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中文摘要：
本文从局部重力场在直角坐标系下的最基本原理边值问题出发,讨论了边值问题在二维和三维直角坐标系下的求解过程,得出了适用于局部重力场的普通解的傅里叶级数表达式;根据傅里叶表达式中三角函数的正交性,得出了其傅里叶系数的积分表达式;根据大地测量学中各物理量之间的关系,分别求得了重力异常和重力梯度垂直分量在二维直角坐标下的傅里叶系数关系式,以及重力场扰动位和重力异常、重力场扰动位及其重力梯度分量在三维直角坐标下的傅里叶系数关系式,并根据实际算例验证了上述表达式的有效性.
英文摘要：
The study first presented the solution procedure of the boundary problem under two and three dimensional Cartesian coordinates to achieve the Fourier series expression of the general solution applied to local gravity field, started with the boundary theory of local gravity field under Cartesian coordinates. Second it derived the integration expression of the Fourier coefficients on the basis of the orthogonality of the trigonometric functions. Ultimately, the Fourier coefficient relation between gravity anomaly and the vertical component of gravity gradient in spectral domain under two dimensional Cartesian coordinates, as well as the relations between the geodetic physical quantities including gravity anomaly, gravity disturbing potential and gravity gradient were calculated. Result of the calculation example proved the feasibility of the relational expressions.
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