基于奇异值分解的定回线源瞬变电磁数据处理算法研究
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摘要
瞬变电磁方法也称时间域电磁法,是一种基于电性差异,寻找低阻目标体,研究浅层至中深层地电结构的一种探测方法,目前广泛应用于寻找矿产资源和水文勘探中。瞬变电磁法比较常用的工作装置有中心回线、重叠回线、定回线源和偶极装置。其中,定回线源装置在实际测量时只需敷设一次发射线圈即可完成整个测区的探测,解决了野外工作中敷设线圈麻烦的难题,提高了工作效率,从而备受关注。
本文主要针对定回线源瞬变电磁数据反演算法进行研究,取得了以下几方面研究成果:首先计算了定回线源的瞬变电磁响应,采用圆回线与方形回线等效的办法,提高了正演速度;其次,计算了定回线源晚期视电阻率拟合方程。将响应电压拟合转换为视电阻率拟合,避免了因响应电压动态范围大而造成的反演计算中雅克比矩阵不稳定等问题,同时,可以通过观察视电阻率随深度的变化特征,估计出地下地质体的相关物理参数作为反演中的初始模型参数;再次,研究了广义逆矩阵理论和奇异值分解方法,通过对比最小二乘法和奇异值分解法在处理瞬变电磁数据时的优缺点,提出了采用加阻尼截断奇异值分解方法对瞬变电磁数据进行反演解释;最后,采用上述方法对内蒙古二连浩特地区野外瞬变电磁数据反演计算,反演结果与视电阻率解释结果一致,验证了本文提出的数据处理方法的正确性和实用性。
Transient electromagnetic method can also be called Time-domain electromagnetic method(TEM),is a kind of geophysical exploration method based on electrical difference of properties for surveying low resistance targets and researching the earth structure of shallow and middle shallow. The most popular devices of TEM are center-loop,overlap-loop and dipole-dipole device,and the data processing softwares of these devices have been used widely.However,when we work outside using these devices,the amount of work is great for we need to move the transmitter loop again when survey another point.So more and more attention is paid to the fixed-loop devices.This paper is based on the SVD,studying the TEM data processing algorithm of fixed-loop. The main research work and achievements are as follows:
1.Know deeply the work principle,equipment and instrument structure of the MRS and TEM associated instrument. Study deeply the basic theory of electromagnetic fields,as for the work equipment of the TEM mode, transient electromagnetic field’s expression is derived for fixed Loop Source on Multilayered.
2. Then, the arithmetic is proved to be feasible and correct by making contrastive research between the center point of the center loop’s transient electromagnetic response and the center point of the fixed Loop’s transient electromagnetic response using several groups of the earth model.At the same time,making the circular loop response equivalent to the square loop response,the forward computing time is decreased greatly. This can provide theoretical basis for the field data’s inversion.
3.Caculate the late time apparent resistivity of the large fixed loop.Using the apparent resistivity to interpret is more visually than using the response voltage,and the apparent resistivity can also be the initial model for the field data’s inversion.
4.Study the generalized inverse theory and singular value decomposition(SVD),compare the SVD method and the damping least square method,and use a new method called damping truncated singular value decomposition(DTSVD) method that can get the mutual complementary of the two methods,reduce the need of the precisiion for initial model parameter estimation,increase the convergence rate,make the inversion time shorter.
5. Simple and easy to operate to TEM inversion for the fixed loop source on layered earth graphical user interface is designed with the graphical user interface tool of MATLAB.
6.By fitting the TEM data of the theoretical model with the damping truncated singular value decomposition, we find that the fitting rate is fast,the fitting result is correct, the inversion arithmetic is proved to be feasible.
7.We studied the DTSVD method inversion for the wild transient electromagnetic data in Erlianhaote in the Inner Mongolia.By making the contrast between the sectional drawing of apparent resistivity , we found that the result was agreetable.the inversion arithmetic is proved to be feasible in the pratical application.
