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
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFDSSPSSP
FFDFFD
KMKM
PSPIPSPI
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
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
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
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
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
FFD MigrationFFD MigrationP(x,z,) = P(x,0 ,) e zik(x)z
FFD MigrationFFD Migrationother term
P(x,z,) = P(x,0 ,) e zik(x)z
FFD MigrationFFD Migration
PDE associated withother term
other term
Rearrange PDE
P(x,z,) = P(x,0 ,) e zik(x)z
FFD MigrationFFD Migration
Substitute FD approximations into above
P(x,z,) = P(x,0 ,) e zik(x)z
FFD MigrationFFD Migration
Substitute FD approximations into above
P(x,z,) = P(x,0 ,) e zik(x)z
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
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFD
PS, SSP, PSPI, FFDPS, SSP, PSPI, FFD
SummarySummaryCost:Cost:
Accuracy:Accuracy: KMKM SSPSSP
PSPIPSPI FFDFFD
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
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
OUTLINEOUTLINE
Theory ITheory I
Theory IITheory II
Numerical ResultsNumerical Results
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
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
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
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) ]
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 , …. +….
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
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
OUTLINEOUTLINE
Theory ITheory I
Theory IITheory II
Numerical ResultsNumerical Results
0Z
k(m
)3
0 X (km) 16
The Marmousi2 Model
The area in the white box is used for S/N calculation.
0 X (km) 16
0Z
k(m
)3
0Z
(k
m)
3
0 X (km) 16
Conventional Source: KM vs LSM (50 iterations)
0 X (km) 16
0Z
k(m
)3
0Z
(k
m)
3
0 X (km) 16
200-source Supergather: KM vs LSM (300 its.)
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
• 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
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
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
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
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
3D SEG Overthrust Model(1089 CSGs)
15 km
3.5 km
15 km
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
OUTLINEOUTLINE
Theory ITheory I
Theory IITheory II
Numerical ResultsNumerical Results
Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term
Time Statics
Time+Amplitude Statics
QM Statics
36
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
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
Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term
35
Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term
Time Statics
Time+Amplitude Statics
QM Statics
36
Crosstalk TermCrosstalk Term
Time Statics
Time+Amplitude Statics
QM Statics
LL dd + +L L dd22 112211
TT TT
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
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
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