2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method

References

1. AstleyR.J. and MacaulayG.J.1994. Mapped wave envelope elements for acoustical radiation and scattering. Journal of Sound and Vibration170, 97–118.
   [Google Scholar]
2. AstleyR.J., MacaulayG.J., CoyetteJ.P. and CremersL.1998. Three‐dimensional wave‐envelope elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency domain. Journal of the Acoustical Society of America103, 49–63.
   [Google Scholar]
3. BettessJ.A. and BettessP.1998. A new mapped infinite wave element for general wave diffraction problems and its validation on the ellipse diffraction problem. Computer Methods in Applied Mechanics and Engineering164, 17–48.
   [Google Scholar]
4. BlomeM., MaurerH.R. and SchmidtK.2009. Advances in three‐dimensional geoelectric forward solver techniques. Geophysical Journal International176, 740–752.
   [Google Scholar]
5. BurnettD.S.1994. A three‐dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. Journal of the Acoustical Society of America96, 2798–2816.
   [Google Scholar]
6. CardarelliE. and FischangerF.2006. 2‐D data modelling by electrical resistivity tomography for complex subsurface geology. Geophysical Prospecting54, 121–133.
   [Google Scholar]
7. CecotW., RachowiczW. and DemkowiczL.2003. An hp‐adaptive finite element method for electromagnetics. Part 3: A three‐dimensional infinite element for Maxwell's equations. International Journal for Numerical Methods in Engineering57, 899–921.
   [Google Scholar]
8. CharlesA., TowersM.S. and McCowenA.1998. A general infinite element for terminating finite element meshes in electromagnetic scattering prediction. IEEE Translation Journal on Magnetics34, 3367–3370.
   [Google Scholar]
9. DemkowiczL.2007. Computing with Hp‐Adaptive Finite Elements. Chapman and Hall/CRC.
   [Google Scholar]
10. DeyA. and MorrisonH.F.1979. Resistivity modeling for arbitrarily shaped tree‐dimensional structures. Geophysical Prospecting27, 106–136.
    [Google Scholar]
11. FuL.Y. and WuR.S.2000. Infinite boundary element absorbing boundary for wave propagation simulations. Geophysics52, 596–602.
    [Google Scholar]
12. GratkowskiS. and ZiolkowskiM.1992. A three‐dimensional infinite element for modeling open‐boundary field problems. IEEE Translation Journal on Magnetics28, 1675–1678.
    [Google Scholar]
13. GratkowskiS. and ZiolkowskiM.1994. On the accuracy of a 3‐D infinite element for open boundary electromagnetic field analysis. Archiv für Elektrotechnik77, 77–83.
    [Google Scholar]
14. HughesT.J.R.1987. The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Prentice Hall, Englewood Cliffs, NJ.
    [Google Scholar]
15. HvozdaraM. and KaikkonenP.1996. The boundary integral solution of a DC geoelectric problem for a 2‐D body embedded in a two‐layered Earth. Journal of Applied Geophysics34, 169–186.
    [Google Scholar]
16. LeeT.1975. An integral equation and its solution for some two and three‐dimensional problems in resistivity and induced polarization. Geophysical Journal of the Royal Astronomical Society42, 81–95.
    [Google Scholar]
17. LiL.X., GuoS.Z. and WangA.Q.2007. The infinite element method and its application. Advances in Mechanics37, 161–174.
    [Google Scholar]
18. LiL.X., SunJ.S. and SakamotoH.2005. A generalized infinite element for acoustic radiation. Journal of Vibration and Acoustics127, 2–11.
    [Google Scholar]
19. LiuD.G., FeiJ.G., YuY.J. and LiG.Y.1980. Fortran calculating program. National Defense Industry Press. Beijing.
    [Google Scholar]
20. McGillivrayP. and OldenburgD.1990. Methods for calculating Fréchet derivatives and sensitivities for the non‐linear inverse problem: a comparative study. Geophysical Prospecting38, 499–524.
    [Google Scholar]
21. MouchaR. and BaileyR.C.2004. An accurate and robust multigrid algorithm for 2‐D forward modelling. Geophysical Prospecting52, 197–212.
