改进的预处理共轭梯度快速算法在三维重力梯度数据反演中的应用（英文）
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摘要
随着全张量重力梯度(FTG)测量技术的不断发展,重力梯度数据的三维反演技术在油气和矿产勘探中日益受到重视与关注。为了快速处理和解释大规模的高精度数据,图形处理器GPU(Graphics Processing Unit)和预处理分解技术(Preconditioning methods)在地球物理反演中的使用变得十分重要。本文结合对称逐次超松弛(SSOR)技术与不完全乔列斯基分解共轭梯度算法(ICCG)提出改进的预处理共轭梯度法,并考虑到方法预处理分解占用额外的时间,开发该算法的GPU并行算法来提高加速效果。然后通过含噪的模型数据反演来证明改进的并行预处理方法在三维全张量重力梯度数据反演中的适应性。由此,基于NVIDIATesla C2050 GPU的并行SSOR-ICCG算法和在2.0GHz CPU上的串行程序比较,达到了大约25倍的加速比。最后,我们将该算法应用于美国路易斯安那州南方Vinton盐丘的实测航空重力梯度数据反演中,反演出良好的反演结果,验证了该方法在三维全张量重力梯度数据快速反演中的优势和可行性。
With the continuous development of full tensor gradiometer(FTG) measurement techniques,three-dimensional(3D) inversion of FTG data is becoming increasingly used in oil and gas exploration.In the fast processing and interpretation of large-scale high-precision data,the use of the graphics processing unit process unit(GPU) and preconditioning methods are very important in the data inversion.In this paper,an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation(SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm(ICCG).Since preparing the preconditioner requires extra time,a parallel implement based on GPU is proposed.The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data.Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit(CPU).Real airborne gravity-gradiometry data from Vinton salt dome(southwest Louisiana,USA) are also considered.Good results are obtained,which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.
With the continuous development of full tensor gradiometer(FTG) measurement techniques,three-dimensional(3D) inversion of FTG data is becoming increasingly used in oil and gas exploration.In the fast processing and interpretation of large-scale high-precision data,the use of the graphics processing unit process unit(GPU) and preconditioning methods are very important in the data inversion.In this paper,an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation(SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm(ICCG).Since preparing the preconditioner requires extra time,a parallel implement based on GPU is proposed.The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data.Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit(CPU).Real airborne gravity-gradiometry data from Vinton salt dome(southwest Louisiana,USA) are also considered.Good results are obtained,which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.
引文
Bell,R.E.,Anderson,R.,and Pratson,L.,1997,Gravity gradiometry resurfaces:Leading Edge,16(1),55-59.
Blakely,R.J.,1995,Potential Theory in Gravity and Magnetic Applications:Cambridge University Press,Cambridge,UK.
Boulanger,O.,and Chouteau,M.,2001,Constraints in 3d gravity inversion:Geophysical Prospecting,49(2),265-280.
Canning,F.X.,and Scholl,J.F.,1996,Diagonal preconditioners for the EFIE using a wavelet basis:IEEE Transactions on Antennas&Propagation,44(9),1239-1246.
Cella,F.,and Fedi,M.,2011,Inversion of potential field data using the structural index as weighting function rate decay:Geophysical Prospecting,60(2),313-336.
Chen,R.S.,Yung,E.K.N.,Chan,C.H.,and Fang,D.G.,2000,Application of preconditioned CG-FFT technique to method of lines for analysis of the infinite-plane metallic grating:Microwave&Optical Technology Letters,24(3),170-175.
Chen,R.S.,Yung,K.N.,Chan,C.H.,Wang,D.X.,and Fang,D.G.,2002,Application of the SSOR preconditioned CG algorithm to the vector fem for 3D full-wave analysis of electromagnetic-field boundaryvalue problems:IEEE Transactions on Microwave Theory&Techniques,50(4),1165-1172.
Chen,Z.,Meng,X.,Guo,L.,and Liu,G.,2012,GICUDA:a parallel program for 3D correlation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA:Computers&Geosciences,46(3),119-128.
Coker,M.O.,Bhattacharya,J.P.,and Marfurt,K.J.,2007,Fracture patterns within mudstones on the flanks of a salt dome:Syneresis or slumping?:Gulf Coast Association of Geological Societies Transactions,57,125-137.
Cuma,M,and Zhdanov,M.S.,2014,Massively parallel regularized 3D inversion of potential fields on CPUs and GPUs:Computers&Geosciences,62(1),80-87.
Ennen,C,and Hall,S.,2011,Structural mapping of the Vinton salt dome,Louisiana,using gravity gradiometry data:81st Annual International Meeting,SEG,Expanded Abstracts,30(1),830-835.
Forsberg R.,1984,A study of terrain reductions,density an omalies and geophysical inversion methods in gravity fie ld modelling:Report 355,Department of Geodetic Scien ce and Surveying,Ohio State University.
