基于交错网格Fourier伪谱微分矩阵算子的地震波场模拟GPU加速方案
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摘要
作为高精度波形反演或逆时偏移的重要组成部分,地震波数值模拟对计算速度和效率提出了更高要求.GPU通用计算技术的产生及其内在数据并行性,为高效地震波数值模拟应用和研究得以有效开展奠定了基础.本文借助交错网格的Fourier伪谱微分矩阵算子和GPU上高效矩阵乘法,实现了复杂介质中地震波模拟的高效算法.数值试验表明,优化后的GPU计算相比CPU单核计算在大规模二维地震波场计算中获得至少100x以上的加速比.这对我们快速分析目标反射层在地震剖面中同相轴位置,制定优化采集方案具有重要意义.
As a crucial part of high-resolution waveform inversion and reverse time migration, seismic modeling demands a high efficiency of computation. The general-purpose GPU computing technology provides a fundamental basis as for GPU was naturally designed with data parallelism. By virtue of staggered-grid Fourier pseudo-spectral differentiation matrix operator, solving wave equation can be easily implemented on GPU by matrix multiplication. In large-scale two-dimensional wavefield computation, optimized single GPU forward seismic modeling can achieve at least 100x faster than that of single CPU using only one core. The high speedup of GPU/CPU implementation enables us to quickly recognize seismic events of the reflectors of different layers in common shot profile, which is helpful for optimizing the acquisition configuration in field work.
As a crucial part of high-resolution waveform inversion and reverse time migration, seismic modeling demands a high efficiency of computation. The general-purpose GPU computing technology provides a fundamental basis as for GPU was naturally designed with data parallelism. By virtue of staggered-grid Fourier pseudo-spectral differentiation matrix operator, solving wave equation can be easily implemented on GPU by matrix multiplication. In large-scale two-dimensional wavefield computation, optimized single GPU forward seismic modeling can achieve at least 100x faster than that of single CPU using only one core. The high speedup of GPU/CPU implementation enables us to quickly recognize seismic events of the reflectors of different layers in common shot profile, which is helpful for optimizing the acquisition configuration in field work.
引文
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[27] http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/NVIDIA_CUDA_Programming_Gui de_2． 3． pdf
[2] http://developer.download.nvidia.com/compute/curia/2 3/docs/CUDA Getting Started 2． 3． Linux.pdf
[3] Owens J D,Houston M,Luebke D,et al.GPU Computing.Proceedings of the IEEE,2008,96(5) :879～899
[4] Nguyen H,Zeller C,Hart E,etal.GPU Gems3． Addison-Wesley Professional,2007
[5] Cohen J M,Molemaker M J.A fast double precision CFD code using CUDA.Proceedings of Parallel CFD,2009
[6] Micikevicius P.3D finite difference computation on GPUs using CUDA.GPGPU-2:Proceeding of 2~(nd)Workshop on General Purpose Processing on Graphics Processing Units(New York,USA),ACM,2009． 79～84
[7] Johansen O.Seismic Shot Processing on GPU[Master's thesis].Norway:Norwegian University of Science and Technology,2009
[8] Abdelkhalek R,Calandra H,Coulaud O,et al.Fast seismic modeling and reverse time migration on a GPU cluster.The 2009 High Performance Computation & Simulation-HPCS' 09,2009
[9] http://www.acceleware.com/tasks/sites/default/assets/pdf/Acceleware_SEG_2009_RTMonGPU.pdf
[10] http://www.geostar.net.cn/show.php?id=85
[11] 李博,刘国峰,刘洪.地震叠前时间偏移的一种图形处理器提速实现方法.地球物理学报,2009,52(1) :245～252 Li B,Liu G F,Liu H.A method of using GPU to accelerate seismic pre-stack time migration.Chinese J.Geophys.(in Chinese),2009,52(1) :245～252
[12] 刘国峰,刘洪,李博等.山地地震资料叠前时间偏移方法及其GPU实现.地球物理学报,2009,52(12) :3101～3108 Liu G F,Liu H,Li B,et al.Method of prestack time migration of seismic data of mountainous regions and its GPU implementation.Chinese J.Geophys.(in Chinese),2009,52(12) :3101～3108
[13] Zhang J H,Wang S Q,Yao Z X.Accelerating 3D Fourier migration with graphics processing units.Geophysics,2009,74(6) :129～139
[14] http://deveioper.download.nvidia.com/compute/cuda/2_3/toolkit/docs/CUBLAS_Library_2． 3． pdf
[15] 龙桂华,李小凡,张美根.错格傅里叶伪谱微分算子在波场模拟中的应用.地球物理学报,2009,52(1) :193～199 Long G H,Li X F,Zhang M G.The application of staggered-grid Fourier pseudospectral differentiation operator in wavefield modeling.Chinese J.Geophys.(in Chinese),2009,52(1) :193～199
[16] Fornberg B.The pseudospectral method:accurate representation of interfaces in elastic wave calculation.Geophysics,1988,53(5) :625～637
[17] Dault C R,Brail L W,Nowack R L,et al.A comparison of finite-difference and Fourier method calculations of synthetic seismograms.Bull.Seism.Am.Soc.,1989,79(4) :1210～1230
[18] zdenvar T,McMechan G A.Cause and reduction of numerical artifacts in pseudo-spectral wavefield extrapolation.Geophys.J.Int.,1996,126(3) :819～828
[19] Bracewe R N.The Fourier transform and its application(2~(nd)Ed.),McGraw-Hill,Inc.,1974
[20] Fornberg B.High-order finite differences and the pseudospectral method on staggered grids.SIAM Journal on Numerical Analysis,1990,27(4) :904～918
[21] 龙桂华.粘弹性介质中的地震波传播与波形反演研究[博士论文].北京:中国科学院地质与地球物理研究所,2009 Long G H.The study of seismic wave propagation and waveform inversion in viscoelastic media[Ph.D.thesis](in Chinese).Beijing:Institute of Geology and Geophysics,Chinese Academy of Sciences,2009
[22] Corrêa G J,Spiegelman M,Carbotle S,et al.Centered and staggered Fourier derivative and Hilbert transforms.Geophysics,2002,67(5) :1558～1563
[23] Bale R A.Staggered grids for 3D pseudospectral modeling in anistropic elastic media.Calgary:CREWES Research Report,2002
[24] Chew W C,Lieu Q.Perfectly matched layers for elastodynamics:a new modified Maxwell's equations with stretched coordinates.Microwave Opt.Technol.Lett.,1996,7:599～604
[25] Cillino F,Tsogka C.Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media.Geophysics,2001,66(1) :294～301
[26] Komatitsch D,Tromp J.A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation.Geophys.J.Int.,2003,154:146～153
[27] http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/NVIDIA_CUDA_Programming_Gui de_2． 3． pdf
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