spectral element method and gpu computing for seismic imaging chaiwoot boonyasiriwat may 1, 2010
TRANSCRIPT
![Page 1: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/1.jpg)
Spectral Element Method andGPU Computing for Seismic Imaging
Chaiwoot BoonyasiriwatMay 1, 2010
![Page 2: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/2.jpg)
Outline
1
• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary
![Page 3: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/3.jpg)
Seismic Imaging
2
• Given a seismic data set )( trueobs A md
• Find a model that best describes the given data or minimizes the misfit function where
)(~ trialcalc A md
2)()( mddm calcobsE
m?CSG
Common shot gather
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Seismic Imaging
3
obsd
m?
• Use iterative gradient-based methods
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Seismic Imaging in 3D
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• Improve efficiency• Forward modeling: use better numerical methods• Improve convergence rate: preconditioning• Use many sources simultaneously
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Forward Modeling
5
• Important component of seismic imaging methods
)(md A
• Numerically solving a wave equation, e.g., acoustic wave equation
spvptt 22
• Numerical methods:• Finite difference• Spectral/pseudo-spectral• Finite element/spectral element
![Page 7: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/7.jpg)
Outline
6
• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary
![Page 8: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/8.jpg)
Finite Element Methods
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![Page 9: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/9.jpg)
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FDM vs FEM
![Page 10: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/10.jpg)
Finite Element Formulation
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Acoustic wave equation),(),()(),( 22 tstpvtptt rrrr
rrr vsdpdvvvpdtt2
Weak form
n
iii tPtp
1
)()(),( rr Linear combination of basis functions
FKPPM tt
rM dM jiijij ][
rK dvK jiijij 2][
where
Matrix form
rdspvpv tt22 Weighted residual method
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Geophysical Applications of FEM
• Global-scale• Exploration-scale
![Page 12: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/12.jpg)
Outline
11
• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary
![Page 13: Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010](https://reader035.vdocuments.net/reader035/viewer/2022062515/56649d215503460f949f709c/html5/thumbnails/13.jpg)
Seismic Imaging on GPUs
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• High performance and large band-width• General-purpose computing on GPUs using CUDA• Advanced hardware (GPUs) + algorithm
(multisource imaging)• Computational steering: computation + visualization
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13Courtesy of NVIDIA
1000
Pea
k G
FL
OP
/s 750
500
250
0
Performance of GPU vs CPU
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Memory Bandwidth of GPU vs CPU
14Courtesy of NVIDIA
120
Bandwidth
GB/s
100
80
60
40
20
0
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Conventional vs Multisource Method
Conventional RTM Image using 200 gathers
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Multisource RTM Image using 20 supergathers
10x speedup
Conventional vs Multisource Method
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Computational Steering
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• Initial model• Line search method• Regularization• Iteration number• Perturb model
manually (steering)
User Interface
Iteration numberM
isfi
t val
ue
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True model
Tomogram 1
Tomogram 218
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Summary
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• Seismic imaging using spectral element methods• Global-scale waveform inversion using SEM• 3D seismic imaging on GPU cluster (CUDA+MPI)• Computational steering on GPU cluster