Direct gravity interpretation of sedimentary basin using digital computer — Part I- art%3A10.1007%2FBF00875068

7/30/2019 Direct gravity interpretation of sedimentary basin using digital computer Part I- art%3A10.1007%2FBF00875068

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P U R E A N D A P P L I E D G E O P H Y S I C SVol . 86 197 1 / I l l

Di r e c t Gr a v i t y I n t e r p r e t a t i o n o f S e d i me n t a r y Ba s i nU s i n g D i g it a l C o m p u t e r - P a r t I

B y B . N . P . A G A R W A L )

Summary - A m e t h o d i s d ev e l o p ed f o r r ap i d g r av i t y i n t e r p r e t a t i o n o f a s ed i men t a r y b a s i n u s i n ga d i g i t a l co m p u t e r . A s s u m i n g a l i n ea r v a r i ab l e d en s it y co n t r a s t ( b o t h v e r t i c a l ly an d h o r i zo n t a l l y ) ,ex p r e s s i o n s h av e b een d e r i v ed f o r t h e g r av i t a t i o n a l a t t r a c t i o n o f a r ec t an g u l a r s t r i p . A n i n t e r p r e t a t i o no f th e s t r u c t u r e o f G o d av a r i V a l l ey ( I n d i a ) h a s b een m ad e u s i n g t h e s e ex p re s s i o n s .

1 . I n t r o d u c t i o n

A b o u g u e r g r a v i ty a n o m a l y c a n b e a t t r ib u t e d t o a n i nf in i te n u m b e r o f m a s sd i s t r i b u t i o n (S K E E L S, [ 7] 2 ), R O Y [ 6] ). D e p e n d i n g u p o n t h e a v a i l a b i l i t y o f g e o l o g i c a la n d g e o p h y s i c a l i n f o r m a t i o n s , i t s h o u l d b e p o s s i b l e t o i n t e rp r e t a g r a v i t y a n o m a l yt o a g r e a t d e g r e e o f a c c u r a c y . T h o u g h i n g e n e r a l , g r a v i t y i n t e r p r e t a t i o n p r o b l e m i sn o t w e l l d e f i n e d , i n s o m e i n s t a n c e s , t h e g e o l o g i c a l s e t t i n g i s s u c h t h a t i t i s p o s s i b l et o c o n s t r u c t a s u it a b l e g e o p h y s i ca l m o d e l w h i c h c a n e a si ly b e b r o u g h t w i t h i n af r a m e w o r k s u i ta b l e f o r c o m p u t e r a p p l ic a t io n .

T h e i n t e r p r e t a t i o n o f g r a v i t y a n o m a l y o v e r s e d i m e n t a r y b a s i n s ( a l lu v i a l f il le dv a l l ey s ) i s a n e x a m p l e o f w e l l s t r u c t u r e d i n t e r p r e t a t i v e p r o b l e m , w h i c h c a n b e s o l v e du s i n g a d i g i t a l c o m p u t e r . U n d e r s u i t a b l e c o n d i t i o n s a n d a s s u m p t i o n s , a b o u g u e rg r a v i ty p ro f il e p r o v i d e s a m e a n s o f e s t im a t i n g t h e d e p t h t o t h e b e d r o c k t h r o u g h t h es e d i m e n t a r y c o v e r . T h e g r a v i t y p r o f i l e i s s e l e c t e d o n a l i n e p e r p e n d i c u l a r t o t h eb o u g u e r g r a v i t y c o n t o u r s . T h e u n d e r g r o u n d s t r u c tu r e i s a s s u m e d t o b e o f u n i f o r mc r o s s s e c t i o n , e x t e n d i n g i n f i n i t e l y i n t h e d i r e c t i o n p e r p e n d i c u l a r t o t h e p r o f i l e . I na d d i t i o n , t h e f o l l o w i n g f a c t o r s a r e s p e c if i e d t o e n s u r e a u n i q u e i n t e r p r e t a t i o n .

