The Correct Application of Kernel in One-Step Inversion

Integral Equations such as one-stepinversion based on the first derivative of the ellipsoidal Poisson’s integral, for transformation of gravity values on theEarth’s surface to the gravity potential on the reference ellipsoid are used for geoid determination. One of the main problems in numerical solution of integral equations is the resolution of input data. In this study, we have shown that the required resolution of the input gravity data on the Earth’s surface for correct one-step inversion depends on the height of the computational region, the fact that if overlooked can cause totally wrong results. For detect that the resolution ofinput data is sufficient, we study the behavior of the integral kernel and change the integral kernel to overcome the adverse effect of insufficient resolution of the input gravity data are the novel contributions of the study. For numerical tests, we have choose a test area with real gravity data in the west of Iran and The numerical results approve the success of our proposed method to solve the problem of insufficient resolution of the input gravity data for correct one-step inversion.