Gravity inversion by improved iteration with variable density and its application in Xujiaweizi area

  • Chong Zhang
  • Dailei Zhang
  • Guochao Wu
  • Zhihui Wang
  • Jiayong YanEmail author
Original Paper


Various methods to calculate the underground interface caused by the density contrast across different media were proposed. The density contrasts of these methods are from the earlier simple constant to the later realistic variable, and the variable density contrast of exponential is mostly used. But these previous approaches still involve a divergent term in the iteration process. In this article, we put forward an improved iteration inversion, which can avoid the divergent term and give an inversion with exponential variable density to fit in with the actual demand. Compared with the original method, this new inversion method obtains a more convergent and reasonable result. The new inversion method is demonstrated on synthetic data, which obtains a more accurate result. And we also apply it to real data of Xujiaweizi area in China to verify the performance of this method.


Gravity inversion Variable density Improved iteration Xujiaweizi area 



The authors would like to thank Professor Xiaojuan Du for providing the real data over Xujiaweizi area and also thank the editors and reviewers for their constructive suggestions and comments on the manuscript to improve it.

Funding information

This work is supported by ‘China Geological Survey Project (DD20179611, DD20160082)’ and ‘Special Funds for Basic Scientific Research & Services of Chinese Academy of Geological Sciences (Pre-research on Comprehensive Method of Deep Exploration: JYYWF20180101)’.


