Theory And Method Of Ellipsoidal’s Second Geodetic Boundary Value Problem

In this paper,we mainly study the theory and method of ellipsoidal’s second geodetic boundary value problem,The research findings and innovations are summarized as follows:（1）With disturbed gravity as boundary value on reference ellipsoid,ellipsoidal’s second geodetic boundary value problem to solve geoid determination,quasigeoid determination and so on.（2）In order to solve the ellipsoidal’s second geodetic boundary value problem on reference ellipsoid,the Helmert perturbation potential model of ellipsoid and ellipsoid kernel function of ellipsoid Hotine integral are derived,We get the exact ellipsoid integral expressions of height anomaly,geoid determination,quasigeoid determination.（3）Ellipsoid harmonic series of earth’s gravitational field about the second kind of associated legendre functions and Its first and second derivatives’s recursive calculation method are derived and compare with the original Jekeli’s recursive method to calculate the second kind of associated legendre functions and Its first and second derivatives.When the relative error between them is about 10^-12,the calculated results are equal,which proves the accuracy of the theory and method of ellipsoidal’s Second geodetic boundary value Problem.（4）To demonstrate the influence of ellipsoidal’s residual topography about geoid determination and quasigeoid determination from indirect topographic effect,and we derive the exact integral of ellipsoidal expression and elliptical’s Helmert harmonic series expansion of the potential model.and Numerical calculation and analysis,when The integral radius are 0.5°、1°、1.5°和2°,we proof the relationship of geoid determination and integral Radius.（5）We derive the ellipsoidal Harmonic series expansion of Helmert disturbance potential model and its practical formula of geoid determination,quasigeoid determination.and we calculate and analyze that the max value quasigeoid-determination is-12.11m,the min about-36.03m,the average value about-23.25m and the root mean square is-24.18m.（6）To downward continuation the disturbed gravity with boundary value from geoid determination to reference ellipsoid,we Research Poisson algorithm of downward continuation about ellipsoidal’s second geodetic boundary value problem.we calculate and analyze that the disturbed gravity’s value are different,separately,High frequency and low frequency.（7）We research the theory of Airy-Heiskanen terrain correction model,and calculate The direct topographical correction in gravimetric geoid determination,and we derive the precise integral formula of ellipsoidal’s roughness topographic potential and ellipsoidal’s Spherical potential.