a ) T h e l o c a t i o n o f t h e s u r f a ce o f th e b e d r o c k - s e d i m e n t a r y c o n t a c t s a r e g iv e n .b ) T h e s e d i m e n t a r y - b e d r o c k d e n s i t y c o n t r a s t i s s p e c if ie d , a n dc ) T h e u n d e r l y i n g b e d r o c k i s n o t u n d e r c u t a t a n y p o i n t b y th e s e d i m e n t a r y f ill.I n t h e p a s t d e c a d e , m a n y t e c h n i q u e s f o r r a p i d i n t e r p r e t a t io n o f g r a v i ty a n o m a l i e s

h a v e b e e n d e v e l o p e d ( T A L W A N I et a l . [ 8] , B O T T [ 1] , M O R G A N a n d G R A N T [ 3] a n dT A N N E R [9 ]). I n p r i n c ip l e , a l l t h e s e m e t h o d s d e p e n d u p o n i d e a li z in g a b o d y b y at w o - d i m e n s i o n a l m a s s d i s t r i b u t i o n w h i c h is , e i th e r , d iv i d e d in t o la r g e n u m b e r o f

1) D e p a r t m e n t o f G e o p h y s i c s, B a n a r a s H i n d u U n i v e r s it y , V a r a n a si - 5, I n d i a .2 ) N u mb er s i n t h e b r ack e t s r e f e r t o Re f e r en ces , p ag e 1 2 .


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6 B . N . P . A g a r w a l ( P a g e o p h ,v e r t i c a l s t r i p s ( B O T T [ 1] a n d T A t , ~ Z R [ 9] ), o r , f i t t e d b y a n n - s i d e d p o l y g o n (T A L W A N Iet al. [ 8] a n d M O R G A N a n d G R A N T [3 ]) , i n o r d e r t o d e t e r m i n e t h e s t r u c t u r a l c o n f i g u -r a t i o n b y t h e m e t h o d o f s u c c e s s iv e a p p r o x i m a t i o n . I n a ll t h e s e m e t h o d s , t h e e f fe c t so f t h e s u r r o u n d i n g m a s s a n d t h e d e p o s i t i o n o f s e d i m e n t s u n d e r t h e in f lu e n c e o fe a r t h ' s g r a v i t a t i o n a l f i e l d o n t h e g r a v i t y p r o f i l e h a v e n o t b e e n a c c o u n t e d i n a r e a l i s t i cw a y .

I n th e p r e s e n t w o r k , t h e m a s s d i s t r ib u t i o n i s a p p r o x i m a t e d b y a l a rg e n u m b e r o fv e r t i c a l st r ip s . T o a c c o u n t f o r t h e e f fe c t o f s u r r o u n d i n g m a s s o n t h e g r a v i t y p r o f il e ,a v a r i a b l e d e n s i t y c o n t r a s t f u n c t i o n i s u s e d t h r o u g h o u t t h e b o d y ( M O RR T S a n d S U L TZ -B A C H [4 ]). W e a l s o a s s u m e t h a t

a ) a ll t h e s t r ip s a r e o f u n i f o r m w i d t h ,b ) t h e g r a v i t y p r o f il e is s y m m e t r i c a b o u t t h e v e r t i c a l a xi s p a s s i n g t h r o u g h t h e

m i n i m u m g r a v i ty v a l u e, a n dc ) t h e l a t e r a l d e n s i t y v a r i a t i o n i s t a k e n i n b o t h t h e d i r e c t i o n s f r o m t h e p o i n t o fm i n i m u m g r a v i ty v a l ue .

T h e s u i ta b i li t y o f p r e s e n t m e t h o d t o v a r io u s p r o b l e m s o f i n t e r p r e ta t i o n h a s b e e nv i n d i c a te d b y d e m o n s t r a t in g o n e p r a c ti c a l c a se . T h e a d v a n t a g e s o f t hi s m e t h o d o v e ro t h e r e x i s t i n g o n e s h a v e b e e n d i s c u s s e d .

