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 theboundary element method (BEM). The direct BEM formulation for the Laplace equationis applied to obtain a numerical solution to the linearized fixed gravimetric boundaryvalueproblem in points at the Earth’s surface. The numerical scheme uses the collocationmethod with linear basis functions. It involves a discretisation of the Earth’s surfacewhich is considered as a fixed boundary. The surface gravity disturbances represent theoblique derivative boundary condition. The geocentric positions of the collocation pointsare 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 NewZealand, the EGM2008 quasigeoid heights, and the mean sea surface topography fromthe DNSC08 marine database. The gravity disturbances are computed using two heterogeneousgravity data sets: the altimetry-derived gravity anomalies from the DNSC08gravity database (offshore) and the observed ground gravity anomalies from the GNSScience gravity database (onshore). The transformation of gravity anomalies to gravitydisturbances is realized using the quasigeoid heights calculated from the EGM2008 globalgeopotential model. The new experimental quasigeoid model NZQM2010 is compiled atthe study area of New Zealand bounded by the parallels of 34 and 47.5 arc-deg southernlatitude and the meridians of 166 and 179 arc-deg eastern longitude. The least-squaresanalysis is applied to combine the gravimetric solution with GPS-levelling data using a7-parameter model. NZQM2010 is validated using GPS-levelling data and compared withthe existing regional and global quasigeoid models NZGeoid2009 and EGM2008.&nbsp