Estimation of distant relief effect in gravimetry

Abstract

We analyze gravitational effects of distant topographic and bathymetric relief beyond the (earth-centered) angular distance of [Formula: see text] (i.e., beyond the outer limit of the Hayford-Bowie zone O, or approximately [Formula: see text]) using a spherical earth model. Our results support current procedures that neglect distant relief effects for most local gravity surveys but show their potential importance for continental- and global-scale surveys. The distant relief can produce horizontal gradients as large as [Formula: see text] [Formula: see text]. In mountainous areas, the gravitational effect of the distant relief is significant, even for local surveys, although the vertical gradient of the distant relief effect never exceeds [Formula: see text] [Formula: see text] on the earth’s surface.

High resolution Slovak Bouguer gravity anomaly map and its enhanced derivative transformations: new possibilities for interpretation of anomalous gravity fields

“…where: g(P ) is the gravitational acceleration at the point of the database, converted to the 1995 gravity system; γ(P 0 ) is the normal gravity field (the so-called formula "Pizetti-Somigliana" for the parameters of the reference system GRS80, Moritz, 1984); δg F (P ) is the "free-air" correction in the approximation of second degree (Wenzel, 1985); δg sph (P ) is the gravitational effect of the truncated spherical layer (Mikuška et al, 2006) with a half apex angle 1 • 29 58 (corresponding to the distance approximately 166.7 km); TC (P ) are terrain corrections for zones of T 1 (0 -250 m), T 2 (250 m -5.24 km), T 31 (5.24 km -28.8 km) and T 32 (28.8 km -166.7 km) and were calculated by program Toposk (Marušiak et al, 2013;Zahorec et al, 2017a). The effects of topographic and bathymetric masses beyond the 166.7 km range were determined by approach of Mikuška et al (2006), but have not been finally included in the resultant presented field due to their small value range; δg atm (P ) is atmospheric correction for atmospheric masses bounded from below by topography (Mikuška et al, 2008).…”

“…The effects of topographic and bathymetric masses beyond the 166.7 km range were determined by approach of Mikuška et al (2006), but have not been finally included in the resultant presented field due to their small value range; δg atm (P ) is atmospheric correction for atmospheric masses bounded from below by topography (Mikuška et al, 2008).…”

Global ellipsoid-referenced topographic, bathymetric and stripping corrections to gravity disturbance

“…In regional and local studies it might be sufficient to evaluate it to some maximum preselected spherical distance only, such as the Hayford-Bowie limit of 167 km, if the truncation error (distant zone contribution) can be safely neglected (cf. Mikuška et al, 2006) as trend of no interest. The same holds true about numerical aspects of evaluating the volume integral of Eq.…”

“…(9) and the bathymetric correction (−δA EW ) is given by Eq.(10). In geophysics, the bathymetric correction is standardly computed using a constant density contrast of water δρ 0 = −1.64 g/cm 3 , since the bathymetric correction is considered as part of the "terrain" ("relief") correction, considering the sea bottom as relief offshore, taking the density contrast of water relative to a shell of average crustal density (Hinze et al, 2005;Mikuška et al, 2006 and references therein regarding the bathymetric correction). This practice is rigorously correct only under an assumption that the shallowest layer (to the depth of the deepest sea, i.e., to some 11 km) of the model normal density distribution ( ) …”

Gravity disturbances in regions of negative heights: A reference quasi-ellipsoid approach

“…Geod., 52 (2008) Our RQE based corrections below adopt an RQE defined by h * = 500 m. Next we shall consider the RQE based topo-correction given by Eq.(6). Its four individual terms are computed by numerical integration over the whole globe without truncating the integration domain to a spherical cap, which has not become in geophysical applications a standard practice yet (see also Mikuška et al, 2006). We do not split the volume integrals into a shell term and a terrain term.…”