Calculation Of Gravity Field Parameters Using Spherical Harmonics

The earth gravity field model is a set of coefficients of the Earth's gravitational force spread by the spherical harmonic function,which is the approximation or fitting of the earth's gravity field.The gravitational field parameters with important and wide application values such as gravity anomalies,height anomalies and vertical deviations can be derived quickly and easily by simply calculating the complex gravity field and applying a simple linear operation to the perturbation function.Therefore,this paper focuses on how to use the spherical harmonic function to calculate the gravity field expansion quickly and accurately.The main research contents and achievements are as follows:(1)One of the key issues in calculating the spherical harmonic function is to quickly and accurately calculate the associated Legendre function.The applicability of four commonly used associative Legendre functions is discussed from two aspects: calculation accuracy and calculation speed.Experiments show that when the order is extremely high,the standard to the forefront and the standard forward to the fastest calculation,but the worst calculation accuracy,cross-order computing speed is slightly faster than beliokv,the two are quite accurate.Through the insertion ratio and other methods to improve the phenomenon of recursive instability,but increased the number of operations,sacrifice the calculation speed.Comprehensive experiment that the cross-order recursive algorithm is more suitable as a recursive algorithm for the super-high order association Legendre function.(2)The use of spherical harmonic function to derive gravity anomalies,height anomalies and vertical deviations have important applications such as gravity field elements.Through the fast calculation of the trigonometric function,the longitude cycle is followed by the longitude cycle and the simplified index of the array index and so on to improve the calculation speed,and the experiment verifies the correctness of the program.Combined with the Horner summation algorithm to improve the summation of the series and further improve the computational efficiency.(3)Taking the quasi geoid as an example,the paper proposes a QR matrix decomposition method to avoid the inverse process in the process of solving the parameters.The influence of the smoothing factor on the conversion precision of the polygon function is analyzed.Based on the gravity field model,the advantages and disadvantages of the four kinds of fitting models are compared and analyzed.The optimal fitting algorithm is used to analyze the influence of different gravity field models on the conversion precision.Experiments show that the quadratic surface method is more suitable for the residual fitting,and the super-high-order gravity field model is not very different in the small engineering area.(4)According to the above research results,using the ASP.NET(Csharp)programming language to achieve the association of the Legendre stability analysis,the calculation of the gravity field,the gravity field data of the two-dimensional visualization and elevation conversion functions,Three-dimensional visualization of gravity field data is realized by using webGL,and a gravity field calculation platform is designed and developed.