位场向下延拓三种迭代方法之比较  

A comparison of three iteration methods for downward continuation of potential fields

作　　者：曾小牛[1] 李夕海[1] 韩绍卿[1] 刘代志[1] 

机构地区：[1]第二炮兵工程学院,西安710025

出　　处：《地球物理学进展》2011年第3期908-915,共8页Progress in Geophysics

基　　金：国家自然科学基金(60705001;40974037);中国博士后科学基金项目(20080430234)联合资助

摘　　要：位场向下延拓在重磁资料解释和用于位场导航的基准数据库构建中发挥着重要作用.本文针对第一类Fredholm积分方程的三种空间域迭代解法:迭代Tikhonov正则化法、Landweber正则化迭代法和积分迭代法,基于算子理论和不适定问题的正则化处理方法,首先利用傅里叶变换将空间域迭代法变换到波数域,然后由数学归纳法推导得到这三种迭代法对应的波数域位场向下延拓算子;由Landweber迭代法和积分迭代法在迭代形式上的相似性,探讨了它们在位场向下延拓中的异同及各自优势.模型对比分析表明:(1)两种迭代正则化方法在正则化参数选择合适的条件下,其向下延拓的效果要明显优于积分迭代法,且当收敛到相同误差水平时,迭代Tikhonov正则化法在迭代次数上要远远小于Landweber迭代法,但迭代Tikhonov正则化方法存在对正则化参数敏感的问题;(2)从实际应用上讲,由于积分迭代法不存在正则化参数的选择问题,所以该迭代法具有较强的实用性,但需考虑其波数域向下延拓算子对噪声的放大效应.Potential field downward continuation plays an important role in gravity-magnetic data interpretation and the building of potential field database which is a precondition of potential field aided navigation. According to three space domain iteration methods of first kind of Fredholm integral equation： iteration Tikhonov regularization, Landweber iteration regularization and integral iteration methods, based on the operator theory and regularization method for ill-posed problems, we use Fourier transform theory to transform space domain iteration methods to the wave number domain. Then, three wave number domain downward continued operators correspond to three iteration methods are deduced from mathematical induction. Similarities and differences of Landweber iteration and integral iteration methods are discussed based on the comparability of their iteration forms. Model comparison analysis shows that： （1） If the choice of regularization parameters is appropriate, the downward continuation effect of two regularization iteration methods is better than the integral iteration method. The iteration numbers of iteration Tikhonov regularization are smaller than Landweber iterative regularization when they convergence to a similar error level but the iteration Tikhonov regularization method is sensitive to regularization parameters. （2） The integral iteration method is more practical because this method does not need the choice of regularization parameters, but the noise amplification of its wave number domain downward continued operator must be considered.

关 键 词：位场 向下延拓 迭代方法 算子理论 正则化 

分 类 号：P318[天文地球—固体地球物理学]