A Note on Stokes Formula in the Form of Spherical and Planar Convolution

This paper discusses the rigidity and approximation of Stokes formula expressed by spherical and planar convolution the difference between the spherical and planar expression derived.The maximal difference value and the induced error effect on geoid undulation computation are then estimated.It is pointed out that the planar convolution form of Stokes formula taking account of all terms of Stokes function is referred to as "rigorous formula" only in the sense of this formula versus the simple planar convolution form of Stokes formula taking account of the first term of Stokes function which is commonly used in local geoid computation,and that the accurate statement of the so-called "rigorous formula" should be "a high accuracy Stokes convolution formula in planar approximation".In theory,the spherical convolution can not rigorously be converted to any equivalent planar convolution.