Application Of Point-mass Kernel Radial Basic Function In Gravity Field

One of the basic scientific tasks of geodesy is to determine the Earth's gravitational field and its time-varying accurately.The high-precision and high-resolution gravity field model is not only the response to the distribution and change of the material in the earth,but also the basis for people to recognize,use and transform geophysics.The radial basis function is a local gravity field modeling method,which has better localized characteristics in both spatial and frequency domains,which uses a variety of observational data as modeling data and is widely used in the field of earth gravity modeling.At present,there are still many problems in the application of radial basis functions,such as the selection of radial basis functions,the solution of the parameters,the rational use of measured data,the ill-posedness in the process of inversion,and the balance of the accuracy and efficiency in disturbance gravitation evaluation.The main work and conclusions are as follows:1.The Tikhonov regularization method is introduced in the modeling of point-mass kernel functions,which eliminates the ill-posed problem of design matrix caused by the uneven distribution of discrete data,making it possible to directly use discrete data modeling.Experiments show that the Tikhonov regularization method and the grid method achieve considerable accuracy under the condition that no error in modeling data.While when 3mGal error is added into the data,theregularization method achieves 27.9%higher accuracy than grid method.In conclusion,the regularization method can improve the model's stability and immunity to interference.2.Aiming at the problems that local quasigeoid/geoid determined by basic function,such as large system error,big amount of basic data requirement,low computational efficiency and singularity of inverse process,a new approach is presented in this paper called semi-free position point mass based on the gravity field approximation principle.Compared with the traditional model,the plan coordinates of the new one are stationary,while the depths are free.The method is established by a kind of iterative algorithms using the relationship between the nearest point.And then,the algorithm is optimized using the weights calculated by surrounding points based on their distances from the calculating point,then to obtain the best fitting result,a kind of new adaptive method to determine the optimal weighted point number is presented.Results shows the theories presented in this paper achieve higher accuracy than traditional ways,with the advantage of little system error,less modeling data,no singularity and higher accuracy.The experimental results show that compared with the traditional mathematical fitting methods,the precision in the experimental area increased by 13.7%to 72.6%respectively.Self-adaptive method improves the computational efficiency in the experimental area by 1.42 to 18.83 times while maintaining the accuracy.In summary,using the methods to fitting local quasigeoid/geoid is feasible,and the adaptive one is better.3.Focusing on the application of point mass kernel basic function in disturbing gravity,the feasibility and necessity of multi-scale modeling are discussed.Taking the traditional empirical model as an example,the parameters and modeling process of the multi-scale point-mass kernel functions are given.The computational efficiency of multi-scale models are analyzed by numerical experiments,which show that multi-scale models have higher accuracy than single-scale models,and three-tier models can take into account both computational efficiency and accuracy,and the accuracy is achieved up to 0.5mGal at 3Km height.4.The application of mobile window control method converts the design matrix into sparse matrices.Combining with the sparse matrix compression storage method,the data storage of equations is greatly reduced.Finally,the fast inversion library of sparse matrices in the MKL mathematics library is used to improve the efficiency of the equation inversion,and the range of the basis function is expanded.Experiments show that the radius of the model has been extended by about 4.2 times on the same computing device.Fundamental computers can solve the models with a radius of 27°(resolution 5').5.In the process of modeling the point-mass kernel functions,the spherical coordinate transform method was introduced to redistribute the basic function grid and the basic data grid in the polar regions,eliminating the ill-posed problem of the design matrix due to spherical coordinate systems,which makes the stability in the polar regions enhanced,simultaneously facilitates the design of the modeling program.6.In order to meet the demand of long range aircraft's disturbing gravity calculation,the“segmentation-splicing" method is used to establish a global-scale multi-scale model.The stitching criteria and data storage form are set.The experiments show that the model realizes the global service of disgravity calculation,and the accuracy of 3Km height layer can be controlled at 0.5mGal.