对迭代法位场向下延拓方法的剖析

doi:10.13278/j.cnki.jjuese.201503302

摘要/Abstract

摘要：

位场向下延拓迭代法的实质内容是"向上延拓而不是向下延拓"和以"迭代的结果趋近于观测值"为标准的操作过程。根据数据操作流程剖析了位场向下延拓迭代法的运行机制,得到了迭代数据在空间域的变化规律,即用迭代法将观测高度的位场向下延拓一个深度h。这实际上是通过不同高度的向上延拓来实现的。也就是说,迭代次数增加一次,涉及的上延平面就增大一个h的高度。一般地,迭代次数n与上延高度h的关系为n~(n+1)h。在空间域中,初值、上延结果、差以及每一次校正后的结果都能用满足莱布尼兹定理的交错级数表示,从而得出了迭代法能够收敛的结论;或者,以"观测高度上的实测值与计算值的差值小到可以忽略"为标准,从数学上也能证明迭代法能够收敛。数学推论和模型试验结果说明了迭代的位场初值可以任意给定。在实际操作中,迭代误差标准的影响和由于迭代误差标准不恰当可能出现不能达到迭代标准的情况,需引起注意,也值得进一步研究。

关键词: 位场, 向下延拓, 收敛性, 空间域, 迭代法, 频率域, 快速傅里叶变换

Abstract:

The substance of the potential field downward continuation iteration method is an operating process of "upward continuation rather than downward continuation" based on the criterion of "iteration result tend to be the observation data". We have analyzed the operational mechanism of the method by chasing its operation routine, and obtained the dynamic rule of the data flow in spatial domain. It turned out that the iteration method for a downward continuation leads to an upward continuation of the potential field on the individual levels. The relationship between the iteration period n and the height h of the upward continuation is n~(n+1)h.Shown in an alternating serie of satisfying Leibniz theorem to each iteration result in spatial domain, the convergence of this method is obtained. The convergence can also be verified by using the criterion of minimizing the difference between measured value and calculated data. The mathematical reasoning and numerical computation results show that an initial value of the iteration method can be arbitrary. Also, we have studied the effect of the iteration tolerance criterion, and pointed out the possibility that a tolerance might never be satisfied in practice if the criterion is not fitted.

Key words: potential field, downward continuation, convergence, spatial domain, iteration method, frequency domain, fast Fourier transformation (FFT)

中图分类号:

P631.2

于德武, 龚胜平. 对迭代法位场向下延拓方法的剖析[J]. 吉林大学学报(地球科学版), 2015, 45(3): 934-940.

Yu Dewu, Gong Shengping. Analysis of the Potential Field Downward Continuation Iteration Method[J]. Journal of Jilin University(Earth Science Edition), 2015, 45(3): 934-940.

参考文献

[1] Fedi M,Florio G.A Stable Downward Continuation by Using the ISVD Method[J].Geophysical Journal International,2002,151(1):146-156.

[2] Cooper G.The Stable Downward Continuation of Potential Field Data[J].Exploration Geophysics,2004,35(2):260-265.

[3] 刘保华,焦湘恒,王重德.位场向下延拓的边界单元法[J].石油地球物理勘探,1990,25(4):495-499. Liu Baohua,Jiao Xiangheng,Wang Chongde.Boundary Element Method for Continuation of Potential Field[J]. Oil Geophysical Prospecting, 1990,25(4):495-499.

[4] 毛小平,吴蓉元,曲赞.频率域位场下延的振荡机制及消除方法[J].石油地球物理勘探,1998,33(2):230-237. Mao Xiaoping,Wu Rongyuan,Qu Zan. Oscillation Mechanism of Potential Field Downward Continuation in Frequency Domain and Its Elimination[J]. Oil Geophysical Prospecting, 1998,33(2):230-237.

[5] 徐世浙,沈晓华,邹乐君,等.将航磁异常从飞行高度向下延拓至地形线[J].地球物理学报,2004,47(6):1127-1130. Xu Shizhe,Shen Xiaohua,Zou Lejun,et al.Downward Continuation of Aeromagnetic Anomaly from Flying Altitude to Terrain[J].Chinese Journal of Geophysics,2004,47(6):1127-1130.

[6] 徐世浙.位场延拓的积分-迭代法[J].地球物理学报,2006,49(4):1176-1182. Xu Shizhe.The Integral-Iteration Method for Continuation of Potential Fields[J].Chinese Journal of Geophysics,2006,49(4):1176-1182.

[7] 徐世浙.迭代法与FFT法位场向下延拓效果的比较[J].地球物理学报,2007,50(1):285-289. Xu Shizhe.A Comparison of Effects Between the Iteration Method and FFT for Downward Continuation of Potential Fields[J].Chinese Journal of Geophysics,2007,50(1):285-289.

[8] 徐世浙,余海龙.位场曲化平的插值-迭代法[J].地球物理学报,2007,50(6):1811-1815. Xu Shizhe, Yu Hailong.The Interpolation-Iteration Method for Potential Field Continuation from Undulating Surface to Plane[J].Chinese Journal of Geophysics,2007,50(6):1811-1815.

[9] 王彦国,王祝文,张凤旭,等. 位场向下延拓的导数迭代法[J].吉林大学学报:地球科学版,2012,42(1): 240-245. Wang Yanguo,Wang Zhuwen,Zhang Fengxu,et al. Derivative-Iteration Method for Downward Continuation of Potential Fields[J]. Journal of Jilin University:Earth Science Edition, 2012,42(1): 240-245.

[10] 张志厚,吴乐园. 位场向下延拓的相关系数法法[J].吉林大学学报:地球科学版,2012,42(6): 1912-1919. Zhang Zhihou,Wu Leyuan. Corelation Coefficient Method for Downward Continuation of Potential Fields[J]. Journal of Jilin University:Earth Science Edition, 2012,42(6): 1912-1919.

[11] 刘东甲,洪天求,贾志海,等.位场向下延拓的波数域迭代法及其收敛性[J].地球物理学报,2009,52(6):1599-1605. Liu Dongjia,Hong Tianqiu,Jia Zhihai,et al.Wave Number Domain Iteration Method for Downward Continuation of Potential Fields and Its Convergence[J].Chinese Journal of Geophysics,2009,52(6):1599-1605.

[12] 骆遥.位场迭代法向下延拓的地球物理含义:以可下延异常逐次分离过程为例[J].地球物理学进展,2011,26(4):1197-1200. Luo Yao.The Integral-Iteration Method for Continuation of Potential Fields: A Case by Computing Regional Anomaly Can be Continued Downward[J].Progress in Geophysics,2011,26(4):1197-1200.

[13] 姚长利,李宏伟,郑元满,等.重磁位场转换计算中迭代法的综合分析与研究[J].地球物理学报,2012,55(6):2062-2078. Yao Changli, Li Hongwei, Zheng Yuanman, et al. Research on Iteration Method Using in Potential Field Transformations[J]. Chinese Journal of Geophysics,2012,55(6):2062-2078.

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