Метод вычислений потенциала, усклонений отвеса и стоксовых постоянных на основе интегрального уравнения молоденского для возмущего потенциала

Summary

Formulas were obtained for expressing corrections of Stokes's approximations of the disturbing potential, plumb-line deflections, and coefficients of expansion of the disturbing potential in terms of spherical harmonics. When used for the computation of plumb-line deflections in any terrain conditions, these formulas will ensure relative accuracy of order of the Earth's flattening if the distance between the given and a current point is greater than 300 km. In conditions of an undisturbed relief, this distance may be diminished and reduced to zero in flat areas. In difficult terrain conditions inside the central zone, the application of Molodensky's equation for the disturbing potential together with the equation for the single layer density is necessary. The projections of the elementary areas onto the reference sphere may be formed by arcs of meridians, parallels and diagonals of the corresponding trapezia. Besides the gravity anomalies and Stokes' approximation values of the disturbing potential, the mean slope of the Earth's surface, and the mean square value of this slope must be known for the elementary area in question.