1. Fast Multisource Least Squares Migration of 3D Marine Data with
Frequency Encoding
Yunsong Huang and Gerard Schuster
KAUST vs

2. RTM Problem & Possible Soln.
Problem: RTM computationally costly; IO high
Solution: Multisource LSM RTM
Preconditioning speeds up by factor 2-3
Encoded LSM reduces crosstalk. Reduced comp. cost+memory
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 2

3. Outline Phase Encoded Multisource LSM Problem with Marine Data
Phase Encoded Multisource LSM with Frequency Selection
Numerical results
Conclusions
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 3

4. Multisource Data vs mmig =[L +L ](d + d ) Time Shift Encoding1
d1+d2 = [L1+L2]m
migrate
m ~ [L1+L2](d1+d2) T
= L1d1+L2d2+L1d2+L2d1 T
standard mig.
crosstalk vs
Benefit: Only one migration
Problem: Low SNR

5. Multisource Migration:
Iterative Phase Encoded Multisource Migration d { L {
d +d =[L +L ]m 1 2
Forward Model:
Multisource Migration:
mmig=LTd
mmig T T
=[L +L ](d + d ) 1 2
Standard migration
mmig T T T T
= L d +L d + 1 2
L d +L d 2 1
Crosstalk noise
mmig T T T T
= L d +L d +
L d +L d 1 1 2 2 1 2 2 1
mmig
= L d +L d 1 1 2 2

6. Phase Encoded Multisrce Least Squares Migration{ L {
d +d =[L +L ]m 1 2
Forward Model:
Multisource Migration:
mmig=LTd
mmig T T
=[L +L ](d + d ) 1 2 T T T T
m = m +
(k+1)
(k)
= L d +L d + 1 2
L d +L d 2 1
Crosstalk noise
Standard migration
K=20
K=1

7. Land SEG/EAGE Salt Reflectivity Model
Z (km)
1.4 6
X (km)
Use constant velocity model with c = 2.67 km/s
Center frequency of source wavelet f = 20 Hz
320 shot gathers, Born approximation
Encoding: Dynamic time, polarity statics + wavelet shaping
Center frequency of source wavelet f = 20 Hz
320 shot gathers, Born approximation

8. Standard Land Phase Shift Migration vs MLSM
Standard Phase Shift Migration (320 CSGs)
1 x
Z k(m)
1.4
X (km) 6
Multisource PLSM (320 blended CSGs, 7 iterations)
Z (km)
1 x 44
1.4
X (km) 6

9. Single-source Land PSLSM
(Yunsong Huang)
1.0
Conventional encoding: Polarity+Time Shifts
Model Error
Jerry,
The multi-source and single-source approaches have used different strategies for the step length. Therefore direct comparison of their misfit error is not applicable. Sorry about that.
Unconventional encoding
0.3
Iteration Number 50

10. Outline Phase Encoded Multisource LSM Problem with Marine Data
Phase Encoded Multisource LSM with Frequency Selection
Numerical results
Conclusions
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 10

11. the acquisition geometry
Land Multisource FWI
Fixed spread
Simulation geometry must be consistent with
the acquisition geometry

12. Marine Multisource FWI
Mismatch solution with marine data
Observed
marine data
Simulated
land data
Freq. encoding
Decode & mute
purify
4 Hz
8 Hz
4 Hz
8 Hz
4 Hz
8 Hz
F.T.,
freq. selec.
wrong
misfit
Blend
Let’s focus on the white receiver…, how the frequency encoding could save the day.
8 Hz
4 Hz

13. Multisource FWI Freq. Sel. Workflow
m(k+1) = m(k) + a L Dd ~T
For k=1:K
end
Select unique frequency for each src
d d 
Filter and blend observed data: dd
dpred dpred 
Purify predicted data: dpreddpred
Let’s focus on the white receiver…, how the frequency encoding could save the day.
Data residual: Dd=dpred-d

14. Outline Aim of the study Multisource Low-discrepancy frequency coding
Mismatch solution with marine data
Low-discrepancy frequency coding
Numerical results
Conclusions 14

15. Low-discrepancy Frequency Encoding
Standard
Source index 1 60
Low-discrepancy
encoding
Frequency index 1 60 60 60
Frequency index
Frequency index 1 1
Source index 1 60

