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* : Z 5 1)3D7' ]Z[ s F3H 2l[]$ s' )3'#B;)9' 2 ;Z['(*)3Z 6"D3)3)3d1q>9y;

1>w-8:>H%Id1'#)9# 1>+ypd1>w;FD9)3$ @1)3'(XZ#$[ 5 @ *FD3)98]d1)9 2 :a D9)32

FL # ' [ B, *# >

-R)9 p'#B X)9D3D9'# (@) $ 2 )9#* D3 @B;1$ D9D3 'I $hZ M# D3cc)3K )CD

F3H ":*)+ B, $)9B * ) > ]A@ c$ p* :*)3'#2 p #)3 l)R2 )9 D w;FH 01#* 'U )3D

]pB,q$ D3D9 8 F3H 2* D3)92 FL #(*' *B, A5q"!D9 'J '# $01 '#BE'#24)3' '# (8)

^[ 1q>9y>

T FH D3D^1>9yX 1>w_1)9' =[*AB; :* ( $)9 @"=H# 01D3DHB;A*#)324'='#BEFD9)3eFH 01(b

* :) )9D3D9'# *' M# X) $ #* a2AA)9#* D9 5[]G)3242A l 8 I)9 >T FH D3D%1>21q)9'

L B, )9 )H$ L#!' @FL #(* K>NP B, )3 Y)K$ QZ[

)3$ D9)3' #7"#B5lD3D9 kH )LB;1$ D9D3 )3 = =FDCA 6"^ 1q>w-8 1)3'#'=)3242A @qb

:R D901'#>g%K*)9D3D3 k VL :*#01242 :7wxnCPRq5g B,H *A 0-. r\IL !'#)9 *

w-. []G)3242A _A )3q" B;'"M# k)+ >

% !"'1

T )3)3 _1>+yU/1>wp1)9' IAk #*Z :* Q*)9D?B;A* )CAD3 =' B FH!D3 F G'# ,)3M# qb

B Z[A='# JFL &01$)9l" FH!D3 Z['# )3Z * ?>1<=D924 #*Z :* Y"= H#!'=FL #(

G)+ J $ L

F

% 6 1q>2;8

(17)

p s

κ , µ , ρ **^{* *}** ^*

Effektive bergartsparametre Teoretiske modeller

Seismiske hastigheter

c ^

Input parametre

^ f

^

V V ^,

α, [α], φ, κ , µ , ρ , κ , ρ _m _m _m _f

-R)9 1>+y#!,!6 ,M ! 8*I>:EI/.0!#!C>EE "! 6 'E( "2!$!

' ! @ ! $ C "2!$!'% !B! , 8I) !!,'!= 6E B",$

>EE "! !;$ #$M% 1!, "! $! ) 2 3> ! ! !# ) :!

!, "! $! !-)+! 2 !+ "#!$! ,!P% ! ! L

+!, "! $! )+ # !#!

%

c b a

b = c > a

-R)9 1q>w EWXFDCAGL B; :* )P> X ,D9 '#* a24'# a) H Q ID9)32A XDC >

(18)

1.0078*

2.7636*

0.6710*

0.6005*

Olje Gass

Inkompressibilitet (GPa) Tetthet (g/cm ) 3 Fluid

Trykk (MPa)

0.8596 10 20

0.6752

0.6675 0.6837

0.7551 0.6674

0.0014

1 35

1 10 20 35

Saltvann (3%)

0.0692

1.0040

0.2908

0.0142 0.1962

2.4952 2.5612 2.6339 0.9958 0.9997

0.0114 0.1515 0.3639

T FH D3D 1>+y B$ !,! 'E !6 )")+! 2 !"J> ,8! "2!$! ,!P% !B$!

!5) !!,'!5 !C7,'E "! 5EC, E $G/% 1EE "!! !B$!

"! !5!N,' N8O #E ,!F)! ! !B$! 8 E EG(,,$B, '%

nA )324' A6 = P 8 6 = P 8 96t '"B

8

)eA(*'kW 1-O>wXQ ;.q>V0qy wq>2O.

)7A# 'G< w-.q>xx ;x>xx wq>2O.

n1$ D9D y 1x>xx wx>xx wq>2Ox

T FH D3D71>w 7> EE "!! !B$!" )I 2 !I "#!$! ,! !L,! >:E

2 EB !B$! ! ,' %

P # '#H 24#" ZD3$?50 y>x x>+y xq>xy x>xxy

P7#' O$ D 5 :x 0 w1>. x>V.

