Pure and Applied Geophysics

, Volume 176, Issue 1, pp 215–234 | Cite as

A Folding Calculation Method Based on the Preconditioned Conjugate Gradient Inversion Algorithm of Gravity Gradient Tensor

  • Yu Tian
  • Xiaoping KeEmail author
  • Yong Wang


To solve the non-uniqueness problem of gravity gradient inversion, we proposed a folding calculation method based on preconditioned conjugate gradient inversion. Compared with the original algorithm in which the entire study area is taken as the research subject and all grids are used simultaneously in the inversion, the proposed folding method divides the research area into several sub-areas. A prism unit from any of the four corner grids is selected for the first iteration, whose density anomaly result is taken as the initial density anomaly for the next iteration of the same sub-area. The folding in the left–right and up–down directions takes turns during the calculation until the inversion calculation has covered the entire research area. This folding algorithm demonstrates strong regularity. The inversion results of multiple synthetic models show that the folding calculation method performs multiple parameter corrections in the initial model. Meanwhile, on the basis that the relative fitting of standard errors of the observed values satisfies the convergence condition, the model errors are constrained, and thus, the model errors of the inversion results are consequently reduced. The 3-D density anomaly pattern over the Craton area in North China was obtained via a joint inversion of the four components (\(\varvec{T}_{\text{xx}} ,\)\(\varvec{T}_{\text{xz}} ,\)\(\varvec{T}_{\text{yy}} ,\) and \(\varvec{T}_{\text{zz}}\)) of the Gravity field and steady-state Ocean Circulation Explorer L2 gravity gradient after preprocessing. We compared the inversion results from the folding calculation method and the original method, and performed detailed analysis and discussion on the inversion results with existing geological and geophysical data. Our analysis shows that the improved calculation method is effectively applicable to the inversion of measured gravity gradient data, and the inversion results provide more detailed and reliable pattern information for the density anomaly.


Gravity gradient tensor preconditioned conjugate gradient inversion algorithm folding calculation method North China Craton 



The authors are grateful to Prof. Josef Sebera in European Space Agency for providing the initial gravity gradiometry data. The authors are also grateful to Prof. Michael S. Zhdanov in University of Utah for providing valuable and constructive comments and suggestions that improved this work. This work was supported by the National Natural Science Foundation of China under Grant No. 41574073 and No. 41621091; the Major State Research Development Program of China under Grant No. 2016YFC0601101; the R&D of Key Instruments and Technologies for Deep Resources Prospecting (the National R&D Projects for Key Scientific Instruments) under Grant No. ZDYZ2012-1-04.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and GeophysicsChinese Academy of SciencesWuhanChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.Consortium for Electromagnetic Modeling and Inversion (CEMI)University of UtahSalt Lake CityUSA

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