Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients

Abstract

A spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients are applied to a spectral representation of Newton's integral. In this study we utilise Molodensky's truncation coefficients in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms of Molodensky's truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data.

Application of Möbius coordinate transformation in evaluating Newton's integral

“…To derive the expressions for the gravitational field quantities generated by the far-zone topography of a constant mean density ρ 0 , we define the farzone spherical height functionsH n in the following form (cf. Tenzer et al, 2011) H n (Ω , ψ 0 ) = 2n + 1 4π…”

“…Studying the gravitational contribution of the far-zone topography, Novák et al (2001) utilised various truncation coefficients to a spectral representation of Newton's integral. The alternative expressions for computing the far-zone contributions to gravity field quantities by means of Molodensky's truncation coefficients can be found in Tenzer et al (2011).…”

The Accuracy Assessment of Lithospheric Density Models

“…In physical geodesy applications, these methods are used to compute topographic and terrain gravity corrections in gravimetric geoid modeling [1][2][3][4][5][6][7][8][9][10][11] and compile isostatic gravity maps [12]. In gravimetric geophysics, these methods are used to compile Bouguer and mantle gravity maps [13][14][15][16][17][18]. Furthermore, numerous techniques have been developed and applied for a gravimetric interpretation of the Earth's inner structure [19][20][21].…”

“…For global (or large-scale regional) applications, synthetic density models should mimic more realistically the Earth's actual shape and inner density structure. Such synthetic density models have already been used to validate numerical techniques involved in gravimetric geoid modeling [43][44][45], studies of the sediment bedrock morphology [46], the lithospheric and mantle density structure [16,47], the crustal thickness [16,18,[47][48][49][50][51][52], the dynamic and residual topography [53][54][55], or the oceanic lithosphere [56]. To construct a global synthetic density model that closely resembles the Earth's shape and inner structure, available global topographic and density structure models could be used for this purpose, together with additional models that provide information about the Earth's inner structure (such as crust and lithospheric thickness models).…”