Abstract
This study presents an optimized gravity-sparse inversion method. The proposed method minimizes the global objective function using interior-point method for boundary constraints and a general weighting function comprising the depth, compactness, and kernel weighting functions of the density models. For the compactness weighting function, practical experiments demonstrate that the recovered model becomes more compact with an increasing value for the relative exponential factor β. However, if no appropriate boundary-constraint method is applied, the inversion results cannot be controlled within the designated constraint bounds when β needs to be set to a large value to obtain compact inversion results. The interior-point method allows the use of a larger β to obtain more compact inversion results without violating the boundary constraints. Additionally, models in close proximity can more clearly be recognized using this method. To improve the computational efficiency and obtain a more accurate regularization parameter, the preconditioned conjugate gradient and L-curve, or line search methods, were also applied. The proposed method was applied for three synthetic examples: two positive bodies adjacent to each other at different depths inverted using noise-free gravity anomaly data, three bodies (positive or negative) at different depths inverted using noise-free or contaminated gravity anomaly data, and three bodies (positive or negative) characterized by a certain dip angle inverted using contaminated gravity anomaly data. This method was also applied for the inversion of a Woodlawn sulfide body, Missouri iron ore body, and granitoid rock body in the Rio Maria region in the state of Para, Brazil. In all six test cases, larger β values were used and the density models were recovered with sharper boundaries within the designated bounds.
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Acknowledgements
This study was funded by the National Key R&D Program of China (Grants Nos 2018YFC1503606 and 2017YFC1500501); the Science and Technology Basic Work (Grant No. 2015FY210400); the Earthquake Industry Research Project (Grant No. 201508009) funded by the Ministry of Science and Technology of the People’s Republic of China; the National Natural Science Foundation of China (Grant No. 41804010); and the Natural Science Foundation of Tianjin (Grant No. 17JCYBJC21600). We would like to thank Prof. Z.L. Li of Hebei University of Engineering and Prof. S. Chen of the Institute of Geophysics, China Earthquake Administration, for providing detailed guidance. We sincerely appreciate the rigorous and careful work of the editor Christian Voigt and two reviewers, who have helped to improve the paper significantly and encourage and guide our future research.
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Zhu, W., Peng, J., Luo, S. et al. Gravity sparse inversion using the interior-point method and a general model weighting function. Stud Geophys Geod 64, 419–435 (2020). https://doi.org/10.1007/s11200-020-0831-5
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DOI: https://doi.org/10.1007/s11200-020-0831-5