Examination of approximation errors caused by Rock-Equivalent Topography (RET) for the topographic gravitational potential and its first and second derivatives.
19/09/2016 | 17:15 | Session 2: Global gravity field modelling
Author(s): Michael Kuhn and Christian Hirt
Michael Kuhn and Christian Hirt
In global gravity forward modelling, the concept of Rock-Equivalent-Topography (RET) is often used to simplify the computation of gravity implied by rock, water, ice and other topographic masses. The RET concept compresses (approximates) topographic masses into equivalent rock, allowing for a simplified modelling with a single constant mass-density value. While providing computational advantages the RET concept comes at the expense of approximation errors. In this study, we provide a comprehensive examination of approximation errors associated with the RET compression for the topographic gravitational potential and its first- and second-order derivatives. Using the Earth2014 (http://ddfe.curtin.edu.au/gravitymodels/Earth2014/) layered topography suite we apply Newtonian integration in the spatial domain to (a) all mass bodies rigorously and (b) approximated masses using the RET concept. The differences between both variants, which reflect the RET approximation error, are studied for an ensemble of 10 different gravity field functionals at three levels of altitude (on and 3 km above the Earth’s surface and at 250 km satellite height).
The approximation errors are found to be largest at the Earth’s surface over RET compression areas (oceans, ice shields) and to increase for the first- and second-order derivatives. Relative errors, computed here as ratio between the range of differences between both variants relative to the range in signal, are at the level of 0.06-0.08 % for the potential, ~3-7% for the first-order derivatives at the Earth’s surface (~0.1 % at satellite altitude). For the second-order derivatives, relative errors are below 1% at satellite altitude, at the 10-20% level at 3 km and reach maximum values as large as ~20 to 110 % near the surface. In addition over continental areas where Earth2014 and RET masses are identical (e.g. dry bedrock above Mean sea Level) some mostly ‘bias-like’ errors are present. As such, the RET approximation errors may be acceptable for functionals computed far away from the Earth’s surface or studies focussing on the topographic potential only. However, for derivatives of the functionals computed near the Earth’s surface, the use of RET introduces very spurious errors, in some cases as large as the signal, rendering it useless for smoothing or reducing of field observation, thus rigorous mass modelling should be used for both spatial and spectral domain methods. The additional computational effort required for rigorous modelling should be acceptable considering advanced computational resources which are often available today.