Improved seismic survey design by maximizing the spectral ...
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Georgia Institute of TechnologySLIM ML4Seismic
Yijun Zhang and Felix J. Herrmann
Improved seismic survey design by maximizing the spectral gap with global optimization
November 23, 2021
Released to public domain under Creative Commons license type BY (https://creativecommons.org/licenses/by/4.0) Copyright (c) 2021, Yijun Zhang (Georgia Tech)
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ML4Seismic
MotivationsSeismic data
‣ expensive to acquire
Random subsampling
‣ increasingly employed in seismic data acquisition
‣ reduce cost
Matrix completion (MC)
‣ reconstruct fully sampled wavefields from sparsely sampled seismic data
‣ computationally efficient method
Goal: Automatically generate sampling schemes that favor recovery by MC.
Rajiv Kumar, Curt Da Silva, Okan Akalin, Aleksandr Y. Aravkin, Hassan Mansour, Ben Recht, and Felix J. Herrmann, “Efficient matrix compleTon for seismic data reconstrucTon”, Geophysics, vol. 80, pp. V97-V114, 2015. Oscar Lopez, Rajiv Kumar, Nick Moldoveanu and Felix J. Herrmann, “Graph Spectrum Based Seismic Survey Design”, Submi_ed to Geophysics , 2020.
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ML4Seismic
MotivationsSimulation-based acquisition design
‣ expensive
‣ time consuming
Uniform & jittered sampling scheme
‣ not optimal
‣ is not flexible - i.e., cannot add constraints
Spectral gap (SG) of sampling mask
‣ the gap between the first & second singular value
‣ a cheap metric to predict a performance of an acquisition design
‣ should be large to ensure success of matrix completion
Come up with a quantity to predict wavefield reconstruction w/ MC
Oscar Lopez, Rajiv Kumar, Nick Moldoveanu and Felix J. Herrmann, “Graph Spectrum Based Seismic Survey Design”, Submi_ed to Geophysics , 2020. Bhojanapalli, Srinadh, and Prateek Jain. "Universal matrix compleTon." Interna'onal Conference on Machine Learning. PMLR, 2014. Burnwal, Shantanu Prasad, and Mathukumalli Vidyasagar. "DeterminisTc compleTon of rectangular matrices using asymmetric ramanujan graphs: Exact and stable recovery." IEEE Transac'ons on Signal Processing 68 (2020): 3834-3848. Mosher, C. C., S. T. Kaplan, and F. D. Janiszewski. "Non-uniform opTmal sampling for seismic survey design." 74th EAGE Conference and Exhibi'on incorpora'ng EUROPEC 2012. European AssociaTon of GeoscienTsts & Engineers, 2012.
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ML4Seismic
relationship between reconstruction quality & sampled matrixMotivation
binary sampling matrix
the first singular value
the second singular value
SG ratio
an average of 100 experiments
Large spectral gap corresponds to small SG ratio
M
σ1( . )
σ2( . )σ2(M)σ1(M)
Oscar Lopez, Rajiv Kumar, Nick Moldoveanu and Felix J. Herrmann, “Graph Spectrum Based Seismic Survey Design”, Submi_ed to Geophysics , 2020.
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ML4Seismic
Problem
Generate sampling scheme w/o expensive wavefield reconstruction
Take advantage of spectral gap, a cheap metric to evaluate an acquisition mask
Start with 2D acquisition on a grid…
Breakout 2. Acquisition design and wavefield reconstruction (code)Hands-on tutorial:
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ML4Seismic2D acquisition
Sources
Rece
iver
s
1
1
1
1
1
1
1
Source
ReceiversSampling mask in source-receiver domain
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ML4Seismic2D acquisition
Sources
Rece
iver
s
Receivers1 0
1 0
1 0
1 0
1 0
1 0
1 0
Sampled mask in source-receiver domain
Source
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ML4Seismic2D acquisition
Sources
Rece
iver
s
Receivers1 0 1
1 0 1
1 0 1
1 0 1
1 0 1
1 0 1
1 0 1
…
Sampled mask in source-receiver domain
Source
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ML4Seismic2D acquisition
Sources
Rece
iver
s
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
ReceiversSampled mask in source-receiver domain
Source
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ML4Seismic2D acquisition
Sources
Rece
iver
s
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
1 0 1 0 0 1 1
Sampled mask in source-receiver domain
0 0 0 0 0 1 1 0 0 0 0 0 0
0 0 0 1 1 0 0 1 1 0 0 0 0
0 1 1 0 0 1 1 0 0 0 0 1 0
1 0 0 1 1 0 0 0 0 1 1 1 1
0 0 1 0 0 0 0 1 1 1 1 0 0
0 0 0 0 0 1 1 1 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
OffsetsM
idpo
ints
Sampled mask in midpoint-offset domain
SG ratio = 0.804
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ML4Seismic2D acquisition
Sources
Rece
iver
s
Sampled mask in source-receiver domain
OffsetsM
idpo
ints
Sampled mask in midpoint-offset domain
SG ratio = 0.804
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ML4Seismic
Optimized problem2D acquisition
Given source locations & subsampling ratio , find subsampling locations
‣ : an operator that transfers the data from SR domain to midpoint-offset domain
‣ and : the first & second singular values
‣ , the number of sources & , the number of receivers.
‣ , the number of midpoints & , the number of offsets
ns r m = ⌊ns × r⌋ × nrX
minimizeX
σ2(𝒮X)σ1(𝒮X)
subject to ∥X∥0 = m, X ∈ [0,1]ns×nr .
