VTI介质弹性体波模式解耦高效算法
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摘要
对于各向异性波场模式解耦来说,常规的散度与旋度运算存在明显误差,而理论上精确的偏振投影算子受介质参数和传播方向共同控制,导致相应的模式解耦算法成本难以承受。在前人研究基础上,开发面向带有垂直对称轴的横向各向同性(VTI)介质的弹性体波模式解耦高效算法。首先,针对依据主能量传播与偏振方向偏差角设计的伪散度/伪旋度算子,借助波场方向分解,考虑偏差角随传播方向的变化,构造出更精确的qP/qS波分离算法。然后,针对理论更完备、适用性更强的偏振投影低秩近似算法,借助模型分区和GPU加速策略,达到了精度与成本的相对平衡。SEG Hess VTI二维模型数值试验揭示了改进的伪散度/伪旋度算法、分区低秩分解GPU算法的特点,同时验证了方法的可靠性。
For the elastic wave mode decoupling in anisotropic media,conventional approaches with divergence and curl operations lead significant errors.The accurate mode decomposition algorithm,however,is prohibitively expensive because the polarization projection operators are model-and direction-dependent.Based on previous work,we focus on developing efficient algorithms for mode decoupling in heterogeneous medium with vertically transverse isotropy(VTI).First,for the pseudo-divergence or pseudo-curl operators constructed by the deviation of propagation and polarization direction of the dominant energy,we improve the accuracy of qP/qS separation by taking into account the variations of the deviation angle with the propagation direction.This improvement is very important when different wave modes overlap in the same spatial zone at the same time.Then,for the accurate but prohibitively expensive algorithm of mode decoupling through polarization projection,based on the existing low-rank approximation of the projection operator,we achieve a balance between the accuracy and computational cost using the strategies of model partitioning and graph processing unit(GPU)acceleration.The example on the SEG Hess VTI model demonstrates the features and validities of the improved pseudo-divergence/pseudo-rotation algorithm and the GPUbased low-rank approximate polarization projection algorithm.
For the elastic wave mode decoupling in anisotropic media,conventional approaches with divergence and curl operations lead significant errors.The accurate mode decomposition algorithm,however,is prohibitively expensive because the polarization projection operators are model-and direction-dependent.Based on previous work,we focus on developing efficient algorithms for mode decoupling in heterogeneous medium with vertically transverse isotropy(VTI).First,for the pseudo-divergence or pseudo-curl operators constructed by the deviation of propagation and polarization direction of the dominant energy,we improve the accuracy of qP/qS separation by taking into account the variations of the deviation angle with the propagation direction.This improvement is very important when different wave modes overlap in the same spatial zone at the same time.Then,for the accurate but prohibitively expensive algorithm of mode decoupling through polarization projection,based on the existing low-rank approximation of the projection operator,we achieve a balance between the accuracy and computational cost using the strategies of model partitioning and graph processing unit(GPU)acceleration.The example on the SEG Hess VTI model demonstrates the features and validities of the improved pseudo-divergence/pseudo-rotation algorithm and the GPUbased low-rank approximate polarization projection algorithm.
引文
[1] Sun R,McMechan G A,Hsiao H,et al.Separating P- and S-waves in prestack 3D elastic seismograms using divergence and curl[J].Geophysics,2004,69(1):286-297.
[2] Yan J and Sava P.Isotropic angle-domain elastic reverse-time migration[J].Geophysics,2008,73(6):S229-S239.
[3] Du Q,Guo C,Zhao Q,et al.Vector-based elastic reverse time migration based on scalar imaging condition[J].Geophysics,2017,82(2):S111-S127.
[4] 王晨龙.各向异性介质多分量全波地震成像方法[D].上海:同济大学,2017.
[5] Wang T F,Cheng J B.Born reflection kernel analysis and wave equation reflection traveltime inversion in elastic media[C].SEG Technical Program Expanded Abstracts,2017,36:1486-1491.
[6] Wang T F,Cheng J B,Guo Q,et al.Elastic wave-equation-based reflection kernel analysis and traveltime inversion using wave mode decomposition[J].Geophysical Journal International,2018,215(1):450-470.
[7] Morse P M and Feshbach H.Methods of Theoretical Physics[M].McGraw-Hill Book Company,New York,1953.
[8] Aki K and Richards P.Quantitative Seismology(2nd Edition)[M].University Science Books,New Jersey,2002.
[9] 马德堂,朱光明.弹性波波场P波和S波分解的数值模拟[J].石油地球物理勘探,2003,38(5):482-486.MA Detang and ZHU Guangming.Numerical mode-ling of P-wave and S-wave separation in elastic wavefield[J].Oil Geophysical Prospecting,2003,38(5):482-486.
