Transcript Extended Diffraction-Slice Theorem for Wavepath Traveltime

Multisource Least-Squares Migration
of Marine Streamer Data with
Frequency-Division Encoding
Yunsong Huang and Gerard Schuster
KAUST
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 …
Multisource (2)
vs
T
T
mmig =[L +L ](d + d )
d2 1
d1
d1+d2 = [L1+L2]m
~
d
migrate
~
L
blended blended forward
data modeling operator
d1 +d2
T
T
m ~ [L1+L2](d1+d2)
= L1standard
d1+Lmig.
2d2+ L1d2+L2d1
crosstalk
T
T
T
T
Multisource LSM
Inverse problem:
arg min J =
m
1
2
~ ~
|| d – L m ||2
misfit
d
Iterative update:
~
T
(k+1)
(k)
m
=m +aLd
K=1
K=10
Outline
• Multisource LSM
• Problem with Marine Data
• Multisource LSM with Frequency
Division
• Numerical results
• Conclusions
Problem with Marine Data
misfit =
observed
data
erroneous
misfit
simulated
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
Frequency Division
R(w)
Nw frequency bands of source spectrum:
Nw = 5 ttrav fpeak
w
152 sources/group
Group 1
2.2 km
Outline
• Multisource LSM
• Problem with Marine Data
• Multisource LSM with Frequency
Division
• Numerical results (2D)
• Conclusions
Migration images (input SNR = 10dB)
an example shot and its aperture
0
304 shots in total
b) Standard Migration
c) Standard Migration with
1/8 subsampled shots
d) 304 shots/gather
0 1.48
Z (km)
a) Original
1.48
Z (km)
26 iterations
0
X (km)
6.75 0
X (km)
6.75
Convergence curves. Input SNR = 10dB
1
Normalized data misfit
Conjugate gradient
Encoding anew and
resetting search direction
0.5
0.4
0.3
0.2
0.1
0
3
6
9
15
21
Iteration number
30
39
Sensitivity to input noise level
9.4
8.0
Computational gain
6.6
5.4
3.8
Conventional migration:
1
38
76
152
Shots per supergather
304
I/O considerations
• 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 cost
i) Data
on hard disk
ii) Data
on tape
Conventional
migration
Proposed
method
Stacked migration vs
successive least-squares
3
1
2
stacked
migration:
0
di  Lim
successive
least-squares:
1
1
2
3
m
(1)
2
m
(2)
3
m = L†1d1 + L†2d2 + L†1d3
 L†d
m
(3)
Outline
• Multisource LSM
• Problem with Marine Data
• Multisource LSM with Frequency
Division
• Numerical results (3D)
• Conclusions
SEG/EAGE Model+Marine Data
100 m
256 sources
40 m
4096 sources
in total
6 km
20 m
3.7 km
16 cables
13.4 km
Numerical Results
6.7 km
3.7 km
13.4 km
8 x gain in computational
efficiency
What have we empirically learned?
Stnd. Mig
Multsrc. LSM
IO
1
~1/36
Cost
1
~0.1
Migration
SNR
Resolution dx
1
~1
1
~double
Cost vs Quality: Can I<<S? Yes.