基于Taylor和Legendre多项式模型的截断阶数和边界效应研究（英文）  

A preliminary study on truncation level and boundary effects of Taylor polynomial and Legendre polynomial

作　　者：冯彦[1] 梅朵 蒋勇[1] 孙涵[3] 

机构地区：[1]南京信息工程大学数学与统计学院,南京210044 [2]青海省都兰县气象局,都兰816100 [3]国家卫星气象中心遥感应用试验基地/广西气象减灾研究所,南宁530022

出　　处：《地球物理学进展》2015年第1期111-120,共10页Progress in Geophysics

基　　金：Supported by the National Natural Science Foundation of China(Grant No:41404053;41174165);National Natural Science Foundation of China(Grant No.14KJB170012);Special Project for Meteo-scientific Research in the Public Interest(Grant No:GYHY201306073)

摘　　要：当利用Taylor多项式和Legender多项式建立区域地磁场模型时,会碰到两个问题:截断阶数的选取与边界效应的控制.现以常用的Taylor多项式模型和Legendre多项式模型为例,结合中国地区1970.0和2000.0年的地磁场实测数据,提出一种可解决以上两种问题的应用方案.为了进行综合比较和研究,还采用了最新的全球模型——IGRF11和CM4.结果显示通过计算两种模型的均方根偏差(RMSE)和AIC(AIC信息标准)值,并与IGRF11及CM4的均方偏差相比较,可以初步确定截断阶数的选取范围,比较各阶截断阶数的AIC值,可进一步获取合适的截断阶数.通过首次提出的"异常区域添加法"和"均匀添加法"逐步增加境外补充点,结果显示当不断增加补充点后,境外的磁异常的分布大为改善,并与IGRF11的分布高度一致.随着补充点的增加,极值点强度逐渐减弱并趋于稳定."均匀添加法"可更好地控制中国地区的地磁场边界效应.提出了一种可通过两个个步骤以确定最适截断阶数的方法,还提出了两个标准从而可初步确定补充点的数量,从而能够较好地控制边界效应.对于两种模型所反映的一些境外磁异常,可通过实地测量或是在磁异常周围增加测点而验证.A representative solution is put forward about two issues,selection of the Truncation Level（TL） and the control of the Boundary Effects（BE）,while the regional models are created based on data fitting.We chosen the Taylor Polynomial（TP） and Legendre Polynomial（LP）,combined with measured data in 1970.0,and 2000.0 over Chinese mainland.To take a comprehensive comparison and investigation,the newest global model,IGRF11 and CM4,were used.Results show that the Root-mean-square Error（RMSE） of two models could roughly determine the range of TL firstly,then better result could be obtained by taking a comparison with AIC values.We gradually add the supplementary points outside the boundary by two methods,Regional anomalous adding method（RA） and Uniformly adding method（UA）.The former is put forward for the first time.As a result,the distributions outside the boundary could be greatly improved and is highly consistent with that of IGRF11.The intensities of extreme points gradually decrease and trend to be stable while adding points more and more.UA achieves a better control over Chinese mainland than RA.We raise a way that involves two steps that could determine the TL,as well as two criteria that could determine the roughly suitable number of supplementary points that BE could be controlled.

关 键 词：边界效应 截断阶数 Taylor多项式 Legengdre多项式 IGRF11 CM4 

分 类 号：P318[天文地球—固体地球物理学]