Finite Element Simulation of 3-D Marine Controlled Source Electromagnetic Fields in Anisotropic Media with Unstructured Tetrahedral Grids

Abstract

Marine controlled-source electromagnetic (CSEM) method has proved to be a powerful tool and found its increasing applications for offshore resource exploration and tectonic studies. However, bathymetric variations and anisotropic structures encountered in practical measurements have posed challenges for reliable interpretation of marine CSEM data collected in increasingly complex geologic settings. In this study, we present a Finite element (FE) based forward algorithm for simulating 3-D marine CSEM responses in geologic settings characterized with rough bathymetry and electrical anisotropy. Unstructured tetrahedral meshes are employed to permit precise descriptions of arbitrary seafloor topography. After validating the accuracy of the algorithm, we investigate the effects of bathymetric variations and complicated electric anisotropy separately and jointly on marine CSEM responses. Numerical results have demonstrated that both the bathymetry and electrical anisotropy can cause significant distortions on marine CSEM responses, but to different extent. The effects of full electrical anisotropy and bathymetry have to be taken into consideration for reliable interpretations of marine CSEM data in practice.

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References

  1. Amestoy, P. R., Duff, I. S., L’Excellent, J.-Y., & Koster, J. (2001). A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications,23(1), 15–41.

    Article  Google Scholar 

  2. Anderson, B., Bryant, I., Luling, M., Spies, B., & Helbig, K. (1994). oilfield anisotropy: Its origins and electrical characteristics. Oilfield Review,6(4), 48–56.

    Google Scholar 

  3. Ansari, S., & Farquharson, C. G. (2014). 3D finite-element forward modeling of electromagnetic data using vector and scalar potentials and unstructured grids. Geophysics,79(4), E149–E165.

    Article  Google Scholar 

  4. Avdeev, D. B., Kuvshinov, A. V., Pankratov, O. V., & Newman, G. A. (2002). Three-dimensional induction logging problems, Part I: An integral equation solution and model comparisons. Geophysics,67(2), 413–426.

    Article  Google Scholar 

  5. Cai, H., Xiong, B., Han, M., & Zhdanov, M. (2014). 3D controlled-source electromagnetic modeling in anisotropic medium using edge-based finite element method. Computers & Geosciences,73, 164–176.

    Article  Google Scholar 

  6. Castillo-Reyes, O., de la Puente, J., & Cela, J. M. (2018). PETGEM: A parallel code for 3D CSEM forward modeling using edge finite elements. Computers & Geosciences,119, 123–136.

    Article  Google Scholar 

  7. Chung, Y., Son, J. S., Lee, T. J., Kim, H. J., & Shin, C. (2014). Three-dimensional modelling of controlled-source electromagnetic surveys using an edge finite-element method with a direct solver. Geophysical Prospecting,62, 1468–1483.

    Article  Google Scholar 

  8. Clavaud, J. B. (2008). Intrinsic electrical anisotropy of shale: The effect of compaction. Petrophysics,49(03), 243–260.

    Google Scholar 

  9. Coggon, J. (1971). Electromagnetic and electrical modeling by the finite element method. Geophysics,36(1), 132–155.

    Article  Google Scholar 

  10. Commer, M., & Newman, G. A (2007). 3D CSEM modeling and inversion for hydrocarbon reservoir mapping: The bathymetry problem. In 2007 SEG Annual Meeting: Society of Exploration Geophysicists.

  11. Constable, S., & Srnka, L. J. (2007). An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration. Geophysics, 72(2), WA3-WA12.

  12. Darnet, M., Choo, M., Plessix, R., Rosenquist, M., Yip-Cheong, K., Sims, E., et al. (2007). Detecting hydrocarbon reservoir from controlled source electromagnetic (CSEM) data in complex settings: Application to deep water Sabah, Malaysia. Geophysics, 72(2), WA97–WA103.

  13. Davydycheva, S., & Frenkel, M. A. (2013). The impact of 3D tilted resistivity anisotropy on marine CSEM measurements. The Leading Edge,32(11), 1374–1381.

