overview of multisource phase encoded seismic inversion
Post on 22-Mar-2016
58 Views
Preview:
DESCRIPTION
TRANSCRIPT
Overview of Multisource Phase
Encoded Seismic Inversion
Wei Dai, Ge Zhan, and Gerard SchusterKAUST
Outline1. Seismic Experiment:
L m = d
L m = d1 1
L m = d2 2...N N
2. Standard vs Phase Encoded Least Squares Soln.
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
3. Theory Noise Reduction 4. Summmary and Road Ahead
Gulf of Mexico Seismic SurveyL m = d
Time (s)
4
0
d
Goal: Solve overdeterminedSystem of equations for m
Predicted data Observed data
m(x,y,z)
Common Shot Gather
Streamer Reel
Streamer Cables
4 km
Details of Lm = d
Time (s)
6 X (km)
4
0
1 d
G(s|x)G(x|g)m(x)dx = d(g|s)
Reflectivityor velocity
model
Predicted data = Born approximationSolve wave eqn. to get G’s
m
Outline1. Seismic Experiment:
L m = d
L m = d1 1
L m = d2 2...N N
2. Standard vs Phase Encoded Least Squares Soln.
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
3. Theory Noise Reduction 4. Summmary and Road Ahead
Conventional Least Squares Solution: L= & d =
Given: Lm=dFind: m s.t. min||Lm-d||2
Solution: m = [L L] L d T T-1
m = m – a L (Lm - d) T(k+1) (k) (k)(k)
or if L is too big
L1
L2
d 1
d 2
= m – a L (L m - d ) (k)
+ L (L m - d ) 1 1 2 2 21
TT[ ]
In general, hugedimension matrix
Conventional Least Squares Solution: L= & d =
Given: Lm=dFind: m s.t. min||Lm-d||2
Solution: m = [L L] L d T T-1
m = m – a L (Lm - d) T(k+1) (k) (k)(k)
or if L is too big
L1
L2
d 1
d 2
= m – a L (L m - d ) (k)
+ L (L m - d ) 1 1 2 2 21
TT[ ]
In general, hugedimension matrix
Note: subscripts agree
Conventional Least Squares Solution: L= & d =
Given: Lm=dFind: m s.t. min||Lm-d||2
Solution: m = [L L] L d T T-1
m = m – a L (Lm - d) T(k+1) (k) (k)(k)
L1
L2
d 1
d 2
= m – a L (L m - d ) (k)
+ L (L m - d ) 1 1 2 2 21
TT[ ]
In general, hugedimension matrix
Problem: Each prediction is a FD solveSolution: Blend+encode Data
Blending+Phase Encoding
2 d = N d + N d + N d211 33
PhasePhaseBlending
Encoding MatrixSupergather
L = N L + N L + N L3 32 21 1m [ ]m
d 1L m=1
Encoded supergather modeler
d 3L m=3d 2L m=2
O(1/S) cost!
Blending
Blended Phase-Encoded Least Squares Solution L = & d = N d + N d
Given: Lm=dFind: m s.t. min||Lm-d||2
Solution: m = [L L] L d T T-1
m = m – a L (Lm - d) T(k+1) (k) (k)(k)
or if L is too big
1N L + N L2 1
= m – a L (L m - d ) (k)
+ L (L m - d ) 1 1 2 2 21
TT[ ]
1 2 1 2 2
In general, SMALLdimension matrix
+ Crosstalk+ L (L m - d ) 2
T
11 + L (L m - d ) 1
T
22
Iterations are proxyFor ensemble averaging
Brief History Multisource Phase Encoded Imaging
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein, Lacasse, SEG, (2009)Virieux and Operto, EAGE, (2009)Dai, and Schuster, SEG, (2009)
Migration
Waveform Inversion and Least Squares Migration
Biondi, SEG, (2009)
Outline1. Seismic Experiment:
L m = d
L m = d1 1
L m = d2 2...N N
2. Standard vs Phase Encoded Least Squares Soln.
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
3. Theory + Numerical Results 4. Summmary and Road Ahead
SEG/EAGE Salt Reflectivity Model
• Use constant velocity model with c = 2.67 km/s • Center frequency of source wavelet f = 20 Hz• 320 shot gathers, Born approximation
Z
(km
)
0
1.4
0 X (km) 6
• Encoding: Dynamic time, polarity statics + wavelet shaping• Center frequency of source wavelet f = 20 Hz• 320 shot gathers, Born approximation
0 X (km) 6
0Z
k(m
)1.
