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位场向下延拓的导数迭代法

Yan-guo WANG,Zhu-wen WANG,Feng-xu ZHANG,Ling-shun MENG, Jin ZHANG,Zhen-hua TAI

Jilin Daxue Xuebao (Diqiu Kexue Ban)/Journal of Jilin University (Earth Science Edition)（2012）

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Abstract
针对向下延拓的不适定问题,提出了一种新的位场向下延拓方法——导数迭代法.从位场垂向一阶导数的定义出发,将观测面和向上延拓、向下延拓同等高度平面上的位场值近似联系起来,采用迭代法进行逐次逼近,推导出空间域位场向下延拓的导数迭代法的递推公式.考虑到空间域向上延拓积分方程实现的复杂性,对递推公式进行快速傅里叶变换,整理得到波数域中的导数迭代公式,同时证明了该方法的收敛性.模型检验和实例分析均表明迭代法相对直接FFT法具有稳定性强和下延深度大的优点.
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Key words
Analytic continuation,Convergence,Derivative iteration method,Fast Fourier transform,Vertical first-order derivatives
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