On Ambiguities in Definitions and Applications of Bouguer Gravity Anomaly
Over decades diverse definitions and use of the Bouguer gravity anomaly found place in geodetic and geophysical applications. We discuss three distinct Bouguer anomalies. Their definitions vary due to the presence or absence of various effects (correction
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On Ambiguities in Definitions and Applications of Bouguer Gravity Anomaly P. Vajda, P. Vaníˇcek, P. Novák, R. Tenzer, A. Ellmann, and B. Meurers
Abstract Over decades diverse definitions and use of the Bouguer gravity anomaly found place in geodetic and geophysical applications. We discuss three distinct Bouguer anomalies. Their definitions vary due to the presence or absence of various effects (corrections), such as the geophysical indirect effect and the secondary indirect effects. Here we discuss the significance and magnitude of these effects. We point out the different understanding of the Bouguer anomaly in geophysics compared to geodesy. We also address the diverse demands on the gravity data in geophysical and geodetic applications, such as the issue of the topographic density and the lower boundary in the volume integral for the topographic correction, as well as the need for the bathymetric correction. Recommendations are made to bring the definitions and terminology into accord with the potential theory.
3.1 Anomalous Gravity – Gravity Anomaly and Disturbance Having the pairs actual potential and actual gravity (g), normal potential and normal gravity (γ ), we would anticipate to encounter the pair disturbing potential (T) and disturbing (anomalous) gravity. In fact, two such anomalous quantities have been used, the gravity anomaly (g) and the gravity disturbance (δg). Both the disturbance, see Eq. (1), and the anomaly, see Eq. (2), can be defined either using actual gravity,
P. Vajda () Geophysical Institute, Slovak Academy of Sciences, Bratislava, 845 28, Slovak Republic e-mail: [email protected]
cf. the left-hand sides of Eqs. (1) and (2), respectively – we refer to such a definition as “point-wise definition” – or using the disturbing potential, cf. the right-hand sides of Eqs. (1) and (2), respectively def
δg(h,) =
def
∂ g(h,) − γ (h,) ∼ = − T(h,), ∂h
(1)
g(h,) =
(2) 2 ∂ ∼ − T(h,). g(h,) − γ (h − Z,) = − ∂h R
The definition of the gravity anomaly using the right-hand side of Eq. (2) is known as the fundamental gravimetric equation (in spherical approximation, R being the mean earth radius). We refer the positions of points in geodetic (Gauss-ellipsoidal) coordinates that are respective to a geocentric properly oriented equipotential reference ellipsoid (RE), such as GRS’80, where h is height above the RE, and denotes the pair of latitude and longitude. The same RE plays the role of the normal ellipsoid generating normal gravity. Above, Z is the vertical displacement, i.e., the separation between the actual and the equivalent normal equipotential surfaces at (h, ), given by the generalized Bruns equation (e.g., Heiskanen and Moritz, 1967) Z(h,) = T(h,)/γ (h,).
(3)
The two sets of definitions in Eqs. (1) and (2), the left-hand vs. right-hand sides, are not rigorously compatible. They differ by the effect of the deflection of the vertical at the order of 10 μgal (e.g., Vaníˇcek et al., 1999, 2004), which is typically negligible in both
S.P. Mertikas (ed.), Gravity,
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