    Article  Google Scholar 

  14. Edwards, N. (2005). Marine controlled source electromagnetics: Principles, methodologies, future commercial applications. Surveys In Geophysics,26(6), 675–700.

    Article  Google Scholar 

  15. Ellingsrud, S., Eidesmo, T., Johansen, S., Sinha, M., MacGregor, L., & Constable, S. (2002). Remote sensing of hydrocarbon layers by seabed logging (SBL): Results from a cruise offshore Angola. The Leading Edge,21(10), 972–982.

    Article  Google Scholar 

  16. Fu, H., Wang, Y., Um, E. S., Fang, J., Wei, T., Huang, X., et al. (2015). A parallel finite-element time-domain method for transient electromagnetic simulation. Geophysics,80(4), E213–E224.

    Article  Google Scholar 

  17. Geuzaine, C., & Remacle, J. F. (2009). Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering,79(11), 1309–1331.

    Article  Google Scholar 

  18. Gould, N. I., Scott, J. A., & Hu, Y. (2007). A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations. ACM Transactions on Mathematical Software (TOMS),33(2), 10.

    Article  Google Scholar 

  19. Haber, E., & Ascher, U. M. (2001). Fast finite volume simulation of 3D electromagnetic problems with highly discontinuous coefficients. SIAM Journal on Scientific Computing,22(6), 1943–1961.

    Article  Google Scholar 

  20. Hansen, K., Panzner, M., Shantsev, D., & Mittet, R. (2016). TTI inversion of marine CSEM data. In SEG Technical Program Expanded Abstracts, 1014–1018.

  21. Hoversten, M. G., Newman, G. A., Geier, N., & Flanagan, G. (2006). 3D modeling of a deepwater EM exploration survey. Geophysics,71(5), G239–G248.

    Article  Google Scholar 

  22. Jahandari, H., & Farquharson, C. (2015). Finite-volume modelling of geophysical electromagnetic data on unstructured grids using potentials. Geophysical Journal International,202(3), 1859–1876.

    Article  Google Scholar 

  23. Jaysaval, P., Shantsev, D. V., de Ryhove, S. D. L. K., & Bratteland, T. (2016). Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner. Geophysical Journal International,207(3), 1554–1572.

    Article  Google Scholar 

  24. Jin, J. (2002). The finite element method in electromagnetics: John Wiley & Sons.

  25. Key, K., & Ovall, J. (2011). A parallel goal-oriented adaptive finite element method for 2.5-D electromagnetic modelling. Geophysical Journal International, 186(1), 137–154. https://doi.org/10.1111/j.1365-246x.2011.05025.x.

  26. Li, X. S. (2005). An overview of SuperLU: Algorithms, implementation, and user interface. ACM Transactions on Mathematical Software (TOMS),31(3), 302–325.

    Article  Google Scholar 

  27. Li, Y., & Constable, S. (2007). 2D marine controlled-source electromagnetic modeling: Part 2The effect of bathymetry. Geophysics, 72(2), WA63-WA71.

  28. Li, Y., & Dai, S. (2011). Finite element modelling of marine controlled-source electromagnetic responses in two-dimensional dipping anisotropic conductivity structures. Geophysical Journal International,185(2), 622–636.

    Article  Google Scholar 

  29. Li, J., Farquharson, C. G., & Hu, X. (2017). 3D vector finite-element electromagnetic forward modeling for large loop sources using a total-field algorithm and unstructured tetrahedral grids. Geophysics,82(1), E1–E16.

    Article  Google Scholar 

  30. MacGregor, L., & Tomlinson, J. (2014). Marine controlled-source electromagnetic methods in the hydrocarbon industry: A tutorial on method and practice. Interpretation, 2(3), SH13–SH32.

  31. Monk, P. (2003). Finite Element Methods for Maxwell’s Equations. Oxford: Oxford University Press.

    Google Scholar 

  32. Newman, G. A., Commer, M., & Carazzone, J. J. (2010). Imaging CSEM data in the presence of electrical anisotropy. Geophysics,75(2), F51–F61.