Geng,M.,Huang,D.,Yang,Q.,and Liu,Y.,2014,3D inversion of airborne gravity-gradiometry data using cokriging:Geophysics,79(4),G37-G47.
Golub,G.H.,and Van Loan,C.F.1996,Matrix computations(3rd edition.):Johns Hopkins University Press,Baltimore,America.
Haaz,I.B.,1953,Relationship between the potential of the attraction of the mass contained in a finite rectangular prism and its first and second derivatives:Geophysical Transactions,II,57-66
Hou,Z.L.,Wei,X.H.,Huang D.N.,et al.,2015,Full tensor gravity gradiometry data inversion:performance analysis of parallel computing algorithms:Applied Geophysics,12(3),292-302
Li X.,and Chouteau M.,1998,Three-dimensional gravity modelling in all space:Survey in Geophysics,19(4),339-368.
Li,Y,and Oldenburg,D.W.,1996,3-D inversion of magnetic data:Geophysics,61(2),394-408.
Li,Y,and Oldenburg,D.W.,1998,3-d inversion of gravity data:Geophysics,63(1),109-119.
Liu,G.,Meng,X.,and Chen,Z.,2012,3D magnetic inversion based on probability tomography and its GPU implement:Computers&Geosciences,48(9),86-92.
Liu,W.,2012,Parallel program design of Matlab:Beihang University Press,Beijing.
Moorkamp,M.,Jegen,M.,Roberts,A.,and Hobbs,R.,2010,Massively parallel forward modeling of scalar and tensor gravimetry data:Computers&Geosciences,36(5),680-686.
NVIDIA,2007,NIVIDIA CUDA compute unified device architecture programming guide.Santa Clara,CA.
Oliveira Jr,V.C,and Barbosa,C.F.,2013,3-D radial gravity gradient inversion:Geophysical Journal International,195(2),883-902.
Pilkington,M.,1997,3-D magnetic imaging using conjugate gradients:Geophysics,62,1132-1142.
Portniaguine,O.,and Zhdanov,M.S.,2002,3-D magnetic inversion with data compression and image focusing:Geophysics,67(5),1532-1541.
Sajo-Castelli A M,Fortes M A.,and Raydan M.,2014,Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell-Sabin triangulations.Journal of Computational&Applied Mathematics,268(1),34-55.
Qin,P.,Huang,D.,Yuan,Y.,Geng,M.,and Liu,J.,2016,Integrated gravity and gravity gradient 3d inversion using the non-linear conjugate gradient:Journal of Applied Geophysics,126,52-73.
Shamsipour,P.,Marcotte,D.,Chouteau,M.,and Keating,P.,2010,3D stochastic inversion of gravity data using cokriging and cosimulation:Geophysics,75(1),11-110.
Smith,G.D.,1985,Numerical solution of partial differential equations:finite difference methods:Oxford University Press,England.
Szymczyk,M.,and Szymczyk,P.,2012,Matlab and parallel computing:Image Processing&Communications,17(4),207-216.
Thompson,S.A.,and Eichelberger,O.H.,1928,Vinton salt dome,Calcasieu Parish,Louisiana:AAPG Bulletin,12,385-394.
Tontini,C.F.,Cocchi,L.,and Carmisciano,C,2006,Depth-to-the-bottom optimization for magnetic data inversion:magnetic structure of the latium volcanic region,Italy:Journal of Geophysical Research Atmospheres,111(B11),220-222.
Zhang,S.,2009,GPU high performance computing of CUDA:China Water&Power Press,Beijing.
Zhdanov,M.S.,2002,Geophysical inverse theory and regularization problems:Elsevier,Salt Lake City,USA.
Blakely,R.J.,1995,Potential Theory in Gravity and Magnetic Applications:Cambridge University Press,Cambridge,UK.
Boulanger,O.,and Chouteau,M.,2001,Constraints in 3d gravity inversion:Geophysical Prospecting,49(2),265-280.
Canning,F.X.,and Scholl,J.F.,1996,Diagonal preconditioners for the EFIE using a wavelet basis:IEEE Transactions on Antennas&Propagation,44(9),1239-1246.
Cella,F.,and Fedi,M.,2011,Inversion of potential field data using the structural index as weighting function rate decay:Geophysical Prospecting,60(2),313-336.
Chen,R.S.,Yung,E.K.N.,Chan,C.H.,and Fang,D.G.,2000,Application of preconditioned CG-FFT technique to method of lines for analysis of the infinite-plane metallic grating:Microwave&Optical Technology Letters,24(3),170-175.
Chen,R.S.,Yung,K.N.,Chan,C.H.,Wang,D.X.,and Fang,D.G.,2002,Application of the SSOR preconditioned CG algorithm to the vector fem for 3D full-wave analysis of electromagnetic-field boundaryvalue problems:IEEE Transactions on Microwave Theory&Techniques,50(4),1165-1172.
