航空瞬变电磁法一维正演模拟与反演解释
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摘要
航空瞬变电磁法(ATEM)具有效率高,成本低等优点,可以广泛应用于地质填图、直接或间接找矿、水工环勘查等各个领域。近些年随着国家的重视,航空瞬变电磁法得到了迅速的发展。
本文主要研究了航空瞬变电磁法的一维正演和一维反演算法。首先从层状半空间上的磁偶极子电磁场公式出发,推导出了偶极-偶极装置的一维正演公式,并应用数学计算领域中一些最新的研究成果对算法进行了改进,编写了正演程序。通过对不同装置类型和不同参数的层状大地模型的理论响应进行对比计算,分析了航空瞬变电磁法探测的特点。
论文系统研究了现有的ATEM数据反演方法,将现有方法分为近似反演方法和定量反演方法两大类。对近似反演方法,本文实现了两种算法：用迭代法求取全区视电阻率法和其中一种电导率快速转换方法——浮动薄板法。对定量反演方法,实现了具有光滑模型约束能力的奥康姆反演法和具有较高反演精度的模型交替调整反演法。
通过上述研究工作,得出以下几点结论：
1)由正演算例表明,ATEM水平共面装置的探测信号最强,因此在实际探测中应用得最多；ATEM对低阻异常体的探测能力要远远强于对高阻异常体的探测能力。
2)近似反演方法因其速度快,是解决现场ATEM海量数据处理最好的方法,而定量反演方法效果好,但其速度较慢,只适用于室内后期研究之用。
3)对近似反演方法,浮动薄板法计算速度快,反映低阻异常的效果明显,电阻率下降最快的深度可以认为为低阻层的上顶界面。
4)在定量反演方法中,能获得光滑模型的奥康姆反演方法适合于电磁法的特点,其稳定性较高；模型交替调整反演算法是一种技巧性方法,模型算例证明了其效果较好,精度较高。
Airborne transient electromagnetic (ATEM), with its high efficiency and low cost, could be widely applied in fields such as geological mapping, direct or indirect mineral prospecting, hydrological investigation, environmental exploration and so on. With the national attention in recent years, ATEM has been developed rapidly.
In this paper, the 1-D ATEM forward modeling and interpretation method are studied. Firstly, the 1-D forward modeling formula of dipole-dipole array is derived from the electromagnetic field expression of a magnetic dipole source above the layered earth, and the algorithm is optimized with new achievements in mathematics. The program is made up, and the features of ATEM exploration method are studied by analysing the responses of layered earth models with different array types, array parameters and model parameters.
All the ATEM data interpretation methods are studied systematically, and classified into approximation interpretation techniques and quantitative inversion methods. For the former, this paper presents two techniques:all-time apparent resistivity abtained by iteration method and one of the conductivity-depth transformation (CDT) methods:S-inversion. For the latter, there are also two methods presented:the Occam inversion method by which a smoothest model could be generated, and the alternate model adjustment method whose results could interpret the data with high precision.
By the studies above, the following conclusions can be acquired:
1) The forward modeling shows that the signal of the horizontal parallel array is stronger than any other array, and that is why this kind is more adoptive in application; the anomaly induced by conductance is much more powerful than the one by resistance.
2) Approximation interpretation techniques are suitable for immediate interpretation for mass field data due to its fast processing speed, while, the quantitative inversion methods which give better results with lower efficiency can be used in later data processing and analysis.
3) The results of the S-inversion method reflect the conductance anomaly obviously, and in whose profile, the depth where resistivity drops most sharply can be considered as the top of conductance layer.
4) Occam inversion method, which generate a smoothest model, is suitable electromagnetic exploration, and its stability is demonstrated by model experiments; the alternate model adjustment method is developed by experiential skill, and the examples prove its higher precision and better results.
本文主要研究了航空瞬变电磁法的一维正演和一维反演算法。首先从层状半空间上的磁偶极子电磁场公式出发,推导出了偶极-偶极装置的一维正演公式,并应用数学计算领域中一些最新的研究成果对算法进行了改进,编写了正演程序。通过对不同装置类型和不同参数的层状大地模型的理论响应进行对比计算,分析了航空瞬变电磁法探测的特点。
论文系统研究了现有的ATEM数据反演方法,将现有方法分为近似反演方法和定量反演方法两大类。对近似反演方法,本文实现了两种算法：用迭代法求取全区视电阻率法和其中一种电导率快速转换方法——浮动薄板法。对定量反演方法,实现了具有光滑模型约束能力的奥康姆反演法和具有较高反演精度的模型交替调整反演法。
通过上述研究工作,得出以下几点结论：
1)由正演算例表明,ATEM水平共面装置的探测信号最强,因此在实际探测中应用得最多；ATEM对低阻异常体的探测能力要远远强于对高阻异常体的探测能力。
2)近似反演方法因其速度快,是解决现场ATEM海量数据处理最好的方法,而定量反演方法效果好,但其速度较慢,只适用于室内后期研究之用。
3)对近似反演方法,浮动薄板法计算速度快,反映低阻异常的效果明显,电阻率下降最快的深度可以认为为低阻层的上顶界面。
4)在定量反演方法中,能获得光滑模型的奥康姆反演方法适合于电磁法的特点,其稳定性较高；模型交替调整反演算法是一种技巧性方法,模型算例证明了其效果较好,精度较高。
Airborne transient electromagnetic (ATEM), with its high efficiency and low cost, could be widely applied in fields such as geological mapping, direct or indirect mineral prospecting, hydrological investigation, environmental exploration and so on. With the national attention in recent years, ATEM has been developed rapidly.
