Reduced-Time Reduced-Time Migration of Migration of Converted Converted Waves Waves David Sheley David Sheley University of University of Utah Utah
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Reduced-Time Reduced-Time Migration of Migration of
Converted WavesConverted Waves
David SheleyDavid SheleyUniversity of UtahUniversity of Utah
OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data Results Synthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work
PP vs PS Transmission MigrationPP vs PS Transmission MigrationD
epth
Dep
th
OffsetOffset
00
ZZ
Rec
eive
r W
ell
Sou
rce
Wel
l
XX00
PP Reflection MigrationPP Reflection Migration
XX
Sou
rce
Wel
l
Rec
eive
r W
ell
PP
P = ?P = ?
PP
=?=?
00
Dep
thD
epth
ZZ00 OffsetOffset
Rec
eive
r W
ell
Converted Wave MigrationConverted Wave MigrationS
ourc
e W
ell
XX
PP
PP PSPS
PSPS
VVpp,V,Vss = ? = ?
=?=?
00
Dep
thD
epth
ZZ00 OffsetOffset
OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data Results Synthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work
Conventional MigrationConventional Migration
m(r) = S(zm(r) = S(zgg, , sr sr ++ rgrg))
srsr rgrgss
rr
gg
PS Transmission MigrationPS Transmission Migration
m(r) = S(zm(r) = S(zgg, d, dsrsr/V/Vp p ++ ddrgrg/V/Vss))
ddsrsr/V/Vpp ddrgrg/V/Vssss gg
rr
km/seckm/sec
6.06.0
5.05.0
7.07.0
ProblemProblem
WellWell
00
2020
4040
6060
505000
ReceiverReceiverWellWell
SourceSource
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
Reduced-Time MigrationReduced-Time Migration• Data time shiftData time shift
S’(g, t) = S(zS’(g, t) = S(zgg, t + , t + sg sg sgsgObserved direct-P timeObserved direct-P time
obsobs
obsobs
Dep
th (
m)
Dep
th (
m)
00
1141142020 3535Time (ms)Time (ms)
Original DataOriginal Data
Dep
th (
m)
Dep
th (
m)
00
1141148822 Time (s)Time (s)
Shifted Muted DataShifted Muted Data
SPSPPSPS
PP
PSPS SS
SPSP
Data ShiftData Shift
Reduced-Time MigrationReduced-Time Migration• Data time shiftData time shift
S’(zS’(zgg, t) = S(z, t) = S(zgg, t + , t + sg sg
sgsgObserved direct-P timeObserved direct-P time
obsobs
obsobs
• Modify the migration equationModify the migration equation
m(r) = S(zm(r) = S(zgg, , sr sr ++ rg rg - - sg sg ++ sg sg ))obsobscalccalc
calccalcm(r) = S’(zm(r) = S’(zgg, , sr sr ++ rg rg –– sg sg ))
OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data Results Synthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work
Error Analysis -- CWMError Analysis -- CWM
• Single traceSingle trace• Homogeneous mediaHomogeneous media• True velocity = True velocity = cc
• Migration velocityMigration velocity
c’ = c + c’ = c + cc• VVpp/V/Vss = = psrpsr
Assumptions:Assumptions:
m(r) = S(zm(r) = S(zgg, , sr sr ++ rg rg psrpsr))
m(r) = S(zm(r) = S(zgg, (d, (dsr sr ++ ddrg rg psrpsr)/)/c’c’ ))
Error Analysis Error Analysis Conventional MigrationConventional Migration
(d(dsr sr ++ ddrg rg psrpsr)/)/c’c’ (d(dsr sr ++ ddrg rg psrpsr)/()/(c + c + c)c)==
~~ (d(dsr sr ++ ddrg rg psrpsr)()(s – s s – s c)c)22~~
(d(dsr sr ++ ddrg rg psrpsr) ) s s cc
22
cmcm
m(r) = S(g,m(r) = S(g,
Error Analysis Error Analysis Reduced-Time MigrationReduced-Time Migration
))obsobscalccalcsr sr ++ rg rg - - sg sg ++ sgsg
Error Analysis Error Analysis Reduced-Time MigrationReduced-Time Migration
obsobscalccalcsr sr ++ rg rg - - sg sg ++ sgsg
==(d(dsr sr ++ ddrg rg psr psr -- ddsgsg)()(s s –– s s c) + c) + ddsg sg ss
22
(d(dsr sr ++ ddrg rg psr psr -- ddsgsg) ) s s cc
rtmrtm22