本文主要针对定回线源瞬变电磁数据反演算法进行研究,取得了以下几方面研究成果:首先计算了定回线源的瞬变电磁响应,采用圆回线与方形回线等效的办法,提高了正演速度;其次,计算了定回线源晚期视电阻率拟合方程。将响应电压拟合转换为视电阻率拟合,避免了因响应电压动态范围大而造成的反演计算中雅克比矩阵不稳定等问题,同时,可以通过观察视电阻率随深度的变化特征,估计出地下地质体的相关物理参数作为反演中的初始模型参数;再次,研究了广义逆矩阵理论和奇异值分解方法,通过对比最小二乘法和奇异值分解法在处理瞬变电磁数据时的优缺点,提出了采用加阻尼截断奇异值分解方法对瞬变电磁数据进行反演解释;最后,采用上述方法对内蒙古二连浩特地区野外瞬变电磁数据反演计算,反演结果与视电阻率解释结果一致,验证了本文提出的数据处理方法的正确性和实用性。
Transient electromagnetic method can also be called Time-domain electromagnetic method(TEM),is a kind of geophysical exploration method based on electrical difference of properties for surveying low resistance targets and researching the earth structure of shallow and middle shallow. The most popular devices of TEM are center-loop,overlap-loop and dipole-dipole device,and the data processing softwares of these devices have been used widely.However,when we work outside using these devices,the amount of work is great for we need to move the transmitter loop again when survey another point.So more and more attention is paid to the fixed-loop devices.This paper is based on the SVD,studying the TEM data processing algorithm of fixed-loop. The main research work and achievements are as follows:
1.Know deeply the work principle,equipment and instrument structure of the MRS and TEM associated instrument. Study deeply the basic theory of electromagnetic fields,as for the work equipment of the TEM mode, transient electromagnetic field’s expression is derived for fixed Loop Source on Multilayered.
2. Then, the arithmetic is proved to be feasible and correct by making contrastive research between the center point of the center loop’s transient electromagnetic response and the center point of the fixed Loop’s transient electromagnetic response using several groups of the earth model.At the same time,making the circular loop response equivalent to the square loop response,the forward computing time is decreased greatly. This can provide theoretical basis for the field data’s inversion.
3.Caculate the late time apparent resistivity of the large fixed loop.Using the apparent resistivity to interpret is more visually than using the response voltage,and the apparent resistivity can also be the initial model for the field data’s inversion.
4.Study the generalized inverse theory and singular value decomposition(SVD),compare the SVD method and the damping least square method,and use a new method called damping truncated singular value decomposition(DTSVD) method that can get the mutual complementary of the two methods,reduce the need of the precisiion for initial model parameter estimation,increase the convergence rate,make the inversion time shorter.
5. Simple and easy to operate to TEM inversion for the fixed loop source on layered earth graphical user interface is designed with the graphical user interface tool of MATLAB.
6.By fitting the TEM data of the theoretical model with the damping truncated singular value decomposition, we find that the fitting rate is fast,the fitting result is correct, the inversion arithmetic is proved to be feasible.
7.We studied the DTSVD method inversion for the wild transient electromagnetic data in Erlianhaote in the Inner Mongolia.By making the contrast between the sectional drawing of apparent resistivity , we found that the result was agreetable.the inversion arithmetic is proved to be feasible in the pratical application.
引文
[1]薛国强,李貅,底青云.瞬变电磁法理论与应用研究进展.地球物理学进展.2007.8.
[2]嵇艳鞠.浅层高分辨率全程瞬变电磁系统中全程二次场提取技术研究[D].吉林大学,2004.
[3]王家礼,朱满座,路宏敏.电磁场与电磁波.西安:西安电子科技大学出版社,2004.
[4]林君,段清明,王应吉等.核磁共振与瞬变电磁联用仪及其方法.专利申请号:200610017226.8
[5]薛国强,李貅,底青云.瞬变电磁法正反演问题研究进展.地球物理学进展.2008.8:1165-1172.
[6]薛国强,李貅,郭文波,底青云.大回线源瞬变电磁场响应特性.石油地球物理勘探,2007.10:586-590.
[7]米萨克. N纳比吉安著.赵经祥译.勘查地球物理电磁法[M] (第一卷).北京:地质出版社,1992.
[8]李建慧,刘树才等.大定源瞬变电磁法矩形发射回线激发的电磁场.物探化探计算技术.2008.3:154-157.
[9]阮百尧,葛为中.奇异值分解法与阻尼最小二乘法的对比.物探化探计算技术,1997.2:47-49.
[10]李平王椿墉.地球物理反演中奇异值分解应用的若干问题探讨.自然科学进展,2001.8:891-895.
[11]黄皓平.电磁法数据处理的奇异值分解法.地球物理报,1991.9:644-649.
[12]刘继东,方文藻.用线性数字滤波法计算大回线源在地下形成的瞬变电磁场.物探化探计算技术,1996.8:231-237.
[13]阮百尧.均匀水平大地上频率域垂直磁偶源电磁场数值滤波解法.桂林工学院学报,2005.1:14-18
[14]熊彬.大回线瞬变电磁法全区视电阻率的逆样条插值计算.吉林大学学报(地球科学版),2005.7:1-5.
[15]孙圣杰.大地电磁测深资料处理中的奇异值分解法.石油地球物理学报,1991.10:625-633.