Chen,Z.,Meng,X.,Guo,L.,and Liu,G.,2012,GICUDA:a parallel program for 3D correlation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA:Computers&Geosciences,46(3),119-128.
Coker,M.O.,Bhattacharya,J.P.,and Marfurt,K.J.,2007,Fracture patterns within mudstones on the flanks of a salt dome:Syneresis or slumping?:Gulf Coast Association of Geological Societies Transactions,57,125-137.
Cuma,M,and Zhdanov,M.S.,2014,Massively parallel regularized 3D inversion of potential fields on CPUs and GPUs:Computers&Geosciences,62(1),80-87.
Ennen,C,and Hall,S.,2011,Structural mapping of the Vinton salt dome,Louisiana,using gravity gradiometry data:81st Annual International Meeting,SEG,Expanded Abstracts,30(1),830-835.
Forsberg R.,1984,A study of terrain reductions,density an omalies and geophysical inversion methods in gravity fie ld modelling:Report 355,Department of Geodetic Scien ce and Surveying,Ohio State University.
Geng,M.,Huang,D.,Yang,Q.,and Liu,Y.,2014,3D inversion of airborne gravity-gradiometry data using cokriging:Geophysics,79(4),G37-G47.
Golub,G.H.,and Van Loan,C.F.1996,Matrix computations(3rd edition.):Johns Hopkins University Press,Baltimore,America.
Haaz,I.B.,1953,Relationship between the potential of the attraction of the mass contained in a finite rectangular prism and its first and second derivatives:Geophysical Transactions,II,57-66
Hou,Z.L.,Wei,X.H.,Huang D.N.,et al.,2015,Full tensor gravity gradiometry data inversion:performance analysis of parallel computing algorithms:Applied Geophysics,12(3),292-302
Li X.,and Chouteau M.,1998,Three-dimensional gravity modelling in all space:Survey in Geophysics,19(4),339-368.
Li,Y,and Oldenburg,D.W.,1996,3-D inversion of magnetic data:Geophysics,61(2),394-408.
Li,Y,and Oldenburg,D.W.,1998,3-d inversion of gravity data:Geophysics,63(1),109-119.
Liu,G.,Meng,X.,and Chen,Z.,2012,3D magnetic inversion based on probability tomography and its GPU implement:Computers&Geosciences,48(9),86-92.
Liu,W.,2012,Parallel program design of Matlab:Beihang University Press,Beijing.
Moorkamp,M.,Jegen,M.,Roberts,A.,and Hobbs,R.,2010,Massively parallel forward modeling of scalar and tensor gravimetry data:Computers&Geosciences,36(5),680-686.
NVIDIA,2007,NIVIDIA CUDA compute unified device architecture programming guide.Santa Clara,CA.
Oliveira Jr,V.C,and Barbosa,C.F.,2013,3-D radial gravity gradient inversion:Geophysical Journal International,195(2),883-902.
Pilkington,M.,1997,3-D magnetic imaging using conjugate gradients:Geophysics,62,1132-1142.
Portniaguine,O.,and Zhdanov,M.S.,2002,3-D magnetic inversion with data compression and image focusing:Geophysics,67(5),1532-1541.
Sajo-Castelli A M,Fortes M A.,and Raydan M.,2014,Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell-Sabin triangulations.Journal of Computational&Applied Mathematics,268(1),34-55.
Qin,P.,Huang,D.,Yuan,Y.,Geng,M.,and Liu,J.,2016,Integrated gravity and gravity gradient 3d inversion using the non-linear conjugate gradient:Journal of Applied Geophysics,126,52-73.
Shamsipour,P.,Marcotte,D.,Chouteau,M.,and Keating,P.,2010,3D stochastic inversion of gravity data using cokriging and cosimulation:Geophysics,75(1),11-110.
Smith,G.D.,1985,Numerical solution of partial differential equations:finite difference methods:Oxford University Press,England.
Szymczyk,M.,and Szymczyk,P.,2012,Matlab and parallel computing:Image Processing&Communications,17(4),207-216.
Thompson,S.A.,and Eichelberger,O.H.,1928,Vinton salt dome,Calcasieu Parish,Louisiana:AAPG Bulletin,12,385-394.
Tontini,C.F.,Cocchi,L.,and Carmisciano,C,2006,Depth-to-the-bottom optimization for magnetic data inversion:magnetic structure of the latium volcanic region,Italy:Journal of Geophysical Research Atmospheres,111(B11),220-222.
Zhang,S.,2009,GPU high performance computing of CUDA:China Water&Power Press,Beijing.
Zhdanov,M.S.,2002,Geophysical inverse theory and regularization problems:Elsevier,Salt Lake City,USA.