<p>This study presents a theoretical and numerical investigation into the role of the vertical gravity gradient (VGG) in the analytical downward continuation of surface gravity data for geoid determination. Several VGG computation techniques, including integral-based, FFT-based, and integrated second vertical derivative (ISVD)-based methods, are evaluated using synthetic, noise-contaminated gravity disturbances at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1'\times 1'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>1</mn> <mo>′</mo> </msup> <mo>×</mo> <msup> <mn>1</mn> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2'\times 2'\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>2</mn> <mo>′</mo> </msup> <mo>×</mo> <msup> <mn>2</mn> <mo>′</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> resolutions. Among these, ISVD-based methods consistently demonstrate better numerical stability and accuracy. A new iterative downward continuation approach is proposed, which uses VGG values computed on the reference ellipsoid. Its performance is compared to the conventional Taylor series expansion and Poisson integral methods. While the Poisson integral achieves slightly better accuracy (2.1 mGal) when optimally regularized, the proposed iterative method attains comparable accuracy (2.4 mGal) using a simpler regularization strategy- fixed truncation after the second iteration. The proposed method also outperforms the Taylor approach under the same regularization conditions. The results further indicate that higher-resolution input data do not necessarily improve downward continuation accuracy; instead, they can amplify high-frequency noise beyond the signal bandwidth. These findings offer practical guidance for selecting VGG computation methods, regularization strategies, and spatial resolutions in geoid modeling applications.</p>

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Evaluation of vertical gravity gradient estimation methods for analytical downward continuation

  • Mehdi Goli

摘要

This study presents a theoretical and numerical investigation into the role of the vertical gravity gradient (VGG) in the analytical downward continuation of surface gravity data for geoid determination. Several VGG computation techniques, including integral-based, FFT-based, and integrated second vertical derivative (ISVD)-based methods, are evaluated using synthetic, noise-contaminated gravity disturbances at \(1'\times 1'\) 1 × 1 and \(2'\times 2'\) 2 × 2 resolutions. Among these, ISVD-based methods consistently demonstrate better numerical stability and accuracy. A new iterative downward continuation approach is proposed, which uses VGG values computed on the reference ellipsoid. Its performance is compared to the conventional Taylor series expansion and Poisson integral methods. While the Poisson integral achieves slightly better accuracy (2.1 mGal) when optimally regularized, the proposed iterative method attains comparable accuracy (2.4 mGal) using a simpler regularization strategy- fixed truncation after the second iteration. The proposed method also outperforms the Taylor approach under the same regularization conditions. The results further indicate that higher-resolution input data do not necessarily improve downward continuation accuracy; instead, they can amplify high-frequency noise beyond the signal bandwidth. These findings offer practical guidance for selecting VGG computation methods, regularization strategies, and spatial resolutions in geoid modeling applications.