[16]陈孝娟,郭文彬.奇异值分解在广义逆中的应用.华东师范大学学报(自然科学版),2008.1:25-29. [17黄皓平,王维中.时间域航空电磁数据的反演.地球物理学报,1990.1:87-96.
[18]陈明生,陈乐寿,王天生,白改先.用改进广义逆矩阵方法解释大地电磁测深及电测深资料.地球物理学报,1983.7:390-399.
[19][美]A. A.考夫曼,G. V.凯勒著.王建谋,杨生译.频率域和时间域电磁测深[M].北京:地质出版社,1987.
[20]翁爱华,李舟波,王雪秋.地表大回线源在任意层状介质中产生磁场的计算.物探化探计算技术.2000.8:245-248.
[21]庞学亮,林春生,张宁.飞机磁场模型系数的截断奇异值分解法估计.探测与控制学报,2009.10:49-51.
[22]P.B.Keating,D.J.Crossley.The inversion of time-domain airborne electromagnetic data using the plate model.Geophysics, 1990.6:705-711.
[23]A.P.Raiche.Transient electromagnetic field computations for polygonal loops on layer earths.Geophysics,1987.6:785-791.
[24]王家映.地球物理反演理论.北京:高等教育出版社,2002.12:43-63.
[25]刘桂芬.回线源层状大地航空瞬变电磁场的理论计算.吉林大学硕士学位论文,2008:7-30.
[26]许小强,程顺有.地球物理找水方法概述[J].地下水,2007,29(3):28-29.
[27]白登海,Maxwell.A.Meju等.时间域瞬变电磁法中心方式全程视电阻率的数值计算[J].地球物理学报,2003,46(5):697-704.
[28]张小华.核磁共振找水仪原理样机的设计与实现[D].吉林大学,2005.
[29]NAGENDRA PRATAP SINGH,TORU MOGI.Electromagnetic Response of a Large Circular Loop Source on a Layered Earth:A New Computation Method.Pure appl.geophys,162(2005)181-200.
[30]嵇艳鞠,林君,程德福,于生宝.瞬变电磁法中数据取样处理方法的研究.物探与化探,2003.4:142-144.
[31]肖枫,伍吉仓.大型广义逆反演中求逆算法的比较.工程勘察,2008:57-60.
[32]张丽艳,殷福亮.一种改进的奇异值分解语音增强方法.电子与信息学报,2008.2:357-360.
[33]翁爱华,高玲玲,刘云鹤.矩形大定源瞬变测深数据模型约束反演.物探化探计算技术,2008.7:314-316.
[34]程伟平,刘国华.基于广义逆理论的河网糙率反演研究.浙江大学学报(工学版),2005.
[35]蒋邦远.实用近区磁源瞬变电磁法勘探.北京:地质出版社,1998.
[36]陈明生.电偶源瞬变电磁测深研究(六):瞬变场资料的反演解释.煤田地质与勘探,2000.2:46-49
[37]P.K.Fullagar,J.E.Reid.Conductivity-Depth Transformation of Fixed Loop TEM Data.Exploration Geophysics(1992)23:515-519.
[38]J.H.Coggon,E.H.Clarke.The Fixed Receiver Electromagnetic(FREM) Method for Drill Hole Surveys. Exploration Geophysics(1987)18: 305-311.
[39]Edward M.Stolz,James Macnae.Evaluating EM waveforms by singular-value decomposition of exponential basis functions. Geophysics,1998:64-74.
[40]孙轶超.瞬变电磁数据改进阻尼最小二乘拟合算法研究.吉林大学硕士学位论文,2009:6-31.
[41]王正林,刘明.精通MATLAB7.北京:电子工业出版社,2006.7.
[42]林君,嵇艳鞠等.二连浩特市供水水资源瞬变电磁法勘探报告.2009.9.
[2]嵇艳鞠.浅层高分辨率全程瞬变电磁系统中全程二次场提取技术研究[D].吉林大学,2004.
[3]王家礼,朱满座,路宏敏.电磁场与电磁波.西安:西安电子科技大学出版社,2004.
[4]林君,段清明,王应吉等.核磁共振与瞬变电磁联用仪及其方法.专利申请号:200610017226.8
[5]薛国强,李貅,底青云.瞬变电磁法正反演问题研究进展.地球物理学进展.2008.8:1165-1172.
[6]薛国强,李貅,郭文波,底青云.大回线源瞬变电磁场响应特性.石油地球物理勘探,2007.10:586-590.
[7]米萨克. N纳比吉安著.赵经祥译.勘查地球物理电磁法[M] (第一卷).北京:地质出版社,1992.
[8]李建慧,刘树才等.大定源瞬变电磁法矩形发射回线激发的电磁场.物探化探计算技术.2008.3:154-157.
