一维大地电磁Occam反演拉格朗日乘子的搜索
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摘要
在大地电磁反演中,Occam法因其在反演稳定性和模型分辨率等方面的优势,得到广泛应用。但由于其每次迭代都需要不断地搜索拉格朗日乘子,因而拉格朗日乘子的搜索效率对Occam法反演的运算速度起着至关重要的作用。为提高拉格朗日乘子的搜索效率,这里提出将拉格朗日乘子的搜索从自然数域中转到以10为底的对数域中进行,同时在区间最小值的搜索中采用二次函数极小值搜索法。通过大量一维大地电磁反演验证,该方法将拉格朗日乘子的搜索效率提高了20%~50%,大大提高了Occam反演的运算速度,方便了其在高维反演中的应用。
In magnetotelluric inversion,because of its stability in inversion and the advantage of model resolution and so on,Occam method is widely used.But in each iteration,Occam's inversion needs to constantly search Lagrange multiplier.The searching efficiency of Lagrange multiplier to Occam's inversion speed plays a vital role.To improve the search efficiency of Lagrange multiplier,a new searching method was presented in this paper.First Lagrange multiplier of transfer from the natural number field to search for the 10 logs base domain.Second in the search of interval minimum search method using quadratic function.Through a number of one-dimensional magnetotelluric inversions,Lagrange multiplier search efficiency is increased by 20%- 50%,and the operation speed of Occam's inversion is greatly improved.
In magnetotelluric inversion,because of its stability in inversion and the advantage of model resolution and so on,Occam method is widely used.But in each iteration,Occam's inversion needs to constantly search Lagrange multiplier.The searching efficiency of Lagrange multiplier to Occam's inversion speed plays a vital role.To improve the search efficiency of Lagrange multiplier,a new searching method was presented in this paper.First Lagrange multiplier of transfer from the natural number field to search for the 10 logs base domain.Second in the search of interval minimum search method using quadratic function.Through a number of one-dimensional magnetotelluric inversions,Lagrange multiplier search efficiency is increased by 20%- 50%,and the operation speed of Occam's inversion is greatly improved.
引文
[1]石应骏,刘国栋,吴广耀,等.大地电磁测深法教程[M].北京:地展出版社,1985.SHI Y J,LIU G D,WU G Y,Tutorial of MT sounding[M].Beijing:Geological Publishing House,1985.(In Chinese)
[2]陈乐寿,刘任,王天生.大地电磁测深资料处理与解释[M].北京:石油工业出版社,1989.CHEN L S,LIU R,WANG T S.Data processing and interpretation of MT sounding[M].Beijing:Petroleum Industry Press,1989.(In Chinese)
[3]王家映.地球物理反演理论[M].北京:高等教育出版社,2002.WANG J Y.Inverse theory in geophysics[M].Beijing:Higher Education Press,2002.(In Chinese)
[4]CONSTABLE S C,PARKER R L,CONSTABLE C G.Occam’s inversion:A practical algorithm for generating smooth models from electromagnetic sounding data[J].Geophysics,1987,52(3):289-300.
[5]DEGROOT-HEDLIN C D,CONSTABLE S C.Occam’s Inversion to Generate Smooth Two Dimensional Models form MagnetotelluricData[J].Geophysics,1990,55(12):1613-1624.
[6]SIRIPUNVARAPORN W,EGBERTG.An efficient data-subspaceinversion method for 2-D magnetotelluricdata[J].Geophysics,2000,65(3):791-803.
[7]SIRIPUNVARAPORN W,UYESHIMA M,EGBERT G.Three dimensional inversion for network-magnetotelluricdata[J].Earth Planets Space,2004,56(9):893-902.
[8]RODI W L,MACKIE R L.Nonlinear conjugate gradients algorithm for 2-D magnetotelluricinversion[J].Geophysics,2001,66(3):174-187.
