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