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Benefits & Limitations of Least Squares Migration W.Dai,D.Zhang,X.Wang,GTS KAUST. RTM Least Squares RTM. GOM RTM GOM LSRTM. Can We Improve Quality Seismic Imaging?. Better Velocity Updates : FWI & MVA. Better Quality Images: LSM & Multiples. - PowerPoint PPT Presentation
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Benefits & Limitations of
Least Squares Migration
W.Dai,D.Zhang,X.Wang,GTS
KAUSTRTM Least Squares RTM
GOM RTM GOM LSRTM
Can We Improve Quality Seismic
Imaging?
Better Velocity Updates: FWI & MVA
Better Quality Images: LSM & Multiples
Outline
1. Theory: Multisource LSM2. Examples: Synthetic & Field Data3. Summary
Standard Migration vs Multisource Migration
Benefit: Reduced computation and memory
Liability: Crosstalk noise …
Given: d1 and d2
Find: mSoln: m=L1 d1 + L2 d2
T T
Given: d1 + d2
Find: m
= L1 d1 + L2 d2T T
+ L1 d2 + L2 d1T T
Soln: m = (L1 + L2)(d1+d2)T
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
K=1K=10
Multisource LSM & FWI
Inverse problem:
|| d – L m ||2~~1
2J =arg min
m
d misfit
m(k+1) = m(k) + a L d~T
Iterative update:
+ L1 d2 + L2 d1T T
L1 d1 + L2 d2T T
Brief Early History Multisource
Phase Encoded Imaging
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein, Lacasse, SEG Zhan+GTS, (2009)Virieux and Operto, EAGE, (2009)Dai, and GTS, SEG, (2009)
Migration
Waveform Inversion and Least Squares Migration
Biondi, SEG, (2009)
Outline
1. Theory: Multisource LSM2. Examples: 2D Marmousi Data3. Summary
0 6.75X (km)
0Z
(km
)1.
48
a) Original b) Standard Migration
Migration Images (input SNR = 10dB)
0 6.75X (km)
c) Standard Migration with 1/8 subsampled shots
0Z
(km
)1.
48
0 6.75X (km)
d) 304 shots/gather26 iterations
304 shots in total an example shot and its aperture
(Huang and Schuster, 2011, Multisource Least-squares Migration of Marine Streamer with Frequency-division Encoding )
38 76 152 304
9.48.06.65.4
1
Shots per supergather
Computational gain
Conventional migration:
SNR=30dB
Com
p. G
ain
38 76 152 304
9.48.0
6.65.4
3.8
1
Shots per supergather
Com
puta
tiona
l gai
n
Conventional migration:
Sensitivity to input noise level
SNR=10dB
SNR=30dB
SNR=20dB
Outline
1. Theory: Multisource LSM2. Examples: 3D SEG Salt3. Summary
a swath
16 swaths, 50% overlap
16 cables
100 m
6 km
40 m 256 sources
20 m
4096 sources in total
SEG/EAGE Model+Marine Data (Yunsong Huang)
13.4 km
3.7 km
Numerical Results(Yunsong Huang)
6.7 km
True reflectivities
3.7 km
Conventional migration
13.4 km
256 shots/super-gather, 1
6 iterations
8 x gain in computational efficiency
3.7 km
Outline
1. Theory: Multisource LSM2. Examples: 2D GOM Data LSRTM3. Summary
Plane-wave LSRTM of 2D GOM Data
0 X (km) 16
0Z
(km
)2.
5
2.1
1.5
km/s
• Model size: 16 x 2.5 km. • Source freq: 25 hz• Shots: 515 • Cable: 6km• Receivers: 480
0 X (km) 16
0Z
(km
)2.
5Conventional GOM RTM (cost: 1)
(Wei Dai)Z
(km
)2.
