Gravitational effect of distant Earth relief within the territory of former Czechoslovakia

Abstract

We analyzed the gravitational effect of topography and bathymetry beyond the angular distance of approximately 1.5 degrees (referred to as the distant relief effect or DRE), and its impact on measured gravity values in the region of the former Czechoslovakia. Our work was strongly motivated by the contents of the pioneering contribution of outstanding Czech geophysicists Miloš Pick, Jan Pícha and Vincenc Vyskočil, which appeared at the turn of the 1950’s and 1960’s. Our numerical calculations were based upon the direct evaluation of the gravitational effects of compartments of a spherical layer, while the respective heights and depths were obtained from the 2 × 2 minutes digital elevation model (DEM) ETOPO2, taking into consideration also the influence of distant bathymetry. Our results are in close agreement with, but not identical to, those of the above cited authors. We also analyzed the influence of the grid cell size of the involved DEM upon the calculation results. We introduced an approximation of the analyzed effect, based on a simple linear relationship between the calculation point height, the DRE and its vertical gradient (VGDRE). Since when calculated at zero elevation the involved quantities DRE and VGDRE are smooth functions of latitude and longitude and can be easily interpolated, the approximation gives acceptable results in terms of desired accuracy of several μGal (1 μGal = 10⁻⁸ m/s²). In general, we can state that within the territories of the Czech and Slovak Republics the studied distant relief effect has negligible impact upon local gravity survey data. However, when applied to regional gravity studies, there could be a question of its possible influence in the form of a quasilinear W-E trend ranging approximately from −106.6 to −102.5 mGal within the territory of former Czechoslovakia. If we wanted to correct for this phenomenon, we should subtract this negative quantity from the standard Bouguer anomalies as they have been defined in the recent geophysical literature, thereby considerably increasing their values. But, instead of straightforward correcting the Bouguer anomalies for DRE only, we would rather recommend to wait until after the crustal and even lithospheric effects have been studied more carefully based upon the present day independent knowledge about the deep seated sources of those effects.