ps, ssp, pspi, ffd
DESCRIPTION
PS, SSP, PSPI, FFD. KM. SSP. PSPI. FFD. z. 2. 2. k = k 1 – k. ~ k (1 – k + ..). x. x. z. k. 2. k. 2. 2. k. z. k. x. ik(x). z. P(x,z, w ) = P(x,0 , w ) e. PS, SSP, PSPI, FFD. 2. 2. 2. k = k 1 – k. k. k. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/1.jpg)
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFDSSPSSP
FFDFFD
KMKM
PSPIPSPI
![Page 2: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/2.jpg)
k
k z
x
k = k 1 – k z
2
k 2x ~ k (1 – k + ..)
2x
k 22
P(x,z,) = P(x,0 ,) e zik(x) z
![Page 3: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/3.jpg)
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFDk = k 1 – k z
2
k 2x
-1 1.2
1
k z ~ k(1 – k ) 2x
k 22
k z ~ k (1 – .43 ) 2
21 -.5
= k 2x
k 2
P(x,z,) = P(x,0 ,) e zik(x)z
k
k
x
z
![Page 4: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/4.jpg)
SSP MigrationSSP Migration
k = k(x) 1 – k z
2
k(x)2x = k 1 – k
2
k 2x - k
0
0
Thin lens
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 5: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/5.jpg)
FFD MigrationFFD Migration
k = k(x) 1 – k z
2
k(x)2x = k 1 – k
2
k 2x - k
0
0
Thin lens
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 6: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/6.jpg)
k = k(x) 1 – k z
2
k(x)2x = k 1 – k
2
k 2x - k
0
0
Thin lens
FFD MigrationFFD MigrationP(x,z,) = P(x,0 ,) e zik(x)z
![Page 7: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/7.jpg)
FFD MigrationFFD MigrationP(x,z,) = P(x,0 ,) e zik(x)z
![Page 8: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/8.jpg)
FFD MigrationFFD Migrationother term
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 9: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/9.jpg)
FFD MigrationFFD Migration
PDE associated withother term
other term
Rearrange PDE
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 10: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/10.jpg)
FFD MigrationFFD Migration
Substitute FD approximations into above
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 11: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/11.jpg)
FFD MigrationFFD Migration
Substitute FD approximations into above
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 12: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/12.jpg)
FFD MigrationFFD Migration
k = k(x) 1 – k z
2
k(x)2x = k 1 – k
2
k 2x - k
0
0
Thin lens
P(x,z,) = P(x,0 ,) e zik(x)z
![Page 13: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/13.jpg)
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFD
![Page 14: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/14.jpg)
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFD
![Page 15: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/15.jpg)
SummarySummaryCost:Cost:
Accuracy:Accuracy: KMKM SSPSSP
PSPIPSPI FFDFFD
![Page 16: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/16.jpg)
Course SummaryCourse Summary
m(x)= (g,s,x) G(g|x)d(g|x)G(x|s)dgdsg,s,
G(g|x) = G(g|x) + G(g|x) d(g|x) = d(g|x) + d(x|g)
G(g|x) = G(g|x) d(g|x) = d(g|x)
Filter
RTM
Asymptotic G
KM Phase Shift Beam
1-way G Asymptotic G+ Fresnel Zone
![Page 17: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/17.jpg)
1980
Multisource SeismicMultisource SeismicImagingImaging
vs
copper
VLIW
Superscalar
RISC
1970 1990 2010
1
100
100000
10
1000
10000
Aluminum
Year
202020001980
CPU Speed vs Year
![Page 18: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/18.jpg)
OUTLINEOUTLINE
Theory ITheory I
Theory IITheory II
Numerical ResultsNumerical Results
![Page 19: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/19.jpg)
RTM Problem & Possible Soln.RTM Problem & Possible Soln.
