Reverse Time Migration =
description
Transcript of Reverse Time Migration =
Reverse Time Migration Reverse Time Migration ==
Generalized Diffraction MigrationGeneralized Diffraction Migration
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
FilteringFilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
d(r)d(r) = = m(x)m(x)G(G(ss|x)|x) G(x|G(x|rr))[[ ]]****
T=0T=0
Reverse Time MigrationReverse Time MigrationGeneralized Diff. MigrationGeneralized Diff. MigrationCalc. Green’s Func. By FD solvesCalc. Green’s Func. By FD solves
= dot product data with hyperbola= dot product data with hyperbolaGeneralized Kirchhoff kernelGeneralized Kirchhoff kernel
Convolution of G(Convolution of G(ss|x) with G(x||x) with G(x|rr))
QED:QED: RTM can now enjoy: RTM can now enjoy:
Anti-aliasing filterAnti-aliasing filter
Obliquity factorObliquity factor
Angle GathersAngle Gathers
UD SeparationUD Separation
Decomplexify back&forwardDecomplexify back&forward
felds according 2 tastefelds according 2 taste
Etc. etc.Etc. etc.
d(r)d(r) = = m(x)m(x)G(G(ss|x)|x) G(x|G(x|rr))[[ ]]****
T=0T=0
Reverse Time MigrationReverse Time MigrationGeneralized Kirch. MigrationGeneralized Kirch. MigrationCalc. Green’s Func. By FD solvesCalc. Green’s Func. By FD solves
= dot product data with hyperbola= dot product data with hyperbolaGeneralized Kirchhoff kernelGeneralized Kirchhoff kernel
Convolution of G(Convolution of G(ss|x) with G(x||x) with G(x|rr))
QED:QED: RTM can now enjoy: RTM can now enjoy:
Anti-aliasing filterAnti-aliasing filter
Obliquity factorObliquity factor
Angle GathersAngle Gathers
UD SeparationUD Separation
Decomplexify back&forwardDecomplexify back&forward
felds according 2 tastefelds according 2 taste
Etc. etc.Etc. etc.
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
FilteringFilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
Resolution of KM vs GDMResolution of KM vs GDM
timetime timetime
MultiplesMultiples
PrimaryPrimaryPrimaryPrimary
Kirchhoff Mig. vs GDMKirchhoff Mig. vs GDM
1. Low-Fold Stack vs Superstack 1. Low-Fold Stack vs Superstack
2. Poor Resolution vs Superresolution 2. Poor Resolution vs Superresolution
MultiplesMultiples
3. Caution: RTM sensitive to mig. vel. errors3. Caution: RTM sensitive to mig. vel. errors
Rayleigh ResolutionRayleigh Resolution
timetime
LL
migratemigrate
x = 0.25x = 0.25z/Lz/L
Is Superresolution by RTM Achievable?
Tucson, Arizona Test
T u n n el a t level 2(30 m from grou n d )
T u n n el a t leve l 3(45 m from grou n d )
Shaf
t G ro u n d S u rfa ce30 m
1 5 m
S h o t loca tio nR ec e iv e r lo ca tio n
S h a ft en tran ce
60 m
Poststack MigrationPoststack Migration
1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8 3 0X (m )
-0 .2
0
0 .2
0 .4
0 .6
0 .8
1
Nor
mal
ized
Am
plitu
de
D irec t - F u ll A p ra tu reD irec t - H a lf A p ra tu reS ca tte re rs - F u ll A p ra tu reS ca tte re rs - H a lf A p ra tu re
S u p er-reso lu tion T est - P o in t # 14 a t X = 2 4m
~Kirchhoff Mig.
~Scattered RTM
This is highest fruit on the tree..who dares pick it?This is highest fruit on the tree..who dares pick it?
(Hanafy et al., 2008)
Can Scatterers Beat the Resolution Limit?