5
Plane-wave RTM (cost: 0.2)Plane-wave LSRTM (cost: 12)Encoded Plane-wave LSRTM (cost: 0.4)
0
0 X (km) 16
0Z
(km
)2.
5Z
(km
)2.
5
Plane-wave RTM (cost: 0.2)Plane-wave LSRTM (cost: 12)Encoded Plane-wave LSRTM (cost: 0.4)
0
RTMLSM
Conventional GOM RTM (cost: 1)(Wei Dai)
Outline
1. Theory: Multisource LSM2. Examples: 2D GOM Data LSRTM3. Summary
1. Theory: Multisource LSM2. Examples: 2D GOM Data KLSM3. Summary
1.5
Z
(km
)
0.9
10.5 X (km) 11.5
1.5
Z
(km
)
0.9
Multisource Least-squares Migration Image (>10X)
Kirchhoff Migration Image (1X)
K MKLS M (X. Wang)
Alias and Gap DataGOM data, aliased source and gap between 9.5 km and 10 km
Model Size: 3407 X 401 Interval: 6.25 m
# of shots: 248, ds = 75 m
# of receiver: 480, dg = 12.5 m
Streamer length: 6 kmRecord length: 10.24 s, dt=2ms
# of shots in supergather: 16
2.5
Z (k
m)
0
Velocity model
0 X( km) 18.8
1.5
2.2km/s
Velocity model is from FWI. (Boonyasiriwat et al., 2010)
A 10-15-70-75 Hz bandpass filter is applied.
# of supergather: 32
Source wave is generated from stacking near offset ocean bottom reflections.
Plane-wave LSRTM of 2D GOM Data
0 X (km) 16
0Z
(km
)2.
5
2.1
1.5
km/s
• Model size: 16 x 2.5 km. • Source freq: 25 hz• Shots: 515 • Cable: 6km• Receivers: 480
Mute 0.5 km data
KM VS LSM VS MSLSM
KM image
KM VS LSM VS MSLSM
LSM Image after 30 Iterations
KM VS LSM VS MSLSM
MSLSM Image after 30 Iterations
Outline
1. Theory: Multisource LSM2. Examples: 2D Salt Body with Multiples3. Summary
X (km) 16
Z (k
m)
RTM SEG Salt Data(Dongliang Zhang)
Z (k
m)
LSRTM with Born Multiples
0
0
16
16
01st-order Multiples
X (km) 16
Z (k
m)
RTM SEG Salt Data(Dongliang Zhang)
Z (k
m)
LSRTM with Born Multiples
0
0
16
16
0LSRTMRTM
X (km) 30
Z (k
m)
GOM Salt Data(Dongliang Zhang)
Z (k
m)
RTM with Multiples
0
0
3.0
3.0
0
X (km) 30
Z (k
m)
Starting Velocity Model
Z (k
m)
0
0
3.0
3.0
0
FWI(Abdullah AlTheyab)
What have we Empirically Learned about Quality?
1. LSM no better than RTM if inaccurate v(x,y,z)
3. Speckle noise in LSM
4. Multiples can be significantly enhanced if separated properly from primaries
5. FWI works for easy GOM data, not for hard salt
6. FWI & LSM quality degrades below 2 km?
7. Why? Unaccounted Physics? 1). Attenuation, 2). V(x,y,z), 3). ???
2. Cost MLSM ~ RTM; MLSM better resolution
0 Z (km) 1.5
0 X (km) 2
0 X (km) 2
1.0 -1.0
True Reflectivity
Acoustic LSRTM
0 X (km) 2
Viscoelastic LSRTM
1.0 -1.0
0 Z (km) 1.5
0 Z (km) 1.5
0 X (km) 2
Q Model
Q=20
Q=20000
IO 1 ~1/36
Cost
Resolution dx 1 ~double
MigrationSNR
Stnd. Mig Multsrc. LSM
~1
1 ~0.1
Cost vs Quality: Can I<<S? Yes.
What have we empirically learned about MLSM?
1