Improvement of the Focusing Inversion of Gravity Data with Hybrid Conjugate Gradient Parameter Method

Document Type : Research - Paper

Authors

1 Ph.D Student, Dept. of Mining, Petroleum and Geophysics, Shahrood University of Technology, Shahrood, Iran

2 Associate Professor, Dept. of Mining, Petroleum and Geophysics, Shahrood University of Technology, Shahrood, Iran

Abstract

Potential field methods, such as the gravity technique, have become essential tools for exploration. Inversion of gravity data is the most important stage in the interpretation of the data. Inversion is a mathematical technique that constructs a geophysical subsurface model automatically from measured data by adding some prior knowledge. Inversion of gravity data is time-consuming and needs a long time because of numerous data and model parameters. Thus, a fast and effective inversion method is necessary to improve the speed of the inversion process. Many algorithms are available for focusing inversion of gravity data, such as the reweighted regularized conjugate gradient (RRCG) method. This method is iterative, and it takes a long time to converge to a solution. In this algorithm, there is a conjugate gradient parameter that is effective in inversion. In this paper, we used a hybrid conjugate gradient parameter method for focusing inversion of gravity data and compared the results with the conventional Fletcher-Reeves (FR) conjugate gradient parameter method. We applied this method for the data from a synthetic model and Shoaz iron ore deposit in Yazd, Iran. The inversion result indicated that the hybrid conjugate gradient parameter method converges to the solution faster than the FR method, while the results from both approaches have remarkable correlations with the true geological structures.

