FVM: A Good Match to Airborne Gravimetry?

Numerical methods like the Finite Element Methods (FEM) or Finite Element Methods (FVM) are widely used in many engineering applications to solve boundary value problems that are hard to find rigorous analytical solutions. These numerical methods have been also applied in geodesy in many previous studies regardless of its huge computation demands. They have arisen due to the fact that the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the bottom boundary Earth' s surface, and the upper boundary even exacerbates the computation loads because of the required discretization in between. Considering that many areas such as the US have uniformly distributed airborne gravity data that are just a few kilometers above the topography, we propose to move the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant reduction in altitudes, dramatically saves the large computation demands in previous FEM or FVM computations. This paper demonstrates this benefit by using FVM for both simulated data and real data in the target area. In the simulated case, the FVM numerical results show that about an order of magnitude precision improvement can be obtained when moving the upper boundary from 250km to 10km, the maximum altitude of GRAV-D. For the real data sets, 2-3 cm level of accurate quasi geoid model can be obtained depending on different schemes used to model the topographic mass. The paper also demonstrates how to find the upper layer in case no airborne data is available. Last but not the least, this study provides a 3D representation of the entire local gravity field instead of a single 2D surface, the (quasi) geoid.