© 2015 Lars Sjöberg, licensee De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. J. Geod. Sci. 2015; 5:115ś118 Research Article Open Access Lars Sjöberg* Rigorous geoid-from-quasigeoid correction using gravity disturbances DOI 10.1515/jogs-2015-0012 Received November 18, 2014; accepted May 4, 2015 Abstract: We present rigorous solutions for the geoid-from- quasigeoid correction (GQC) using Taylor expansions of surface gravity disturbances along the vertical from the Earth’s surface to the geoid. One solution takes advantage of the topographic potential bias at the geoid, which can be expressed by a simple formula. This implies that the ac- curate GQC does not need a terrain correction. Keywords: geoid-from-quasigeoid correction; gravity dis- turbance; topographic compensation 1 Motivation The classical approximate expression for the geoid-from- quasigeoid height correction (GQC) is the product of the Bouguer gravity anomaly and the orthometric height di- vided by mean normal gravity (cf. Heiskanen and Moritz 1967, Sect. 8-13). Helmert (1890) knew that this formula was not precise enough in mountainous areas, and it was fur- ther studied by Niethammer (1932). Sjöberg (1995) added a term related with the vertical gradient of the gravity anomaly, and Flury and Rummel (2009) augmented the classical formula by adding a term that includes the topo- graphic potential diference at the geoid and the surface point. While the classical formula estimates the peak GQC in the Himalayas to be of the order of −2 m, Sjöberg and Bagherbandi (2012) estimated it to −5.5 m from a more ac- curate expression with direct geoid and height anomaly diferences estimated by an Earth Gravitational Model complete to degree and order 2160. Although most formu- las are approximate, Tenzer et al. (2006), Sjöberg (2010) and (2012) published some strict approaches to solve the problem. Tenzer et al. (ibid) used the mean gravity distur- bance between the geoid and Earth’s surface, including the topographic attraction determined by the Newton in- *Corresponding Author: Lars Sjöberg: Royal Institute of Technol- ogy (KTH) Stockholm, Sweden, E-mail: lsjo@kth.se tegral of all topographic masses, which is not well known. The goal of the present work is also to derive explicit for- mulas for the GQC using gravity disturbances, but avoid- ing the inaccurate and cumbersome Newton integral. 2 Recent formulas The classical formula for determining the GQC is (cf. Heiskanen and Moritz 1967, Sect. 8-13) GQC = N − ζ ≈ ∆g B ¯ γ H P , (1) where N is the geoid height, ζ is the height anomaly, ∆g B is the simple Bouguer gravity anomaly, ¯ γ is the mean nor- mal gravity between the reference ellipsoid and normal height, and H P is the orthometric height at the computa- tion point P. Flury and Rummel (2009) showed that this formula needs an improvement in mountainous regions to (cf. Flury and Rummel 2009, Eq. 24) GQC ≈ ∆ ⌢ g B ¯ γ H P + V T g − V T P ¯ γ , (2) where ∆ ⌢ g B is the refned Bouguer anomaly, V T is the topo- graphic potential , and subscripts g and P denote locations at the geoid and Earth’s surface, respectively. Sjöberg (2010) and (2012) developed the formula fur- ther to rigorous expressions for surface gravity anoma- lies, the latter using gravity anomaly ∆g c P , which replaces the Bouguer correction with an arbitrary compensation scheme (cg. Sjöberg 2012, Eq. 7a), yielding GQC = ∆g c P ¯ γ H P + dV T g γ 0 − dV T P γ Q + res , (3a) where dV = V T −V c , V c being the compensation potential, and res = H P ∫ 0 ∆g c γ dh − ∆g c P ¯ γ H P (3b) is a residual height, which is assumed to be negligible in most situations and is therefore not explicitly expressed in a practical form.