The modified integral method for the determination of gravity disturbance near the Earth’s surface

Abstract For the calculation of gravity disturbance in the Earth’s external gravity field, the Stokes-Pizzetti integral is a commonly used method. However, when the target point approaches the Earth’s surface, such problems as singularity and discontinuity arise due to the Stokes kernel structure itself. To settle the problems, firstly the reason for singularity and discontinuity was discussed, and then modification was made to the integral formula, by which the singularity at the surface point is eliminated. Finally the non-singular integral formulas for the calculation of disturbing gravity were derived. In numerical experiments, an area in China was selected to test the modified formula. Numerical results show that the modified formula performs much better than classical Stokes-Pizzetti integral formula when dealing with the calculation of the radial component of gravity disturbance near the Earth’s surface.