Local Gravity Field Solution from Goce Mission by 1DFFT Integral Inversion of the Potential Second Radial Derivative
Garcia, Ramon; Lopez-Moreno, Manuel; Balderrama-Corral, Rigoberto; Arana-Medina, Anibal; Guzman-Galindo, Tiojary; Monjardin, Jesus
University Autonomous of Sinaloa, MEXICO

An analysis is made on the geopotential solution in the space domain using the second radial derivative of the gravitational potential produced by a gradiometric satellite mission like GOCE. The model presented is based on a close form integral that relates the disturbing potential T(R) at the Earth’s surface to its second radial derivative Trr(r) at satellite altitude. The integral involved is inverted using 1D-FFT to solve for T(R) at the Earth surface. Regularization is required to stabilize the system. The Tikhonov method is employed for this purpose. Nine monthly data set of the mission were used in the simulation test, the EGM2008 geopotential model was employed as measured and true field. The solutions were obtained on a quasi-global scope (polar gap), avoiding the cyclic convolution errors along the parallels. The optimum regularization parameter was estimated by iteration, by comparing to the true values in the simulation process, and using the selected one for the corresponding configuration when applying to real measurements. Results indicate that with the method presented and the expected GOCE errors for Trr with nine months of data, a 7 cm geoid with 100 km resolution and 3cm geoid with 200 km resolution are possible. However, when using the real data the estimated errors were about twice larger. Nevertheless, they were smaller than the estimated errors of published geopotential models.