Topographic gravitational potential up to second - order 5 derivatives : an examination of approximation errors caused by 6 rock - equivalent - topography

19 In gravity forward modelling, the concept of Rock-Equivalent-Topography (RET) is often used 20 to simplify the computation of gravity implied by rock, water, ice and other topographic 21 masses. In the RET concept topographic masses are compressed (approximated) into 22 equivalent rock, allowing the use of a single constant mass-density value. Many studies 23 acknowledge the approximate character of the RET, but few have attempted yet to quantify 24 and analyse the approximation errors in detail for various gravity field functionals and heights 25 of computation points. Here we provide an in-depth examination of approximation errors 26 associated with the RET compression for the topographic gravitational potential and its first27 and second-order derivatives. Using the Earth2014 layered topography suite we apply 28 Newtonian integration in the spatial domain in the variants (a) rigorous forward modelling of 29 all mass bodies, (b) approximative modelling using RET. The differences among both variants, 30 which reflect the RET approximation error, are formed and studied for an ensemble of 10 31