• Problem:Problem: RTM computationally costly RTM computationally costly
• Solution:Solution: Multisource LSM RTM Multisource LSM RTM
1919
Preconditioning speeds up by factor 2-3Preconditioning speeds up by factor 2-3
LSM reduces crosstalkLSM reduces crosstalk
5
![Page 20: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/20.jpg)
Multisource Migration:Multisource Migration: mmmigmig=L=LTTdd
Forward Model:Forward Model:
Multisource Least Squares Migration Multisource Least Squares Migration
d +d +dd =[ =[L +L +LL ]m ]m11 222211
LL{dd{
=[=[L +L +LL ]( ](dd + + dd ) ) 11 222211
TT TT
= = L d +L d +L dL d + + 11 222211
TT TT
LL dd + +L L dd22 112211
Crosstalk noiseCrosstalk noiseStandard migrationStandard migration
TT TT
![Page 21: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/21.jpg)
Multisource Least Squares Phase-encoded Multisource Least Squares Phase-encoded Migration Migration
=[=[NN L +L +N LN L ](N ](N dd + + NN dd ) ) 11 222211 22 221111
mmmigmig
==N*NN*N L d +L d +N*N L dN*N L d + N* + N*NN L L dd + + N*N*NN L L dd 11 2211 22 221111 11 11 11 22 1122 22 22 22
TT TT
TT TT TT TT
** **
= = L d +L d + L d L d11 11 22 22
Standard migrationStandard migration
If <N N > = If <N N > = (i-j)(i-j)i j
Crosstalk noiseCrosstalk noise
Orthogonal phase encoding s.t. <Orthogonal phase encoding s.t. <N* N* N >=0N >=01 1 22
![Page 22: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/22.jpg)
Key AssumptionKey Assumption
d(t) =d(t) =
Zero-mean white noise: <N(t)>=0; <N(t) N(t’) >=0
++ M= Stack Number
Am
plit
ude
k=1k=1
MM
N(t )N(t )(k)(k)
<N(t)> ~<N(t)> ~
k=1k=1
MM
[ S(t) ][ S(t) ]22
M1
SNR SNR
M
M vs M
k=1k=1
MM
[ N(t) ][ N(t) ]22
~
(k)(k)
(k)(k)
[ S(t) ][ S(t) ]22
k=1k=1
MM
[ N(t) ][ N(t) ]22 22
~(k)(k)
MM22
[ S(t) ][ S(t) ]22
~MM
22
M M
k=1k=1
MM
[S(t) +N(t) ][S(t) +N(t) ]
![Page 23: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/23.jpg)
Multisource S/N RatioMultisource S/N Ratio
# geophones/CSG# geophones/CSG
# CSGs# CSGs
L [d + d +.. ]1 221
d +d T d , d 2211
L [d + d + … ]1 2
T , …. +….
![Page 24: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/24.jpg)
Multisrc. Migration vs Standard Migration
# iterations# iterations
Iterative Multisrc. Migration vs Standard Migration
vs
vs
MSMSS-1
M~~
# geophones/CSG# geophones/CSG # CSGs# CSGs
MSMI
![Page 25: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/25.jpg)
SummarySummary
Time Statics
Time+Amplitude Statics
QM Statics
1. Multisource crosstalk term analyzed analytically1. Multisource crosstalk term analyzed analytically
2. Crosstalk decreases with increasing 2. Crosstalk decreases with increasing , randomness, , randomness, dimension, iteration #, and decreasing depthdimension, iteration #, and decreasing depth
3. Crosstalk decrease can now be tuned3. Crosstalk decrease can now be tuned
4. Some detailed analysis and testing needed to refine 4. Some detailed analysis and testing needed to refine predictions.predictions.
LL dd + +L L dd22 112211
TT TT
![Page 26: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/26.jpg)
OUTLINEOUTLINE
Theory ITheory I
Theory IITheory II
Numerical ResultsNumerical Results
![Page 27: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/27.jpg)
0Z
k(m
)3
0 X (km) 16
The Marmousi2 Model
The area in the white box is used for S/N calculation.
![Page 28: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/28.jpg)
0 X (km) 16
0Z
k(m
)3
0Z
(k
m)
3
0 X (km) 16
Conventional Source: KM vs LSM (50 iterations)
![Page 29: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/29.jpg)
0 X (km) 16
0Z
k(m
)3
0Z
(k
m)
3
0 X (km) 16
200-source Supergather: KM vs LSM (300 its.)
![Page 30: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/30.jpg)
S/N
0
1 Number of Iterations 300
S/N =7
The S/N of MLSM image grows as the square root of the number of iterations.
I
![Page 31: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/31.jpg)
• Fast Multisource Least Squares Fast Multisource Least Squares Phase Shift.Phase Shift.
