A comparison of different methods for determining the topographic - condensation mass effects at airborne altitude

Abstract

Airborne gravimetry is a fast and sufficiently accurate gravity measurement technique to derive high resolution geoids in not easily accessible regions. Under optimal conditions the measurement accuracy varies around 1 to 2 mGal for a spatial resolution of approximately 2 km. The downward continuation of these observations requires data filtering to reduce the intrinsic instabilities. To ease the downward continuation procedure it is helpful to additionally apply a remove-restore technique based on gravity field information provided by digital elevation models, available nowadays for most parts of the world. This paper discusses three different methods for determining the effects of topographic masses at aircraft altitude. In the first method, the topographic condensation masses are expanded into a spherical harmonic expansion up to a maximum degree of approximately 360, which corresponds to a resolution of approximately 30 arc minutes block size. In addition, the residual fine structure of the topography is modeled by a spherical spline representation. A second method is based again on the spherical harmonic expansion of the topography, but the fine structure is modeled by the integral over the residual topography, numerically evaluated by a quadrature method based on digital elevation blocks with a resolution of 2.5 arcmin side length. The third method consists in the integration over the complete topographic masses, again numerically evaluated by an elevation block quadrature formula. The integration area is restricted to a specific region and the far zone effect is estimated based on a technique proposed by Molodenskii. These three methods are compared by a numerical example of the Canadian Rocky Mountains. The results are validated by evaluating the integral of topography over the whole earth.