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8/9/2019 AGSC PowerPoint Oral Presentation
1/22
APPLICATION OF MATLAB IN SEISMICINTERFEROMETRY FOR ACCURATE IMAGING
OF RESERVOIRS USING MIGRATIONMETHODS.
BY: ISAAC KUMA YEBOAH.
Department of Engineering,
Regent Universit Co!!ege ofS"ien"e an# $e"%no!og.
isaa"&e'oa%(()a%oo."o.*&
mailto:isaackyeboah77@yahoo.co.ukmailto:isaackyeboah77@yahoo.co.uk
8/9/2019 AGSC PowerPoint Oral Presentation
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Content.
1. Motivations.
2. Mt!o"o#o$%.
3.3. Super-Resolution and Super-Stacking.Super-Resolution and Super-Stacking.
4. Local Matching Filter.
5. Prestack Modeling.
&. Si'(#ation Rs(#ts in MATLAB o)
Di*+a,tion Sta,- Mi$+ation.
7. Conclusion.
8/9/2019 AGSC PowerPoint Oral Presentation
3/22
Motivations
Problem: Receiverinterval of OBS data is(sometimes) too large
Solution: Interferometricinterpolation
Water
Water
Benets of Interferometric Benets of Interferometric Interpolation: Interpolation:
• Accuracy (ave!e"uation based Accuracy (ave!e"uation based
sc#eme)sc#eme)•
8/9/2019 AGSC PowerPoint Oral Presentation
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Mt!o"o#o$%
Applying t#e far!eld appro%imation Applying t#e far!eld appro%imation
xd n
GG
n
GGGG
xS x
2000
*)()(
)(*)()*()(
∂
∂−
∂
∂=− ∫
B|xx|A
x|AB|xB|AB|A
*)(*)()(2)( 02
0 B|AB|xx|AB|A G xd GGik GS
+= ∫
OBSOBS OBSOBS S&P S&P OBSOBS
'!state reciprocity e"uation of t#e '!state reciprocity e"uation of t#ecorrelation typecorrelation type
(ong and Sc#uster '*+ Ram,re- et(ong and Sc#uster '*+ Ram,re- etal./ '*)al./ '*)
Interferometry Interferometry artifacts (spuriousartifacts (spuriousmultiples):multiples):
0ocal matc#in lter 0ocal matc#in lter
8/9/2019 AGSC PowerPoint Oral Presentation
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uper! eso u on an uper!uper! eso u on an uper!Stac1ingStac1ing
Super!stac1ingSuper!stac1ing NM vsvs.. N
Super!resolutionSuper!resolution
8/9/2019 AGSC PowerPoint Oral Presentation
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8/9/2019 AGSC PowerPoint Oral Presentation
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G(x|G(x| x’ x’ ) = ) =
x x x’ x’
eei|x!i|x!
x’ x’
|"#|"#
$%ase $%ase|x!|x! x’ x’ || Ge&m.Ge&m.
Sprea Sprea
G*’s +,*-TI* G*’s +,*-TI*
|x!|x! x’ x’ ||
8/9/2019 AGSC PowerPoint Oral Presentation
8/22
Prestack MigrationPrestack Migration
Mi$+ation is t! #ast 'a/o+ 0+o,ss t!at isa00#i" to sis'i, "ata )o+ it is int+0+t".
T!is is #i-#% to #a'" )o+ a## so+t o) t!in$s#i- in,onsistnt a'0#it("s an" #a,- o)
st+(,t(+a# "tai#s vn t!o($! t!s 0+o#'s'a% a+is )+o' a,(isition o+ a+#i+0+o,ssin$ st0s.
Mi$+ation ,an ,#assi3" as P+sta,-
'i$+ation o+ Poststa,- 'i$+ation. Mi$a+tion is 0+)o+'" on 0+sta,-" "ata
it!+ on s!ot $at!+s o+ CMP "ata.
8/9/2019 AGSC PowerPoint Oral Presentation
9/22
$resta#k /&'elin $resta#k /&'elin D(+in$ t! a,(isition4 t! sa' s(s(+)a, 0oint
'a% !it sv+a# ti' % 'itt" 5avs4 5 5i##t!+)o+ !av '(#ti0# in)o+'ation )+o' t! sa'0oint.
In ,#assi, 0oststa,- 0+o,ssin$4 t! 'o"# is ass('"
to a st o) 6at4 !o+i7onta# an" !o'o$no(s#a%+s !n, !%0+o#i, 'ovo(t ,(+vs )o+ sta,-in$.
P+sta,- ti' 'i$+ation is n,ssa+% 5!n t!$o#o$i,a# st+(,t(+s 0+snt ,on6i,tin$ "i0s4
+s(#tin$ in ,on6i,tin$ sta,-in$ v#o,itis. P+)o+'in$ 'i$+ation "i+,t#% in "0t! an" )+o' t!
0+sta,- "ata is t!+)o+ n,ssa+% in ,as o)va+io(s "i0s an" #at+a# v#o,it% va+iations.
