SEG2015_Li_Zhao_Reduced_Rank_LSRTMcbs.pdf

An Imaging Perspective of Low-
Rank Seismic Data Reconstruction

1. An Imaging Perspective of Low-
Rank Seismic Data Reconstruction
W. Li and Y. Zhao

2. •We recommend integrated data reconstruction and imaging
–Reconstruct data that directly contribute to improved image
–Avoid complexity and storage due to independent data reconstruction
Why:
•Low-rank data reconstruction done independent of imaging
–Large complexity overhead, SNR metric inconsistent with imaging
performance
•Migration based imaging
–Migration acts as data interpolator, quality of which depends on wave physics
Main Points

3. LS Migration of Incomplete Data – version 1999
Imaging can be robust to missing data

4. •Data approximation with rank constraints
•Assumptions
-Clean/complete data would be low-rank (in certain transformed domain)
-Effect of noise or missing traces increases the rank of the data
-Data reconstruction improves imaging
Low-Rank Data Reconstruction: Overview
rank constraints:
sum of singular values
Approximation error
at observed traces
sampling
operator
domain
transform
measured
traces

5. •Existing methods
-Truncated SVD (e.g. SSA/Cadzow) [Trickett2010), Oropeza & Sacchi 2011]
-Matrix completion ,efficient optimization instead of SVD [Yang2012, Lee2010, Aravkin2014],
-Tensor based methods [Kreimer&Sacchi 2012; Ely2013; Da Silva &Herrmann2013]
•Potential drawbacks
-Complexity: e.g. �(�
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��
� �� ��) with � the approximate rank, large overhead
cost
-Domain transform for low rank can be case-dependent
Low-Rank Data Reconstruction: Status

6. Low-Rank Data Reconstruction: Performance
•Quality metrics
synthetic data: real data:
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2
2
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2
2
10푙�?
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2
2
�(�−�
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•Performance trade-off
–Distortion in observed traces while reduce noises or completing traces
•Limitation: pure data metrics, may not be consistent with imaging performance
� - sampling operator
� - reconstructed data
�
����- true complete data
�
�����- observed data

7. •What is the NET GAIN in imaging from doing data reconstruction?
•Can reconstruction be image-oriented at lower cost?
•Would an integrated approach be a better option
–improved image quality than RTM of incomplete/noisy data
–reduced complexity than reconstruction+RTM
That Brings the Questions:

8. An Integrated Approach
Low-Rank Data
Reconstruction
Imaging
6000
0
600040002000
Receiver Receiver
Depth (m)
Horizontal distance (m)

9. An Integrated Approach
6000
0
600040002000
Reduced-Rank
LSRTM Imaging

10. •We recommend integrated data reconstruction and imaging
–Reconstruct data that directly contribute to improved image
–Avoid complexity and storage due to independent data reconstruction
Why:
•Low-rank data reconstruction done independent of imaging
–Large complexity overhead, SNR metric inconsistent with imaging
performance
•Migration based imaging
–Migration acts as data interpolator, quality of which depends on wave physics
Main Points