Transcript Slide 1

Multi-source Wave Equation Least-squares
Migration with a Deblurring Filter
Wei Dai
Jan. 7, 2010
Outline
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Motivation
Theory
Numerical Tests
Conclusion
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Motivation
Multi-source least-squares migration reduces the data size by
hundreds of times, thus lifts the I/O burden and saves computation
time.
The multi-source least-squares migration algorithm can be applied
with reverse time migration with two advantages:
1.RTM usually produces images of better quality than KM
does in complex medium.
2.Significant increase in computational efficiency can be achieved.
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Theory
With multi-source data
shots, the supergathers:
is the time delay operator
multi-source modeling
operator as
Is modeling operator associated
with individual shot
multi-source migration
operator as
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Theory
2-4 stagged grid finite difference
forward modeling operator:
Linearized forward
modeling operator:
no born approximation
is the scattered field
is the reflectivity model
Is the background velocity
model
Reverse time migration
operator:
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Theory
Standard migration image:
signal
(KM image)
noise
Least-squares migration image:
Goal:
1. Suppress crosstalk noise
2. Invert the Hessian
Advantage:
Modeling and migrating all the multiple sources together to increase
the computational efficiency.
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Numerical Tests
Model: Marmousi2
Size: 800X100
Grid interval: 20 m
Source: 800
Receiver: 800
0
m/s
3000
Z (m)
4500
1500
0
X (m)
Figure 1. Decimated Marmousi2 Model.
16000
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Background Velocity Model
3000
Z (m)
0
m/s
4500
0
X (m)
16000
1500
Figure 2. Smooth background velocity model.
(Marmousi2 model after 7x7 moving average filtering)
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3000
Z (m)
0
Standard RTM image
0
X (m)
16000
Figure 3. RTM image with conventional source.
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3000
Z (m)
0
Standard RTM image after Laplacian filtering
0
X (m)
16000
Figure 4. RTM image with conventional source
after Laplacian filtering.
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3000
Z (m)
0
Single Source LSRTM image:
15 iterations
25 times computation
0
X (m)
16000
Figure 5. LSRTM image with conventional source after
15 iterations. Total computation is about 25 times
compared to RTM (Figure 3).
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3000
Z (m)
0
Deblurred image: 2 times computation
0
X (m)
16000
Figure 6. RTM image with conventional source
after deblurring filtering.
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3000
Z (m)
0
RTM image of 100-shot supergathers:
1/100 computation
0
X (m)
16000
Figure 7. RTM image of 100-shot supergathers.
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3000
Z (m)
0
LSRTM image of 100-shot supergathers:
15 iterations
¼ computation
0
X (m)
16000
Figure 8. LSRTM image of 100-shot supergather after
15 iterations.
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3000
Z (m)
0
LSRTM of 100-shot supergathers V.S. Standard RTM
(after Laplacian filtering)
X (m)
16000
3000
Z (m)
0
0
0
X (m)
16000
15
3000
Z (m)
0
LSRTM of 100-shot supergathers with a
deblurring filter: ¼ computation.
0
X (m)
16000
Figure 10. LSRTM image of 100-shot supergathers
after 15 iterations with a deblurring filter.
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0.4
Data Residual
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Convergence Curves of LSRTM of 100-shot
Supergathers with and without deblurring
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Iterations
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Figure 11. Convergence curves of LSRTM of 100-shot
supergathers, with and without the deblurring filter.
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Conclusion
• LSM can suppress cross-talk noise in multi-source
data when supergathers consist 100 shots.
• Computation cost is reduced to ¼ compared to
standard RTM.
• The deblurring filter removes the migration
artifacts and accelarates convergence
• The data size is reduced by 100 times. Thus, our
algorithm is perfect for implementations of GPUs.
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Limitations
• The deblurring filter introduces artifacts.
• LSM introduces high frequency noise.
• More iterations cannot improve the LSRTM
image.
Future work
• Improve the deblurring filter
• The multi-source LSRTM algorithm can be
applied with VIT/TTI medium.
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Acknowledgement
We would like to thank the
UTAM 2009 sponsors for their
support.
Thank You
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