重力场径向基函数多尺度分析的直接解算方法  

Direct calculation method for multi-scale analysis of the gravity field with radial basis functions

作　　者：马志伟 陆洋[1,2] 方剑 

机构地区：[1]中国科学院测量与地球物理研究所,大地测量与地球动力学国家重点实验室,武汉430077 [2]中国科学院大学,北京100049

出　　处：《地球物理学进展》2017年第4期1474-1482,共9页Progress in Geophysics

基　　金：国家重点基础研究发展计划(973计划)(2013CB733301);国家自然科学基金(41274025,41674085)联合资助

摘　　要：利用径向基函数的多尺度分析方法可以对地球重力场进行分解,提取出细节的地球物理信息.目前通常采用离散积分法进行解算,但信号分解并重构后,所得信号并不能与原始重力场信号完全符合,分解过程中出现了信号泄露.针对这一现象,本文在最小二乘算法和方差分量估计的基础上,提出了新的在各个尺度上直接解算基函数系数的算法(直接法),有效的减少了重力场分解过程中的信号泄露.以南海地区DTU13重力异常数据为例,分别运用离散积分法和直接法对重力异常进行多尺度分解,结果显示:直接法的5个尺度上的信号泄露误差相对离散积分法减小约39%~79%;直接法总的泄露误差为±1.12 m Gal,明显小于离散积分法的±4.04 m Gal,直接法具有更优的效果.The radial basis function can be used to multi-scale analysis of the gravity field,and then extract the detail geophysical information.However,due to the signal leakage problem,the reconstructed signal cannot be fully consistent with the original gravity field,which is often overlooked.In order to reduce the leakage error,we present a new multi-scale analysis algorithm,which using least squares and the variance component estimate method,directly calculate the radial basis function coefficients on each scale（direct method）.Comparing to the former algorithm,the direct method reduces signal leakage error significantly.Taking the gravity anomaly（DTU13） of the South China Sea as an example,we try to decompose the gravity field using the two methods mentioned above.Results show that the signal leakage error of the new method on the five scales reduced by about 39%～79%.The total leakage error of the direct method is ±1.12 mgal,which is obviously smaller than the corresponding value of the discrete integral method（±4.04 m Gal）.The direct method has better decomposition results than the discrete integral method.

关 键 词：多尺度分析 重力异常 径向基函数 直接法 离散积分法 

分 类 号：P312[天文地球—固体地球物理学]