位场向下延拓的导数迭代法  

Derivative-Iteration Method for Downward Continuation of Potential Fields

作　　者：王彦国[1] 王祝文[1] 张凤旭[1] 孟令顺[1] 张瑾[1] 邰振华[1] 

机构地区：[1]吉林大学地球探测科学与技术学院,长春130026

出　　处：《吉林大学学报（地球科学版）》2012年第1期240-245,共6页Journal of Jilin University：Earth Science Edition

基　　金：国家自然科学重点基金项目(40739905);国家油气选区项目(14B09XQ1201)

摘　　要：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。We present a new approach for downward continuation of potential fields： a derivative-iteration method in the case of that downward continuation is an unstable problem.From the definition of vertical first-order derivatives,we connect the values of the potential fields of observation planes with the values of the planes of upward continuation in a certain height and downward continuation in the same height.We use also the iterative method to successive approximation.Thus we deduce the recursive formula of the derivative-iteration method for continuation downward of potential fields in space domain.Taking the complexity of achieving upward continuation integral equations in spatial domain into accout,the fast Fourier transform is adopted in the recurrence formula.Then it gets the derivative iteration formula in wavenumber domain.It also proves the convergence of this method.The analysis of model tests and a practical example indicate that,comparing with the immediate FFT method,advantages of the iteration method are strong stability and a great downward continuation depth.

关 键 词：解析延拓 垂向一阶导数 导数迭代法 快速傅里叶变换 收敛性 

分 类 号：P631.1[天文地球—地质矿产勘探]