Making the Most from the Least (Squares Migration) G. Dutta, Y. Huang, W. Dai, X. Wang, and Gerard...

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