2. Formulation of the problemT h e g e o m e t r y o f" t h e s t r i p h a s b e e n s h o w n i n fi g u r e 1 . T h e B o u g u e r g r a v i t ya n o m a l y v a l u e s g ( ~ ) , a t e q u i s p a c e d p o i n t s (~ i, 0 ) w h e r e i = 1 , 2 , . . . n (n b e i n g t h e

P ( ~ i , O )~ ( 0 , 0 ) J , ~

2~o,~b - -

-rLF i g u r e 1

G e o m e t r y o f t h e s t r ip


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Vol. 86 , 19 71 /III) Direct Gravi ty In terpre tat ion of Sedimentary Basin - Par t I 7n u m b e r o f p o i n t s a n d a l so t h e n u m b e r o f s tr ip s ), a r e k n o w n a l o n g t h e h o r iz o n t a la x is . T h e g r a v i t y e f f ec t a t e a c h p o i n t ( ~ i, 0 ) c a n b e c o m p u t e d b y s o l v i n g t h e f o l l o w i n gi n t e g r a l ( H E m A N D [ 2 ] )

r f2(~)g ( 4 ,) = 2 G tl 2 + ( ~ _ 4) 2 (1 )

~ ' f l ( g )w h e r e~ ( 4 , t/) v a r i a b l e d e n s i t y c o n t r a s t f u n c t i o n ;4 ' a n d 4 " t h e c o o r d i n a t e s o f ~ t r o m a r b i t r a r y o r i g i n f o r f ix i n g t h e e x t e n t o f t h e

b a s i n ;f l ( 4) c o m p l i c a t e d f u n c t io n s o f d e p t h s f o r u p p e r a n d l o w e r b o u n d a r i e s o f

a n d f 2 ( r t h e b a s i n ;a n d G u n i v e r s a l g r a v i t a t i o n a l c o n s t a n t .

T h e e x a c t s o l u ti o n o f i n te g r al , g i v e n i n e q u a t i o n ( 1) c a n n o t b e o b t a i n e d b e c a u s et h e d e p t h f u n c t i o n s f 1 4 ) a n d f z ( 4 ) a r e u n k n o w n a n d a r e ra t h e r c o m p l i c a t e d . A s i m p l ea p p r o x i m a t i o n is m a d e f o r t h e i n t e r p re t a t io n o f s e d i m e n t a r y b a s i n s b y c h o o s i n g

f 1 ( 4 ) = 0 a n d a p p r o x i m a t i n g f 2 ( 4 ) b y s m a l l h o r iz o n t a l l in e s o f c o n s t a n t l e n g th b u t o fd i f f e re n t d e p t h s . F u r t h e r m o r e , t h e d i s t a n c e s b e t w e e n t h e c o o r d i n a t e s ( ~ ' , 0 ) a n d(4", 0 ) a r e d i v i d e d i n t o n - s t r ip s o f e q u a l w i d t h b . T h u s t h e s o l u t i o n o f i n t e g r a l g i v e ni n e q u a t i o n ( l ) c a n b e o b t a i n e d b y s u m m i n g u p t h e g r a v i t y e ff e c t o f a l l t h e s tr ip s . T h ee q u a t i o n ( 1) c a n n o w b e w r i tt e n a s

n ~ ' + j b t lj

g ( 4, ) = 2 G 2 + ( { i - 4) 2-j = l { ' + ( j - 1 ) b 0

o r (2 )g (4 i) = 2 G ) , A j g(4 i )

/..,dj = lw h e r e 0 2 (4 , t /) t h e v a r i a b l e d e n s i t y f u n c t i o n i n j t h s t r i p

r /j t h e d e p t h s t o t h e l o w e r s u r f a c e o f j t h s t ri pa n d d j g ( ( i ) g r a v i t a t i o n a l a t t r a c t i o n o f t h e j t h s t r ip a t t h e p o i n t ( ~ i , 0 ) .I t i s t h e p u r p o s e o f t h e p r e s e n t p a p e r t o o b t a i n t h e s o l u t i o n o f e q u a t i o n ( 2) a n d

u s e it i n th e i n t e r p r e t a t i o n o f t h e s t r u c t u r e o f a g i v en s e d i m e n t a r y b a s i n .W e s h a l l m a k e t h e f o l l o w i n g a s s u m p t i o n s w i t h r e g a r d t o t h e v a r i a b l e d e n s i t y

