重力学反问题中零外部位密度的研究

对重力学反问题研究中零外部位密度的数学性质及物理意义进行了系统研究和分析．首先从基本定义及条件的描述入手，推演出其数学表示和限制，由此揭示重力学反问题的非适定性形态，进而论及其与非零外部位密度之间的数学关系．由此证明对应于给定外部位的场源函数可以分解成零外部位密度与调和密度的直和．通过对其物理意义的讨论，为地球物理反演非零外部位场源及物理大地测量学构制等效场源提供理论依据．

A RESEARCH ON DENSITY OF NULL EXTERNAL POTENTIAL

As a important theoretical problem in geophysics and geodesy the mathematical characters(representations and classifications) and physical significances of the densities corresponding to a null external potential are researched and proven systematecally and deeply.With the beginning of basic definitions and conditions being made,the density functions of null external Potential are derived, which reveals the nonuniqueness of gravity inversion. Furthermore, the intrinsic relations between the densities corresponding to null external potential and non-null external potential are analysed. At last the physical significances of the results above are discussed so as to provide some theoretical arguments for gravity inversion.