扩散蒙特卡罗反演方法及应用
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摘要
扩散蒙特卡罗方法是量子力学中研究多体系统的一种有效数值计算方法,具有较强非线性搜索能力,能够更好地求得全局最优解。本文将该方法从量子力学范畴引入到地震反演这样的经典系统,通过数值模拟试验验证了该方法的可行性。在此基础上,进行了实际地震资料的反演,获得了较好的反演结果,表明把扩散蒙特卡罗方法应用于地球物理反问题的求解是成功的,它适合于非线性、多极值的地球物理反演问题,在避免陷入局部极小等方面有着一定的优势。
Diffusion Monte Carlo method,an effective numerical simulation way for many-body system research in quantum mechanics,has strong nonlinear searching capability for getting global optimal solution.This paper introduces diffusion Monte Carlo method from the domain of quantum mechanics to seismic inversion,which results show the feasibility of the method.On that basis,the inversion of real seismic data gets preferable result,which denotes that diffusion Monte Carlo method has successful application in seismic inversion,has some advantages for avoiding being trapped in local minimum and is suitable for nonlinear,multi-maximum geophysical inverse problem.
Diffusion Monte Carlo method,an effective numerical simulation way for many-body system research in quantum mechanics,has strong nonlinear searching capability for getting global optimal solution.This paper introduces diffusion Monte Carlo method from the domain of quantum mechanics to seismic inversion,which results show the feasibility of the method.On that basis,the inversion of real seismic data gets preferable result,which denotes that diffusion Monte Carlo method has successful application in seismic inversion,has some advantages for avoiding being trapped in local minimum and is suitable for nonlinear,multi-maximum geophysical inverse problem.
引文
[1]黄绪德.反褶积与地震道反演.北京:石油工业出版社,1992
[2]俞寿朋.高分辨率地震勘探.北京:石油工业出版社,1993
[3]李庆忠.走向精确勘探的道路.北京:石油工业出版社,1994
[4]Ceperley D M,Alder B J.Ground state of the elec-tron gas by a stochastic method.Phys Rev Lett,1980,45(7):566~569
[5]Hammond B L,Lester W A,Reynolds P J.MonteCarlo methods in ab initio quantumchemistry.Singa-pore:World Scientific,1994
[6]Anderson J B.A random-walk si mulation of theSchr dinger equation:H3+.J Chem Phys,1975,63(4):1499~1503
[7]Anderson J B.Quantumchemistry by random walk.J Chem Phys,1976,65(10):4121~4127
[8]Reynolds P J,Ceperley D M.Fixed-node quantumMonte Carlo for molecules.J Chem Phys,1982,77(11):5593~5603
[9]Umrigar C J,Nightingale MP,Runge KJ.Adiffu-sion Monte Carlo algorithm with very small ti me-steperrors.J Chem Phys,1993,99(4):2865~2890
[10]Kosztin I,Faber B,Schulten K.Introduction to thediffusion Monte Carlo method.Am J Phys,1996,64(5):633~644
[11]Rapisarda F,Senatore G.Diffusion Monte Carlo studyof electrons in two-di mensional layers.Aust J Phys,1996,49(1):161~182
[12]Pederiva F,Umrigar CJ,Lipparini E.Diffusion MonteCarlo study of circular quantum dots.Phys Rev B2000,62(12):8120~8125
[13]Anderson J B.Diffusion and Green’s functionquantum Monte Carlo methods in quantum si mula-tions of complex many-body systems:fromtheorytoalgorithms(Lecture Notes).2002,25~50
[14]Guclu A D,Wang J S,Guo H.Disordered quantumdots:A diffusion Monte Carlo study.Phys Rev B,2003,68(3)
[15]Makrini M El,Jourdain B,Lelievre T.DiffusionMonte Carlo method:numerical analysis in a si mplecase.Mathematical Modeling and Numerical Anal-ysis,2007,41(2):189~213
[16]Santoro G E,Tosatti E.Opti mization using quantummechanics:quantumannealing through adiabatic evo-lution.J Phys A:Math Gen,2006,39(36):393~431
[17]Anderson J B.Quantumchemistry by random walk:higher accuracy.J Chem Phys,1980,73(8):3897~3899
[18]Mentch F,Anderson J B.Quantumchemistry by ran-dom walk:i mportance sampling for H3+.J ChemPhys,1981,74(11):6307~6311
[19]Alder B J,Ceperley D M,Reynolds P J.Stochasticcalculation of interaction energies.J Phys Chem,1982,86(7):1200~1204
[20]Moskowitz J W,Kalos M H.A newlook at correla-tions in atomic and molecular systems I:Applicationof fermion Monte Carlo variational method.Int JQuantum Chem,1981,20(5):1107~1119
