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一种物理上合理的顾及局部地形效应的外部边值问题的解应该是:包含在解中的表征地表重力场全球特性的所谓长波长效应,必须和表征场的局部细节的所谓短波长影响相匹配。本文从泛函分析理论出发,研究有限离散型边界约束情况,得出如下结论:1。所谓虚拟点质量解不是最佳逼近和最小模逼近解;2。Riesz表示子逼近普遍地存在于一般的Hilbert空间,而所谓物理大地测量最小二乘配置只不过是一种特殊的所谓带核Hilbert空间的Ricsz表示子逼近。解的最终形式表示为两部分之和:近区,为积分给出;远区,为球函数级数给出。这种解介于最佳核插值逼近解与球函数解之间,因而自然能兼备此二者之优点,克服各自之缺点。解对观测数据的类型没有任何要求,因此是一种联合解。
A physically reasonable solution to the exterior boundary value problem that takes into account the local topographic effects should be that the so-called long wavelength effect of the global properties of the surface gravitational field contained in the solution must be related to the so-called short wavelength-influencing phase characterizing the local details of the field match. Based on the functional analysis theory, this paper studies the finite discrete boundary constraints, and draws the following conclusions: 1. The so-called virtual point of mass solution is not the best approximation and the minimum modulus approximation solution; 2. Riesz said that the sub-approximation exists universally in the general Hilbert space, and the so-called physical geodetic least squares configuration is only a special kind of Ricsz representation sub-approximation with the so-called kernel Hilbert space. The final form of the solution is expressed as the sum of two parts: the near area, given for the integral; the far area, given for the series of spherical functions. This solution between the best kernel interpolation approximation solution and the solution of the ball function, so naturally both can take advantage of both to overcome their shortcomings. Solution does not have any requirement on the type of observation data, so it is a joint solution.