16. Outline Aim of the study Multisource Low-discrepancy frequency coding
Mismatch solution with marine data
Low-discrepancy frequency coding
Numerical results
Conclusions 16

17. Multisource Least Squares Migration Marine Geometry
m’ = m LT[Lm - d]
f ~ [LTL]-1 f
Steepest Descent
Preconditioned
z (km) 4 8
x (km)

18. Multisource Least-squares vs Standard Migration
a) Original
b) Standard Migration
Z (km)
1.48
c) 4 groups
50 iterations
d) 1 group
50 iterations
Z (km)
1.48
X (km)
6.75
X (km)
6.75

19. Conventional Migration
64 shots/gather
128 shots/gather
32 shots/gather
256 shots/gather
Conventional Migration
‘14%’ is chosen to equate the computational complexity of this migration (with fewer # of sources) with that of Least Squares multisource migration.
The idea is, less computation can be achieved simply by using fewer CSGs. The point made in this plot is, this naïve approach yields poor result, as indicated by the dashed yellow line, of relatively large model error.
N_{shots}/ gather: # of shots contained in a super-gather
SNR: the observed data (which forms the objective function of LS) has been intentionally added with random band-limited noise, such that the SNR=10dB. This is to study the robustness of our approach.
Red dots signify where the LS multisource migration results are perceptually comparable to that of the standard migration.
The computational cost of the LS multisource migration is computed based on those numbers.

20. SEG/EAGE Model+Marine Data
sources in total
40 m
100 m
16 swaths,
50% overlap
256 sources
a swath
6 km
3.7 km
20 m
16 cables
13.4 km

21. Numerical Results 8 x True reflectivities Conventional migration
6.7 km
True reflectivities
Conventional migration
3.7 km
256 shots/super-gather, 16 iterations
The multisource result is of slightly higher resolution than the conventional shot-gather migration; indistinguishable in this size on screen.
13.4 km
8 x

22. Frequency-selection FWI of 2D Marine Data
Shots: 60
Source freq: 8 Hz
Receivers/shot: 84
Cable length: 2.3 km
Z (km)
1.5
4.5
(km/s)
1.5
6.8
X (km)

23. FWI images Actual model Starting model Standard FWI Multisource FWI
Z (km)
1.5
Starting model
Standard FWI
(69 iterations)
Z (km)
1.5
X (km)
6.8
Multisource FWI
(262 iterations)
X (km)
6.8

24. Conclusions Frequency selection is implemented in FDTD
2 x time steps per forward or backward modeling
Low-discrepancy frequency encoding
affects no asymptotic rate of convergence
helps to reduce model error in the beginning of simulation
4x speedup for the multisource FWI on the synthetic marine model 24

25. Step 1: Frequency Selection/Shot Step 2: Pass only red to right of
Pass only green between
d = [L mk - d]
Simulation result
Observed data
Still mismatch between d and L mk  erroneous big d
combined by
frequency selective multisource

26. Outline Phase Encoded Multisource LSM Problem with Marine Data
Phase Encoded Multisource LSM with Frequency Selection
Numerical results
Conclusions
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 26

27. Multisource Data mmig =[L +L ](d + d ) mmig =[L +L ](d + d )
Time Shift Encoding
d1 +d2
mmig T T
=[L +L ](d + d )
Time
d d2 1
d1+d2 = [L1+L2]m
migrate
m ~ [L1+L2](d1+d2) T
= L1d1+L2d2+L1d2+L2d1 T
crosstalk
Time Shift + Frequency Encoding
S(w)
Time 1 T
d1 +d2
mmig T
=[L +L ](d + d ) w
d d2 2
d1+d2 = [L1+L2]m
migrate
m ~ [L1+L2](d1+d2) T
= L1d1+L2d2+L1d2+L2d1 T

28. Frequency Selection per Shot Gather
R(w)
Frequency bands of source spectrum w
20 m
216 channels
Group 1
76 sources/group
The colors of every hydrophone denote its ‘pass frequency’. That is, non-colored frequency bands are filtered out.
By this frequency-selection mechanism, we can winnow out the undesired contributions at each hydrophone from other sources when these sources are grouped together for simulation.
2.2 km

