multisource least-squares migration multisource least-squares migration of marine streamer data with...
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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