1887
Volume 42, Issue 2
  • ISSN: 0263-5046
  • E-ISSN: 1365-2397

Abstract

Abstract

This study introduces a DC 2D inversion algorithm that employs conjugate gradients relaxation to solve the maximum likelihood inverse equations. The adoption of the maximum likelihood algorithm was motivated by its advantage of not requiring the calculation of electrical field derivatives. While the inversion algorithm based on the maximum likelihood inverse theory has been extensively described for 3D DC inversion using finite differences modelling, its application in the 2D finite element method has received limited attention. A significant difference between 3D finite difference modelling and 2D finite element methods lies in the integration variable lambda. In our 2D case, the electrical potential is initially calculated in the Laplace and Fourier domains, which include the stiffness matrix. However, to obtain the stiffness matrix in the Cartesian domain, we had to develop a suitable transformation method since no existing resources in the literature addressed this specific condition. In this study, we successfully transformed the stiffness matrix using a similar approach to the potential calculation. The results obtained from synthetic and real models demonstrate the method’s potential for various applications, as exemplified by the hydrogeological study presented in this work.

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2024-02-01
2025-06-13
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References

  1. Almeida, E.R., Porsani, J.L., Monteiro dos Santos, F. A., Bortolozo, C. A. [2017]. 2D TEM Modeling for a Hydrogeological Study in the Paraná Sedimentary Basin, Brazil.International Journal of Geosciences (ON LINE), v. 08, p. 693–710.
    [Google Scholar]
  2. Ashby, B., Bortolozo, C., Lukyanov, A. and Pryer, T. [2021]. Adaptive modelling of variably saturated seepage problems.The Quarterly Journal of Mechanics and Applied Mathematics, 74(1), pp.55–81.
    [Google Scholar]
  3. Bokhonok, O., Diogo, L.A., Bortolozo, C.A., Mendonça, C.A. and Slob, E. [2015]. Residual function dispersion maps to evaluate multidimensional objective function topography: Near surface geophysical inverse problems. Resultados Preliminaries: 14th International Congress of the Brazilian Geophysical Society & EXPOGEF.
    [Google Scholar]
  4. Bortolozo, C.A., Porsani, J.L., Pryer, T., Benjumea, J.L.A., dos Santos, F.A.M., Couto Jr, M.A., Pampuch, L.A., Mendes, T.S.G., Metodiev, D., de Moraes, M.A.E., Mendes, R.M. and de Andrade, M.R.M. [2023]. Curupira V1.0: Joint Inversion of VES and TEM for Environmental and Mass Movements Studies. International Journal of Geosciences, 14, 1160–1176.
    [Google Scholar]
  5. Bortolozo, C.A., Bokhonok, O., Porsani, J.L., Monteiro dos Santos, F.A., Diogo, L.A. and Slob, E. [2017]. Objective Function Analysis for Electric Soundings (VES), Transient Electromagnetic Soundings (TEM) and Joint Inversion VES/TEM.Journal of Applied Geophysics, 146, 120–137.
    [Google Scholar]
  6. Bortolozo, C.A. [2011]. Inversão conjunta 1D e 2D de dados de Eletrorresistividade e TDEM aplicados em estudos de hidrogeologia na bacia do Paraná. (PhD Thesis). Universidade de São Paulo, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Departamento de Geofísica.
    [Google Scholar]
  7. Bortolozo, C.A., Couto, M.A., Porsani, J.L., Almeida, E.R. and Monteiro dos Santos, F.A. [2014]. Geoelectrical characterization using joint inversion of VES/TEM data: A case study in Paraná Sedimentary Basin, São Paulo State, Brazil.Journal of Applied Geophysics, 11, 33–46.
    [Google Scholar]
  8. Bortolozo, C.A., Porsani, J.L., Monteiro dos Santos, F.A. and Almeida, E. R. [2015]. VES/TEM 1D joint inversion by using Controlled Random Search (CRS) algorithm.Journal of Applied Geophysics, 112, 157–174.
    [Google Scholar]
  9. Campana, J.D.R., Porsani, J.L., Bortolozo, C. A., Serejo, G. and Monteiro dos Santos, F.A. [2017]. Inversion of TEM data and analysis of the 2D induced magnetic field applied to the aquifers characterization in the Paraná basin, Brazil.Journal of Applied Geophysics, p. 233–244.
    [Google Scholar]
  10. Dey, A. and Morrison, F. [1979]. Resistivity modeling for arbitrarily shaped two-dimensional structures.Geophysical Prospecting, 27, 106–136.
    [Google Scholar]
  11. Dong, Z., Georgoulis, E.H. and Pryer, T. [2020]. Recovered finite element methods on polygonal and polyhedral meshes.ESAIM: Mathematical Modelling and Numerical Analysis, 54(4), pp.1309–1337.
    [Google Scholar]
  12. Iritani, M.A. and Ezaki, S. [2012]. As águas subterrâneas do estado de são Paulo. Governo do Estado de São Paulo secretaria do meio ambiente. Instituto Geológico publication.
    [Google Scholar]
  13. Leite, D.N., Bortolozo, C.A., Porsani, J.L., Couto, M.A., Campana, J.D.R., Monteiro dos Santos, F.A., Rangel, R.C., Hamada, L.R., Sifontes, R.V., Serejo, G. and Stangari, M.C. [2018]. Geoelectrical Characterization with 1D VES/TDEM Joint Inversion in Urupês-SP Region, Paraná Basin: Applications to Hydrogeology.Journal of Applied Geophysics, 151, 205–220.
    [Google Scholar]
  14. Mackie, R.L., Bennett, B.R. and Madden, T.R. [1988]. Long-period magnetotelluric measurements near the central California coast: A land-locked view of the conductivity structure under the Pacific Ocean: Geophysics Journal, 95, 181–194.
    [Google Scholar]
  15. Mackie, R.L. and e Madden, T.R. [1993]. Three-dimensional magne-totelluric inversion using conjugate gradients:Geophysics Journal International, 115, 215–229.
    [Google Scholar]
  16. Madden, T.R. [1990]. Inversion of low-frequency electromagnetic data, in oceanographic and geophysical tomography: Elsevier Science Publ., 337–408.
    [Google Scholar]
  17. Milani, E., Melo, J., Souza, P., Fernandes, L. and França, A.B. [2007]. Bacia do Paraná.Boletim de Geociências da Petrobrás, 15, n° 1, 265–287. Rio de Janeiro, Brasil.
    [Google Scholar]
  18. Rijo, L. [1977]. Modeling of electric and electromagnetic data. Ph.D. Thesis, University of Utah.
    [Google Scholar]
  19. Tarantola, A. and Valette, B. [1982]. Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion:Reviews of Geophysics and Space Physics, 20, 219–232.
    [Google Scholar]
  20. Tarantola, A. [1987]. Inverse Problem Theory. Elsevier.
    [Google Scholar]
  21. Telford, W.M., Geldart, L.P. and Sheriff, R.E. [1990]. Applied Geophysics. 2nd Edition, Cambridge University Press, Cambridge, 770.
    [Google Scholar]
  22. Tikhonov, A.N. and e Arsenin, V.I. [1977]. Solutions of ill-posed problems. VH Winston & Sons, Washington, DC.
    [Google Scholar]
  23. Zhang, J., Mackie, R.L. and Madden, T.R. [1995]. 3-D resistivity forward modeling and inversion using conjugate gradients.Geophysics, 60(5), 1313–1325.
    [Google Scholar]
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