Omission Error, Data Requirements, and the Fractal Dimension of the Geoid

Abstract

The newest global geopotential model, EGM08, yields significantly improved height anomaly (and geoid undulation) estimates, but not yet at the level of 1cm accuracy. Achieving this goal requires higher resolution gravimetric data (among other advancements, both theoretical and numerical). To determine the necessary data resolution, a statistical approach using the power spectral density (psd) of the height anomaly may be used to relate resolution to standard deviation in omission error. Kaula’s rule was the first such relationship based on a power-law approximation to the psd. It is shown that the Earth’s topography, whose fractal nature implies a power-law attenuation of its psd, and which in many cases is linearly correlated with the gravity anomaly on the basis of Airy’s isostatic assumption, can be used to design approximations to the psd of the local height anomaly, thus leading to estimates of the data resolution required to support the 1cm accuracy level.