c o n t r a s t f u n c t i o n1 ) T h e d e n s i t y c o n t r a s t v a r i e s l i n e a r l y i n l a t e r a l a s w e l l a s i n v e r t i c a l d i r e c t i o n i n

a s t r ip .2 ) T h e v a r i a t i o n o f d e n s i t y c o n t r a s t a l o n g t h e v e r t i c a l d ir e c t i o n i s s u c h t h a t i t

a s s u m e s a c o n s t a n t d e n s i t y c o n t r a s t a t th e l o w e r b o u n d a r y o f t h e s t ri p.T h e s e c o n d a s s u m p t i o n i s m a d e b e c a u s ea ) t h e v a r i a t i o n a l o n g t h e v e r ti c a l d i r e c t i o n i s n o t k n o w n ,


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8 B.N .P . Agarwa l (Pageoph ,b ) a l o n g t h e b o u n d a r y ( lo w e r ) o f t h e s e d i m e n t a r y b a s i n , a c o n s t a n t d e n s i ty c o n -

t r a s t is a s s u m e d . W h e n t h e n u m b e r o f s t r ip s a r e l a r g e e n o u g h , t h e v a r i o u s d e p t h s o ft h e s t ri p s c a n b e ta k e n a s t h e b o u n d a r y o f t h e s e d i m e n t a r y b a s in .

3. Calculation o f density functionT h e g e o m e t r y o f t h e s t r i p h a s b e e n s h o w n i n fi g u re 1 . L e t t h e d e n s i t y v a l u e s a t

t h e u p p e r c o r n e r s o f a s t r ip b e 0 1 a n d 0 2 r e s p e c t i v e l y a n d 0 3 a t t h e l o w e r b o u n d a r yo f th e s t ri p a n d i s c o n s t a n t t h r o u g h o u t t h e w i d t h o f t h e s tr ip . L e t u s c h o o s e t h ep o i n t s P 1 a n d P 2 a t a d e p t h t / f r o m t h e g r o u n d s u r fa c e . T h e n t h e d e n s i t y f u n c t io n s0 , ( t / ) a n d 0 2 ( t /) , b y a s s u m p t i o n , a r e g i v e n b y

a n dw h e r e

a n d

o ~ ( ~ ) = < [ i + ~ I ( , - , 1 ) ] ( 3 )"103 - 01 [f i l -L, ' ( ~ z - ~ 1 ) ( 4 )!

~ 3 - - 0 2 [f l 2 - ~ 2 " ( ~ 2 - * / 1 ) " JS i n c e t h e d e n s i t y v a r i e s l i n e a r l y b e t w e e n t h e p o i n t s P 1 a n d P2 , t h e y m u s t s a t i s f y t h er e l a t i o n 02(t1) = 01(t1)(1 -{- ( b )

0 2 ( ~ ) - ~ ( ~ ) ( 5 )0 . ( , ) b

T h e r e f o r e t h e d e n s i t y f u n c t i o n 0 ( # , ~/) a t a p o i n t P3(~ , /7 ) f r o m t h e o r i g i n w i l l b eg iv en b y 0 (~ , t /) = 01 (*/ ) (1 + ~ ~) . (6 )

S u b s t i t u t i n g t h e ' v a lu e s o f 01 (t/) a n d ~ f r o m e q u a t i o n s ( 3 ) a n d ( 5) w e g e t a f t e r s o m es i m p l i f i c a t i o nw h e r e

a n d~ 2 - - ~I

01b ( 7 )0 2 f 1 2 - - 0 1 f l ly - 0 1 b

W h e n ~]1 = 0 i .e . th e u p p e r s u r f a c e o f t h e s t r i p c o i n c i d e s w i t h t h e h o r i z o n t a l g r o u n ds u r f a c e , t h e n 0 ( { , ~/) b e c o m e s

o ( ~ . ~ ) = o i [ ~ + ~ ~ + / h ~ + ~ , I ] . ( 8 )


