spectral element method and gpu computing for seismic imaging chaiwoot boonyasiriwat may 1, 2010
TRANSCRIPT
Spectral Element Method andGPU Computing for Seismic Imaging
Chaiwoot BoonyasiriwatMay 1, 2010
Outline
1
• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary
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
Seismic Imaging
3
obsd
m?
• Use iterative gradient-based methods
Seismic Imaging in 3D
4
• Improve efficiency• Forward modeling: use better numerical methods• Improve convergence rate: preconditioning• Use many sources simultaneously
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
Outline
6
• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary
Finite Element Methods
7
8
FDM vs FEM
Finite Element Formulation
9
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
10
Geophysical Applications of FEM
• Global-scale• Exploration-scale
Outline
11
• Introduction to Seismic Imaging• Spectral Element Method• GPU Computing and Computational Steering• Summary
Seismic Imaging on GPUs
12
• High performance and large band-width• General-purpose computing on GPUs using CUDA• Advanced hardware (GPUs) + algorithm
(multisource imaging)• Computational steering: computation + visualization
13Courtesy of NVIDIA
1000
Pea
k G
FL
OP
/s 750
500
250
0
Performance of GPU vs CPU
Memory Bandwidth of GPU vs CPU
14Courtesy of NVIDIA
120
Bandwidth
GB/s
100
80
60
40
20
0
15
Conventional vs Multisource Method
Conventional RTM Image using 200 gathers
16
Multisource RTM Image using 20 supergathers
10x speedup
Conventional vs Multisource Method
Computational Steering
17
• Initial model• Line search method• Regularization• Iteration number• Perturb model
manually (steering)
User Interface
Iteration numberM
isfi
t val
ue
True model
Tomogram 1
Tomogram 218
Summary
19
• 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