making the most from the least (squares migration) g. dutta, y. huang, w. dai, x. wang, and gerard...
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Making the Most from the Least (Squares Migration)
G. Dutta, Y. Huang, W. Dai, X. Wang, and Gerard SchusterKAUST
Standard Migration Least Squares Migration
Outline
• Summary and Road Ahead
• Problems with LSM: Cost and V(x,z) Sensitivity
• Multisource LSM: Gulf of Mexico Data
• Least Squares Migration:
• Examples of LSM:
• Viscoacoustic LSM: Marmousi & GOM data
x-yx-z
Problem: mmig=LTd
Migration Problems
Soln: m(k+1) = m(k) + a L Dd(k)T
Solution: Least squares migration
Given: d = Lmpredicted observed
= LModeling operatord
Find: min ||Lm - d ||2
m
defocusing
aliasing
Least Squares Migrationm(k+1) = m(k) + a L Dd(k)T
m = [LTL]-1LT d
Geom. Spreading: 1 -1 1 1 r4 r2 r2
Anti-aliasing:
[w(t) w(t)]-1w(t) w(t) Source Decon:
1/r 1/r
Aliasingartifacts
migrate model
Inconsistent events
Brief History of Least Squares Migration
Romero et al. (2000)
Tang & Biondi (2009), Dai & GTS (2009), Dai (2011, 2012),Zhang et al. (2013), Dai et al. (2013), Dutta et al (2014)
Multisource Migration
Multisource Least Squares Migration
Lailly (1983), Tarantola (1984)Linearized Inversion
Least Squares MigrationCole & Karrenbach (1992), GTS (1993), Nemeth (1996)Nemeth et al (1999), Duquet et al (2000), Sacchi et al (2006)Guitton et al (2006),
Outline
• Summary and Road Ahead
• Problems with LSM: Cost and V(x,z) Sensitivity
• Multisource LSM: Gulf of Mexico Data
• Least Squares Migration:
• Examples of LSM:
• Viscoacoustic LSM: Marmousi & GOM data
Acquisition Footprint Mitigation
0 10 0 10X (km)
0
10
Y (
km)
Standard Migration LSM
X (km)
5 sail lines200 receivers/shot45 shot gathers
RTM vs LSM
6.3 9.9X (km)
0.8
1.2
Z (
km)
Reverse Time Migration0.8
1.2
Z (
km)
Plane-Wave LSM
6.3 9.9X (km)
Outline
• Summary and Road Ahead
• Problems with LSM: Cost and V(x,z) Sensitivity
• Multisource LSM: Gulf of Mexico Data
• Least Squares Migration:
• Examples of LSM:
• Viscoacoustic LSM: Marmousi & GOM data
Problem #1 with LSMProblem: High Sensitivity to Inaccurate V(x,y,z)
b) Iterative LSM+MVA
LSM LSM+Statics
RTM+MVARTM+Traveltime Tomo
LSM CSG1
LSM CSG2
Partial Solutions: a) Statics corrections
Sanzong Zhang (2014)
Problem #2 with LSMProblem: LSM Cost >10x than RTM
Solution: Migrate Blended Supergathers
Standard Migration vs Multisource LSM
Given: d1 and d2
Find: m
Soln: m=L1 d1 + L2 d2T T
Given: d1 + d2
Find: m
= m(k) + a[L1 d1 + L2 d2 T T
+ L1 d2 + L2 d1T T
Soln: m(k+1) = m(k) + a (L1 + L2)(d1+d2)
T
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Iteratively encode data soL1T d2 = 0 and L2T d1 = 0
1 RTM to migrate manyshot gathers
1 RTM pershot gather
]
Benefit: 1/10 reduced cost+memory
0 6.75X (km)
0Z
(km
)1.
48
a) Original b) Standard Migration
Multisource LSM(304 blended shot gathers)
0 6.75X (km)
c) Standard Migration with 1/8 subsampled shots
0Z
(k
m)
1.48
0 6.75X (km)
d) 304 shots/gather26 iterations
38 76 152 304
9.4
5.4
1
Shots per supergather
Computational gain
Conventional migration:
SNR=30dB
Com
p. G
ain
Outline
• Summary and Road Ahead
• Examples of LSM:
• Problems with LSM: Cost and V(x,z) Sensitivity
• Multisource LSM: 3D SEG Salt Model
• Least Squares Migration:
• Viscoacoustic LSM: Marmousi & GOM data
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/s
uper-gather, 1
6 iterations
8 x gain in computational efficiency
3.7 km
Outline
• Summary and Road Ahead
• Examples of LSM:
• Problems with LSM: Cost and V(x,z) Sensitivity
• Multisource LSM: Gulf of Mexico Data
• Least Squares Migration:
• Viscoacoustic LSM: Marmousi & GOM data
Plane-wave LSRTM of 2D GOM Data
0 X (km) 16
0Z
(k
m)
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
(k
m)
2.5
Conventional 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
(k
m)
2.5
Z (
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
• Summary and Road Ahead
• Examples of LSM:
• Problems with LSM: Cost and V(x,z) Sensitivity
• Multisource LSM: 3D SEG Salt Model
• Least Squares Migration:
• Viscoacoustic LSM: Marmousi & GOM data
Viscoacoustic Least Squares Migration
m(k+1) = m(k) + a L Dd(k)T
L = viscoacoustic wave equation
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
Viscoacoustic 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
Road Ahead Summary
3. Sensitivity: Quality LSM = RTM if inaccurate v(x,y,z)
1. LSM Benefits: Anti-aliasing, better resolution, focusing
5. Broken LSM: Multiples. Quality degrades below 2 km? Collect 4:1 data?
2. Cost: MLSM ~ RTM, MLSM has better resolution
4. Viscoacoustic LSM: Required if Q<25?
6. Road Ahead: Iterative MVA+MLSM+Statics