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<p>Compared to traditional gravity measurements, gravity gradiometry provides multi-component and high-precision gravitational field information. Therefore, in theory, gravity anomalies recovered from gravity gradients demonstrate higher accuracy, making them more suitable for geophysical geodesy studies such as geoid recovery. In our study, we propose a strategy for calculating gravity anomalies from gravity gradients based on Stokes' formula and variable-order numerical integration. Due to the discrete nature of measured data, we discretize the Stokes' formula computation, and variable-order numerical integration is employed to enhance computational accuracy and address singularity issues. During the inversion process, a regularization method is adopted to mitigate the ill-posed problem in large-scale matrix inversion, while GPU parallel computing is utilized to further accelerate the computation speed. We utilized the CUGB2023GRAD data and the SIO gravity gradient model as the original datasets, selecting the areas [1°W, 2°W][2°S, 3°S] and [0.5°E, 1.5°E][30°S, 31°S] in our experiments. For the CUGB2023GRAD data, calculations were performed using the principal components of gravity gradients tensors: <i>T</i><sub><i>xx</i></sub>, <i>T</i><sub><i>yy</i></sub> and <i>T</i><sub><i>zz</i></sub>. The computed results were compared with the gravity anomaly data from the SIO model. The root mean square (RMS) of the differences in the two experimental areas are 1.98 mGal and 4.17 mGal, respectively, outperforming the traditional algorithm without numerical integration, which yielded RMS values of 2.46 mGal and 5.38 mGal. Furthermore, the parallel computing achieved a speed-up ratio of up to 26.73, validating the accuracy and efficiency of the proposed algorithm.</p>

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Gravity anomaly recovery using the gravity gradient tensors based on variable-order numerical integration

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Jingyu Bu,
  • Zhourun Ye,
  • Xinghui Liang,
  • Lintao Liu,
  • Jinzhao Liu,
  • Shaofeng Bian,
  • Tianshuo Fu

摘要

Compared to traditional gravity measurements, gravity gradiometry provides multi-component and high-precision gravitational field information. Therefore, in theory, gravity anomalies recovered from gravity gradients demonstrate higher accuracy, making them more suitable for geophysical geodesy studies such as geoid recovery. In our study, we propose a strategy for calculating gravity anomalies from gravity gradients based on Stokes' formula and variable-order numerical integration. Due to the discrete nature of measured data, we discretize the Stokes' formula computation, and variable-order numerical integration is employed to enhance computational accuracy and address singularity issues. During the inversion process, a regularization method is adopted to mitigate the ill-posed problem in large-scale matrix inversion, while GPU parallel computing is utilized to further accelerate the computation speed. We utilized the CUGB2023GRAD data and the SIO gravity gradient model as the original datasets, selecting the areas [1°W, 2°W][2°S, 3°S] and [0.5°E, 1.5°E][30°S, 31°S] in our experiments. For the CUGB2023GRAD data, calculations were performed using the principal components of gravity gradients tensors: Txx, Tyy and Tzz. The computed results were compared with the gravity anomaly data from the SIO model. The root mean square (RMS) of the differences in the two experimental areas are 1.98 mGal and 4.17 mGal, respectively, outperforming the traditional algorithm without numerical integration, which yielded RMS values of 2.46 mGal and 5.38 mGal. Furthermore, the parallel computing achieved a speed-up ratio of up to 26.73, validating the accuracy and efficiency of the proposed algorithm.