Fixed Gravimetric BVP for the Vertical Datum Problem

Abstract

AbstractThis paper discusses advantages of the fixed gravimetric boundary value problem (FGBVP) for precise gravity field modeling that is necessary for a unification of local vertical datums (LVDs). Our objective is to show how inconsistencies of input gravity data due to shifts and tilts of LVDs can influence precise solutions. Such systematic errors can backward affect estimations of the shifts and tilts of LVDs. This drawback completely vanishes in case of FGBVP. Terrestrial gravimetric measurements accompanied by the precise 3D positioning by GNSS yield globally consistent surface gravity disturbances that are fully independent from any LVD (assuming the same gravity datums). Since terrestrial gravity data from the past are related to LVDs, we try to reconstruct their ellipsoidal heights using available geoid/quasi-geoid models as well as shifts and tilts of LVDs modeled from GPS/Leveling data. In this way we simulate consistent surface gravity disturbances that represent oblique derivative boundary condition for FGBVP. In the numerical experiments we deal with (i) the global gravity field modeling using the boundary element method (BEM), and with (ii) the continental modeling using the finite volume method (FVM). In both cases we compare the numerical solutions obtained with and without taking into account corrections from the shifts and tilts of LVDs in the input data. It shows how an absolute precision of vertical positions of terrestrial gravity data influence precise numerical solutions.KeywordsBoundary Element MethodGravity DataGeopotential ModelEllipsoidal HeightGlobal Geopotential ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.