Error FunctionsError FunctionsCWM vs. RTM CWM vs. RTM
rtmrtm(d(dsr sr ++ ddrg rg psr psr -- ddsgsg) ) s s cc
22
cmcm(d(dsr sr ++ ddrg rg psrpsr) ) s s cc
22
rtmrtm
cmcm
00
0000
00250250
250250
500500
500500
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
00
1212
88
44
1616
Imaging-Time ErrorImaging-Time Error
ImagingImaging ErrorError (ms)(ms)
OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data ResultsSynthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work
Crosswell ModelCrosswell Model
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m) 11411400114114
00
VV22
VV11
V = 5500 m/sV = 5500 m/s22
V = 5000 m/sV = 5000 m/s11
VVpp /V /Vss = 1.5 = 1.5
Well Separation Well Separation = 100 m= 100 m
Source = 1500 HzSource = 1500 Hzds = 2 mds = 2 mdg = 2 mdg = 2 m
Synthetic DataSynthetic DataD
epth
(m
)D
epth
(m
)
00
1141142020 3535Time (ms)Time (ms)
Original DataOriginal Data
Dep
th (
m)
Dep
th (
m)
00
1141148822 Time (s)Time (s)
Shifted Muted DataShifted Muted Data
SPSPPSPS
PP
PSPS SS
SPSP
PS Transmission Migration PS Transmission Migration True VelocityTrue Velocity
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)00114114
00
114114
Conventional PS MigrationConventional PS Migration+ 10 % Velocity+ 10 % Velocity
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)00114114
00
114114
Reduced-Time PS MigrationReduced-Time PS Migration+ 10% Velocity+ 10% Velocity
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)00114114
00
114114
OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data ResultsSynthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work
• Time Delay = 3 ms ?Time Delay = 3 ms ?
• Well locationWell location
• Velocity ModelVelocity Model
Data ProblemsData Problems
km/seckm/sec
6.06.0
5.05.0
7.07.0
Kidd CreekKidd Creek
WellWell
00
2020
4040
6060
505000
ReceiverReceiverWellWell
SourceSource
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
66Time (ms)Time (ms)
00
2020
4040
6060
Dep
th (
m)
Dep
th (
m)
00
Time Shifted CRGTime Shifted CRG
Conventional PS MigrationConventional PS Migration00
2020
4040
6060
505000
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
Reduced-Time PS MigrationReduced-Time PS Migration00
2020
4040
6060
505000
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
RTM-PS CRG #8RTM-PS CRG #800
2020
4040
6060
505000
Dep
th (
m)
Dep
th (
m)
Offset (m)Offset (m)
Kidd CreekKidd Creek00
2020
4040
6060
505000 Offset (m)Offset (m) 505000 Offset (m)Offset (m)
OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data ResultsSynthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work
Discussion & ConclusionsDiscussion & Conclusions
• PS migration can image structure PS migration can image structure invisible to reflection migration.invisible to reflection migration.
• Reduced-time migraton decreases the Reduced-time migraton decreases the error of an incorrect velocity model. error of an incorrect velocity model.
• Converted wave reduced-time Converted wave reduced-time migration can successfully image a migration can successfully image a transmitting boundary.transmitting boundary.
Future WorkFuture Work• Model and migrate salt proximity Model and migrate salt proximity
VSP data with converted wave VSP data with converted wave RTM. RTM.
• Model and test PP RTM.Model and test PP RTM.• Search for other applications of Search for other applications of
RTM.RTM.• Graduate.Graduate.
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