40
Z (k
m)
1.4
0 X (km) 6
Standard Phase Shift Migration (320 CSGs)
Standard Phase Shift Migration vs MLSM (Yunsong Huang)
Multisource PLSM (320 blended CSGs, 7 iterations)
1 x
1 x
44
Single-source PSLSM(Yunsong Huang)
Mod
el E
rror
1.0
0.30 50Iteration Number
Unconventional encoding
Conventional encoding: Polarity+Time Shifts
Multi-Source Waveform Inversion Strategy(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 gathers
3D SEG Overthrust Model(1089 CSGs)
15 km
3.5 km
15 km
3.5 km
Dynamic QMC Tomogram (99 CSGs/supergather)
Static QMC Tomogram(99 CSGs/supergather)
15 km
Dynamic Polarity Tomogram(1089 CSGs/supergather)
Numerical Results
1000x
300x
300x
Outline1. Seismic Experiment:
L m = d
L m = d1 1
L m = d2 2...N N
2. Standard vs Phase Encoded Least Squares Soln.
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
3. Theory + Numerical Results 4. Summmary and Road Ahead
Multisource Migration: mmig=LTd
Forward Model:
Multisource Least Squares Migration
d +d =[L +L ]m1 221
L{d{Standard migration
Crosstalk term
Phase encoding
Kirchhoff kernel
34
Multisource Least Squares Migration Crosstalk term
Crosstalk Prediction FormulaL (L m - d ) 2
T
11 + L (L m - d ) 1
T
22 e-s w2 2
O( )~X =
X
s .01 1.0
Standard Migration SNR
GS# geophones/CSG
# CSGs
SNR= ...migrate
SNR=
d(t) = Zero-mean white noise [S(t) +N(t) ] Neglect geometric spreading
Standard Migration SNR
Standard Migration SNR
Assume:
migrate+++
stack
S1
SGS G~~
iterate
GI
Iterative Multisrc. Mig. SNR
# iterations
SNR=
Cost ~ O(S)
Cost ~ O(I)
SNR
0
1 Number of Iterations 300
7The SNR of MLSM image grows as the square root of the number of iterations.
SNR = GI
IO 1 1/320
Cost ~
Resolution dx 1 1
SNR~
Stnd. Mig Multsrc. LSM
Less 1
1 <1/44
Cost vs Quality
Summary
1
L1
L2
d 1
d 2m = N L + N L
1 21 2[ ]m = [N d + N d ]
1 21 2
Multisource FWI Summary(We need faster migration algorithms & better velocity models)
Future: Multisource MVA, Interpolation, Field Data, Migration Filtering, LSM
Issues: Optimal encoding strategies, datacompression, loss of information.
Summary(We need faster migration algorithms & better velocity models)
IO 1 vs 1/20 or better
Cost 1 vs 1/20 or better
Resolution dx 1 vs 1
Sig/MultsSig ?
Stnd. FWI Multsrc. FWI
Multisource Migration: mmig=LTd
Forward Model:
Multisource Least Squares Migration
d +d =[L +L ]m1 221
L{d{Standard migration
Crosstalk term
Phase encoding
Kirchhoff kernel
34
Multisource Least Squares Migration Crosstalk term
Numerical Result of Multi-source Super stacking Reflectivity model
5.9X (km)0
Z (k
m)
1. 40
KM of 320 Single Source CSG
5.9X (km)0
Z (k
m)
1. 40
Narrowed Spectrum Wavelet
0.5time (s)0
Am
plitu
de
- 0. 3
0.4
Signal
FT of Wavelet
0.5Frequency (Hz)0
04.
5
50
Dominant frequency
(Xin Wang)
Numerical Result of Multi-source Super stacking KM of 320 Shots Supergather w/o
PE
5.9X (km)0
Z (k
m)
1. 40
-0.05
040
00
0.05
KM of 3000 Stacking Supergather
5.9X (km)0
Z (k
m)
1. 40
320 × 3000
0
KM of 320 Shots Supergather with PE
5.9X (km)
Z (k
m)
1. 40
Gaussian Distribution
0.05-0.05
05 0 320
Signal + Noise Singal + Noise
Singal + Noise
(Xin Wang)
Numerical Result of Multi-source Super stacking Noise
= Σ Σ Γ(g,x,s)* D0 (g|s)sg + R Σ Σ Σ Γ (g,x,s)* D0 (g|s’)
sg s≠s’
= Signal + Noise − Signal
= < N (g,s) N (g,s’)* > if s≠s’ R = e-2ω σ2 2Crosstalk damping coefficientR (σ) / R (σ0) = e 2ω (σ0 - σ )2 2 2
(Xin Wang)
0Z
k(m
)3
0 X (km) 16
The Marmousi2 Model(Wei Dai)
The area in the white box is used for SNR calculation.