T FL D9D$1>21?> 1 !2 89$!,6E!$! 5 ,M * =! E$ +*' !!P%

(19)

∆ P

P

∆ V V

V 2

P

1 1

P ₁

1

1 P 2

"!"#%$'&()* +",-/.1023546#+!87:9;+&!=<6!">"?'9;!"

!""9;?:?'!A@(?'CBEDF?'&()HGI"J!!H/.10KK.L?NM"&(K<I$# +"'K+!9:!"O!""9:?;?'!

PRQHS#TU&(V+WX<6!"$'Y$'&()* +"'ZPRQ[KT\=&()]&(GG "!=46A546A!""9;?:?'! +IC268^B`_B

ab Vc b ed\fhg;ihj b j b6k jLlm b hn;=j bEkAop qKb rj b jhjhs b j b6k jhLld\f bEtRu lLlb jvf pwxb vj b jhjhs b j b6k

jlAy;f; kbEkb z{n:jhhy5i b6k pw|b }lLXjflfLn~5s bEk

b j b

Of;j-

b bet

fihgy*d3W8

kkbb

j b

zZdLhihy

t

f;hsfl a z b

llLfzz bEa

Lz

b

jhi bb

yj~

b

j b jhjhs b jf"s3n:ijs b j(3hIs=; t f b ilLf b j b zdhLiy tf;hsfl a LIsAilf~U

p VI' ¢¡£

¤¥

F ¦¨§

b jhj b©b b6k hf~ªjl k3« zZk o flL k k bEkªb fz¬j b6k jZmhy b lL tfz{n:j b Nn;lb

ihf;z ihn;ljZfªn k s

u5a

jj(V

b j b

{i bEkb

b

f;j

t

fhigyd®¯

kkb¢b6k

z b k g u n;yj

tfsfl a ihm b ihy ~ b lLi b n(~°sn;ijhLs b j8f±j b jhjs b j o z b6a jhn k id k yjhIsAi8lLf~\

²L k k

³~5i

b

en:j´d\fhgij b j o

dUf bEtRu

lLl

o z b j k k

in

a

flLXjflf5d3(~5Lhy

b

´mly j

b

j=

j

bEkµt

f;

b6k

m b

hn;=j(3

b

hz b6a

~5LlAf;i¶s3n;i=jL;s b j

b6k

d3(~5Lhy

b

iE

· b jhjhs b j b6k n~ jn;8z bEa g;y b6kab d\fhg;ihj b j o z b6k lLy j tf tfhiy6 b lLlL±d\f btRu lLl¸Of bEtRu lLl

z

b6a

lNn(~{j

b

jjs b j

o3t

g

b

Vjln:j8mlyj

b

jj bEk

n(~ jIn;

t

f;j b b z

b6a

dUf;hgij b j

bEk

·- u y y b jy¹n k d3(~¦hy b d\fgihXj b j o d\f b 3a f ab hz b6a j b jhjhs b j b6k b6k m b hn;=j(º Ub yj b

n(~,j u y5y a Lihy j b b iAy¹n;djj b lA³

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Ó k y:fzZd b iihmLlj b j bEk{Ô jl b j´zZn:j b hNn:lb;o:b tfsfl ab jrz b llLfzÕj u y y:gy k k b6k f; ab6k

b ihlXj b b6kab b lLn:jX~ b ~f;lLz b6ka hk b6k R3

Ô{×ÖZØvÙ

Ö

ØOÚ

Û

¡¸Ü ÛÝ

Û ¡

×ÖZÞ¶Ø

ß Û

Û ¡

pÞ¶Ø

Þ p

F ¦à

(20)

P

ψ

s

-R)9K1><; 1,'!"2$! F/8 6 >:E 2#) >: 89* % #MF 89!!" 6E

E$!FEL #2 82 L" #2! )N>: 89* -,I2!$! :E

89*,I /89 6!P3>,',B%2%

: A )9 "(* m)kD9)3)3 f2B,B, m AmD3B, mB,)3'#2 ,]p*(0q242A

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GD9 G2AB, )9B; F[5mZ[Ak$ #B; $D3d ?>

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OA ' )CAD9*(01212A 5 # # 6 1q>0-8

