用数值模式匹配算法高效仿真轴对称型散射体海洋可控源电磁响应
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摘要
圆盘、球体以及球冠状体是地球物理研究中非常重要的一类散射类型.在海洋环境中,圆盘可以用于描述玄武岩基岩以及油气圈闭构造等电阻率异常体,而球冠可以近似描述某些基岩隆起或起伏地形等.这类散射体的一个重要特征是其电阻率空间分布具有轴对称性.如果能够针对这类形状的散射体研究建立一套有效的海洋可控源电磁数值模拟方法,对于认识复杂地层条件下海洋电磁响应的变化特征、研究建立相关的资料处理和解释方法具有非常重要的意义.本文根据电导率轴对称分布特征,设法用一个或多个不同半径、不同厚度的水平同心圆盘逼近这类轴对称电导率散射体,并将这些同心圆盘与海洋环境中的空气、海水、沉积层和基岩等背景介质结合,形成一个在水平方向电导率具有轴对称分布、在垂直方向又具有分层特征的水平层状非均质模型.在此基础上,应用数值模式匹配法研究水平电偶极子天线电磁场的数值模拟方法,给出位于对称轴上的水平发射天线电磁场在层状非均质地层中的半解析解,建立海洋可控源电磁响应高效算法.最后通过数值模拟结果对该算法进行检验并考察海洋可控源三维电磁响应特征.
Horizontal disk, sphere, and spherical crown are a very important type of scatter in geophysics research. In the marine environment, a disk-like scatter can be used to describe several resistive targets, e.g., basaltic sills and stratigraphic hydrocarbon reservoirs while spherical crown can be used to approximately depict the topography of interface for basement rock. This type of scatter has characteristics of axisymmetrical distribution of the conductivity.If some approaches can be established to efficiently simulate the marine controlled source electromagnetic(MCSEM)response to this scatter, it will be meaningful to investigate the nature of MCSEM responses in complex formation and to build appropriate method of processing and explaining MCSEM data. In this paper, the resistive scatters are approximated by one or several horizontal concentric disks with different radii and thickness values, based on the axially symmetrical spatial distribution of conductivity. Then, a combination of these concentric disks with air, sea water and surrounding beds will construct a horizontally stratified inhomogeneous formation with common axis-center, whose spatial distribution of conductivity is layered in the vertical direction and axisymmetric in the horizontal direction. Based on the approximations mentioned above, the computation of MCSEM response excited by horizontal electrical dipole(HED) located at the z-axis is entirely transformed into two axially symmetrical problems for the Fourier harmonic components of the electromagnetic(EM) fields. The differential operators about the horizontal magnetic components and transformation of horizontal electrical components and other EM components from horizontal magnetic components are derived. Then, the numerical mode matching approach is extended to the simulation of the EM field and threedimensional(3D) MCSEM responses excited by the HED in the formation. The procedure for solving the EM field is presented. The semi-analytic solution of EM field in the whole space is obtained to efficiently and numerically model MCSEM response in the complex formation. Finally, the efficiency and accuracy of the present method are demonstrated numerically. The characteristics of 3D MCSEM responses in three different cases are further investigated.
Horizontal disk, sphere, and spherical crown are a very important type of scatter in geophysics research. In the marine environment, a disk-like scatter can be used to describe several resistive targets, e.g., basaltic sills and stratigraphic hydrocarbon reservoirs while spherical crown can be used to approximately depict the topography of interface for basement rock. This type of scatter has characteristics of axisymmetrical distribution of the conductivity.If some approaches can be established to efficiently simulate the marine controlled source electromagnetic(MCSEM)response to this scatter, it will be meaningful to investigate the nature of MCSEM responses in complex formation and to build appropriate method of processing and explaining MCSEM data. In this paper, the resistive scatters are approximated by one or several horizontal concentric disks with different radii and thickness values, based on the axially symmetrical spatial distribution of conductivity. Then, a combination of these concentric disks with air, sea water and surrounding beds will construct a horizontally stratified inhomogeneous formation with common axis-center, whose spatial distribution of conductivity is layered in the vertical direction and axisymmetric in the horizontal direction. Based on the approximations mentioned above, the computation of MCSEM response excited by horizontal electrical dipole(HED) located at the z-axis is entirely transformed into two axially symmetrical problems for the Fourier harmonic components of the electromagnetic(EM) fields. The differential operators about the horizontal magnetic components and transformation of horizontal electrical components and other EM components from horizontal magnetic components are derived. Then, the numerical mode matching approach is extended to the simulation of the EM field and threedimensional(3D) MCSEM responses excited by the HED in the formation. The procedure for solving the EM field is presented. The semi-analytic solution of EM field in the whole space is obtained to efficiently and numerically model MCSEM response in the complex formation. Finally, the efficiency and accuracy of the present method are demonstrated numerically. The characteristics of 3D MCSEM responses in three different cases are further investigated.