[9]韩波,胡祥云,何展祥,等.大地电磁反演方法的数学分类[J].石油地球物理勘探,2012,47(1):177-187.HAN B,HU X Y,HE ZH X,et al.Mathematical classification of magnetotelluric inversion methods[J].Oil Geophysical Prospecting,2012,47(1):177-187.(In Chinese)
[10]陈小斌,赵国泽,汤吉,等.大地电磁自适应正则化反演算法[J].地球物理学报,2005,48(4):937-946.CHEN X B,ZHAO G Z,TANG J,et al.An adaptive regularized inversion algorithm for magnetotelluric data[J].Chinese J Geophys,2005,48(4):937-946.(In Chinese)
[11]吴小平,徐果明.大地电磁数据的OCCAM反演改进[J].地球物理学报,1998,41(4):547-554.WU X P,XU G M.Improvement of OCCAM's inversion for MT date[J].Chinese J Geophys,1998,41(4):547-554.(In Chinese)
[12]朴英哲,李桐林,刘永亮.在大地电磁二维Occam反演中求取拉格朗日乘子方法改进[J].吉林大学学报:地球科学版,2014,44(2):660-667.PAK Y C,LI T L,LIU Y L.Improvement of choosing lagrange multiplier on MT 2D Occam inversion[J].Journal of Jilin University:Earth Science Edition,2014,44(2):660-667.(In Chinese)
[13]刘俊峰,邓居智,陈辉,等.一种用于Occam反演中搜索拉格朗日乘子的方法[J].工程地球物理学报,2013,10(3):344-350.LIU J F,DENG J Z,CHEN H,et al.A method used for searching lagrange multiplier in Occam inversion[J].Chinese journal of engineering geophysics,2013,10(3):344-350.(In Chinese)
[2]陈乐寿,刘任,王天生.大地电磁测深资料处理与解释[M].北京:石油工业出版社,1989.CHEN L S,LIU R,WANG T S.Data processing and interpretation of MT sounding[M].Beijing:Petroleum Industry Press,1989.(In Chinese)
[3]王家映.地球物理反演理论[M].北京:高等教育出版社,2002.WANG J Y.Inverse theory in geophysics[M].Beijing:Higher Education Press,2002.(In Chinese)
[4]CONSTABLE S C,PARKER R L,CONSTABLE C G.Occam’s inversion:A practical algorithm for generating smooth models from electromagnetic sounding data[J].Geophysics,1987,52(3):289-300.
[5]DEGROOT-HEDLIN C D,CONSTABLE S C.Occam’s Inversion to Generate Smooth Two Dimensional Models form MagnetotelluricData[J].Geophysics,1990,55(12):1613-1624.
[6]SIRIPUNVARAPORN W,EGBERTG.An efficient data-subspaceinversion method for 2-D magnetotelluricdata[J].Geophysics,2000,65(3):791-803.
[7]SIRIPUNVARAPORN W,UYESHIMA M,EGBERT G.Three dimensional inversion for network-magnetotelluricdata[J].Earth Planets Space,2004,56(9):893-902.
[8]RODI W L,MACKIE R L.Nonlinear conjugate gradients algorithm for 2-D magnetotelluricinversion[J].Geophysics,2001,66(3):174-187.
[9]韩波,胡祥云,何展祥,等.大地电磁反演方法的数学分类[J].石油地球物理勘探,2012,47(1):177-187.HAN B,HU X Y,HE ZH X,et al.Mathematical classification of magnetotelluric inversion methods[J].Oil Geophysical Prospecting,2012,47(1):177-187.(In Chinese)
[10]陈小斌,赵国泽,汤吉,等.大地电磁自适应正则化反演算法[J].地球物理学报,2005,48(4):937-946.CHEN X B,ZHAO G Z,TANG J,et al.An adaptive regularized inversion algorithm for magnetotelluric data[J].Chinese J Geophys,2005,48(4):937-946.(In Chinese)
[11]吴小平,徐果明.大地电磁数据的OCCAM反演改进[J].地球物理学报,1998,41(4):547-554.WU X P,XU G M.Improvement of OCCAM's inversion for MT date[J].Chinese J Geophys,1998,41(4):547-554.(In Chinese)
[12]朴英哲,李桐林,刘永亮.在大地电磁二维Occam反演中求取拉格朗日乘子方法改进[J].吉林大学学报:地球科学版,2014,44(2):660-667.PAK Y C,LI T L,LIU Y L.Improvement of choosing lagrange multiplier on MT 2D Occam inversion[J].Journal of Jilin University:Earth Science Edition,2014,44(2):660-667.(In Chinese)
[13]刘俊峰,邓居智,陈辉,等.一种用于Occam反演中搜索拉格朗日乘子的方法[J].工程地球物理学报,2013,10(3):344-350.LIU J F,DENG J Z,CHEN H,et al.A method used for searching lagrange multiplier in Occam inversion[J].Chinese journal of engineering geophysics,2013,10(3):344-350.(In Chinese)