Anomalous potential modelling in Brazilian Vertical Datum aiming at its new definition

Abstract

The Brazilian Vertical Datum (BVD) was established by the mean sea level (MSL)
from tide gauge observations. However, in this MSL local effects linked to the shift
between the MSL from a equipotential surface W0 best fitted to the global MSL
were not taken into account. The relationship between the BVD and W0 can be
determined by its gravity potential Wi. The potential difference ∆W = Wi – W0 is
related to the topography of the mean sea level (better known in English as sea
surface topography, SSTop) in the datum region by SSTop = ∆W/γ, where γ is the
normal gravity in the considered point. However, the computation of the potential
difference ∆W is strongly affected by the local components of the Disturbing
Potential T not predicted in global geopotential models. The determination of these
local components is part of the Geodetic Boundary Value Problem – GBVP. In the
classical approach, the solution of GBVP is based on the use of gravity anomalies in
the computations by Stokes’ integral formula, which depends on the local vertical
reference frame. The alternative presented here is based in the solution of the GBVP
by using gravity disturbances in the context of Molodenskii’s solution associated with the known Earth surface.