c i a g e o l o g i c a l das Guianas ( B r a z i l ) , S i x t h , Div.
G e o l . M i n e r a l . , no. 41, p. 143-150.
129
B a r t a , R u d o l f , 1967, C o n t r i b u t i o n t o t h e s o l u t i o n o f t o p o g r a p h i c e f f e c t s
in g e o e l e c t r i c a l s u r v e y i n g :
Cesk. Akad. Ved, S b o r n i k G e o l . Ved
U z i t a G e o f y z . , no. 6 , p. 2 7- 4 0 .
B a r t o n , Donald C . , 1927, A p p l i e d g e o p h y s i c a l methods in America:
G e o l . , v. 2 2 , no. 7, p, 6 49 -6 6 8.
B a r u s , Carl W., 1882, On t h e e l e c t r i c a l a c t i v i t y o f
Geology o f t h e Comstock Lode (ed . George F.
S u r v . , Monograph, no. 3, p. 30 9- 367 .
Econ.
o r e b o d i e s : in
B e c k e r ) , U. S. Ge ol,
B e c k e r , Alex and T e l f o r d , W. M ., 1965, Sp on ta n e ou s p o l a r i z a t i o n s t u d i e s :
Geophys. P r o s p e c t . (The H a g u e ) , v. 13, no. 2, p. 173-188.
B e l l u i g i , A r n a l d o , 1929, I n t r o d u z i o n e a l i a G e o f i s i c a M i n e r a r i a :
1 1 i n d u s t r i a l M i n e r a r i a , 88 p.
-
e d . de
B e l l u i g i , A r n a l d o , 1925, The need o f r e v i s i n g t h e a p p a r a t u s employed in
t h e measurement o f an e l e c t r o c h e m i c a l e f f e c t o f t h e grou nd:
B e i t r . Angew. G e o p h y s . , v. 5, no. 2 ,
p. 169-177.
B e l l u i g i , A r n a l d o , 1939, T h e o r e t i s c h e Grundzuge d e r S e l b s t p o t e n t i a l messungen u b e r E r z l a g e r s t a t t e n ( T h e o r e t i c a l f o u n d a t i o n s o f s e l f p o t e n t i a l : measu re men ts above o r e d e p o s i t s ) :
B e i t r . Angew.
G e o p h y s . , v. 7, p. 172-178.
B e n n e t s , J o h n , 1833, On t h e e l e c t r o m a g n e t i s m
o f v e i n s o f c o p p e r o r e in
C o r n w a ll : P h i l o s . Mag., v. 3, p. 17-18.
B e n v e n u t i , G . , 1969, Study o f a g r a p h i t e m i n e r a l i z a t i o n ( a t Monte ros so
C a l a b ro ) by measurements o f S. P. and I , P . :
B oll. Geofis.
T e o r . A p p l . , v. 11, no. 4 3 - 4 4 , p. 131-139.
B e r d i c h e v s k i y , M. N. , 1965, G e o l o g i c a l i n t e r p r e t a t i o n o f t h e r e s u l t s
o f t e l l u r i c c u r r e n t s u r v e y s : in E l e c t r i c a l P r o s p e c t i n g w i t h
t h e T e l l u r i c C u r r e n t Method ( t r a i n s . George V, K e l l e r ) , Colo,
Sch. Mines, Q u a r t . , v. 6 0 , no. 1, p. 176-208.
B e r g e y , W. R . , I9 6 0, G e o ph ys ic al and g eoc he mi ca l s u r v e y s in t h e Connors
a r e a , S t. C atherine, Jamaica:
G e o n o te s , v. 3, p a r t 4 , pp. 121123.
Berg ey, W. R . , C l a r k , A. R . , F r a n t z , J . C . , K e e v i l , N. B. and Sm it h,
F. Gordon, 1959, D is c o v e r y o f c o p p e r n i c k e l o r e b o d i e s a t t h e
Temagarni mine, O n t a r i o :
in Methods and c a s e h i s t o r i e s in mining
g e o p h y s i c s ( C a n a d a ) , Commonwealth Mining and M e t a l l u r g i c a l
C o n g r e s s , S i x t h , p. 168-175-
130
B e r g s tr o m , G . , 1925, E l e c t r i c a l p r o s p e c t i n g : J . Chem. Metal 1. Min.
Soc. S. A f r . , v. 25, no. 5, p. 138-148.
B e r n s t e i n , F. and S c a l a , C . , 1959, Some a s p e c t s o f t h e s t r e a m i n g p o t e n ­
t i a l and t h e e l e c t r o c h e m i c a l S. P. in s h a l e s :
J. Petrol.
T e c h n o 1 . , v. 7, no. 12, p. 7 6- 7 7 .
B i l i n s k y . S . , 1938, E l e c t r i c a l e x p l o r a t i o n o f d r i l l
R e v . , p . 12-16.
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