The quasigeoid modelling in New Zealand using the boundary element method

Abstract

We compile a quasigeoid model at the study area of New Zealand using the
boundary element method (BEM). The direct BEM formulation for the Laplace equation
is applied to obtain a numerical solution to the linearized fixed gravimetric boundaryvalue
problem in points at the Earth’s surface. The numerical scheme uses the collocation
method with linear basis functions. It involves a discretisation of the Earth’s surface
which is considered as a fixed boundary. The surface gravity disturbances represent the
oblique derivative boundary condition. The geocentric positions of the collocation points
are determined combining the digital elevation data and the a priori quasigeoid model
(onshore) and the mean sea surface topography (offshore). In our numerical realization,
we use the global elevation data from SRTM30PLUS V5.0, the detailed DTM of New
Zealand, the EGM2008 quasigeoid heights, and the mean sea surface topography from
the DNSC08 marine database. The gravity disturbances are computed using two heterogeneous
gravity data sets: the altimetry-derived gravity anomalies from the DNSC08
gravity database (offshore) and the observed ground gravity anomalies from the GNS
Science gravity database (onshore). The transformation of gravity anomalies to gravity
disturbances is realized using the quasigeoid heights calculated from the EGM2008 global
geopotential model. The new experimental quasigeoid model NZQM2010 is compiled at
the study area of New Zealand bounded by the parallels of 34 and 47.5 arc-deg southern
latitude and the meridians of 166 and 179 arc-deg eastern longitude. The least-squares
analysis is applied to combine the gravimetric solution with GPS-levelling data using a
7-parameter model. NZQM2010 is validated using GPS-levelling data and compared with
the existing regional and global quasigeoid models NZGeoid2009 and EGM2008.