8/9/2019 AGSC PowerPoint Oral Presentation
10/220 m 30 m0 m 30 m
0 km0 km
30 m30 m
#&rner #&rner
8/9/2019 AGSC PowerPoint Oral Presentation
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1&rn /&'elin 1&rn /&'elin
x x x’’ x’’
S#atterer S#atterer x’ x’
m&'el m&'el 'ata'ata ∫ /&'el /&'el
Spa#e Spa#e
'(x)'(x) == (x| (x| x’ x’ )( )( x’ x’ |x’’)|x’’) &(x’)'x’ &(x’)'x’ 2( 2( ω ) )
8/9/2019 AGSC PowerPoint Oral Presentation
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'(x’’|(x’’| x x )= )=
S#atterer S#atterer
τ x x x’ x’
ee
!i !i
(x (x x’ x’ ) )
τ x’ x’ x’’ x’’
ee!i !i
(x’’ (x’’ x’ x’ ) )&(x’)&(x’)
x x
x’ x’
x’’ x’’
∑ x’ x’ ω
66
1&rn /&'elin 1&rn /&'elin
(7! 8# " #09 )(7! 8# " #09 )!6#!6#
!6!6 66
2( 2( ω
) )
8/9/2019 AGSC PowerPoint Oral Presentation
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Time!D&mainTime!D&main
Di::ra#ti&n Sta#k /&'elin Di::ra#ti&n Sta#k /&'elin
2( 2( ω
) )
(x (x x’ x’ ) )
τ x x x’ x’ i i ee
∑
x’ x’
τ x’ x’ x’’ x’’ i i
ee (x’’ (x’’ x’ x’ ) )
'(x) ='(x) = &(x’)&(x’) ∫ ' ' ω
i i ω
t t ee' '
ω
i i ω
t t ee∫
!! !!
( t!( t!τ
!!τ
) ) x x
x’ x’
x’ x’
x’’ x’’
(x (x x’ x’ ) )
∑
x’ x’ (x’’ (x’’ x’ x’ ) )
&(x’)&(x’)== .. ..
8/9/2019 AGSC PowerPoint Oral Presentation
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(x;)(x;)
66 66
8/9/2019 AGSC PowerPoint Oral Presentation
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(x;)(x;)
(x 0)(x 0)ss
1&rn /&'elin 1&rn /&'elin
(x 0)(x 0)
( t!( t!τ
!!τ
) ) x x x’ x’ x’ x’ x’’ x’’
(x (x x’ x’ ) )
∑
x’ x’ (x’’ (x’’ x’ x’ ) )
&(x’)&(x’)=='(x)'(x) == .. ..
-an#elati&n-an#elati&n
8/9/2019 AGSC PowerPoint Oral Presentation
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8/9/2019 AGSC PowerPoint Oral Presentation
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1&rn ppr&ximati&n 1&rn ppr&ximati&n
∫ /&'el /&'el Spa#e Spa#e
'(x)'(x) == G(x|G(x| x’ x’ )G( )G( x’ x’ |x’’)|x’’) &(x’)'x’ &(x’)'x’
e:le#tiit> e:le#tiit>'ata'ata
2( 2( ω
) )
2aelet 2aelet
Spe#trum Spe#trum
$r&paates S#attere' $r&paates S#attere'
ner> :r&m S#att. at ner> :r&m S#att. at
x’ x’ t& e#eier att& e#eier at x x
$r&paates ner> :r&m $r&paates ner> :r&m
Sr# at Sr# at x’’ x’’ t& S#atterer att& S#atterer at x’ x’
8/9/2019 AGSC PowerPoint Oral Presentation
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8/9/2019 AGSC PowerPoint Oral Presentation
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Si'(#ation Rs(#ts in MATLAB o)Di*+a,tion Sta,- Mi$+ation.
S,//B
8/9/2019 AGSC PowerPoint Oral Presentation
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S,//B S,//B
7. xpl&'in e:le#t&r /&'elin = Di::ra#ti&n Sta#k /&'elin 7. xpl&'in e:le#t&r /&'elin = Di::ra#ti&n Sta#k /&'elin
(x (x x’ x’ ) )
(x’) (x’)
re:le#tiit>re:le#tiit>
Ge&m.Ge&m.sprea'in sprea'in
S&ur#e aelet S&ur#e aelet
Sum &er Sum &er
re:le#t&rsre:le#t&rs
6. Ci% +reuen#> ppr&ximati&n (i.e #(x) ariati&ns E 3? 6. Ci% +reuen#> ppr&ximati&n (i.e #(x) ariati&ns E 3?
) )
3. ppr&ximates Finemati#s &: Data @ut n&t D>nami#s3. ppr&ximates Finemati#s &: Data @ut n&t D>nami#s
((τ
8/9/2019 AGSC PowerPoint Oral Presentation
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Conclusion. MATLAB )o+ t,!ni,a# ,o'0(tin$ a00#i" to
sis'i, int+)+o't+i, % (sin$ G+n8s )(n,tion#a"in$ to s(0+ +so#(tion o) t! i'a$.
A 'a/o+ n3t o) sis'i, int+)+o't+i, is t!atso(+, +,iv+ a++a%4 a)t+ int+)+o't+i,
+"at('in$ ,o's ,#os+ to t! i'a$in$ ta+$t.
T!is 'ans t!at t! "isto+tin$ *,ts o) t!(nint+stin$ 0a+t o) t! '"i(' a+ avoi""
#a"in$ to tt+ i'a$ +so#(tion o) t! ta+$t. T!is $ivs a v+% ,#a+ i'a$ 5!i,! ,an s!o5 t!)o+'ation o) t! a+t! an" 0ossi# !%"+o,a+on"0osit" in t!at 0a+t o) t! s(s(+)a,.
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