关键词: 局部重力场建模, 径向基函数, 点质量核基函数, Tikhonov正则化, Kriging格网化

Abstract: 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.

Key words: regional gravity field modeling, radial basis functions, point-mass kernel, Tikhonov regularization, Kriging gridding method