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Vol. 86, 197 1/III ) D irec tG ravity Interpretation of SedimentaryBasin - Par t I 94 . C a l c u l a t i o n o f g r a v i t a t i o n a l a t t r a c t i o n o f a r e c ta n g u l a r s t r ip w i th v a r i a b l e d e n s i t y

c o n t r a s t f u n c t i o n ~ ( { , ~ )L e t u s c o n s i d e r a p o i n t P a t a d i s t a n c e { ~ f r o m t h e o r i g i n o f c o o r d i n a t e s y st em( F i g u r e 1 ) . T h e g r a v i t a t i o n a l a t t r a c t i o n A j g ( r f o r a r e c t a n g u l a r s t r i p o f v a r i a b l ed e n s i t y c o n t r a s t f u n c t i o n ~ ( ~ , / / ) , d e fi n ed b y e q u a t i o n ( 7 ), is g iv e n b y (H E IL A N D [ 2 ])

b t'12A~ g (~ i) = 2 G f f ~,[1 + ~ { + fl1(////2-+//')({, _ 7{(//{)2 / / 1 ) ] / / de d// (9)

o r ,

o r

0 r/1b r/2 b ~2

A j g( r = 2 G 0 2 / / 2 + ( r _ 0 2 + ~ I /2 + ( r - {)20 ~i 0 ~/j

b ~2 b ~/2

+ & ,~ + (~ ,_ 02 & ,~ r + (~ ,_ r0 ql 0 r /1

b ~/2 b ~/2

- ~- ~ . / / 2 .~ _ ( ~ i - r ~ / / 1 / ~ 2 .O f_ r ~ ? ) 2 ]0 ~/1 0 ~/1

(10)

Ai g ( ~ ,) = 2 G O j [ I i + a I2 + f l l Ia - f l , / /1 I , + y I4 - Y / /~ I 2 ] .T h e s e i n t e g r a l s h a v e b e e n s o l v e d a n d t h e c o n c e r n e d e x p r e s s i o n s f o r t h e i n t e g r a l s/ 1 , / 2 , I 3 a n d I 4 c a n b e w r i tt e n a s

1 1 = r ++t / 2 (t a n - 1\

- ~ / l ( t a n -%

1 2 = 2 //z l n / / 2 + ~ //~

{ 2 , / / / 2 + ( { , _ b )2r ({, - b ) l n v t h + ({ i b ) 21 / 2~ - t a n - * ~ t]2 - b ){--~ - t a n - 1 { , - b ~~ i / / i /l n ~ / / } + ( r b ) 2

/ 2 q_ r_2"~In / t 1 2 2 + ( r ~ ~ / ~ .n // /2 gi |+ ( { i - b ) 2 ~ / / / 2 + ( r b ) 2 //1 g , d~ 2l n / / / 2 + { , / / 2 + ( ~ , b ) 2+ r r ' 4 / / ~ + # - ( ~ - b ) I n ~ + ( r b ) 2

t/~ "- - t a n - x ~'~i2)1~ / l ( ta n _ 1 r t a n _ l ~ ) _ t / 2 ( t a n _ 1 r b

(11)

(:2)


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10 B.N .P. Agarwal (Pageoph,' I ( + ' ( + + + + b )/3 = ~ t/~ t a n -1 . . . ./2 ta n - t/z-- - / ? 2 ta n -1--t/ t - tan -1b( t /2 - t /1) + ~ 2(an - l+ th - t an -1 t /2 '] (13 )e 7

- ( ~ . i - b ) / ' ( t a n - t ~ i t / l - - b t a n - I : i t / ~ ) ? -- + ' 11 + ( + , : - b) 2

+ r - l t / 2 t an - 1 t /l ~ _e T - rx ( t a n - l - - ~ - t a n -~ ib ~i th b ) + b ( t / 2 - t h ) ( b - 2 ~ i ) ] (14)+ 89~[ t / zz ' ( t an - 1 ~--i - t a n - 1 ~ /~ b )/2_ t h " t an - 1 ~ i ~ i - - b l t /2~

