Inverse Neumann Problem and Inverse Stokes Formula on Exterior Sphere

An integral for the upward continuation of the disturbing potential is presented based on modified Poisson's integral in which the zero and the first degrees of spherical harmonics are excluded.Differentiating the integral expression with respect to the geocentric distance of computing point,the solution in a closed integral form for the inverse Neumann's exterior problem is then obtained.The closed integral expression for upward continuation of the solutions for inverse Stokes formula is derived in terms of the fundamental differential equation in physical geodesy.