Keywords

References

  1. نوروزی، غ.؛ 1388؛ "ژئوفیزیک اکتشافی". چاپ اول، انتشارات دانشگاه تهران.
  2. Foks, N. L., Krahenbuhl, R., and Li, Y. (2014). “Adaptive sampling of potential field data: A direct approach to compressive inversion Adaptive sampling and compressive inversion”. Geophysics, 79(1): IM1-IM.
  3. رضایی، م.، مرادزاده، ع.، نجاتی، ع.، آقاجانی، ح.؛ 1393؛ "انتخاب خودکار پارامتر منظم سازی به روش اعتبار سنجی متقاطع تعمیم یافته در وارون‌سازی سه‌بعدی داده‌های گرانی". سی و سومین گردهمایی ملی علوم زمین، سازمان زمین‌شناسی ایران، 3 و 4 اسفند.
  4. Blakely, R. J. (1996). “Potential theory in gravity and applications”. Cambridge University Press, pp. 441.
  5. Aster, R. C., Borchers, B., and Thurber, C. H. (2013). “Parameter Estimation and Inverse Problems”. Second Edition, Academic Press. US, pp. 360.
  6. Tikhonov, A. N., and Arsenin, V., I. (1977). “Solutions of ill-posed problems”. Washington: New York: Winston; Distributed Solely by Halsted Press, pp. 258.‏‏
  7. Li, Y., and Oldenburg, D. W. (1998). “3-D inversion of gravity data”. Geophysics, 63(1): 109-119.
  8. Portniaguine, O., and Zhdanov, M. S. (1999). “Focusing geophysicalinversion images”. Geophysics, 64: 874-887.
  9. Portniaguine, O., and Zhdanov, M. S. (2002). “3-D magnetic inversion with data compression and image focusing”. Geophysics, 67(5): 1532-1541.
  10. Farquharson, C. G., Ash, M. R., and Miller, H. G. (2008). “Geologically constrained gravity inversion for the Voisey’s Bay ovoid deposit”. The Leading Edge, 27(1): 64-69.‏
  11. Zhdanov, M. S. (2002). “Geophysical inverse theory and regularization problems”. Amsterdam: Elsevier Science, pp. 609.
  12. Zhdanov, M. S. (2009). “New advances in regularized inversion of gravity and electromagnetic data”. Geophysical Prospecting, 57(4): 463-478.‏
  13. Čuma, M., Wilson, G. A., and Zhdanov, M. S. (2012). “Large-scale3D inversion of potential field data”. Geophysical Prospecting, 60: 1186-1199.
  14. Čuma, M., and Zhdanov, M. S. (2014). “Massively parallel regularized 3D inversion of potential fields on CPUs and GPUs”. Computers and Geosciences, 62: 80-87.‏
  15. Rezaie, M. (2019). “3D non-smooth inversion of gravity data by zero order minimum entropy stabilizing functional”. Physics of the Earth and Planetary Interiors, 294: 106275.‏
  16. Xiang, Y., Yu, P., Zhang, L., Feng, S., and Utada, H. (2017). “Regularized magnetotelluric inversion based on a minimum support gradient stabilizing functional”. Earth, Planets and Space, 69(1): 158.‏
  17. Hestenes, M. R., and Stiefel, E. (1952). “Methods of conjugate gradients for solving linear systems”. Research of the National Bureau of Standards, 49(6): 409-436.
  18. Zhdanov, M. S. (2015). “Inverse theory and applications in geophysics”. Elsevier Science, pp. 730.‏
  19. Rezaie, M., Moradzadeh, A., Kalate, A. N., Aghajani, H., Kahoo, A. R., and Moazam, S. (2017). “3D modelling of Trompsburg Complex (in South Africa) using 3D focusing inversion of gravity data”. Journal of African Earth Sciences, 130: 1-7.‏
  20. Sun, Y., Meng, Z., and Li, F. (2018). “Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method”. Pure and Applied Geophysics, 175(3): 1065-1084.
  21. Wei, Z., Yao, S., and Liu, L. (2006). “The convergence properties of some new conjugate gradient methods”. Applied Mathematics and computation, 183(2): 1341-1350.
  22. Mtagulwa, P., and Kaelo, P. (2019). “A convergent modified HS-DY hybrid conjugate gradient method for unconstrained optimization problems”. Journal of Information and Optimization Sciences, 40(1): 97-113.
  23. Polak, E., and Ribiere, G. (1969). “Note on the convergence of conjugate direction methods”. ESAIM: Mathematical Modeling and Numerical Analysis, 3(R1): 35-43. (In French).‏
  24. Fletcher, R., and Reeves, C. M. (1964). “Function minimization by conjugate gradients”. the Computer Journal, 7(2): 149-154.‏
  25. معظم، س.، آقاجانی، ح.، نجاتی، ع.؛ 1399؛ "بهبود محاسبه ماتریس هسته در مدل‌سازی وارون داده‌های گرانی به روش ترکیبی". مجله پژوهش‌های ژئوفیزیک کاربردی، آماده انتشار.
  26. Hajar, N., Shapiee, N., Abidin, Z. Z., Khadijah, W., Rivaie, M., and Mamat, M. (2017). “A new modified conjugate gradient coefficient for solving system of linear equations”. In Journal of Physics: Conference Series, 890(1): 012108. IOP Publishing.
  27. Salleh, Z., and Alhawarat, A. (2016). “An efficient modification of the Hestenes-Stiefel nonlinear conjugate gradient method with restart property”. Journal of Inequalities and Applications, 110(2016). DOI: https://doi.org/10.1186/s13660-016-1049-5.‏
  28. Abdullahi, I., and Ahmad, R. (2017). “Global convergence analysis of a new hybrid conjugate gradient method for unconstrained optimization problems”. Malaysian Journal of Fundamental and Applied Sciences, 2(13): 40-48.‏
  29. Abdullahi, I., and Ahmad, R. (2016). “Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems”. Indian Journal of Science and Technology, 9: 1-9.
  30. Abdullahi, I., and Ahmad, R. (2015). “Convergence analysis of a new conjugate gradient method for unconstrained optimization”. Applied Mathematical Sciences, 9: 6969-6984.
  31. Hu, Y. F., and Storey, C. (1991). “Global convergence result for conjugate gradient methods”. Journal of Optimization Theory and Applications (JOTA), 71(2): 399-405.
  32. Hager, W. W., and Zhang, H. (2006). “A survey of nonlinear conjugate gradient methods”. Pacific Journal of Optimization, 2(1): 35-58.
  33. Zhang, L., Koyama, T., Utada, H., Yu, P., and Wang, J. (2012). “A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint”. Geophysical Journal International, 189(1): 296-316.
  34. قلعه نویی، م. ح.؛ 1397؛ "وارون‌سازی داده‌های میدان پتانسیل: روشی برای مدل‌سازی شکل هندسی توده‌ها و ساختار زمین‌شناسی". رساله دکتری، دانشگاه یزد.

Files

History

  • Receive Date: 06 December 2020
  • Revise Date: 31 January 2021
  • Accept Date: 25 April 2021

Share

How to cite

Statistics