2.5-D DC resistivity modeling considering flexibility and accuracy

Abstract

We highlighted the flexibility of using unstructured mesh together with the local refinement by a resistivity model with complicated topography. The effect of topography is emphasized. Based on this, we calculated a specific class of layered models and found that the accuracy is not always satisfactory by utilizing the standard approach. As an improvement, we employed the layered earth as the reference model to calculate the wavenumbers. The comparison demonstrates that the accuracy is considerably improved by using this enhanced approach.

Keywords

2-D topography / 2.5-D DC resistivity modeling / layered earth

References

[1] Coggon J. H.. Electromagnetic and Electrical Modeling by the Finite Element Method. Geophysics, 1971, 36(1): 132-155.

[2] Dey A., Morrison H. F.. Resistivity Modelling for Arbitrarily Shaped Two-Dimensional Structures. Geophysical Prospecting, 1979, 27(1): 106-136.

[3] Erdogan E., Demirci I., Candansayar M. E.. Incorporating Topography into 2D Resistivity Modeling Using Finite-Element and Finite-Difference Approaches. Geophysics, 2008, 73(3): F135-F142.

[4] Fox R. C., Hohmann G. W., Killpack T. J., . Topographic Effects in Resistivity and Induced-Polarization Surveys. Geophysics, 1980, 45(1): 75-93.

[5] Frey, P. J., 2001. MEDIT—An Interactive Mesh Visualization Software. INRIA Technical Report 0253. http://www-rocq.inria.fr/gamma/medit/medit.html. Accessed November 26, 2007

[6] Hvozdara M., Kaikkonen P.. The Boundary Integral Solution of a DC Geoelectric Problem for a 2-D Body Embedded in a Two-Layered Earth. Journal of Applied Geophysics, 1996, 34(3): 169-186.

[7] Lesur V., Cuer M., Straub A.. 2-D and 3-D Interpretation of Electrical Tomography Measurements, Part 1: The Forward Problem. Geophysics, 1999, 64(2): 386-395.

[8] Li J. M.. Geoelectric Field and Electric Prospecting, 2005, Beijing: Geological Publishing House 473

[9] Li Y. G., Spitzer K.. Three-Dimensional DC Resistivity Forward Modelling Using Finite Elements in Comparison with Finite-Difference Solutions. Geophysical Journal International, 2002, 151(3): 924-934.

[10] Mufti I. R.. Finite-Difference Resistivity Modeling for Arbitrarily Shaped Two-Dimensional Structures. Geophysics, 1976, 41(1): 62-78.

[11] Mundry E.. Geoelectrical Model Calculations for Two-Dimensional Resistivity Distributions. Geophysical Prospecting, 1984, 32(1): 124-131.

[12] Pidlisecky A., Knight R.. FW2_5D: A MATLAB 2.5-D Electrical Resistivity Modeling Code. Computers & Geosciences, 2008, 34(12): 1645-1654.

[13] Ruan B. Y.. 2-D Electrical Modeling due to a Current Point by FEM with Variation of Conductivity within Each Triangular Element. Guangxi Sciences, 2001, 8(1): 1-3.

[14] Scalicky, T., 1996. LASPack Reference Manual. http://www.netlib.org. Accessed September 9, 2007

[15] Shewchuk, J. R., 1996. Triangle: A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. WACG, 1st Workshop on Applied Computational Geometry. 124–133. http://www.cs.cmu.edu/~quake/triangle.html. Accessed March 12, 2007

[16] Snyder D. D.. A Method for Modeling the Resistivity and IP Response of Two-Dimensional Bodies. Geophysics, 1976, 41(5): 997-1015.

[17] Tang J. T., Wang F. Y.. 2.5-D Direct Current Resistivity Simulation Based on the Unstructured Mesh. Computing Techniques for Geophysical and Geochemical Exploration, 2008, 30(5): 413-418.

[18] Tang J. T., Wang F. Y., Ren Z. Y.. 2.5-D DC Resistivity Modeling by Adaptive Finite-Element Method with Unstructured Triangulation. Chinese J. Geophys., 2010, 53(3): 708-716.

[19] Tsourlos P. I., Szymanski J. E., Tsokas G. N.. The Effect of Terrain Topography on Commonly Used Resistivity Arrays. Geophysics, 1999, 64(5): 1357-1363.

[20] Xiong B., Ruan B. Y.. A Numerical Simulation of 2-D Geoelectric Section with Biquadratic Change of Potential for Resistivity Sounding by the Finite Element Method. Chinese Journal of Geophysics, 2002, 45(2): 285-295.

[21] Xu S. Z., Duan B. C., Zhang D. H.. Selection of the Wavenumbers K Using an Optimization Method for the Inverse Fourier Transform in 2.5D Electrical Modeling. Geophysical Prospecting, 2000, 48(5): 789-796.

[22] Xu S. Z., Zhao S. K., Ni Y.. A Boundary Element Method for 2-D DC Resistivity Modeling with a Point Current Source. Geophysics, 1998, 63(2): 399-404.

[23] Zienkiewicz O. C., Taylor R. L.. The Finite Element Method, Volume I: The Basic, 2000 Fifth Edition Woburn, MA: Butterworth-Heinemann 347

[24] Zienkiewicz O. C., Zhu J. Z.. The Superconvergent Patch Recovery and a Posteriori Error Estimates. Part 1: the Tecovery Technique. International Journal for Numerical Methods in Engineering, 1992, 33(7): 1331-1364.

[25] Zienkiewicz O. C., Zhu J. Z.. The Superconvergent Patch Recovery and a Posteriori Error Estimates. Part 2: Error Estimates and Adaptivity. International Journal for Numerical Methods in Engineering, 1992, 33(7): 1365-1382.