29. Outline Phase Encoded Multisource LSM Problem with Marine Data
Phase Encoded Multisource LSM with Frequency Selection
Numerical results: 2D
Conclusions
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 29

30. Sensitivity to Noise Level
SNR=30dB
SNR=10dB
SNR=20dB
LSFDMS stands for Least-squares Frequency Selection Multi-Source
Different noise levels have been tried, with essentially the same results.
Here, strict frequency selection is honored, that is, simultaneous sources have absolutely non-overlapping frequency channels.
This restriction precludes more aggressive multi-sourcing. Thus the speedup factor is smaller than the eyebrow-raising 40ish.
256 frequency channels are assumed to be available. Thus each super-gather can meaningfully include at most about 256 sources.

31. Outline Phase Encoded Multisource LSM Problem with Marine Data
Phase Encoded Multisource LSM with Frequency Selection
Numerical results: 3D
Conclusions
My talk is organized in the following way:
1. The first part is motivation. I will talk about a least squares migration (LSM ) advantages and challenges.
2. The second part is theory for a deblurring filter, which is an alternative method to LSM.
3. In the third part, I will show a numerical result of a deblurring filter.
4. The fourth is the main part of my talk.
Deblurred LSM (DLSM) is a fast LSM with a deblurring filter.
I will explain how to use the filter in LSM algorithm.
5. Then I will show numerical results of the DLSM.
6. Then I will conclude my presentation.
Each figure has a slide number is shown at the footer. 31

32. Cost vs Quality: Can I<<S? Yes.
What have we empirically learned?
Stnd. Mig Multsrc. LSM
IO /320
Cost ~ 1 ~1
SNR~
Resolution dx double
Cost vs Quality: Can I<<S? Yes.

33. Conclusions Mig vs MLSM1.
SNR: VS GS GI
# geo
# srcs
# iterations
2. Memory: 1/S Cost: O(1/10)
2. Cost: S vs I
3. Caveat: Mig. & Modeling were adjoints of one another. LSM sensitive starting model
Second I compute reflectivity model within this offset range from the velocity and density models.
I also created a source wavelet that mimics an air gun source signature.
Fdom = 25 Hz.
4. Unconventional encoding: I << S
Next Step: Sensitivity analysis to starting model 33

34. Acknowledgments Schlum-WesternGeco Aramco Total BP Tullow Chevron
Thanks Sponsors of Center for Seimsic Imaging
And Fluid Modeling (CSIM) at KAUST
Schlum-WesternGeco
Total
Tullow
Veritas
Aramco BP
Chevron
Pemex
Petrobras
Second I compute reflectivity model within this offset range from the velocity and density models.
I also created a source wavelet that mimics an air gun source signature.
Fdom = 25 Hz. 34

35. Land Data: Src shootsall phones, so does FD modeler. This is good.
Marine Data: Src shootslimited phones, but FD modeler shoots all. This is bad.
d = [L mk - d]
Simulation result
Observed data
combined by
multisource
Mismatch between d and L mk  erroneous big d

36. Outline Aim of the study Multisource Migration
Mismatch solution with marine data
Low-discrepancy frequency coding
Numerical results
Conclusions 36

37. low-discrepancy encoding
Convergence Rates
Waveform error
Faster initial convergence rate of the white curve 1
1 supergather,
standard encoding
Same asymptotic convergence rate of the red and white curves
Log normalized
by individual sources
1 supergather,
low-discrepancy encoding
3.8 x
0.025 1 69
262
Log iteration number

38. low-discrepancy encoding
Convergence Rates
Speedup
60 / 2 / 2 / 3.8 = 4
Velocity error 1
Gain
60: sources
Overhead factors:
2 x FDTD steps
2 x domain size
3.8 x iteration number
1 supergather,
standard encoding
Log normalized
by individual sources
1 supergather,
low-discrepancy encoding
3.8 x
0.35 1 69
262
Log iteration number

39. Low-discrepancy encoding is 12% to 3x faster initially than
Convergence Rates
Velocity error (normalized)
Low-discrepancy encoding is
12% to 3x faster initially than
Standard encoding 1
standard encoding 10
0.75 1
iteration number