New views of the spherical Bouguer gravity anomaly

Abstract

S U M M A R YThis paper presents a number of new concepts concerning the gravity anomaly. First, it identifies a distinct difference between a surface (2-D) gravity anomaly (the difference between actual gravity on one surface and normal gravity on another surface) and a solid (3-D) gravity anomaly defined in the fundamental gravimetric equation. Second, it introduces the 'no topography' gravity anomaly (which turns out to be the complete spherical Bouguer anomaly) as a means to generate a quantity that is smooth, thus suitable for gridding, and harmonic, thus suitable for downward continuation. It is understood that the possibility of downward continuing a smooth gravity anomaly would simplify the task of computing an accurate geoid. It is also shown that the planar Bouguer anomaly is not harmonic, and thus cannot be downward continued.

From Discrete Gravity Survey Data to a High-resolution Gravity Field Representation in the Nordic-Baltic Region

“…Note that the alternative spherical Bouguer anomalies (see e.g. Vaníček, Novák, and Martinec 2001;Vaníček et al 2004;Novák et al 2001;Kuhn, Featherstone, and Kirby 2009) are not considered in this contribution.…”

Computation of precise geoid model of Auvergne using current UNB Stokes-Helmert’s approach

“…In the first step, the observed free-air gravity anomalies are converted to Helmert gravity anomalies, one of the couple of anomalies known to be "solid" and thus capable of being continued downwards to the geoid (Vaníček et al, 2004). This conversion consists of adding the direct topographical and atmospheric effects (DTE) and (DAE), the secondary indirect topographical and atmospheric effects (SITE) and (SIAE) and, if the topographical density model is available, also the direct topographical density effect (DDE).…”

“…They have opted for using the physically rigorous approach formulated by Poisson (MacMillan, 1930) and the results of their studies of Poisson's method for the downward continuation of harmonic functions are documented in several publications, e.g., Sun and Vaníček, 1998;Kingdon and Vaníček, 2010). As a by-product of their investigation they discovered that in order to downward continue a gravity anomaly, the anomaly must be of a "solid" type (Vaníček et al, 2004), which rules out the use of free-air as well as planar Bouguer gravity anomalies.…”

Comparison of Helmert and rigorous orthometric heights over Japan

“…Vaníček et al 1999Vaníček et al , 2004 Figure 2 Distribution of gravity data over the four Japanese main islands.…”

“…Vaníček et al 2004). The gravitational attraction generated by the topography can be decomposed into the gravitational acceleration generated by Bouguer shell (g B T ), terrain roughness residual to the Bouguer shell (g R T ) and the lateral variations in massdensity within the topography (g δρ ).…”