[21]Moskowitz J W,Schmidt K E,Lee MAet al.MonteCarlo variational study of Be:Asurvey of correlatedwave functions.J Chem Phys,1982,76(2):1064~1067
[22]曾谨言.量子力学(第三版).北京:科学出版社,2000
[23]Foulkes W MC,Mitas L,Needs RJ et al.QuantumMonte Carlo si mulations of solids.Rev Mod Phys,2001,73(1):33~83
[24]马文淦.计算物理学.北京:科学出版社,2005
[25]Al偄n A G,William A L.Quantum Monte Carlo meth-ods for the solution of the Schr dinger equation formolecular systems.Handbook for Numerical Analy-sis.Special Volume of Computational Chemistry(10),2003:485~535
[26]魏超,朱培民,王家映.量子退火反演的原理和实现.地球物理学报,2006,49(2):577~583Wei Chao,Zhu Pei-min,Wang Jiang-ying.Quantumannealing inversion and its i mplementation.ChineseJournal of Geophysics,2006,49(2):577~583
[27]Pang T.An Introduction to Computational Physics.Cambridge University Press,2006
[2]俞寿朋.高分辨率地震勘探.北京:石油工业出版社,1993
[3]李庆忠.走向精确勘探的道路.北京:石油工业出版社,1994
[4]Ceperley D M,Alder B J.Ground state of the elec-tron gas by a stochastic method.Phys Rev Lett,1980,45(7):566~569
[5]Hammond B L,Lester W A,Reynolds P J.MonteCarlo methods in ab initio quantumchemistry.Singa-pore:World Scientific,1994
[6]Anderson J B.A random-walk si mulation of theSchr dinger equation:H3+.J Chem Phys,1975,63(4):1499~1503
[7]Anderson J B.Quantumchemistry by random walk.J Chem Phys,1976,65(10):4121~4127
[8]Reynolds P J,Ceperley D M.Fixed-node quantumMonte Carlo for molecules.J Chem Phys,1982,77(11):5593~5603
[9]Umrigar C J,Nightingale MP,Runge KJ.Adiffu-sion Monte Carlo algorithm with very small ti me-steperrors.J Chem Phys,1993,99(4):2865~2890
[10]Kosztin I,Faber B,Schulten K.Introduction to thediffusion Monte Carlo method.Am J Phys,1996,64(5):633~644
[11]Rapisarda F,Senatore G.Diffusion Monte Carlo studyof electrons in two-di mensional layers.Aust J Phys,1996,49(1):161~182
[12]Pederiva F,Umrigar CJ,Lipparini E.Diffusion MonteCarlo study of circular quantum dots.Phys Rev B2000,62(12):8120~8125
[13]Anderson J B.Diffusion and Green’s functionquantum Monte Carlo methods in quantum si mula-tions of complex many-body systems:fromtheorytoalgorithms(Lecture Notes).2002,25~50
[14]Guclu A D,Wang J S,Guo H.Disordered quantumdots:A diffusion Monte Carlo study.Phys Rev B,2003,68(3)
[15]Makrini M El,Jourdain B,Lelievre T.DiffusionMonte Carlo method:numerical analysis in a si mplecase.Mathematical Modeling and Numerical Anal-ysis,2007,41(2):189~213
[16]Santoro G E,Tosatti E.Opti mization using quantummechanics:quantumannealing through adiabatic evo-lution.J Phys A:Math Gen,2006,39(36):393~431
[17]Anderson J B.Quantumchemistry by random walk:higher accuracy.J Chem Phys,1980,73(8):3897~3899
[18]Mentch F,Anderson J B.Quantumchemistry by ran-dom walk:i mportance sampling for H3+.J ChemPhys,1981,74(11):6307~6311
[19]Alder B J,Ceperley D M,Reynolds P J.Stochasticcalculation of interaction energies.J Phys Chem,1982,86(7):1200~1204
[20]Moskowitz J W,Kalos M H.A newlook at correla-tions in atomic and molecular systems I:Applicationof fermion Monte Carlo variational method.Int JQuantum Chem,1981,20(5):1107~1119
[21]Moskowitz J W,Schmidt K E,Lee MAet al.MonteCarlo variational study of Be:Asurvey of correlatedwave functions.J Chem Phys,1982,76(2):1064~1067
[22]曾谨言.量子力学(第三版).北京:科学出版社,2000
[23]Foulkes W MC,Mitas L,Needs RJ et al.QuantumMonte Carlo si mulations of solids.Rev Mod Phys,2001,73(1):33~83
[24]马文淦.计算物理学.北京:科学出版社,2005
[25]Al偄n A G,William A L.Quantum Monte Carlo meth-ods for the solution of the Schr dinger equation formolecular systems.Handbook for Numerical Analy-sis.Special Volume of Computational Chemistry(10),2003:485~535
[26]魏超,朱培民,王家映.量子退火反演的原理和实现.地球物理学报,2006,49(2):577~583Wei Chao,Zhu Pei-min,Wang Jiang-ying.Quantumannealing inversion and its i mplementation.ChineseJournal of Geophysics,2006,49(2):577~583
[27]Pang T.An Introduction to Computational Physics.Cambridge University Press,2006
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