Extent and resolution requirements for the residual terrain effect in gravity gradiometry

Gravity gradiometry, whether from ground or airborne surveys, for geodesy and geophysics typically requires that the gravitational effect of the visible terrain is removed from the measured values. A systematic, algorithmic approach is developed to determine the extent of terrain data needed to maintain a truncation error below a desired level. The algorithm is based on a geostatistical analysis of the topography and applies to gradient differences over a particular size of survey area. It was found that a suitable modification of the kernel of the integral for the terrain effect can reduce the needed extent significantly in some cases. The determination of the needed extent for a given truncation error (standard deviation) and survey area size requires knowing a reasonable amplitude of the power spectral density (PSD) of the local topography, but otherwise is based on the fractal nature of topography, which also assumes that it is stationary. The algorithm is illustrated for ground and airborne cases in both moderate and rough terrain. For example, for an airborne gradiometer survey at 5 km altitude over 50 km of moderate terrain, the algorithm predicts requiring a topographic data extent of about 48 km for 1 Eotvos error (standard deviation) in the terrain effect. This extent can be reduced to 35 km with the kernel modification. In addition, the developed PSD models may be extended to determine the data resolution required for the terrain effect using a simple analytic formula.