地震波散射非线性反演的不动点方法(英文)
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摘要
旨在构造一种新的地震波散射非线性反演方法.将函数论中的不动点理论引入到地震波散射非线性反演中,并构造出了波相空间里关于速度参数的具体的压缩映射算子,从而从理论上保证了速度参数不动点的存在性和寻找途径.在此基础上还证明了利用此速度参数的不动点和正演所得到的相应的波值也是波函数本身的不动点,并利用不动点的稳定属性得出此不动点是一个最优的点.最后,文中还用该方法给出了具体的数值算例,间接地证实了本方法的实用性.
The work described in this paper focuses on making a new method of nonlinear inversion for seismic scattering. The fixed-point theory is incorporated into the nonlinear seismic scattering inversion and the method to create a series of contractive mappings of velocity parameter’s in the mapping space of wave is given. The existence of fixed point of velocity parameter is testified by the results and the method to find it is given. Furthermore, it is proved that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Because of the stabilities quality of the fixed point, it is the global optimum. The given numerical example shows the validity of the method.
The work described in this paper focuses on making a new method of nonlinear inversion for seismic scattering. The fixed-point theory is incorporated into the nonlinear seismic scattering inversion and the method to create a series of contractive mappings of velocity parameter’s in the mapping space of wave is given. The existence of fixed point of velocity parameter is testified by the results and the method to find it is given. Furthermore, it is proved that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Because of the stabilities quality of the fixed point, it is the global optimum. The given numerical example shows the validity of the method.
引文
[1]AKI K,RICHARDS P G.Quantitative seismology theory and methods[M].San Francisco:Freeman Company,1980.
[2]COWIE P A,VANNESTE C,SORNETTE D.Statis-tical physics model for the spatiotemporal evolution of faults[J].J Geophys Res,1993,98:21809-21821.
[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.
[4]TARENTOLA A,VALATTE B.Generalized nonlin-ear inverse problems solved using the least squares cri-terion[J].Review of geophysics space physics,1982,20:219-232.
[5]TARANTOLA A,VALETTE B.Inverse problems=quest for information[J].J Geophys,1984,50:159-170.
[6]MORA P.Inversion=migration+tomography[J].Geophysics,1989,54(12):1575-1586.
[7]杨晓春,李小凡,张美根.地震波反演方法研究的某些进展及其数学基础[J].地球物理学进展,2001,16(2):96-109.
[8]INGBER L.Genetic algorithms and very fast si mula-ted reannealing:a comparison[J].Math Comput Mod-eling,1992,16:87-100.
[9]DJURDJE C,JACEK K.Taboo search:an approach to the multiple mini ma problem[J].Science,1995,267(3):664-671.
[10]DEAN V B,MICHAEL M M.Temporal Informa-tion transformed into a spatial code by a neural net-work with realistic properties[J].Science,1995,267(17):1028-1031.
[11]SAMBRIDGE M S.Geophysical inversion with a neighborhood algorithm-Ⅰsearching a parameter space[J].Geophys J Int,1999,138:479-494.
[12]SAMBRIDGE M S.Geophysical inversion with a neighborhood algorithm-Ⅱappraising the ensemble[J].Geophys J Int,1999,138:727-746.
[13]VORONOI M G.Nouvelles applications des parame-ters continue a la theorie des formes quadratiques[J].J Reine Angew Math,1908,134:198-287.
[14]杨文采.地球物理反演问题的遗传算法[J].石油物探,1995,341:116-122.
[15]杨文采.地震道的非线性混沌反演-Ⅰ理论和数值试验[J].地球物理学报,1993,36(2):222-232.
[16]杨文采.非线性地震道的混沌反演-Ⅱ关于L指数和吸引子[J].地球物理学报,1993,36(3):376-386.
[17]杨磊,张向君,李幼铭.地震到非线性反演的参数反馈控制及效果[J].地球物理学报,1999,42(5):677-684.
[18]SCHECHTER M.Principles of functional analysis[M].Burlingtom MA:Academic Press,1971.
[19]SMART D R.Fixed point theorems[M].Cam-bridge:Cambridge University,1980.
[20]顾本立.地球物理衍射CT应用地震层析成像[M].北京:地质出版社,1993.
[2]COWIE P A,VANNESTE C,SORNETTE D.Statis-tical physics model for the spatiotemporal evolution of faults[J].J Geophys Res,1993,98:21809-21821.
[3]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.
[4]TARENTOLA A,VALATTE B.Generalized nonlin-ear inverse problems solved using the least squares cri-terion[J].Review of geophysics space physics,1982,20:219-232.
[5]TARANTOLA A,VALETTE B.Inverse problems=quest for information[J].J Geophys,1984,50:159-170.
[6]MORA P.Inversion=migration+tomography[J].Geophysics,1989,54(12):1575-1586.
[7]杨晓春,李小凡,张美根.地震波反演方法研究的某些进展及其数学基础[J].地球物理学进展,2001,16(2):96-109.
[8]INGBER L.Genetic algorithms and very fast si mula-ted reannealing:a comparison[J].Math Comput Mod-eling,1992,16:87-100.
[9]DJURDJE C,JACEK K.Taboo search:an approach to the multiple mini ma problem[J].Science,1995,267(3):664-671.
[10]DEAN V B,MICHAEL M M.Temporal Informa-tion transformed into a spatial code by a neural net-work with realistic properties[J].Science,1995,267(17):1028-1031.
[11]SAMBRIDGE M S.Geophysical inversion with a neighborhood algorithm-Ⅰsearching a parameter space[J].Geophys J Int,1999,138:479-494.
[12]SAMBRIDGE M S.Geophysical inversion with a neighborhood algorithm-Ⅱappraising the ensemble[J].Geophys J Int,1999,138:727-746.
[13]VORONOI M G.Nouvelles applications des parame-ters continue a la theorie des formes quadratiques[J].J Reine Angew Math,1908,134:198-287.
[14]杨文采.地球物理反演问题的遗传算法[J].石油物探,1995,341:116-122.
[15]杨文采.地震道的非线性混沌反演-Ⅰ理论和数值试验[J].地球物理学报,1993,36(2):222-232.
[16]杨文采.非线性地震道的混沌反演-Ⅱ关于L指数和吸引子[J].地球物理学报,1993,36(3):376-386.
[17]杨磊,张向君,李幼铭.地震到非线性反演的参数反馈控制及效果[J].地球物理学报,1999,42(5):677-684.
[18]SCHECHTER M.Principles of functional analysis[M].Burlingtom MA:Academic Press,1971.
[19]SMART D R.Fixed point theorems[M].Cam-bridge:Cambridge University,1980.
[20]顾本立.地球物理衍射CT应用地震层析成像[M].北京:地质出版社,1993.
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