/ 7 1 t /1 ~ i ~i//_ ( ~ i _ b ) e . ( t a n - 1 /71 t a n - 1 t/2 ) 1~ i - b ~ , Z b + b( t/2 - t / l)

w h e r e ' l n ' d en o t e s t h e n a t u r a l l o g a r i t h m .U s i n g t h e ex p r e s si o n s f o r 11, Iz , 13 an d I 4 and equ at ion (10) we ca n eas i ly ca l cu l a te

the va lue o f g (~ i) f rom equ at ion (2 ).5 . M e t h o d o f c o m p u t at io n

Th e a l g o r i t h m d ev e l o p e d f o r ca l cu l a ti n g th e s h ap e o f t h e s ed i m en t a r y b as in ,us ing equ at ions (7 ) and (10) t o (14) is s imi l a r t o t he one descr ibed by BOTT [1 ] excep tt h a t f ew m o d i f ica t i o n s h av e b ee n i n co r p o r a t ed t o t ak e i n t o a cco u n t t h e v a r i ab l ed en s i t y co n t r a s t w i t h t h e a s s u m p t i o n t h a t b a s i n ex t en d s f r o m t h e h o r i zo n t a l p l an eof o bse rvat io n, i .e ., J71 = 0 in eq ua t ions (10) to (14).

Le t t h e s p an o f t h e b as i n ' 2 a ' be d iv ided in to ' 2n ' ver t i ca l s tr ips o f equal w id thb ( b = a / n , w h er e n = 1, 2 , 3 .. .) . A s s u m i n g t h e m ax i m u m an d m i n i m u m d en s i t y co n -t ras ts as ~max an d 0 , ,i ,, w e have O~max - - ~m inc~ - (1 5)a Q m i n

Th erefo re , t he den s i ty va lues a t t he co rne r s o f t he every s t r ip c an be c a l cu l a t ed byo ~ i = O , ~ i , ( l + ~ i b ) fo r i = 0 , 1 , 2 . .. . n ]an d j (16)

0 n + i= ~ ~ fo r i = 1 , 2 , 3 . .. . n .


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V o l . 86 , 1 9 7 1 / I I / ) D i r ec t G r a v i t y I n t e r p r e t a t i o n o f Sed i m en t a r y Bas i n - Pa r t I 11Before going to an iterative process for least square fitting of the Bouguer gravity

anomaly (Gb ) , prior knowledge of the approximate depths of each strip is essential.The approximate depths are calculated from the Bouguer slab equation g = 2 Ir G ~ hwhere h is the thickness of the slab.In the present case, the first approximate depths r/~j are calculated by

r l ~ j G b J= j = 1 , 2 , 3 . . . . . 2 n . ( 1 7 )The second and other higher approximate depths are calculated exactly with the

same method as adopted by BOTT [1].6 . A p p l i c a t i o n

In a sedimentary basin, the condition of deposition of sediments under earth'sgravity action gives rise to a density gradient in the vertically downward direction.Also, one may assume a suitable density contrast from the centre of the basin towardsits edges to account for the effect of the surrounding mass on the gravity profile.

We have estimated the shape of the Godavari Basin (India), on the basis ofBouguer anomaly map (QURESHVe t a l . [5]) along a profile C C' north of Nagpur(Latitude 21~ ' N, longitude 79~ ` E). The values of g(~i) have been calculated bymeans of a computer program developed for use on IBM 1620, using equations (10)to (17). The figure 2 shows the various shapes of the basin obtained by assuming thedensity function to be