200 CSGs.
Born Approximation
Conventional Encoding: Static Time Shift & Polarity Statics
0 X (km) 16
0Z
k(m
)3
0Z
(km
)3
0 X (km) 16
Conventional Source: KM vs LSM (50 iterations)Conventional KM
50x
1x
Conventional KLSM
0 X (km) 16
0Z
k(m
)3
0Z
(km
)3
0 X (km) 16
Multisource KM (1 iteration)
200-source Supergather: Multisrc. KM vs LSM
Multisource KLSM (300 iterations)
1 x200
Outline
1. Migration Problem and Encoded Migration
2. Standard vs Monte Carlo Least Squares Soln.
3. Numerical Results: Kirchhoff, Phase Shift, RTM
4. Summary
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
SEG/EAGE Salt Reflectivity Model
• Use constant velocity model with c = 2.67 km/s • Center frequency of source wavelet f = 20 Hz• 320 shot gathers, Born approximation
Z
(km
)
0
1.4
0 X (km) 6
• Encoding: Dynamic time, polarity statics + wavelet shaping• Center frequency of source wavelet f = 20 Hz• 320 shot gathers, Born approximation
0 X (km) 6
0Z
k(m
)1.
40
Z (k
m)
1.4
0 X (km) 6
Standard Phase Shift Migration (320 CSGs)
Standard Phase Shift Migration vs MLSM (Yunsong Huang)
Multisource PLSM (320 blended CSGs, 7 iterations)
1 x
1 x
44
Single-source PSLSM(Yunsong Huang)
Mod
el E
rror
1.0
0.30 50Iteration Number
Unconventional encoding
Conventional encoding: Polarity+Time Shifts
Outline
1. Migration Problem and Encoded Migration
2. Standard vs Monte Carlo Least Squares Soln.
3. Numerical Results: Kirchhoff, Phase Shift, RTM
4. Summary
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
3D SEG Overthrust Model(1089 CSGs, Chaiwoot)
15 km
3.5 km
15 km
3.5 km
Dynamic QMC Tomogram (99 CSGs/supergather)
Static QMC Tomogram(99 CSGs/supergather)
15 km
Dynamic Polarity Tomogram(1089 CSGs/supergather)
Numerical Results(Chaiwoot Boonyasiriwat)
1000x
300x
300x
IO 1 1/320
Cost ~
Resolution dx 1 1/2
SNR~
Stnd. Mig Multsrc. LSM
I=7
1 1/44
Cost vs Quality: Can I<<S? Yes.
What have we empirically learned?
S=320
Outline
1. Migration Problem and Encoded Migration
2. Standard vs Monte Carlo Least Squares Soln.
3. Numerical Results
4. S/N Ratio
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
Standard Migration SNR
GS# geophones/CSG
# CSGs
SNR= ...migrate
SNR=
d(t) = Zero-mean white noise [S(t) +N(t) ] Neglect geometric spreading
Standard Migration SNR
Standard Migration SNR
Assume:
migrate+++
stack
S1
SGS G~~
iterate
GI
Iterative Multisrc. Mig. SNR
# iterations
SNR=
Cost ~ O(S)
Cost ~ O(I)
SNR
0
1 Number of Iterations 300
7The SNR of MLSM image grows as the square root of the number of iterations.
SNR = GI
Summary
IO 1 1/100
Cost ~
Resolution dx 1 1/2
SNR
Stnd. Mig Multsrc. LSM
GS GI
S I
Cost vs Quality: Can I<<S?
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
Outline• Motivation• Multisource LSM theory• Signal-to-Noise Ratio (SNR)• Numerical results • Conclusions
Conclusions Mig vs MLSM
1.
2. Cost: S vs I
3. Caveat: Mig. & Modeling were adjoints of one another. LSM sensitive starting model
5. Next Step: Sensitivity analysis to starting model
SNR: VSGS GI
4. Unconventional encoding: I << S
2. Memory 1 vs 1/S
Back to the Future?
Poststackencoded migration
DMO Prestackmigration
1980s 1980s-2010 2010?
Evolution of Migration
Poststackmigration
1960s-1970s
1980
Multisource SeismicImaging
vs
copper
VLIW
Superscalar
RISC
1970 1990 2010
1
100
100000
10
1000
10000
Aluminum
Year202020001980
Spee
d
CPU Speed vs Year
Multisource Migration: mmig=LTd
Forward Model:
Multisource Phase Encoded Imaging
d +d =[L +L ]m1 221
L{d{
=[L +L ](d + d ) 1 221
T T
= L d +L d + 1 221
T T
L d +L d2 121
Crosstalk noiseStandard migration
T T
m = m +(k+1) (k)
FWI Problem & Possible Soln.• Problem: FWI computationally costly
• Solution: Multisource Encoded FWI Preconditioning speeds up by factor 2-3
Iterative encoding reduces crosstalk
Outline
1. Migration Problem and Encoded Migration
2. Standard vs Monte Carlo Least Squares Soln.
3. Numerical Results: Kirchhoff, Phase Shift, RTM
4. Summary
L1
L2
d 1
d 2m = vs N L + N L1 21 2[ ]m = [N d + N d ]1 21 2
top related