• Multisource Waveform Inversion (Ge Zhan)Multisource Waveform Inversion (Ge Zhan)
• Theory of Crosstalk Noise (Schuster)Theory of Crosstalk Noise (Schuster)
8
Multisource TechnologyMultisource Technology
![Page 32: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/32.jpg)
The True Model
• use constant velocity model with c = 2.67 km/s
• center frequency of source wavelet f = 20 Hz
X (km)
Z (
km)
Reflectivity, SEG/EAGE Salt Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
1.2
![Page 33: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/33.jpg)
Multi-source PSLSM
X (km)
Z (k
m)
Reflectivity, Ten 10-source supergathers
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
1.2
• 645 receivers and 100 sources, equally spaced 10 sets of sources, staggered; each set constitutes a supergather
• 50 iterations of steepest descent
![Page 34: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/34.jpg)
Single-source PSLSM
• 645 receivers and 100 sources, equally spaced 100 individual shots
• 50 iterations of steepest descent
X (km)
Z (k
m)
Reflectivity, 100 single source gathers
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
1.2
![Page 35: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/35.jpg)
Multi-Source Waveform Inversion StrategyMulti-Source Waveform Inversion Strategy(Ge Zhan) (Ge Zhan)
Generate multisource field data with known time shift
Generate synthetic multisource data with known time shift from estimated
velocity model
Multisource deblurring filter
Using multiscale, multisource CG to update the velocity model with
regularization
Initial velocity model
144 shot gathers144 shot gathers
![Page 36: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/36.jpg)
3D SEG Overthrust Model(1089 CSGs)
15 km
3.5 km
15 km
![Page 37: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/37.jpg)
3.5 km
Dynamic QMC TomogramDynamic QMC Tomogram (99 CSGs/supergather)(99 CSGs/supergather)
Static QMC TomogramStatic QMC Tomogram(99 CSGs/supergather)(99 CSGs/supergather)
15 km
Dynamic Polarity TomogramDynamic Polarity Tomogram(1089 CSGs/supergather)(1089 CSGs/supergather)
Numerical ResultsNumerical Results
![Page 38: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/38.jpg)
OUTLINEOUTLINE
Theory ITheory I
Theory IITheory II
Numerical ResultsNumerical Results
![Page 39: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/39.jpg)
Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term
Time Statics
Time+Amplitude Statics
QM Statics
36
![Page 40: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/40.jpg)
SummarySummaryCrosstalk term
Time Statics
Time+Amplitude Statics
QM Statics
1. Multisource crosstalk term analyzed analytically1. Multisource crosstalk term analyzed analytically
2. Crosstalk decreases with increasing 2. Crosstalk decreases with increasing , randomness, , randomness, dimension, and decreasing depthdimension, and decreasing depth
3. Crosstalk decrease can now be tuned3. Crosstalk decrease can now be tuned
4. Some detailed analysis and testing needed to refine 4. Some detailed analysis and testing needed to refine predictions.predictions.
37
![Page 41: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/41.jpg)
Multisource Migration:Multisource Migration: mmmigmig=L=LTTdd
Forward Model:Forward Model:
Multisource Least Squares Migration Multisource Least Squares Migration
d +d =[d +d =[L +L ]mL +L ]m11 222211
LL{dd{Standard migration
Crosstalk term
Phase encodingPhase encoding
Kirchhoff kernelKirchhoff kernel
34
![Page 42: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/42.jpg)
Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term
35
![Page 43: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/43.jpg)
Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term
Time Statics
Time+Amplitude Statics
QM Statics
36
![Page 44: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/44.jpg)
Crosstalk TermCrosstalk Term
Time Statics
Time+Amplitude Statics
QM Statics
LL dd + +L L dd22 112211
TT TT
![Page 45: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/45.jpg)
SummarySummaryCrosstalk term
Time Statics
Time+Amplitude Statics
QM Statics
1. Multisource crosstalk term analyzed analytically1. Multisource crosstalk term analyzed analytically
2. Crosstalk decreases with increasing 2. Crosstalk decreases with increasing , randomness, , randomness, dimension, and decreasing depthdimension, and decreasing depth
3. Crosstalk decrease can now be tuned3. Crosstalk decrease can now be tuned
4. Some detailed analysis and testing needed to refine 4. Some detailed analysis and testing needed to refine predictions.predictions.
37
![Page 46: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/46.jpg)
Multisource FWI SummaryMultisource FWI Summary(We need faster migration algorithms & better velocity models)(We need faster migration algorithms & better velocity models)
IO 1 vs 1/20
Cost 1 vs 1/20 or better
Resolution dx 1 vs 1
Sig/MultsSig ?
Stnd. FWI Multsrc. FWIStnd. FWI Multsrc. FWI
![Page 47: PS, SSP, PSPI, FFD](https://reader033.vdocument.in/reader033/viewer/2022061612/56815a33550346895dc772bc/html5/thumbnails/47.jpg)
Key AssumptionKey Assumption
<d(t)>= <S(t)> + <N(t)><d(t)>= <S(t)> + <N(t)>
Zero-mean white noise: <N>=0; <N N >=0i j
++ n= Stack Number
Am
plit
ude
<N(t)> ~ <N(t)> ~ 22 n <S(t)> ~ <S(t)> ~
22 n 22
k=1k=1
nn
N(t )N(t )(k)(k)
<N(t)> ~<N(t)> ~1/n
<N(t) > ~<N(t) > ~ 22
k=1k=1
nn
[ N(t ) ][ N(t ) ](k)(k) 22
1/n
<N(t) > ~<N(t) > ~ 22
k=1k=1
nn
[ N(t ) ][ N(t ) ](k)(k) 22
1/n