基于局部重力场建模的Tikhonov正则化点质量核径向基函数方法

Point-Mass Kernel RBF Model Based on Tikhonov Regularization

针对点质量核径向基函数应用于局部重力场建模中的设计矩阵严重病态问题,本文引入Tikhonov正则化方法对传统点质量核径向基函数方程进行改造,建立了相应的正则化模型。通过模拟数据进行仿真实验,以传统格网化方法作为对比试验,利用"标靶法"确定两种模型的最优结构。实验结果表明:正则化点质量核径向基函数可以直接利用离散数据进行局部重力场建模。在两种模型的最优结构下,当实测数据无污染时,正则化方法达到与传统格网化方法相当的精度;当实测值中加入3 mGal的高斯白噪声时,正则化方法的精度获得了27.9%的提升。这说明本文方法可以应用于局部重力场建模中,且模型结构更优,抗干扰能力更强。

To solve the singularity of design matrix using the discretized data during the process in regional gravity modeling,the Tikhonov regularization method is introduced to transform the traditional point-mass kernel radial basis function model,and a corresponding regularization model is established.Experiments are conducted using some simulation data sets which are for model setting and model testing,besides a comparative experiment is designed based on traditional way in which the discretized data is gridded.Meanwhile the optimal structure of the two models are determined by ranging the parameters of them,such as the depth and the resolution.The results show that the regularized point mass kernel radial basis function can directly use the discretized data to model the local gravitational field.And the accuracy of the two models is equal when they are in their separate optimal structures with no error in the modeling data;while with 3 mGal-error White Gaussian Noise input,the regularization method put forward in this paper has improved by 27.9%,which means it can effectively restrain the error amplification caused by ill-conditioned design matrix,and the accuracy and stability are improved.