  1. Agarwal BNP (1971) Direct gravity interpretation of sedimentary basin using digital computer-part I. Pure Appl Geophys 86(1):5–12CrossRefGoogle Scholar
  2. Barbosa VC, Silva JB, Medeiros WE (1999a) Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth. Geophysics 64(5):1429–1437CrossRefGoogle Scholar
  3. Barbosa VC, Silva JB, Medeiros WE (1999b) Stable inversion of gravity anomalies of sedimentary basins with nonsmooth basement reliefs and arbitrary density contrast variations. Geophysics 64(3):754–764CrossRefGoogle Scholar
  4. Bott MHP (1960) The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins. Geophys J Int 3(1):63–67CrossRefGoogle Scholar
  5. Chai Y, Hinze WJ (1988) Gravity inversion of an interface above which the density contrast varies exponentially with depth. Geophysics 53(6):837–845CrossRefGoogle Scholar
  6. Cheng R, Wang P, Liu W, Shan X, Chen S (2003) Volcanic massif and sedimentary facies belts controlled by Xujiaweizi fault terrace belts in Songliao basin. Oil Gas Geol 24(2):126–129Google Scholar
  7. Cordell L (1973) Gravity analysis using an exponential density-depth function—San Jacinto Graben, California. Geophysics 38(4):684–690CrossRefGoogle Scholar
  8. Cordell L, Henderson RG (1968) Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics 33(4):596–601CrossRefGoogle Scholar
  9. Feng J, Zhang S, Meng X (2016) Constraint 3d density interface inversion from gravity anomalies. Arab J Geosci 9(1):56CrossRefGoogle Scholar
  10. Garcia-Abdeslem J (1992) Gravitational attraction of a rectangular prism with depth-dependent density. Geophysics 57(3):470–473CrossRefGoogle Scholar
  11. García-Abdeslem J (1996) GL2D: a Fortran program to compute the gravity anomaly of a 2-d prism where density varies as a function of depth. Comput Geosci 22(7):823–826CrossRefGoogle Scholar
  12. Gendzwill DJ (1970) The gradational density contrast as a gravity interpretation model. Geophysics 35(2):270–278CrossRefGoogle Scholar
  13. Gómez-Ortiz D, Agarwal BN (2005) 3DINVER. M: a MATLAB program to invert the gravity anomaly over a 3D horizontal density interface by Parker-Oldenburg’s algorithm. Comput Geosci 31(4):513–520CrossRefGoogle Scholar
  14. Granser H (1987) Three-dimensional interpretation of gravity data from sedimentary basins using an exponential density-depth function. Geophys Prospect 35(9):1030–1041CrossRefGoogle Scholar
  15. Guspí F (1990) General 2D gravity inversion with density contrast varying with depth. Geoexploration 26(4):253–265CrossRefGoogle Scholar
  16. Guspi F (1992) Three-dimensional Fourier gravity inversion with arbitrary density contrast. Geophysics 57(1):131–135CrossRefGoogle Scholar
  17. Hubbert MK (1948) A line-integral method of computing the gravimetric effects of two-dimensional masses. Geophysics 13:215–225CrossRefGoogle Scholar
  18. Jiang W, Zhou L, Xiao D, Gao J, Yuan S, Tu G, Zhu D (2006) The characteristics of crust structure and the gravity and magnetic fields in northeast region of China. Prog Geophys (in Chinese) 21(3):730–738Google Scholar
  19. Lefort JP, Agarwal BNP (2000) Gravity and geomorphological evidence for a large crustal bulge cutting across Brittany (France): a tectonic response to the closure of the bay of Biscay. Tectonophysics 323(3–4):149–162CrossRefGoogle Scholar
  20. Li Y, Gao R, Yao Y, Mi S, Li W, Xiong X, Gao J (2014) The crust velocity structure of a Da Hinggan Ling orogenic belt and the basins on both sides. Prog Geophys (in Chinese) 29(1):73–83Google Scholar
  21. Martin-Atienza B, Garcia-Abdeslem J (1999) 2-D gravity modeling with analytically defined geometry and quadratic polynomial density functions. Geophysics 64(6):1730–1734CrossRefGoogle Scholar
  22. Meng L (2001) Application of universal Kriging to the density modeling in north western Xujiaweizi area of Daqing oil field. Geophysical Prospecting for Petrole 40(1):88–96Google Scholar
  23. Murthy IR, Rao DB (1979) Gravity anomalies of two-dimensional bodies of irregular cross-section with density contrast varying with depth. Geophysics 44(9):1525–1530CrossRefGoogle Scholar
  24. Negi JG, Garde SC (1969) Symmetric matrix method for rapid gravity interpretation. J Geophys Res 74(15):3804–3807CrossRefGoogle Scholar
  25. Oldenburg DW (1974) The inversion and interpretation of gravity anomalies. Geophysics 39(4):526–536CrossRefGoogle Scholar
  26. Parker RL (1973) The rapid calculation of potential anomalies. Geophys J Int 31(4):447–455CrossRefGoogle Scholar
  27. Pilkington M, Crossley DJ (1986) Determination of crustal interface topography from potential fields. Geophysics 51(6):1277–1284CrossRefGoogle Scholar
  28. Rao DB (1986) Modelling of sedimentary basins from gravity anomalies with variable density contrast. Geophys J Int 84(1):207–212CrossRefGoogle Scholar
  29. Rao DB (1990) Analysis of gravity anomalies of sedimentary basins by an asymmetrical trapezoidal model with quadratic density function. Geophysics 55(2):226–231CrossRefGoogle Scholar
  30. Rao DB, Prakash MJ, Babu NR (1990) 3D and 2D modelling of gravity anomalies with variable density contrast. Geophys Prospect 38(4):411–422CrossRefGoogle Scholar
  31. Rao CV, Chakravarthi V, Raju ML (1993) Parabolic density function in sedimentary basin modelling. Pure Appl Geophys 140(3):493–501CrossRefGoogle Scholar
  32. Rao CV, Pramanik AG, Kumar GVRK, Raju ML (1994) Gravity interpretation of sedimentary basins with hyperbolic density contrast. Geophys Prospect 42(7):825–839CrossRefGoogle Scholar
  33. Silva Dias FJ, Barbosa VC, Silva JB (2007) 2D gravity inversion of a complex interface in the presence of interfering sources. Geophysics 72(2):I13–I22CrossRefGoogle Scholar
  34. Talwani M, Worzel JL, Landisman M (1959) Rapid gravity computations for two-dimensional bodies with application to the Mendocino submarine fracture zone. J Geophys Res 64(1):49–59CrossRefGoogle Scholar
  35. Xiong X, Gao R, Zhang X, Li Q, Hou H (2011) The Moho depth of North China and Northeast China revealed by seismic detection. Acta Geosci Sin 32(1):46–56Google Scholar
  36. Xu SZ (2006) The integral-iteration method for continuation of potential fields. Chin J Geophys 49(4):1054–1060CrossRefGoogle Scholar
  37. Yang B, Tang J, Li Q, Wang J, Faisal SA, Li R et al (2004) Crustal reflection structure in the uplifting zone of Songliao Basin and disconnecting Moho interface. Sci China Ser D Earth Sci 47(6):514–521CrossRefGoogle Scholar
  38. Zhang E, Jiang C, Zhang Y, Li Z, Feng X, Wu J (2010) Study on the formation and evolution of deep structure of Xujiaweizi fault depression. Acta Petrol Sin 26(1):149–157Google Scholar
  39. Zhang C, Huang D, Wu G et al (2015) Calculation of Moho depth by gravity anomalies in Qinghai–Tibet plateau based on an improved iteration of Parker-Oldenburg inversion. Pure Appl Geophys 172:1–12CrossRefGoogle Scholar
  40. Zhang C, Huang D, Zhang K, Pu Y, Yu P (2016) Magnetic interface forward and inversion method based on Padé approximation. Appl Geophys 13(4):712–720CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  1. 1.China Deep Exploration Center (SinoProbe Center)Chinese Academy of Geological SciencesBeijingChina
  2. 2.College of Geo-Exploration Science and TechnologyJilin UniversityChangchunChina
  3. 3.Key Laboratory of Submarine Geosciences, State Oceanic AdministrationSecond Institute of Oceanography, Ministry of Natural ResourcesHangzhouChina

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