[10] 李振春,张华,刘庆敏,等.弹性波交错网格高阶有限差分法波场数值模拟[J].石油地球物理勘探,2007,42(5):510-515.LI Zhenchun,ZHANG Hua,LIU Qingmin,et al.Numeric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm[J].Oil Geophysical Prospecting,2007,42(5):510-515.
[11] 吴潇,刘洋,蔡晓慧.弹性波波场分离方法对比及其在逆时偏移成像中的应用[J].石油地球物理勘探,2018,53(4):710-721.WU Xiao,LIU Yang,CAI Xiaohui.Elastic wavefield separation methods and their applications in reverse migration[J].Oil Geophysical Prospecting,2018,53(4):710-721.
[12] Crampin S.Effective anisotropic elastic constants for wave propagation through cracked solids[J].Geophysical Journal of the Royal Astronomical Society,1984,76(1):135-145.
[13] Dellinger J.Anisotropic Seismic Wave Propagation[D].Stanford University,1991.
[14] Yan J and Sava P.Elastic wave-mode separation for VTI media[J].Geophysics,2009,74(6):WB19-WB32.
[15] Zhang Q and McMechan G A.2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media[J].Geophysics,2010,75(3):D13-D26.
[16] Cheng J B and Fomel S.Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media[J].Geophysics,2014,79(4):C97-C110.
[17] Alkhalifah T.An acoustic wave equation for aniso-tropic media[J].Geophysics,2000,65(4):1239-1250.
[18] Liu F,Morton S A,Jiang S,et al.Decoupled wave equations for P and SV waves in an acoustic VTI media[C].SEG Technical Program Expanded Abstracts,2009,28:2844-2848.
[19] Cheng J B,Kang W.Simulating propagation of separated wave modes in general anisotropic media,Part Ⅰ:qP-wave propagators[J].Geophysics,2014,79(1):C1-C18.
[20] Cheng J B,Kang W.Simulating propagation of separated wave modes in general anisotropic media,Part Ⅱ:qS-wave propagators[J].Geophysics,2016,81(2):C39-C52.
[21] Dellinger J and Etgen J.Wavefield separation in two-dimensional anisotropic media[J].Geophysics,1990,55(7):914-919.
[22] 魏石磊,张大洲,李明智,等.VTI介质中波场分离算子特征研究[J].石油地球物理勘探,2016,51(3):506-512.WEI Shilei,ZHANG Dazhou,LI Mingzhi,et al.Wave separation operator characteristics in the VTI medium[J].Oil Geophysical Prospecting,2016,51(3):506-512.
[23] Yan J and Sava P.Improving the efficiency of elastic wave-mode separation for heterogeneous tilted transverse isotropic media[J].Geophysics,2011,76(4):T65-T78.
[24] Engquist B and Ying L.Fast directional multilevel algorithms for oscillatory kernels[J].SIAM Journal on Scientific Computing,2007,29(4):1710-1737.
[25] Wang W L,Hua B L,McMechan G,et al.P- and S-decomposition in anisotropic media with localized low-rank approximations[J].Geophysics,2018,83(1):C13-C26.
[26] 芦永明,张剑锋,杨凯,等.二维TI介质非结构网格弹性波矢量逆时偏移[J].地球物理学报,2017,60(12):4776-4789.LU Yongming,ZHANG Jianfeng,YANG Kai,et al.Vector elastic reverse time migration based on unstructured mesh for tilted TI medium[J].Chinese Journal of Geophysics,2017,60(12):4776-4789.
[27] Zhou Y and Wang H Z.Efficient wave-mode separation in vertical transversely isotropic media[J].Geophysics,2017,82(2):C35-C47.
[28] Tang C and McMechan G.Multidirectional slowness vector for computing angle gathers from reverse time migration[J].Geophysics,2016,81(2):S55-S68.
[29] 赵虎,武泗海,尹成,等.基于OpenACC编程模型的逆时偏移多级并行的设计与优化[J].石油地球物理勘探,2018,53(6):1307-1313,1325.ZHAO Hu,WU Sihai,YIN Cheng,et al.Multi-level parallel design and optimization for reverse migration based on OpenACC programming mode[J].Oil Geophysical Prospecting,2018,53(6):1307-1313,1325.
[2] Yan J and Sava P.Isotropic angle-domain elastic reverse-time migration[J].Geophysics,2008,73(6):S229-S239.
[3] Du Q,Guo C,Zhao Q,et al.Vector-based elastic reverse time migration based on scalar imaging condition[J].Geophysics,2017,82(2):S111-S127.
[4] 王晨龙.各向异性介质多分量全波地震成像方法[D].上海:同济大学,2017.
[5] Wang T F,Cheng J B.Born reflection kernel analysis and wave equation reflection traveltime inversion in elastic media[C].SEG Technical Program Expanded Abstracts,2017,36:1486-1491.
[6] Wang T F,Cheng J B,Guo Q,et al.Elastic wave-equation-based reflection kernel analysis and traveltime inversion using wave mode decomposition[J].Geophysical Journal International,2018,215(1):450-470.
