phone +7 (3412) 91 60 92

Archive of Issues


Russia Izhevsk
Year
2020
Volume
30
Issue
4
Pages
696-710
<<
Section Computer science
Title A priori estimations of geometric parameters of an anomalous object in modeling the soil structure using RES3DINV software
Author(-s) Nemtsova O.M.a, Bannikova T.M.b, Nemtsov V.M.a
Affiliations Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciencesa, Udmurt State Universityb
Abstract We discuss the problem of proper use of software packages that implement methods for solving ill-posed problems. Most of the problems of processing experimental data belong to ill-posed problems. When using methods for solving ill-posed problems, there is a problem of non-uniqueness of the solution, which is solved by introducing a priori information. Obtaining a priori information is possible in different ways, but quantitative estimates involve the use of additional methods for data analysis. Obviously, additional methods should not be more complicated and labor intensive than the main data processing method. Using the RES3DINV electrical prospecting data analysis software as an example, the role of a priori information for obtaining reliable results is demonstrated. The RES3DINV software is used to build a soil model from the measured values of resistivity using electrical survey’s methods. When using the inversion method implemented in the software package, it is necessary to set the input parameters describing the geometric dimensions of the anomalous resistance object, which are usually unknown a priori. By model objects we demonstrate how the incorrect setting of input parameters affects the result of data interpretation. We show that the vector analysis method can be used as a way to obtain a priori information. This method allows us to obtain estimates of the geometric parameters of an anomalous object, does not involve high time and resource expenses, and can be used directly at the site of field experimental measurements.
Keywords ill-posed problems, data interpretation, a priori information, geometric parameters, vector analysis
UDC 519.677, 519.688
MSC 65J20, 86-10
DOI 10.35634/vm200411
Received 17 August 2020
Language Russian
Citation Nemtsova O.M., Bannikova T.M., Nemtsov V.M. A priori estimations of geometric parameters of an anomalous object in modeling the soil structure using RES3DINV software, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2020, vol. 30, issue 4, pp. 696-710.
References
  1. Ogorodnikov I.N. Vvedenie v obratnye zadachi fizicheskoi diagnostiki (Introduction to inverse problems of physical diagnostics), Yekaterinburg: Ural University Press, 2017. https://www.elibrary.ru/item.asp?id=29050248
  2. Kabanikhin S.I. Obratnye i nekorrektnye zadachi (Inverse and ill-posed problems), Novosibirsk: SB RAS Publishing House, 2018. http://doi.org/10.15372/INVERSE2018KSI
  3. Krogstad H.E. An introduction to inverse problems, TMA 4180 Optimeringsteori, IMF, 2007. https://folk.ntnu.no/hek/Optimering2010/InverseProblems_2010.pdf
  4. Sumin M.I. Metod regulyarizatsii A.N. Tikhonova dlya resheniya operatornykh uravnenii pervogo roda (The regularization method of A.N. Tikhonov for solving operator equations of the first kind), Nizhny Novgorod: Nizhny Novgorod State University, 2016. http://www.lib.unn.ru/students/src/Posobie-2016_1.pdf
  5. Sergeev V.V., Denisova A.U. An iterative method for reconstructing piecewise-constant images with known domain boundaries, Computer Optics, 2013, vol. 37, no. 2, pp. 239-243 (in Russian). http://www.computeroptics.smr.ru/KO/Annot/KO37-2/15.html
  6. Gavin H.P. The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems, Department of Civil and Environmental Engineering, Duke University, 2016.