B, $ 2AA '#2M zJ B,q$D3 #*#01242 ''#B "#ZD9$ QB, D9D3B ' 2M zJ#' L )9

' 2M zJ#$ "#B A'"M##6"^[ 1><;8 #

W q'(O$ ' B ' 2M zJ FL!D3 2 )3) AzJ' 2 S #L 'M#[DIB; $

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' 242 :XFL #I2 )V 2 D9 _*)9D9" D3D3 ='#2M zJ#FH!D3 IF a' ;)3M# B L SR[)3$ 5

[];' # 242 ` &01 S $ 1'#*$ FL!D9 o2AA * )9 )IzJ'#2 ?5

h 8 6(y@:-:x8 > Nq2M zJ FL!D3 'R ' 2 l )3D1]I )9l)1 _zJ'#2 J "# 2 qb

'*1Z )3>

%G*A21'#)3'X @B;A*'#*$ cB;' 2M zJ $ "#B 'M#S) A' '@YAzJ'#2 U' ]YDC f2

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' UD9)3)91>wq>

(21)

8

κ

µ

∗

Elastiske moduler (GPa)

Gassmetning (%)

m

* κ*

µ

V

G V G

Elastiske moduler (GPa)

Leirinnhold (%)

# ¨§5A<}<(")*!"' }3?:!G54Ã+KX<(!">"?'G5<6=<6)*!" BV46V¹<("7 &(>+!V

,$(<6)*!"!!}J"¹<6"!}@(?'C2$:

<C$:!=<Ã)9'K.R&("!W

BJV!)*&(!<6!"!He!"¨.R>

546v>}:!"&:+ =Iv ¶7 !r<6 +"! B

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b b6k iy:n:d b 6 b j b f b jhLihy b zZf ab lLl bEkb ifz mlb¬a Lihy j b =j*y¹n;dXjhj b l{y¹n k m b6ku jhj b i

tf}¬ kkbHab ( b6kk fzZi k jjlL b8b llb bEUb yjh~ b*b lNn;i=jLiy bWb b6k ihy¹n;d b6kb jlm b n;j b6k

n;yjf

b

Yifz

a

L

b

yj

b

y¹n

k

d3(~5Ly

b}abEk¶bEUb

yjX~

b k

y:fzd

b

ihihmLlj b j

bEk

fKihy6

«

hzf a

lb6k jhLl b6k m b hn:j b sf'~ b6a ihn;y b lLWdUf;hgij b j o d\f btRu ll o d\f b b fz b j o z b j k k in a

fµl b Lhkk sf;la UL; bEkb ¨§°f© µlLlLij b b Ws~f; a n kab jj b ~¦lY~5Lhy b kk d3 ab

b

lLn;ijhLiy

b

zf

a

l bEkb

Ozf ab

lLl b6k

ihfz m b6ku

jhj

b

i6OL à§{n}~5Li

b

Wn:j~

bEa

k jf

a

y

i1f k n~¬m3n; bt Wdhf;i b6k jvn:ihir bEk ~:n kk z b jj b jYm b hn;=j o ~¦l abEk¶bEUb yjX~ b k y;fzd b ihi

LmLlLXj b j b6k n~ jn a n;i=jLiy m b n;j b6k b6kbEUb yjX~ b ihy6 « hzf a lbEk d~5hy b ied*lLn k ;j

k3« Vih z ub n~Zn;iiVm b n;=j b6k Ór3em b bEUb yj bEk n~Zgyj}l b Lkk sfla Uz{n:jhhy5i

ijhgh bHtf ab6kµbEUb yjh~ b ihy6 « zZf a lb6k%b6kkµabEkbEUb yjh~ b k y;fzd b ihiLmlLXj b j b6k

ÓK3;¬ ¦àµnW;n;id b y j t fhsflab j°R3¦ t n%dUf; b *z b6a ¥ jlri t « Lihy b

d\f

b

Hz

bEa ¥

A

b

b¶ab±bb

y jh~

bb

lNn;i=jihy

b

zf

a

l bEkb

gy

b

*y n

t

jhL

k

;Hy;f k

i bEk jn:i1f kbEk n(~©i t « hihy b dUf b gy b 6 b6kab6k bb y jh~ b k y;fzd b ihiLmlLj b j b6k gy b

z b ij6L°m {~¦i b ©s~f; a n k s3n;ijhLs b j bEk n(~ jIn; tf%gy b6kab dUf;hgij b j%f lLy j