    Article  Google Scholar 

  33. Operto, S., Virieux, J., Amestoy, P., L’Excellent, J.-Y., Giraud, L., & Ali, H. B. H. (2007). 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study. Geophysics, 72(5), SM195–SM211.

  34. Pek, J., & Santos, F. A. (2002). Magnetotelluric impedances and parametric sensitivities for 1-D anisotropic layered media. Computers & Geosciences,28(8), 939–950.

    Article  Google Scholar 

  35. Peng, R. H., Hu, X. Y., Chen, B., & Li, J. H. (2018). 3-D marine controlled-source electromagnetic modeling in electrically anisotropic formations using scattered scalar-vector potentials. IEEE Geoscience and Remote Sensing Letters,15(10), 1500–1504.

    Article  Google Scholar 

  36. Puzyrev, V., Koric, S., & Wilkin, S. (2016). Evaluation of parallel direct sparse linear solvers in electromagnetic geophysical problems. Computers & Geosciences,89, 79–87.

    Article  Google Scholar 

  37. Saad, Y. (2003). Iterative methods for sparse linear systems: Siam.

  38. Sasaki, Y. (2011). Bathymetric effects and corrections in marine CSEM data. Geophysics,76(3), 139–146.

    Article  Google Scholar 

  39. Schenk, O., & Gärtner, K. (2006). On fast factorization pivoting methods for sparse symmetric indefinite systems. Electronic Transactions on Numerical Analysis, 23, 158–179.

    Google Scholar 

  40. Schwarzbach, C., Börner, R.-U., & Spitzer, K. (2011). Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics-a marine CSEM example. Geophysical Journal International,187(1), 63–74.

    Article  Google Scholar 

  41. Si, H. (2015). TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator. ACM Transactions on Mathematical Software (TOMS),41(2), 11.

    Article  Google Scholar 

  42. Streich, R. (2009). 3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy. Geophysics,74(5), F95–F105.

    Article  Google Scholar 

  43. Um, E. S., Commer, M., & Newman, G. A. (2013). Efficient pre-conditioned iterative solution strategies for the electromagnetic diffusion in the Earth: Finite-element frequency-domain approach. Geophysical Journal International,193, 1460–1473.

    Article  Google Scholar 

  44. Wang, F., Morten, J. P., & Spitzer, K. (2018). Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids. Geophysical Journal International,213, 1056–1072.

    Article  Google Scholar 

  45. Weiss, C. J., & Constable, S. (2006). Mapping thin resistors and hydrocarbons with marine EM methods, Part II—Modeling and analysis in 3D. Geophysics,71(6), G321–G332.

    Article  Google Scholar 

  46. Werthmüller, D. (2017). An open-source full 3D electromagnetic modeler for 1D VTI media in Python: empymod. Geophysics, 82(6), WB9WB19.

  47. Yan, L., Lines, L. R., & Lawton, D. C. (2004). Influence of seismic anisotropy on prestack depth migration. The Leading Edge,23(1), 30–36.

    Article  Google Scholar 

  48. Zhdanov, M. S., Lee, S. K., & Yoshioka, K. (2006). Integral equation method for 3D modeling of electromagnetic fields in complex structures with inhomogeneous background conductivity. Geophysics,71(6), G333–G345.

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 41704133, 41630317), and Hubei subsurface multi-scale imaging key laboratory (No. SMIL-2018-03). Ronghua Peng would like to express his gratitude to Dr. Piyoosh Jaysaval for providing the reference data of the 1-D shallow-water TTI model used in Fig. 4. We wish to express our gratitude to the editor, Raúl Periáñez, and three anonymous reviewers for their comments and suggestions that helped clarify and improve the manuscript.

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Correspondence to Xiangyun Hu.

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Peng, R., Hu, X., Li, J. et al. Finite Element Simulation of 3-D Marine Controlled Source Electromagnetic Fields in Anisotropic Media with Unstructured Tetrahedral Grids. Pure Appl. Geophys. (2020). https://doi.org/10.1007/s00024-020-02514-z

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Keywords

  • Controlled source electromagnetics
  • electrical anisotropy
  • bathymetric effect
  • finite element method
  • unstructured tetrahedral grids