~. - I C

- 2 s

E I 4 C

Z - 5 C0 - -- 6 s K I L O M E T E R S

2 0 4 0 6 0N o s i z 3 4 5 6 7

8 O,? I 0 0 1 2 0 g 4 0I z I 3 1 4 1 5 1 6 I I ~ ~ a' ~ . L . ~ _ ~ . L 9 I c '~ . =- s ~ ' " ! E ~ ,

. . . . . 23

V E R T I C A L S C A L E E X A G G E R A T E D

F i g u r e 2S t r u c t u r a l co n f i g u r a t i o n b e l o w a p r o f i l e a c r o s s G o d av a r i V a l l ey ( I n d i a ) o b t a i n ed b y a s s u mi n g :1 ) co n s t an t d en s i t y co n t r a s t ( - - 0 . 4 g i n / c r u Z ) ( - . -) ; 2 ) l a t e r a l d en s i t y v a r i a t i o n ( - - ) ; 3 ) v e r t i c a l an dl a t e r a l d e n si t y v a r i a t i o n ( - - ) . M a x i m u m a n d m i n i m u m d e n s it y c o n t ra s t s a r e - - 0 . 4 g m / c m 3 a n d- - 0 . 3 g m / cm ~ r e s p ec t iv e l y


8/8

12 B .N .P . Aga rwa la ) c o n s t a n t ( d e n si ty c o n t r a s t - 0 . 4 g m / c m 3)b ) o f l a t e r a l v a r i a t i o n ( m a x i m u m a n d m i n i m u m d e n s it y c o n t r as t - 0 . 4 g m / c m 3

a n d - 0 . 3 g m / c m 3 r e s p e c ti v e l y .c ) o f l a t e ra l a n d v e r t i ca l v a r i a t i o n .

7. ConclusionT h e p r e s e n t m e t h o d p r o v i d e s a m o r e a c c u r a t e i n t e r p r e ta t i o n o f g r a v i t y a n o m a l y

o v e r s e d i m e n t a r y b a s i n b y a s s u m i n g t h e c o n t i n u o u s v a r i a t i o n o f d e n s i t y i n l a te r a l a sw e l l a s i n v e r t i c a l d i r e c t i o n .

8. AcknowledgementsA u t h o r i s g r a t e f u l t o M r . T AR KE SH W AR L A L f o r h i s c o n t i n u e d i n t e r e st a n d e n -

c o u r a g e m e n t t h r o u g h o u t t h e w o r k . A u t h o r i s a ls o t h a n k f u l t o D i re c t o r, R e g i o n a lR e s e a r c h L a b o r a t o r y , H y d e r a b a d f o r p r o v id i n g c o m p u t i n g f ac il i ti es . P a r t o f t h e w o r kw a s d o n e w h il e a u t h o r w a s J u n i o r R e s e a r c h F e l l o w ( C . S . I .R . ) a t N a t i o n a l G e o -p h y s i c a l R e s e a r c h I n s t it u t e , H y d e r a b a d .

REFERENCES[1] M. H. P. BOTT,The use o f rapid digital computing methods for direct gravity interpretation ofsedimentary basins, Geophys. J . Roy. Astron. Soc. 3 (1960), 63.[2] C. A. HEILAND,Geophysical Exploration (Prentice Hall Inc., New York 1946), 151.[3] N. A. MORGANand F. S. GRANT, High speed calculation of gravity and magnetic profiles acrosstwo dimensional bodies having an arbitrary cross-section, Geophys . Prosp . 11 (1963), 10.[4] D. B. MoRms and R. A. SULTZSACH, Gravity data reduction and interpretation using a digitalcomputer, a case history, Mining Geophysics 2 (1967), 630.[5] M. N. QURESHY,N . KRISHNABRAHMAN,S. C. GARDE and B. K. MATHUR,Gravity anomalies andGodavari Rift, India, Bull. Geol. Soc. Am. 79 (1968), 1221.[6] A. RoY, Ambiguity in Geophysical interpretation, Geophysics 27 (1962), 90.[7] D. C. SKEELS,Ambiguity in gravity interpretation, Geophysics 12 (1947), 43.[8] M . TALW ANI, J. LAMARWORZEL, an d MA RK LANDISMAN,Rapid gravity computations for two

dimensional bodies with application to the Mendocino submarine fracture zone, J . Geophys . Res .64 (1959), 49.[9] J. G. TANNER, An automated method of gravity interpretation, Geophys . J . Roy. Astron. Soc .13 (1967), 339.(Received 2nd July 1970)

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Direct gravity interpretation of sedimentary basin using digital computer — Part I- art%3A10.1007%2FBF00875068