    [Google Scholar]
22. MuftiI.R.1976. Finite‐difference resistivity modeling for arbitrary shaped two‐dimensional structures. Geophysics41, 62–78.
    [Google Scholar]
23. MundryE.1984. Geoelectrical model calculations for two‐dimensional resistivity distributions. Geophysical Prospecting32, 124–131.
    [Google Scholar]
24. PanK.J. and TangJ.T.2.5 D and 3 D resistivity modelling using an extrapolation cascadic multigrid method. Geophysical Journal International197, 1459–1470.
    [Google Scholar]
25. QiangJ.K., HanX., and DaiS.K.2013. 3‐D DC resistivity inversion with topography based on regularized conjugate gradient method. International Journal of Geophysics, Article ID 931876.
    [Google Scholar]
26. RenZ.Y. and TangJ.T.2010. 3‐D direct current resistivity modeling with unstructured mesh by adaptive finite‐element method. Geophysics75, 7–17.
    [Google Scholar]
27. RückerC., GüntherT. and SpitzerK.2006. Three‐dimensional modelling and inversion of dc resistivity data incorporating topography‐I. Modelling. Geophysical Journal International166, 495–505.
    [Google Scholar]
28. SunY.2005. Numerical analysis for three‐dimensional resistivity model by using finite element/infinite element methods. Chinese Journal of Geotechnical Engineering27, 733–737.
    [Google Scholar]
29. SpitzerK.1995. A 3‐D finite‐difference algorithm for DC resistivity modelling using conjugate gradient methods. Geophysical Journal International123, 903–914.
    [Google Scholar]
30. TangJ.T. and GongJ.Z.2010. 3‐D DC resistivity forward modeling by finite‐infinite element coupling method. Chinese Journal of Geophysics53, 717–728.
    [Google Scholar]
31. TangJ.T. and WangF.Y.2010. 2.5‐D DC resistivity modeling by adaptive finite‐element method with unstructured triangulation. Chinese Journal of Geophysics53, 708–716.
    [Google Scholar]
32. TowersM.S., McCowenA. and MacnabJ.A.R.1993. Electromagnetic scattering from an arbitrary, inhomogeneous 2‐D object‐a finite and infinite element solution. IEEE Transactions on Antennas and Propagation41, 770–777.
    [Google Scholar]
33. TrippA.C., HohmannG.W., and SwiftC.M.1984. Two‐dimensional resistivity inversion. Geophysics49, 1708–1717.
    [Google Scholar]
34. WuX.P.2003. A 3‐D finite‐element algorithm for DC resistivity modeling using the shifted incomplete Cholesky conjugate gradient method. Geophysical Journal International154, 947–956.
    [Google Scholar]
35. XuS.Z.1994. The Finite Element Method in Geophysics. Science Press. Science Press, Beijing.
    [Google Scholar]
36. XuS.Z., DuanB.C. and ZhangD.H.2000. Selection of the wavenumbers k using an optimization method for the inverse Fourier transform in 2.5‐D electrical modeling. Geophysical Prospecting48, 789–796.
    [Google Scholar]
37. XuS.Z., ZhaoS.K. and YiN.1998. A boundary element method for 2‐D dc resistivity modeling with a point current source. Geophysics63, 399–404.
    [Google Scholar]
38. XuT.J. and ChengB.J.2008. Multi‐scale analysis of seismic signal in wavelet domain by mixed programming with Compaq visual Fortran and MATLAB. Computing Techniques for Geophysical and Geochemical Exploration30, 185–190.
    [Google Scholar]
39. ZienkiewiczO.C., BettessK., EmsonC. and ChiamT.C.1985. Mapped infinite element for exterior wave problem. International Journal for Numerical Method in Engineering21, 1229–1251.
    [Google Scholar]
40. ZienkiewiczO.C. and TaylorR.L.2000. The Finite Element Method. Fifth Edition. Volume 1: The Basis. Butterworth Heinemann, Oxford.
    [Google Scholar]