[9]阮百尧,葛为中.奇异值分解法与阻尼最小二乘法的对比.物探化探计算技术,1997.2:47-49.
[10]李平王椿墉.地球物理反演中奇异值分解应用的若干问题探讨.自然科学进展,2001.8:891-895.
[11]黄皓平.电磁法数据处理的奇异值分解法.地球物理报,1991.9:644-649.
[12]刘继东,方文藻.用线性数字滤波法计算大回线源在地下形成的瞬变电磁场.物探化探计算技术,1996.8:231-237.
[13]阮百尧.均匀水平大地上频率域垂直磁偶源电磁场数值滤波解法.桂林工学院学报,2005.1:14-18
[14]熊彬.大回线瞬变电磁法全区视电阻率的逆样条插值计算.吉林大学学报(地球科学版),2005.7:1-5.
[15]孙圣杰.大地电磁测深资料处理中的奇异值分解法.石油地球物理学报,1991.10:625-633.
[16]陈孝娟,郭文彬.奇异值分解在广义逆中的应用.华东师范大学学报(自然科学版),2008.1:25-29. [17黄皓平,王维中.时间域航空电磁数据的反演.地球物理学报,1990.1:87-96.
[18]陈明生,陈乐寿,王天生,白改先.用改进广义逆矩阵方法解释大地电磁测深及电测深资料.地球物理学报,1983.7:390-399.
[19][美]A. A.考夫曼,G. V.凯勒著.王建谋,杨生译.频率域和时间域电磁测深[M].北京:地质出版社,1987.
[20]翁爱华,李舟波,王雪秋.地表大回线源在任意层状介质中产生磁场的计算.物探化探计算技术.2000.8:245-248.
[21]庞学亮,林春生,张宁.飞机磁场模型系数的截断奇异值分解法估计.探测与控制学报,2009.10:49-51.
[22]P.B.Keating,D.J.Crossley.The inversion of time-domain airborne electromagnetic data using the plate model.Geophysics, 1990.6:705-711.
[23]A.P.Raiche.Transient electromagnetic field computations for polygonal loops on layer earths.Geophysics,1987.6:785-791.
[24]王家映.地球物理反演理论.北京:高等教育出版社,2002.12:43-63.
[25]刘桂芬.回线源层状大地航空瞬变电磁场的理论计算.吉林大学硕士学位论文,2008:7-30.
[26]许小强,程顺有.地球物理找水方法概述[J].地下水,2007,29(3):28-29.
[27]白登海,Maxwell.A.Meju等.时间域瞬变电磁法中心方式全程视电阻率的数值计算[J].地球物理学报,2003,46(5):697-704.
[28]张小华.核磁共振找水仪原理样机的设计与实现[D].吉林大学,2005.
[29]NAGENDRA PRATAP SINGH,TORU MOGI.Electromagnetic Response of a Large Circular Loop Source on a Layered Earth:A New Computation Method.Pure appl.geophys,162(2005)181-200.
[30]嵇艳鞠,林君,程德福,于生宝.瞬变电磁法中数据取样处理方法的研究.物探与化探,2003.4:142-144.
[31]肖枫,伍吉仓.大型广义逆反演中求逆算法的比较.工程勘察,2008:57-60.
[32]张丽艳,殷福亮.一种改进的奇异值分解语音增强方法.电子与信息学报,2008.2:357-360.
[33]翁爱华,高玲玲,刘云鹤.矩形大定源瞬变测深数据模型约束反演.物探化探计算技术,2008.7:314-316.
[34]程伟平,刘国华.基于广义逆理论的河网糙率反演研究.浙江大学学报(工学版),2005.
[35]蒋邦远.实用近区磁源瞬变电磁法勘探.北京:地质出版社,1998.
[36]陈明生.电偶源瞬变电磁测深研究(六):瞬变场资料的反演解释.煤田地质与勘探,2000.2:46-49
[37]P.K.Fullagar,J.E.Reid.Conductivity-Depth Transformation of Fixed Loop TEM Data.Exploration Geophysics(1992)23:515-519.
[38]J.H.Coggon,E.H.Clarke.The Fixed Receiver Electromagnetic(FREM) Method for Drill Hole Surveys. Exploration Geophysics(1987)18: 305-311.
[39]Edward M.Stolz,James Macnae.Evaluating EM waveforms by singular-value decomposition of exponential basis functions. Geophysics,1998:64-74.
[40]孙轶超.瞬变电磁数据改进阻尼最小二乘拟合算法研究.吉林大学硕士学位论文,2009:6-31.
[41]王正林,刘明.精通MATLAB7.北京:电子工业出版社,2006.7.
[42]林君,嵇艳鞠等.二连浩特市供水水资源瞬变电磁法勘探报告.2009.9.