Multisource Least-Squares Migrationof Marine Streamer Data withFrequency-Division Encoding

Yunsong Huang and Gerard SchusterKAUST

Outline

• Multisource LSM• Problem with Marine Data• Multisource LSM with Frequency

Division• Numerical results • Conclusions

Multisource

vs

Benefit:Reduction in computation and memory

Liability:Crosstalk noise …

d1+d2 = [L1+L2]m

=[L +L ](d + d ) 1

T TmmigTim

e

crosstalk

migrate m ~ [L1+L2](d1+d2)T T

= L1d1+L2d2+ L1d2+L2d1TT T T

d1 d2 d1 +d2

vs

standard mig.

Multisource (2)

d~

blended data

L~

blended forward modeling operator

K=1K=10

Multisource LSM

Inverse problem:

|| d – L m ||2~~1

2J =arg min

m

d misfit

m(k+1) = m(k) + a L d~T

Iterative update:

Outline

• Multisource LSM• Problem with Marine Data• Multisource LSM with Frequency

Division• Numerical results • Conclusions

observeddata

simulateddata

misfit = erroneous

misfit

Problem with Marine Data

Outline

• Multisource LSM• Problem with Marine Data• Multisource LSM with Frequency

Division• Numerical results • Conclusions

Solution- Every source sends out a unique identifier that

survives LTI operations- Every receiver acknowledge the contribution from

the ‘correct’ sources.

observed simulated

152 sources/group

R( )w

Group 1

Nw frequency bands of source spectrum:

Frequency Division

2.2 km

w

N w = 5 ttrav fpeak

Outline

• Multisource LSM• Problem with Marine Data• Multisource LSM with Frequency

Division• Numerical results (2D) • Conclusions

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

Iteration number

0.5

0.4

0.3

0.2

0.13 6 9 15 21 30 39

1

0

Convergence curves. Input SNR = 10dBN

orm

aliz

ed

dat

a m

isfi

t

304 shots/gather

38 shots/gather

Conjugate gradient

Encoding anew andresetting search direction

38 76 152 304

9.48.0

6.6

5.4

3.8

1

Shots per supergather

Co

mp

uta

tion

al g

ain

Conventional migration:

Sensitivity to input noise level

SNR=10dB

SNR=30dB

SNR=20dB

• Ns: # shots subsumed in a supergather• Nit: # of iterations that call for new encoding

(i.e., new frequency division scheme)

i) If data is stored on hard disk– The I/O cost of our proposed method is Nit/Ns

times that of standard migration.

ii) If data is stored on tape– The I/O cost of our proposed method is 1+ e

times that of standard migration.

I/O considerations

Conventional migration

Proposed method

I/O cost

i) Dataon hard disk

ii) Data on tape

3

Stacked migration vs successive least-squares

(1)m

stacked migration:

successiveleast-squares:

i id L m

21

321

† † †1 1 2 2 1 3m = L d + L d + L d†L d

1

0

2(2)m

3

(3)m

Outline

• Multisource LSM• Problem with Marine Data• Multisource LSM with Frequency

Division• Numerical results (3D)• Conclusions

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

13.4 km

3.7 km

Numerical Results

3.7 km

6.7 km

True reflectivities

Conventional migration

13.4 km

256 shots/s

uper-gather, 1

6 iterations

8 x gain in computational efficiency

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?

1