一种改进的基于导数迭代的磁场向下延拓方法  

Improved downward continuation method of magnetic field based on derivative iteration

作　　者：王泽 陈棣湘[1] 刘中艳 潘孟春 陈卓[1] 王振雄[1] 任鑫田 徐昱静 胡佳飞 张琦[1] WANG Ze;CHEN DiXiang;LIU ZhongYan;PAN MengChun;CHEN Zhuo;WANG ZhenXiong;REN XingTian;XU YuJing;HU JiaFei;ZHANG Qi(School of Intelligent Science Rational University of Defense Technology of the People's Liberation Army,Changsha 410005,China)

机构地区：[1]中国人民解放军国防科技大学智能科学学院,长沙410005

出　　处：《地球物理学进展》2022年第1期284-290,共7页Progress in Geophysics

摘　　要：高精度的地磁场数据库是地磁匹配导航的基础.在构建地磁数据库时,需要将空中的航磁测量数据向下延拓至某一水平面,而向下延拓在数学上具有不适定性,通常利用迭代方法逐次逼近"适定最优解".本文针对导数迭代法在迭代过程中的噪声累积问题,提出一种改进方法,首先利用稳定的向上延拓将观测面和向上延拓、向下延拓同等高度平面上的磁场值联系起来,再通过垂向一阶导数关系构造残差项,为了抑制高频噪声的干扰,采用向上延拓算子对残差项进行低通滤波,最后更新迭代值.在不同噪声水平的仿真条件下,改进方法的延拓误差仅为导数迭代法的四分之一,表明改进方法的抗噪能力与精度远远优于导数迭代法,同时实测数据也验证了改进方法可以实现稳定的磁场向下延拓.High precision geomagnetic database is the basis of geomagnetic matching navigation. In the construction of geomagnetic database, it is necessary to extend the airborne aeromagnetic data down to a certain horizontal plane, and the downward continuation is not well posed mathematically, so the iterative method is usually used to approach the “well posed optimal solution” step by step. In this paper, an improved method is proposed to solve the problem of noise accumulation in the iterative process of derivative iteration method. Firstly, the stable upward continuation is used to connect the magnetic field values on the observation plane and the plane with the same height of upward continuation and downward continuation. Then, the residual term is constructed by the vertical first-order derivative relationship. In order to suppress the interference of high-frequency noise, the upward continuation operator is used to calculate the residual term Low pass filtering, and finally update the iterative value. Under the simulation conditions of different noise levels, the continuation error of the improved method is only one fourth of that of the derivative iteration method, which shows that the anti noise ability and accuracy of the improved method are far better than that of the derivative iteration method. At the same time, the measured data also verify that the improved method can achieve stable downward continuation of the magnetic field.

关 键 词：地磁数据库 向下延拓 导数迭代法 滤波 高频噪声 抗噪能力 

分 类 号：P631[天文地球—地质矿产勘探]