引文
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[13]Chen G B,Wang H N,Yao J J,Han Z Y,Yang S W2009 Acta Phys.Sin.58 1608(in Chinese)[陈桂波,汪宏年,姚敬金,韩子夜,杨守文2009物理学报58 1608]
[14]Chen G B,Wang H N,Yao J J,Han Z Y 2009 Acta Phys.Sin.58 3848(in Chinese)[陈桂波,汪宏年,姚敬金,韩子夜2009物理学报58 3848]
[15]Kong F N,Johnstad S E,R?sten T,Westerdahl H 2008Geophysics 73 F9
[16]Wang H N,Tao H G,Yao J J,Zhang Y 2012 IEEETrans.Geosci.Remote Sens.50 3383
[17]Wang H N,Tao H G,Yang S W 2008 Chin.J.Geophys.51 1591
[18]Liu Q H,Chew W C 1992 Radio Sci.27 569
[19]Wang H N 2011 IEEE Trans.Geosci.Remote Sens.494483
[20]Wang H N,So P M,Yang S W,Hoefer W J R,Du H L2008 IEEE Trans.Geosci.Remote Sens.46 1134
[21]Zhu T Z,Yang S W,Bai Y,Chen T,Wang H N 2017Chin.J.Geophys.60 1221(in Chinese)[朱天竹,杨守文,白彦,陈涛,汪宏年2017地球物理学报60 1221]
[22]Chew W C 1990 Waves and Fields in Inhomogeneous Media(New York:van Nostrand Reinhold)
[2]Constable S 2010 Geophysics 75 75A67
[3]Yuan J,Edwards N 2000 Geophys.Res.Lett.27 2397
[4]Weiss C J,Constable S 2006 Geophysics 71 G321
[5]Constable S C,Weiss C J 2006 Geophysics 71 G43
[6]Hoversten G M,Newman G A,Geier A,Flanagan G2006 Geophysics 71 G239
[7]Wang J X,Wang H N,Zhou J M,Yang S W,Liu X J,Yin C C 2013 Acta Phys.Sin.62 224101(in Chinese)[汪建勋,汪宏年,周建美,杨守文,刘晓军,殷长春2013物理学报62 224101]
[8]Li Y G,Dai S K 2011 Geophys.J.Int.185 622
[9]Xu Z F,Wu X P 2010 Chinese J.Geophys.53 1931(in Chinese)[徐志锋,吴小平2010地球物理学报53 1931]
[10]Shen J S 2003 Chin.J.Geophys.46 280(in Chinese)[沈金松2003地球物理学报46 280]
[11]Streich R 2009 Geophysics 74 F95
[12]Zhou J M,Zhang Y,Wang H N,Yang S W,Yin C C2014 Acta Phys.Sin.63 159101(in Chinese)[周建美,张烨,汪宏年,杨守文,殷长春2014物理学报63 159101]
[13]Chen G B,Wang H N,Yao J J,Han Z Y,Yang S W2009 Acta Phys.Sin.58 1608(in Chinese)[陈桂波,汪宏年,姚敬金,韩子夜,杨守文2009物理学报58 1608]
[14]Chen G B,Wang H N,Yao J J,Han Z Y 2009 Acta Phys.Sin.58 3848(in Chinese)[陈桂波,汪宏年,姚敬金,韩子夜2009物理学报58 3848]
[15]Kong F N,Johnstad S E,R?sten T,Westerdahl H 2008Geophysics 73 F9
[16]Wang H N,Tao H G,Yao J J,Zhang Y 2012 IEEETrans.Geosci.Remote Sens.50 3383
[17]Wang H N,Tao H G,Yang S W 2008 Chin.J.Geophys.51 1591
[18]Liu Q H,Chew W C 1992 Radio Sci.27 569
[19]Wang H N 2011 IEEE Trans.Geosci.Remote Sens.494483
[20]Wang H N,So P M,Yang S W,Hoefer W J R,Du H L2008 IEEE Trans.Geosci.Remote Sens.46 1134
[21]Zhu T Z,Yang S W,Bai Y,Chen T,Wang H N 2017Chin.J.Geophys.60 1221(in Chinese)[朱天竹,杨守文,白彦,陈涛,汪宏年2017地球物理学报60 1221]
[22]Chew W C 1990 Waves and Fields in Inhomogeneous Media(New York:van Nostrand Reinhold)