d\f btRu

ll¸vf;ji

b

jj

t

n¯z bEa

~:n kk

ifz dUf;

bEtRu

ll

o

n(~5jn;,/s3n;ijhLs b j

bEk

z b

b6kk

s3n;i=js b j b6kµk ;}d\fhg;ihj b j b6k gy b 6

Wab b ab jj b y¹n;djhj b lb jihy¹n;l ab j tfy i b b iKd3{s~f a n k¢t n;yjhf bEkb ihf;zÌ~5hy b Wkk

d3

p o\Ô

f; s3n:}

kk

~5Ly k k

±d3

ab

i b LizZihy

b

s3n:ijs b j

b6kb

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Ä"! #%$ÇAËÈEÍ#°ÆVËV¼

& u llLbKb j}n;l¸A=§:´k jhhf a i b j b ~ bEa jha i bEkk fzi k jhjhihlL k k bEk s3n:ijs b j b6k b6k

d\fhgi}m b n;=j8ihfz t k y i1f k n~,dUfgihXj b j o d\f bEtRu lLlAf;zZn:jhhLy iE

(22)

)U)+ * D$1 N1 )3'#B;)9' 2A XZ['# )3Z * k,FH (*'#[*AB; :*

8

µ ∗ κ ∗

Konsentrasjon av sfæriske porer (%)

Elastiske moduler (GPa)

0 25 50 75 100

^F8

20

15 25 25

20 10 κ∗

µ

10 ∗ 15

(%) O G V, O

G

Porøsitet

Elastiske moduler (GPa)

V

-R)9 1>VO G& ! $ "2B$!5 8OB ;;*!5 8F $!%#)HG 1*' ! ,

+/82$2 2,">: ! $ "#B$! "! , $!%

L

% 6 1q>VQ8

$ G$ F3H 2*)+ PRb&Z['(*)9Z Q) FL # ?5 PRb Z['# )3Z * )KB A )921'

Z[A'#*)9Z :* o)GH# 01D3D9 >]T )9)9 1)3'# Y L !' )9 ?57L SR[)3$K5j

B;A*#)324' '#2 H RqM#!# $ J"RZ['(*)9Z l )3D1FH!D3 p' B F# '# X)3M# B

B, $)9B; :>

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* )3 B ]AD3)3

L

% 6 1q>V:8

L

6 1>+ydx8

T )3)3C1>V: M# D9$ _"l2A' D3)3$ # YFL # 5RB; '1>+ydx M# D3$ _"p2' D9)3$qb

(* Z[1F' $)3B, * > v Z)9 6(yG:X:.-8U1)9'#* Q D3)9)3C1>2: )9lB, )9'(b

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L !'#)9 5qB; $Q[*AB; :* ( $)9 k' B )9 J)KOFL D9D3 _1>wp/1>V1q>[ I2AB;B,

(23)

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Effekter av trykk på seismiske hastigheter - modellerte og observerte sammenhenger

2.

3.

1.

4.

C A

B

C

D

A

B C

D

A

B

, µ f k

k*

, µ k m , µ m

k m m

f , µ∗

α = b a b

a

* µ *

k , k , * *

µ

µ∗= L k*=kL, µ *

µ L=

kL=k*, µ2= µ m

k1=km, µ2

µ

k2,

p s

κ , µ , ρ * * *

Effektive bergartsparametre Teoretiske modeller

Seismiske hastigheter

c ^

Input parametre

^ f

^

V V ,

α, [α], φ, κ , µ , ρ , κ , ρ m m m f

c b a

b = c > a

1.0078*

2.7636*

0.6710*

0.6005*

Olje Gass

Inkompressibilitet (GPa) Tetthet (g/cm ) 3 Fluid

Trykk (MPa)

0.8596 10 20

0.6752

0.6675 0.6837

0.7551 0.6674

0.0014

1 35

1 10 20 35

Saltvann (3%)

0.0692

1.0040

0.2908

0.0142 0.1962

2.4952 2.5612 2.6339 0.9958 0.9997

0.0114 0.1515 0.3639

∆ P

P

P

∆ V V

V 2

P

1 1

P 1

1

1

P 2

P

ψ

s

κ

µ

∗

µ∗= L k=kL, µ

κ , µ , ρ **^{* *}** ^*

V V ^,

α, [α], φ, κ , µ , ρ , κ , ρ _m _m _m _f

P ₁