Research On Boundary Value Problem And Data Processing For Airborne Gravimetry

With the development of gravity field detection technology,gravity field measurement presents a multi-means,multi-type andmulti-level information acquisition pattern from the ground,the ocean,the air to the space.The determination of the earth's gravity field by airborne gravimetry can be attributed to solving a special boundary value problem of physical geodesy.This paper focuses on airborne gravity boundary value problems and processing and application of gravity disturbance data.The main work and innovations are:1.This paper studies the method of remove integrating irregularity of center region of Hotine integral and method to correct kernel function,combination of the improved Hotine kernel function and gravity disturbances data are used to determine the regional geoid.2.The formula of calculating gravity disturbance vector from gravity disturbances and the Green integral with real terrain surface is deduced,and the formula of calculating gravity disturbance vector from gravity disturbances and the Hotine integral is deduced.3.The Tikhonov regularization method of point mass model is studied for the morbid problem of the coefficient matrix of point mass model,and the downward continuation of combine ground and airborne gravity data is completed by using the regularized point mass model.4.Aiming at the different problems of different height measurement in the actual area of airborne gravity measurement,a leveling scheme based on the radial derivative formula of gravity disturbance is put forward.5.The theory and method of the downward continuation of airborne gravity data are studied,Numerical experiments are designed to compare and analyze different methods,so as to provide a method selection for downward continuation processing of actual airborne gravity data.6.The band-limited kernel function solution of band limited boundary value problem commonly used by the continuation of airborne gravity data is derived.The integral solution and discrete approximation algorithm for local application of band-limited boundary value problem for downward continuation of airborne gravity are established.As a result,the problem of instability of continuation has been solved well and the necessary technical foundation has been laid for the expansion of the engineering application of airborne gravimetry data.7.An integer degree recursive interpolation algorithm for calculation of Legendre functions with Non-integer degree is proposed and a Spherical cap harmonic harmonic approximation model for fusion processing of aerial and ground gravity disturbance and height anomaly is constructed.It is applied to the downward continuation experiment and good results are obtained.8.Based on the basic observation equation of geopotential model and the diagonalization of normal matrix block,the problems of storage and low computational efficiency of large Matrix were solved by combining the equator symmetry characteristic of Legendre function,reduction of the matrix solution equation and design of the calculation and storage method of Legendre function.9.The toroidal harmonic analysis method is improved and two improved algorithms proposed that are convenient for parallel implementation are proposed.This work greatly improves the efficiency of spherical harmonic analysis and processing and provides a tool for the spherical harmonic analysis of high-resolution data.