Generalisation and improvement of the compact gravity inversion method
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RESEARCH ARTICLE - APPLIED GEOPHYSICS
Generalisation and improvement of the compact gravity inversion method Wenwu Zhu1,2 · Junhuan Peng1 · Sanming Luo2 · Xiangang Meng2 · Jinzhao Liu2 · Chuandong Zhu2 Received: 5 May 2020 / Accepted: 26 September 2020 © Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2020
Abstract Compact gravity inversion (CGI) is widely used to invert gravity data following the principle of minimising the volume of the causative body due to its simplicity, high efficiency, and sharp-boundary inversion results. In this study, the compactness weighting function is generalised and the depth weighting function is introduced to CGI to obtain the reweighted CGI (RCGI) method. Although RCGI exhibits better flexibility than CGI, selecting an appropriate compactness factor α and depth weighting function β is difficult, and we design a parameter selection rule to search the proper 𝛼 and 𝛽 quantitively. Furthermore, we improve RCGI for boasting superior computational efficiency by gradually eliminating the model blocks that reach the designated boundaries in the iterative algorithm of inversion. This approach is termed the reweighted and element-elimination CGI (REECGI) method. The inversion results show that both RCGI and REECGI result in better inversion accuracy than CGI, and REECGI has higher computational efficiency than RCGI and CGI, which increases with the number of iterations. Keywords Compact gravity inversion · Inversion theory · Compactness factor · Weighting function · Inversion accuracy · Computational efficiency
Introduction Gravity inversion is a practical method that has been extensively applied in hydrology, oil and gas exploration, mineral exploration, and geological surveys (Blakely 1995; Chen et al. 2008; Karaoulis et al. 2014; Li and Oldenburg 1998; Mendonca and Silva 1994, 1995; Pilkington 1997, 2009; Portniaguine and Zhdanov 1999; Roland et al. 2013; Zhdanov 2015). Owing to the instability and non-uniqueness of inversion, which is known as the ill-posed problem (Hadamard 1902), it is difficult to obtain inversion information that accurately reflects the real geological conditions below the Earth’s surface. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11600-020-00495-0) contains supplementary material, which is available to authorised users. * Wenwu Zhu [email protected] 1
China University of Geosciences (Beijing), Beijing 100083, China
The First Crust Monitoring and Application Centre, China Earthquake Administration, Tianjin 300180, China
2
Researchers have made numerous attempts to overcome the ill-posed problem; one solution is to find the appropriate stability function combined with the error function. Constable et al. (1987) and Smith et al. (1991) introduced the minimum norm of the Laplace operator of the model, which can produce a smooth inversion solution; however, this method usually fails to accurately describe the true massive geological structure. Rudin et al. (1992) pr
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