[7] Morse P M and Feshbach H.Methods of Theoretical Physics[M].McGraw-Hill Book Company,New York,1953.
[8] Aki K and Richards P.Quantitative Seismology(2nd Edition)[M].University Science Books,New Jersey,2002.
[9] 马德堂,朱光明.弹性波波场P波和S波分解的数值模拟[J].石油地球物理勘探,2003,38(5):482-486.MA Detang and ZHU Guangming.Numerical mode-ling of P-wave and S-wave separation in elastic wavefield[J].Oil Geophysical Prospecting,2003,38(5):482-486.
[10] 李振春,张华,刘庆敏,等.弹性波交错网格高阶有限差分法波场数值模拟[J].石油地球物理勘探,2007,42(5):510-515.LI Zhenchun,ZHANG Hua,LIU Qingmin,et al.Numeric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm[J].Oil Geophysical Prospecting,2007,42(5):510-515.
[11] 吴潇,刘洋,蔡晓慧.弹性波波场分离方法对比及其在逆时偏移成像中的应用[J].石油地球物理勘探,2018,53(4):710-721.WU Xiao,LIU Yang,CAI Xiaohui.Elastic wavefield separation methods and their applications in reverse migration[J].Oil Geophysical Prospecting,2018,53(4):710-721.
[12] Crampin S.Effective anisotropic elastic constants for wave propagation through cracked solids[J].Geophysical Journal of the Royal Astronomical Society,1984,76(1):135-145.
[13] Dellinger J.Anisotropic Seismic Wave Propagation[D].Stanford University,1991.
[14] Yan J and Sava P.Elastic wave-mode separation for VTI media[J].Geophysics,2009,74(6):WB19-WB32.
[15] Zhang Q and McMechan G A.2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media[J].Geophysics,2010,75(3):D13-D26.
[16] Cheng J B and Fomel S.Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media[J].Geophysics,2014,79(4):C97-C110.
[17] Alkhalifah T.An acoustic wave equation for aniso-tropic media[J].Geophysics,2000,65(4):1239-1250.
[18] Liu F,Morton S A,Jiang S,et al.Decoupled wave equations for P and SV waves in an acoustic VTI media[C].SEG Technical Program Expanded Abstracts,2009,28:2844-2848.
[19] Cheng J B,Kang W.Simulating propagation of separated wave modes in general anisotropic media,Part Ⅰ:qP-wave propagators[J].Geophysics,2014,79(1):C1-C18.
[20] Cheng J B,Kang W.Simulating propagation of separated wave modes in general anisotropic media,Part Ⅱ:qS-wave propagators[J].Geophysics,2016,81(2):C39-C52.
[21] Dellinger J and Etgen J.Wavefield separation in two-dimensional anisotropic media[J].Geophysics,1990,55(7):914-919.
[22] 魏石磊,张大洲,李明智,等.VTI介质中波场分离算子特征研究[J].石油地球物理勘探,2016,51(3):506-512.WEI Shilei,ZHANG Dazhou,LI Mingzhi,et al.Wave separation operator characteristics in the VTI medium[J].Oil Geophysical Prospecting,2016,51(3):506-512.
[23] Yan J and Sava P.Improving the efficiency of elastic wave-mode separation for heterogeneous tilted transverse isotropic media[J].Geophysics,2011,76(4):T65-T78.
[24] Engquist B and Ying L.Fast directional multilevel algorithms for oscillatory kernels[J].SIAM Journal on Scientific Computing,2007,29(4):1710-1737.
[25] Wang W L,Hua B L,McMechan G,et al.P- and S-decomposition in anisotropic media with localized low-rank approximations[J].Geophysics,2018,83(1):C13-C26.
[26] 芦永明,张剑锋,杨凯,等.二维TI介质非结构网格弹性波矢量逆时偏移[J].地球物理学报,2017,60(12):4776-4789.LU Yongming,ZHANG Jianfeng,YANG Kai,et al.Vector elastic reverse time migration based on unstructured mesh for tilted TI medium[J].Chinese Journal of Geophysics,2017,60(12):4776-4789.
[27] Zhou Y and Wang H Z.Efficient wave-mode separation in vertical transversely isotropic media[J].Geophysics,2017,82(2):C35-C47.
[28] Tang C and McMechan G.Multidirectional slowness vector for computing angle gathers from reverse time migration[J].Geophysics,2016,81(2):S55-S68.
[29] 赵虎,武泗海,尹成,等.基于OpenACC编程模型的逆时偏移多级并行的设计与优化[J].石油地球物理勘探,2018,53(6):1307-1313,1325.ZHAO Hu,WU Sihai,YIN Cheng,et al.Multi-level parallel design and optimization for reverse migration based on OpenACC programming mode[J].Oil Geophysical Prospecting,2018,53(6):1307-1313,1325.
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