𝒮
σ1( . ) σ2( . )
ns nr
nm no
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ML4Seismic
Simulated annealing (SA)Combinatorial search techniqueOutline:
‣Select a neighbor at random
- If better than current state, update the state (improving move)
- Otherwise, update current state w/ some probability (worsening move)
‣Probability goes down with time
High probability means diversify (many worsening moves)
Low probability means intensify (focus on improving moves)
Kirkpatrick, Scott, C. Daniel Gelatt, and Mario P. Vecchi. "Optimization by simulated annealing." science 220.4598 (1983): 671-680.Černý, Vladimír. "Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm." Journal of optimization theory and applications 45.1 (1985): 41-51.From: Ümit V. Çatalyürek; CSE 6140/ CX 4140: Computational Science and Engineering ALGORITHMS
?
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ML4SeismicSelect a neighbor at random
Previous state
Fix 80% subsampled positions, move 20% subsampled positions
Set move range
Move range = 2New neighbor state
: all possible locations; : initial subsampled locations; : to be moved location; : the new neighbor subsampled location
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ML4Seismic
Stylized example w/ equal source/receiver dimension (300 300)×
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ML4Seismic
Experiment 1Optimal SG ratio w/ simulated annealing
Mask dimension: 300 x 300
Subsampling ratio:
Source and receiver sampling interval: 12.5 m
Decrease the SG ratio of given initial subsampling masks:
‣ uniform random subsampling
‣ optimal jittered subsampling
33 %
Herrmann, Felix J., and Gilles Hennenfent. "Non-parametric seismic data recovery with curvelet frames." Geophysical Journal International 173.1 (2008): 233-248.
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ML4SeismicUniform random mask Initial state (input) of the optimal method
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ML4SeismicImproved random mask Output of the optimal method w/ SA algorithm
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ML4SeismicOptimal jittered maskInitial state (input) of the optimal method
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ML4SeismicImproved jittered maskOutput of the optimal method w/ SA algorithm
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ML4SeismicSG ratio comparisonW/ 10 independent tests
Uniform random
Improved random
Optimal jittered
Improved jittered
0.2
0.25
0.3
0.35
0.4
SG ra
tio
Subsampling ratio = 33%
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ML4Seismic
Synthetic example
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ML4Seismic
Experiment 2Test masks by using wavefield reconstruction (LR matrix completion)
Data dimension: 300 x 300 x 1024 (nr x ns x nt)
Dimension of each frequency slice: 300 x 300
Source sampling interval: 12.5 m
Receiver sampling interval: 12.5 m
Time sampling interval: 0.002 s
Rajiv Kumar, Curt Da Silva, Okan Akalin, Aleksandr Y. Aravkin, Hassan Mansour, Ben Recht, and Felix J. Herrmann, “Efficient matrix compleTon for seismic data reconstrucTon”, Geophysics, vol. 80, pp. V97-V114, 2015.
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ML4Seismic2D synthetic Compass dataset
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ML4Seismic
Scenarios
Use wavefield reconstruction to recover the subsampled data w/ 4 masks
‣Uniform random
‣ Improved random mask w/ proposed optimized method
‣Optimal jittered (w/ max gap control)
‣ Improved jittered subsampling w/ proposed optimized method
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ML4SeismicRecovery & differenceUniform random mask Difference = ground truth - recovery
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ML4SeismicRecovery & differenceImproved uniform random mask
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ML4SeismicRecovery & differenceOptimal jittered mask
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ML4SeismicRecovery & differenceImproved jittered mask w/ proposed method
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ML4SeismicSNR comparisonW/ 10 independent tests
Uniform random
Improved random
Optimal jittered
Improved jittered
11
11.5
12
12.5
13
13.5
14
14.5
SNR
[dB]
Subsampling ratio = 33%
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ML4SeismicSG ratio comparison vs. SNR comparisonW/ 10 independent tests
Uniform random
Improved random
Optimal jittered
Improved jittered
11
11.5
12
12.5
13
13.5
14
14.5
SNR
[dB]
Subsampling ratio = 33%
Uniform random
Improved random
Optimal jittered
Improved jittered
0.2
0.25
0.3
0.35
0.4
SG ra
tio
Subsampling ratio = 33%
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ML4Seismic
Stylized example w/ unequal source/receiver dimension (300 150)×
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ML4Seismic
Experiment 3Optimal SG ratio w/ simulated annealing
Mask dimension:
Subsampling ratio:
Source & receiver sampling interval: 12.5 m
Decrease SG ratio of given initial subsampling masks:
‣ uniform random subsampling
‣ optimal jittered subsampling
300 × 150
20 %
Herrmann, Felix J., and Gilles Hennenfent. "Non-parametric seismic data recovery with curvelet frames." Geophysical Journal International 173.1 (2008): 233-248.
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ML4SeismicSubsampled mask in source-receiver domainSubsampling ratio = 20 %
Sources
Receivers
Extension
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ML4SeismicSubsampled mask in source-receiver domainSubsampling ratio = 20 %
Reciprocity
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ML4SeismicUniform random mask Initial state (input) of the optimal method
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ML4SeismicImproved random mask Output of the optimal method w/ SA algorithm
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ML4SeismicOptimal jittered maskInitial state (input) of the optimal method
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ML4SeismicImproved jittered maskOutput of the optimal method w/ SA algorithm
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ML4SeismicSG ratio comparisonW/ 10 independent tests
Uniform random
Improved random
Optimal jittered
Improved jittered
0.24
0.26
0.28
0.3
0.32
0.34
Spec
tral r
atio
Subsampling ratio = 20%
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ML4Seismic
Conclusion & future works
Improved seismic survey design w/o expensive wavefield reconstruction
Proposed optimization scheme that finds subsampling masks w/ small SG ratio
Optimized masks improve wavefield reconstruction
Test reconstruction quality w/ unequal source/receiver dimension
3D seismic data survey design
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ML4Seismic
Thank you for your attention!