Recorded Green’s functions G(s|x) divided into:
- Shot gathers with direct arrivals only
- Shot gathers with scattered arrivals only
0 20 4 0 60 80 1 0 0 1 2 0
D ista n ce (m )
0 .5
0 .4
0 .3
0 .2
0 .1
0
Time
(ms)
G reen 's F u n ctionA fter b an d -p ass filter
0 20 40 60 8 0 10 0 12 0
D ista n ce (m )
0 .5
0 .4
0 .3
0 .2
0 .1
0
Time
(ms)
G reen 's F u n ctio nA fter b a n d -p a ss filter
0 20 40 60 80 1 0 0 1 2 0
D ista n ce (m )
0 .5
0 .4
0 .3
0 .2
0 .1
0
Time
(ms)
G reen 's F u n ctionA fter b an d -p ass filter
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
Filtering: 1Filtering: 1stst Arrival Filtering Arrival FilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
[[GG((ss|x)G(x|g)]* d(s|g) |x)G(x|g)]* d(s|g) s,g
1. RTM: 1. RTM: [{[{ } {} { } ]* d(s|g) } ]* d(s|g)
GG((ss|x)|x) GG((ss|x)|x) GG(x|g) (x|g) GG(x|g)(x|g)++ ++s,g==
dd (x) = (x) =
GG((ss|x)|x) GG(x|g)(x|g){ }s,g~~ ** d(s|g) d(s|g)
Super-wide Angle PhaseSuper-wide Angle Phase
Shift MigrationShift Migration
First Arrival FilterFirst Arrival Filter
Single Arrival KirchhoffSingle Arrival Kirchhoffw/o high-freq. appoxw/o high-freq. appox
Early Arrival FilterEarly Arrival Filter
Multiple Arrival KirchhoffMultiple Arrival Kirchhoffw/o high-freq. appoxw/o high-freq. appox
(or Super beam migration)(or Super beam migration)
Frechet DerivativeFrechet Derivative
True RTMTrue RTM
Phase Shift, Beam, Kirchhoff Migrations Phase Shift, Beam, Kirchhoff Migrations
are Special Cases of True RTMare Special Cases of True RTM
dsds
First Arrival FilterFirst Arrival Filter
& U p+Down filter& U p+Down filter
Efficient RT Migration OperatorsEfficient RT Migration Operators
SALTSALTFD only in FD only in
expanding boxexpanding box
Example Example (Min Zhou, 2003)(Min Zhou, 2003)
Standard FD Wavefront G(s|x)Standard FD Wavefront G(s|x) Early Arrival FD Wavefront G(s|x)Early Arrival FD Wavefront G(s|x)
Standard RTM vs Early Arrival RTMStandard RTM vs Early Arrival RTM
Standard FDStandard FD
0 4.5 km0 4.5 km
00
1.5 km1.5 km
Wavefront FDWavefront FDEfficient RT Migration OperatorsEfficient RT Migration Operators
FD/ Wavefront FD CostFD/ Wavefront FD Cost
# Gridpts along side# Gridpts along side500 3000500 3000
4545
55
FD/ W
avef
ront
FD
Cos
tFD
/ Wav
efro
nt F
D C
ost
ModelModel
0 4.5 km0 4.5 km
00
1.5 km1.5 km
00
1.5 km1.5 km
Wavefront Migration ImageWavefront Migration Image
1.5 km/s1.5 km/s2.2 km/s2.2 km/s
1.8 km/s1.8 km/s
Wavefront Migration ImageWavefront Migration Image
Reverse Time MigrationReverse Time Migration
00
1.5 km1.5 km
0 4.5 km0 4.5 km
00
1.5 km1.5 km
1.5 km/s1.5 km/s2.2 km/s2.2 km/s
1.8 km/s1.8 km/s
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
Filtering: 1Filtering: 1stst Arrival Filtering Arrival FilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
SALTSALT
Filtering of Wave Equation Filtering of Wave Equation Migration OperatorsMigration Operators
SALTSALT
Truncation: anti-aliasingTruncation: anti-aliasing
SALTSALT
Slant stackSlant stack
Filtering of Wave Equation Filtering of Wave Equation Migration OperatorsMigration Operators
Filtering of Filtering of WaveWave Equation Migration Operators Equation Migration Operators
0 s0 s
1.0 s1.0 s
Tim
e (s
)T
ime
(s)
0 km 0 km 4.5 km 4.5 km X (km)X (km) 0 km 0 km 4.5 km 4.5 km X (km)X (km)
0 s0 s
1.0 s1.0 s
0 s0 s
1.0 s1.0 s
COG Mig. Op.COG Mig. Op. Filtered COG Mig. Op.Filtered COG Mig. Op.
