位场向下延拓的迭代最小二乘法  

The iterative Least Square method for downward continuation of potential fields

作　　者：陈龙伟[1] 徐世浙[2] 胡小平[1] 吴美平[1] 张辉[1] 

机构地区：[1]国防科技大学机电工程与自动化学院,长沙410073 [2]浙江大学地球科学系,杭州310027

出　　处：《地球物理学进展》2011年第3期894-901,共8页Progress in Geophysics

基　　金：国家自然科学基金项目(40774059);教育部博士点基金项目(20070335090)联合资助

摘　　要：将位场向下延拓作为一种反问题,结合正则化方法和快速傅里叶算法的优点,本文提出了一种解决位场向下延拓问题的迭代最小二乘法,新方法将位场向下延拓问题转化为最小二乘问题,采用梯度下降法对最小二乘问题进行迭代求解,在迭代过程中,利用快速傅里叶变换方法解决了计算量大的问题,新方法对延拓数据中的噪声具有很好的抑制作用,利用不合噪声和含有噪声的模型数据对新方法进行了验证,结果表明新方法快速、稳定、抗干扰能力强,向下延拓距离大.To treat potential field downward continuation problem as an inverse problem and to make full use of advantage of regularization method and fast Fourier algorithm, this paper presents an iterative least square method to deal with downward continuation of potential field. The presented method converts downward continuation problem to a least square problem, and adopts gradient descent iteration method to search for the solution of the least square problem. In the process of iteration, fast Fourier algorithm is used to deal with computation problem. New method is not sensitive to the noise in original data. Model data with and without noise is simulated to test the presented method. The result shows that the new method is fast, stable, robust and has a large downward continuation distance.

关 键 词：位场向下延拓 迭代最小二乘法 正则化方法 梯度下降法 快速傅里叶算法 

分 类 号：P631[天文地球—地质矿产勘探]