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在瞬变电磁法的实际应用中，由于发射回线和发射波形的不规则性而导致其发射源成为时空展源. 展源效应的忽略会造成正反演和数据解释的差错，因此开展展源效应的研究对于瞬变电磁法的实际应用具有重要的意义. 对于空间展源，本文以磁偶极子的响应为基响应，应用有源空间的互易定理和第二类曲线积分，提出了一种可基于发射回线数值坐标求取任意形状发射回线响应的计算方法. 同时对于时间展源，以阶跃波形的响应为基响应，对阶跃响应的特性进行了分析，提出了一种对发射信号进行非均匀采样的高效时间域计算方法，解决了对数采样的基响应与高密度采样的发射波形之间进行常规卷积时所面临的时间与精度之间的矛盾. 通过对层状大地上展源响应的模拟仿真和对比验证显示了本文所提出方法的正确性. 最后本文考察了几种常见时空展源在常规近似前后响应的差别，并给出了相关结论.In practical applications of transient electromagnetic methods, irregularity of the transmitting loop or current waveform makes the source an extended one. Since neglect of the effect of the extended source will cause some errors in both forward modeling and data interpretation, it makes great sense to calculate the responses that take this effect into account. For a spatially extended source over layered medium, step response is firstly calculated and taken as the basic response, then principle of reciprocity and the integral of the second kind are used to propose a new method that can compute the response based on the coordinates of the loop. For an extended source in time, an improved step-function summation method is proposed to deal with the contradiction between the precision of result and consuming of time. Comparisons with the published work have proved the validity and accuracy of our methods. The effect of the traditional approximations of the extended source is also investigated and some analysis for the numerical results is presented for advanced usage.
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Keywords:
- stratified medium /
- extended source /
- principle of reciprocity /
- nonuniform sampling
[1] Zhdanov M S 2010 Geophysics 75 75A49
[2] Huang L, Zeng Z F, Wang M N, Wang Z J 2007 Applied Geophysics 4 301
[3] Zhou J M, Wang H N, Yao J J, Yang S W, Ma Y Z 2012 Acta Phys. Sin. 61 089101 (in Chinese) [周建美, 汪宏年, 姚敬金, 杨守文, 马寅芝 2012 61 089101]
[4] Zhang Y, Zhang X J, Fang G Y 2012 Acta Phys. Sin. 61 184203 (in Chinese) [张宇, 张晓娟, 方广有 2012 61 184203]
[5] Zhang Y, Zhang X J, Fang G Y 2013 Acta Phys. Sin. 62 044204 (in Chinese) [张宇, 张晓娟, 方广有 2013 62 044204]
[6] Ren X C, Guo L X 2008 Chin. Phys. Lett. 25 101
[7] Wang A Q, Guo L X, Chai C 2011 Chin. Phys. B 20 050202
[8] Ji W J, Tong C M 2013 Chin. Phys. B 22 020301
[9] Singh N P, Mogi T 2003 Earth Planets and Space 55 301
[10] Singh N P, Mogi T 2005 Pure and Appl. Geophy. 162 181
[11] Singh N P, Utsugi M, Kagiyama T 2009 Pure Appl. Geophy. 166 2037
[12] Cheng G B, B J, Wang J B, Chen X Y, Sun G C, Lu J 2011 Acta Phys. Sin. 60 094102 (in Chinese) [陈桂波, 毕娟, 汪剑波, 陈新邑, 孙贯成, 卢俊 2011 60 094102]
[13] Jang H, Jang H, Lee K H, Kim H J 2013 J. Geophy. Eng. 10 025011
[14] Christiansen A V, Auken E, Viezzoli A 2011 Geophysics 76 43
[15] Ji Y J, Lin J, Yu S B, Wang Z, Wang J 2006 Chinese J. Geophys. 49 1884 (in Chinese) [嵇艳鞠, 林君, 于生宝, 王忠, 王静 2006 地球 49 1884]
[16] Niu Z L 2007 Transient Electromagnetic Methods (Changsha: Central South University Press) p31 (in Chinese) [牛之琏 2007 时间域电磁法原理(长沙: 中南大学出版社) 第31页]