Z=70 mZ=70 m
Z=270 mZ=270 m
Z=1190 mZ=1190 m
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
Filtering: 1Filtering: 1stst Arrival Filtering Arrival FilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
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Standard Reverse Time RedatumingStandard Reverse Time Redatuming
Cost = 10 FD SolvesCost = 10 FD Solves
to get G(to get G(xx||xx))
Special case:Special case: 10 Shot Gathers at the Surface, 3 Receivers at Depth10 Shot Gathers at the Surface, 3 Receivers at Depth
Procedure:Procedure: Compute 10 FD Solves, one for each shot at z=0Compute 10 FD Solves, one for each shot at z=0
DatumDatum
Special case:Special case: 10 Shot Gathers at the Surface, 3 Receivers at Depth10 Shot Gathers at the Surface, 3 Receivers at Depth
Procedure:Procedure: Compute 3 FD Solves, one for each shot at z=datumCompute 3 FD Solves, one for each shot at z=datum
Cost = 3 FD SolvesCost = 3 FD Solves
to get to get GG((xx||xx))
Trick:Trick: By ReciprocityBy Reciprocity GG((xx||xx)=)=GG((xx||xx))
Target Oriented Reverse Time RedatumingTarget Oriented Reverse Time Redatuming
DatumDatum
Benefit: Several ordersBenefit: Several orders
magnitude less expensivemagnitude less expensive
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Dep
th (K
m)
Dep
th (K
m)
00
WW EE
3.53.5Offset (km)Offset (km)00
22.0.0
A slice of 3D SEG/EAGE model at x=2.0 kmA slice of 3D SEG/EAGE model at x=2.0 km
1.241.24
3D Synthetic Data (Dong)3D Synthetic Data (Dong)
Kirchhoff MigrationKirchhoff Migration
Redatum + KMRedatum + KM
33.5.5Offset (km)Offset (km)00
Z (k
m)
Z (k
m)
00
8.08.0
y (km)y (km)
6.06.0
00
x (km)x (km)1212
00
Interval velocity model
3D Field Data Test3D Field Data Test
OBC geometry:
50,000 shots
180 receivers per shot
Datum depth:
1.5 km
RVSP Green’s functions:
5,000 shots
180 receivers per shot
km/s5.55.5
1.51.5
New Datum
3D Field Data Test3D Field Data Test
y (km)y (km)00 4.54.5
Tim
e (s
)Ti
me
(s)
00
6.06.0
Original CSG
y (km)y (km)00 4.54.5
Tim
e (s
)Ti
me
(s)
00
6.06.0
Redatumed CSG
KM of RTD data
Z (k
m)
Z (k
m)
00
88
y (km)y (km)
55
00
x (km)x (km)1212
00
KM of redatumed data
Z (k
m)
Z (k
m)
00
88
y (km)y (km)
55
00
x (km)x (km)1212
00
KM of original data
3D Field Data Test3D Field Data Test
( Inline No. 61 )( Inline No. 61 )
X (km)X (km)00 1212
Z (k
m)
Z (k
m)
00
8.08.0
KM of RTD data
X (km)X (km)00 1212
Z (k
m)
Z (k
m)
00
8.08.0
3D Field Data Test3D Field Data Test
KM of original data
( Crossline No. 41 )( Crossline No. 41 )
Y (km)Y (km)00 5.05.0
Z (k
m)
Z (k
m)
00
8.08.0
KM of RTD data
Y (km)Y (km)00 5.05.0
Z (k
m)
Z (k
m)
00
8.08.0
3D Field Data Test3D Field Data Test
KM of original data
( Crossline No. 61 )( Crossline No. 61 )
Y (km)Y (km)00 5.05.0
Z (k
m)
Z (k
m)
00
8.08.0
KM of RTD data
Y (km)Y (km)00 5.05.0
Z (k
m)
Z (k
m)
00
8.08.0
3D Field Data Test3D Field Data Test
KM of original data
( Depth 2.0 km )( Depth 2.0 km )
X (km)X (km)00 1212
Y (k
m)
Y (k
m)
00
5.05.0
KM of RTD data
X (km)X (km)00 1212
Y (k
m)
Y (k
m)
00
5.05.0
3D Field Data Test3D Field Data Test
KM of original data
( Depth 2.5 km )( Depth 2.5 km )
X (km)X (km)00 1212
Y (k
m)
Y (k
m)
00
5.05.0
KM of RTD data
X (km)X (km)00 1212
Y (k
m)
Y (k
m)
00
5.05.0
3D Field Data Test3D Field Data Test
KM of original data
( Depth 4.0 km )( Depth 4.0 km )
X (km)X (km)00 1212
Y (k
m)
Y (k
m)
00
5.05.0
KM of RTD data
X (km)X (km)00 1212
Y (k
m)
Y (k
m)
00
5.05.0
3D Field Data Test3D Field Data Test
KM of original data
RTM (CPU-hours)
RTD (CPU-hours)
Speed up
3D field data test 5,000,000 (estimated) 52,000 100
Computational CostsComputational Costs
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
Filtering: 1Filtering: 1stst Arrival Filtering Arrival FilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
Motivation (Ge Zhan)Motivation (Ge Zhan)• ProblemProblem
Conventional RTM suffers from imaging artifacts.Conventional RTM suffers from imaging artifacts.
