Precise Modelling of the Static Gravity Field from GOCE Second Radial Derivatives of the Disturbing Potential Using the Method of Fundamental Solutions

Abstract

The method of fundamental solutions (MFS) is used to derive the disturbing potential and gravity disturbances from the second derivatives observed by the GOCE satellite mission. Namely, the radial components T _rr of the gravity disturbing tensor available from the EGG_TRF_2 product are processed to evaluate the unknown coefficients in the source points that are located directly on the real Earth’s surface. MFS as a mesh-free boundary collocation technique uses the fundamental solution of the Laplace equation as its basis functions. Hence, the system matrix is created by the second radial derivatives of the fundamental solution that depend solely on 3D positions of the GOCE observations and the source points. Once the coefficients are evaluated, the disturbing potential and gravity disturbance can be computed in any point above the Earth’s surface. This paper presents results of processing 20 datasets of the GOCE measurements, each for different 2-months period. To obtain “cm-level” precision, the source points are uniformly distributed over the Earth’s surface with the high-resolution of 0.075° (5,760,002 points). For every dataset the radial components T _rr as input data are filtered using the nonlinear diffusion filtering. The large-scale parallel computations are performed on the cluster with 1.2 TB of the distributed memory. A combination of numerical solutions obtained for different datasets/periods yields the final static gravity field model. Its comparison with the SH-based satellite-only geopotential models like GOCO03S, GOCE-TIM5 or GOCE-DIR5 indicates its high accuracy. Standard deviation of differences evaluated at altitude 235 km above the reference ellipsoid is about 0.05 m²s⁻² (∼5 mm) in case of the disturbing potential, and 0.01 mGal for gravity disturbances.