Spectral Element Method and GPU Computing for Seismic Imaging Chaiwoot Boonyasiriwat May 1, 2010

Outline 1 Introduction to Seismic ImagingIntroduction to Seismic Imaging Spectral Element MethodSpectral Element Method GPU Computing and Computational SteeringGPU Computing and Computational Steering SummarySummary

Seismic Imaging 2 Given a seismic data setGiven a seismic data set Find a model that best describes the given data or minimizes the misfit function whereFind a model that best describes the given data or minimizes the misfit function where m?m?m?m? CSG Common shot gather

Seismic Imaging 3 m?m?m?m? Use iterative gradient-based methodsUse iterative gradient-based methods

Seismic Imaging in 3D 4 Improve efficiencyImprove efficiency Forward modeling: use better numerical methodsForward modeling: use better numerical methods Improve convergence rate: preconditioningImprove convergence rate: preconditioning Use many sources simultaneouslyUse many sources simultaneously

Forward Modeling 5 Important component of seismic imaging methodsImportant component of seismic imaging methods Numerically solving a wave equation, e.g., acoustic wave equationNumerically solving a wave equation, e.g., acoustic wave equation Numerical methods:Numerical methods: Finite differenceFinite difference Spectral/pseudo-spectralSpectral/pseudo-spectral Finite element/spectral elementFinite element/spectral element

Outline 6 Introduction to Seismic ImagingIntroduction to Seismic Imaging Spectral Element MethodSpectral Element Method GPU Computing and Computational SteeringGPU Computing and Computational Steering SummarySummary

Finite Element Methods 7

8 FDM vs FEM

Finite Element Formulation 9 Acoustic wave equation Weak form Linear combination of basis functions  where Matrix form Weighted residual method

10 Geophysical Applications of FEM Global-scaleGlobal-scale Exploration-scaleExploration-scale

Outline 11 Introduction to Seismic ImagingIntroduction to Seismic Imaging Spectral Element MethodSpectral Element Method GPU Computing and Computational SteeringGPU Computing and Computational Steering SummarySummary

Seismic Imaging on GPUs 12 High performance and large band-widthHigh performance and large band-width General-purpose computing on GPUs using CUDAGeneral-purpose computing on GPUs using CUDA Advanced hardware (GPUs) + algorithm (multisource imaging)Advanced hardware (GPUs) + algorithm (multisource imaging) Computational steering: computation + visualizationComputational steering: computation + visualization

13 Courtesy of NVIDIA 1000 Peak GFLOP/s Performance of GPU vs CPU

Memory Bandwidth of GPU vs CPU 14 Courtesy of NVIDIA 120 BandwidthGB/s

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 number Misfit value

True model Tomogram 1 Tomogram 2 18

Summary 19 Seismic imaging using spectral element methodsSeismic imaging using spectral element methods Global-scale waveform inversion using SEMGlobal-scale waveform inversion using SEM 3D seismic imaging on GPU cluster (CUDA+MPI)3D seismic imaging on GPU cluster (CUDA+MPI) Computational steering on GPU clusterComputational steering on GPU cluster