[17] Xue G Q, Yan S, Zhou N N 2011 Chinese J. Geophys. 54 2389 (in Chinese) [薛国强, 闫述, 周楠楠 2011 地球 54 2389]
[18] Zhdanov M S 2009 Geophysical Electromagnetic Theory and Methods (Amsterdam: Elsevier) p200
[19] Chen S D, Lin J, Zhang S 2012 Chinese J. Geophys. 55 709 (in Chinese) [陈曙东, 林君, 张爽 2012 地球 55 709]
[20] Qi Y Z, Huang L, Wu X, Zhu W H, Fang G Y 2011 Proceedings of the IEEE 4th International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (MAPE) Beijing, China. November 1–3, 2011 p179
[21] Kong F N 2007 Geophysical Prospecting 55 83
[22] Yang R G 2008 Advanced Electromagnetic Theory (Beijing: Higher Education Press) p162 (in Chinese) [杨儒贵 2008 高等电磁理论(北京: 高等教育出版社) 第162页]
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[1] Zhdanov M S 2010 Geophysics 75 75A49
[2] Huang L, Zeng Z F, Wang M N, Wang Z J 2007 Applied Geophysics 4 301
[3] Zhou J M, Wang H N, Yao J J, Yang S W, Ma Y Z 2012 Acta Phys. Sin. 61 089101 (in Chinese) [周建美, 汪宏年, 姚敬金, 杨守文, 马寅芝 2012 61 089101]
[4] Zhang Y, Zhang X J, Fang G Y 2012 Acta Phys. Sin. 61 184203 (in Chinese) [张宇, 张晓娟, 方广有 2012 61 184203]
[5] Zhang Y, Zhang X J, Fang G Y 2013 Acta Phys. Sin. 62 044204 (in Chinese) [张宇, 张晓娟, 方广有 2013 62 044204]
[6] Ren X C, Guo L X 2008 Chin. Phys. Lett. 25 101
[7] Wang A Q, Guo L X, Chai C 2011 Chin. Phys. B 20 050202
[8] Ji W J, Tong C M 2013 Chin. Phys. B 22 020301
[9] Singh N P, Mogi T 2003 Earth Planets and Space 55 301
[10] Singh N P, Mogi T 2005 Pure and Appl. Geophy. 162 181
[11] Singh N P, Utsugi M, Kagiyama T 2009 Pure Appl. Geophy. 166 2037
[12] Cheng G B, B J, Wang J B, Chen X Y, Sun G C, Lu J 2011 Acta Phys. Sin. 60 094102 (in Chinese) [陈桂波, 毕娟, 汪剑波, 陈新邑, 孙贯成, 卢俊 2011 60 094102]
[13] Jang H, Jang H, Lee K H, Kim H J 2013 J. Geophy. Eng. 10 025011
[14] Christiansen A V, Auken E, Viezzoli A 2011 Geophysics 76 43
[15] Ji Y J, Lin J, Yu S B, Wang Z, Wang J 2006 Chinese J. Geophys. 49 1884 (in Chinese) [嵇艳鞠, 林君, 于生宝, 王忠, 王静 2006 地球 49 1884]
[16] Niu Z L 2007 Transient Electromagnetic Methods (Changsha: Central South University Press) p31 (in Chinese) [牛之琏 2007 时间域电磁法原理(长沙: 中南大学出版社) 第31页]
[17] Xue G Q, Yan S, Zhou N N 2011 Chinese J. Geophys. 54 2389 (in Chinese) [薛国强, 闫述, 周楠楠 2011 地球 54 2389]
[18] Zhdanov M S 2009 Geophysical Electromagnetic Theory and Methods (Amsterdam: Elsevier) p200
[19] Chen S D, Lin J, Zhang S 2012 Chinese J. Geophys. 55 709 (in Chinese) [陈曙东, 林君, 张爽 2012 地球 55 709]
[20] Qi Y Z, Huang L, Wu X, Zhu W H, Fang G Y 2011 Proceedings of the IEEE 4th International Symposium on Microwave, Antenna, Propagation, and EMC Technologies for Wireless Communications (MAPE) Beijing, China. November 1–3, 2011 p179
[21] Kong F N 2007 Geophysical Prospecting 55 83
[22] Yang R G 2008 Advanced Electromagnetic Theory (Beijing: Higher Education Press) p162 (in Chinese) [杨儒贵 2008 高等电磁理论(北京: 高等教育出版社) 第162页]
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