In this paper, the 1-D ATEM forward modeling and interpretation method are studied. Firstly, the 1-D forward modeling formula of dipole-dipole array is derived from the electromagnetic field expression of a magnetic dipole source above the layered earth, and the algorithm is optimized with new achievements in mathematics. The program is made up, and the features of ATEM exploration method are studied by analysing the responses of layered earth models with different array types, array parameters and model parameters.
All the ATEM data interpretation methods are studied systematically, and classified into approximation interpretation techniques and quantitative inversion methods. For the former, this paper presents two techniques:all-time apparent resistivity abtained by iteration method and one of the conductivity-depth transformation (CDT) methods:S-inversion. For the latter, there are also two methods presented:the Occam inversion method by which a smoothest model could be generated, and the alternate model adjustment method whose results could interpret the data with high precision.
By the studies above, the following conclusions can be acquired:
1) The forward modeling shows that the signal of the horizontal parallel array is stronger than any other array, and that is why this kind is more adoptive in application; the anomaly induced by conductance is much more powerful than the one by resistance.
2) Approximation interpretation techniques are suitable for immediate interpretation for mass field data due to its fast processing speed, while, the quantitative inversion methods which give better results with lower efficiency can be used in later data processing and analysis.
3) The results of the S-inversion method reflect the conductance anomaly obviously, and in whose profile, the depth where resistivity drops most sharply can be considered as the top of conductance layer.
4) Occam inversion method, which generate a smoothest model, is suitable electromagnetic exploration, and its stability is demonstrated by model experiments; the alternate model adjustment method is developed by experiential skill, and the examples prove its higher precision and better results.
引文
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[7]Sasaki Y, Hiroomi Nakazato. Inversion of airborne EM data accounting for terrain and inaccurate flight height[A]. SEG Technical Program Expanded Abstracts[C],2004,648-651.
[8]Brodie R, Sambridge M. A holistic approach to inversion of frequency-domain airborne EM data. Geophysics,2006,71(6):G301-312.
[9]Wolfgram P, Sattel D, Christensen N B. Approximate 2D inversion of AEM data. Exploration Geophysics,2003,34:29-33.
[10]Christensen N B. Electromagnetic subsurface imaging, a cace for an adaptive born approximation. Surveys in Geophysics,1997,18:477-510.
[11]Viezzoli A, Auken E, Munday T. Spatially constrained inversion for quasi 3D modelling of airborne electromagnetic data—an application for environmental assessment in the Lower Murray Region of South Australia. Exploration Geophysics,2009,40:173-183.
[12]Sattel D, Reid J. Modelling of airborne EM anomalies with magnetic and electric dipoles buried in a layered earth. Exploration Geophysics,2006,37 254-260.
[13]Wilson G, Raiche A, Sugeng F. Practical 3D AEM inversion using 2.5D modeling. AESC2006, Melbourne, Australia.
[14]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,2008,23(4)：1165-1172.
[15]雷栋,胡祥云,张素芳.航空电磁法的发展现状.地质找矿论丛,2006,21(1)：40-53.
[16]罗延钟,张胜业,王卫平.时间域航空电磁法一维正演研究.地球物理学报,2003,46(5)：719-724.
[17]刘桂芬.回线源层状大地航空瞬变电磁场的理论计算[硕士论文].长春：吉林大学,2008.
[18]Wooden B, Azari M, Soliman M. Well test analysis benefits from new method of Laplace space inversion. Oil & gas Journal,1992,90:29,108-110.
[19]Guptasarma D, Singh B. New digital linear filters for Hankel JO and J1 transforms. Geophysical prospecting,1997,45(5):745-762.
[20]Knight J H, Raiche A P. Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method. Geophysics,1982, 47(1):47-50.
[21]方文藻,李予国.瞬变电磁测深法原理.西安：西北工业大学出版社,1993.54-58.
[22]Nabighian M N. Electromagnetic Methods in Applied Geophysics, Volume 1, Theory. Tulsa:Society of Exploration Geophysicists,1988.
[23]昌彦君,张桂青.电磁场从频率域转换到时间域的几种算法比较.物探化探计算技术,1995,17(3)：25-29.
[24]Anderson W L. Computer program numerical integration of related Hankel transform, of order 0 and 1 by adaptive digital filtering. Geophysics,1979,44(7): 1287-1305.
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