用椭球函数解Molodensky问题  

SOLVING MOLODENSKY'S WITH ELLIPSOID FUNCTION

作　　者：张赤军[1] 骆鸣津 柳林涛[1] 方剑[1] 唐元义[3] 

机构地区：[1]中国科学院测量与地球物理研究所大地测量与地球动力学国家重点实验室,武汉430077 [2]河南省地震局,郑州450003 [3]湖北大学,武汉430062

出　　处：《大地测量与地球动力学》2014年第6期148-156,共9页Journal of Geodesy and Geodynamics

基　　金：国家自然科学基金项目(90814009;41021003)

摘　　要：椭球域外的扰动位T(u,θ,λ)在外空为调和函数,可以用椭球调和函数的级数之和表示,对T(u,θ,λ)沿法线n方向求导,仅需对各项级数中含u的因子Qmn(u)求导,而其中含θ、λ的因子包括Tmn(b,θ,λ)在内都保持不变(b为常数)。用地面观测点的椭球坐标(u,θ,λ)代入T、T/n以及它们的线性组合之中,可分别构成第一、第二、第三边值方程,其一端为边界条件即地球表面的观测值,再将另一端级数中的Qmn(u)和Qmn(un)/n展为Δu的泰勒级数,其中Δu=u-b。由于边界条件和Δu己知,可由各边值方程求解出椭球坐标下的Tmn(b,θ,λ),然后推算出地面点及其外空一点处的扰动位T(uR,θ,λ)。由于解算时没有把椭球面视为球面,并用椭球函数的级数求解,如此可更接近于实际的地球。还可将地面观测值(包括高程)一并使用,避开了莫氏用单层位求解中地面倾角多变的困难。For a harmonic function in outer space, ellipsoid lay outside the disturbance T（ u, 0, A ） can be ex- pressed by a series of harmonic functions ellipsoid, said to T（ u, 0, A ） along the normal （n） direction derivation, only to the various series contains u factor derivation Qm （ u）, and contain the factors ： u, 0, A include remain ~＇ （ b, 0, A ） unchanged （including b for constant）. T OT, the linear combination of, unobserved ground ellipsoid coordinate u, 0, On A, can be used to establish respectively the first second and third boundary value equation, end for boundary condi- tions that observation of the surface of the earth, then the other end the series and generative Taylor series of Au, in- cluding Au = u - b. Due to the boundary conditions and Au are known, then the equation of the ellipsoid T~ （ b, 0, A ） can be solved , and then the disturbance （ u~, 0, A ） on the ground point or in outer space are calculated. As the ellipsoid is not used as the sphere, and ellipsoid function and the series solution are used, the results with the solu-tion are closer to the actual the earth. Moreover, the method combining ground observation data（ such as elevation） can avoid difficult of the changeable in use of a single layer＇ s inclination.

关 键 词：重力第一、第二、第三边值问题 级数解 积分解 椭球调和函数 

分 类 号：P223[天文地球—大地测量学与测量工程]