  7. Vasin V.V., Ageev A.L. Ill-posed problems with a priori information, VSP, 1995. https://doi.org/10.1515/9783110900118
  8. Onak O.N., Dogrusoz Y.S., Weber G.W. Effects of a priori parameter selection in minimum relative entropy method on inverse electrocardiography problem, Inverse Problems in Science and Engineering, 2018, vol. 26, issue 6, pp. 877-897. https://doi.org/10.1080/17415977.2017.1369979
  9. Bhatt R.N. Positron emission tomography (PET) tumor segmentation and quantification: development of new algorithms, Electronic Theses and Dissertations: Florida International University, 2012. https://doi.org/10.25148/etd.FI12121004
  10. Prakash J., Sanny D., Kalva S.K., Pramanik M., Yalavarthy P.K. Fractional regularization to improve photoacoustic tomographic image reconstruction, IEEE Transactions on Medical Imaging, 2019, vol. 38, no. 8, pp. 1935-1947. https://doi.org/10.1109/TMI.2018.2889314
  11. Programmnyi kompleks «Rus'» «Okhrana okruzhayushchei sredy» (Software package “Rus” “Environmental protection”). http://aieco.ru/programms_main_oos.html (accessed 13 August 2020)
  12. Holmes J., Chambers J., Meldrum P., Wilkinson P., Boyd J., Williamson P., Huntley D., Sattler K., Elwood D., Sivakumar V., Reeves H., Donohue S. Four-dimensional electrical resistivity tomography for continuous, near-real-time monitoring of a landslide affecting transport infrastructure in British Columbia, Canada, Near Surface Geophysics, 2020, vol. 18, issue 4, pp. 337-351. https://doi.org/10.1002/nsg.12102
  13. Loke M.H. Rapid 3D resistivity and IP inversion using the least-squares method: geoelectrical imaging 2D and 3D, Geotomo Software, Malaysia, 2011. https://www.geotomosoft.com/gs_brochure3d.pdf
  14. Loke M.H., Barker R.D. Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method, Geophysical Prospecting, 1996, vol. 44, issue 1, pp. 131-152. https://doi.org/10.1111/j.1365-2478.1996.tb00142.x
  15. Li K., Yin X.-Y., Zong Z.-Y. Reliability enhancement of mixed-domain seismic inversion with bounding constraints, Inverse Problems in Science and Engineering, 2019, vol. 27, issue 2, pp. 255-277. https://doi.org/10.1080/17415977.2018.1456536
  16. Reichel L., Rodriguez G. Old and new parameter choice rules for discrete ill-posed problems, Numerical Algorithms, 2013, vol. 63, pp. 65-87. https://doi.org/10.1007/s11075-012-9612-8
  17. Hochstenbach M.E., Reichel L., Rodriguez G. Regularization parameter determination for discrete ill-posed problems, Journal of Computational and Applied Mathematics, 2015, vol. 273, pp. 132-149. https://doi.org/10.1016/j.cam.2014.06.004
  18. Bianchi D., Buccini A., Donatelli M., Serra-Capizzano S. Iterated fractional Tikhonov regularization, Inverse Problems, 2015, vol. 31, no. 5, 055005. https://doi.org/10.1088/0266-5611/31/5/055005
  19. Kaltenbacher B. Minimization based formulations of inverse problems and their regularization, SIAM Journal on Optimization, 2018, vol. 28, issue 1, pp. 620-645. https://doi.org/10.1137/17M1124036
  20. Lelièvre P.G., Farquharson C.G. Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes, Geophysical Journal International, 2013, vol. 195, issue 1, pp. 330-341. https://doi.org/10.1093/gji/ggt255
  21. Johansson B., Jones S., Dahlin T., Flyhammar P. Comparisons of 2D- and 3D-inverted resistivity data as well as of resistivity and IP-surveys on a landfill, Procs. Near Surface 2007 - 13th European Meeting of Environmental and Engineering Geophysics, Istanbul, Turkey, 3-5 September, 2007, p. P42. https://portal.research.lu.se/portal/files/5819684/4934437.pdf
  22. Gündoğdu N.Y., Candansayar M.E. Three-dimensional regularized inversion of DC resistivity data with different stabilizing functionals, Geophysics, 2018, vol. 83, issue 6, pp. E399-E407. https://doi.org/10.1190/geo2017-0558.1
  23. Loke M.H. Tutorial: 2-D and 3-D electrical imaging surveys, Geotomo Software, Malaysia, 2019. https://sites.ualberta.ca/~unsworth/UA-classes/223/loke_course_notes.pdf
  24. MacLennan K. Methods for addressing noise and error in controlled source electromagnetic data, Mines Theses and Dissertations, Digital Collections of Colorado, 2013. https://mountainscholar.org/bitstream/handle/11124/77966/MacLennan_mines_0052E_10119.pdf
  25. Arato A., Piro S., Sambuelli L. 3D inversion of ERT data on an archaeological site using GPR reflection and 3D inverted magnetic data as a priori information, Near Surface Geophysics, 2015, vol. 13, issue 6, pp. 545-556. https://doi.org/10.3997/1873-0604.2015046
  26. Nemtsova O., Zhurbin I., Zlobina A. Vector analysis of pole-pole array for determining the 3D boundary of object, Near Surface Geophysics, 2019, vol. 17, issue 5, pp. 563-575. https://doi.org/10.1002/nsg.12065
  27. Buccini A. Regularizing preconditioners by non-stationary iterated Tikhonov with general penalty term, Applied Numerical Mathematics, 2017, vol. 116, pp. 64-81. https://doi.org/10.1016/j.apnum.2016.07.009
  28. Zlobina A.G., Dogadin S.E., Zhurbin I.V., Nemtsov V.M. System for diagnostics of natural and anthropogenic environments by shallow electrical profiling, Khimicheskaya Fizika i Mezoskopiya, 2019, vol. 21, no. 3, pp. 455-464 (in Russian). https://doi.org/10.15350/17270529.2019.3.49
Full text
<< Previous article