• SolutionSolution
Wavelet compression of Green’s functions (10x or more).Wavelet compression of Green’s functions (10x or more).
Compressed generalized diffraction-stack migration (GDM) .Compressed generalized diffraction-stack migration (GDM) .
Kirchhoff (diffraction-stack) migration is efficient Kirchhoff (diffraction-stack) migration is efficient
but with a high-frequency approximation.but with a high-frequency approximation.
WEM method (RTM)WEM method (RTM) is accurate but computationallyis accurate but computationally
intensive compared to KM.intensive compared to KM.
Least squares algorithm.Least squares algorithm.
Migration OperatorMigration Operator
Size = nx*nz*ns*ng*nt = 645*150*323*176*1001*4 = 20 TB
Too big to store.
G G2D Wavelet Transform
rr
xx
ss
( | )G s x ( | )G x r
appropriate threshold
10x compression
TheoryTheory
G(s|x)G(x|g) (5 dimensions)
Green’s Function trace
Can Scatterers Beat the Resolution Limit ?
TheoryTheory
Numerical ResultsNumerical ResultsSEG/EAGE Salt Model
X (km)
Z (k
m)
0 15
0
3
X (km)
Z (k
m)
0 15
0
3
Zoom View
323 shots
176 geophones
peak freq = 13 Hz
dx = 24.4 m
dg = 24.4 m
ds = 48.8 m
nsamples = 1001
dt = 0.008 s
1.5
2.5
3.5
4.5
km/s
Calculated GF
Tim
e (s
)
Trace #
4
0
4011Ti
me
(s)
Trace#
4
1.5
4011
Trace Comparison
101 201 301
200 MB
Trace #4011
Reconstructed GF
20 MB
Wavelet Transform CompressionWavelet Transform Compression
Numerical ResultsNumerical Results
Early-arrivals
Tim
e (s
)
Trace#
4
0
4011 Trace# 4011
Multiples
Numerical ResultsNumerical Results
X (km)
Z (k
m)
0 15
0
3
(a) GDM using Early-arrivals
X (km)0 15
(b) GDM using Full Wavefield
X (km)
Z (k
m)
0 15
0
3
(c) GDM using Multiples
X (km)0 15
(d) Optimal Stack of (a) and (c)
Numerical ResultsNumerical Results
OutlineOutline1. RTM = GDM1. RTM = GDM2. Implications2. Implications
Filtering: 1Filtering: 1stst Arrival Filtering Arrival FilteringSuperresolutionSuperresolution
Target Oriented RTMTarget Oriented RTMFast LSMFast LSMDiffraction SelectiveDiffraction Selective
Perfect Migration OperatorsPerfect Migration Operators
Exact Migration Operators from VSP Exact Migration Operators from VSP IMPLICATION #2IMPLICATION #2
SALTSALT
g(s|x)g(s|x)
SALTSALT
**Exact Migration Operators from VSP Exact Migration Operators from VSP
IMPLICATION #2IMPLICATION #2
g(r|x)g(r|x) g(s|x)g(s|x)**
Exxon RVSP DataExxon RVSP Data0 s0 s
0.5 s0.5 s
Z = .18 kmZ = .18 km
DirectDirectReflections Reflections
MultiplesMultiples
0 km 0 km 0.2 km 0.2 km XX
FocusingFocusing
OperatorOperatorg(x|r)g(x|r)g(s|x)g(s|x)
Exxon RVSP Data Exxon RVSP Data
0 km 0 km 0.2 km 0.2 km
0 km 0 km 0.2 km 0.2 km XX
XX
Prim Refl. Focusing OperatorPrim Refl. Focusing Operator 0.2 s0.2 s
0.28 s0.28 s
Interbed Multiple Refl. Focusing OperatorInterbed Multiple Refl. Focusing Operator 0.31 s0.31 s
0.37 s0.37 s