Skip to main content
SpringerLink
Log in

Three-Dimensional Transient Electromagnetic Modeling Based on Fictitious Wave Domain Methods

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

Abstract

Finite-difference time domain (FDTD) methods, which have been widely employed in three-dimensional transient electromagnetic (TEM) modeling, require very small time steps to simulate the electromagnetic fields and this will be time consuming. We present an efficient numerical method for three-dimensional TEM forward modeling. Its key features are based on a correspondence principle between the diffusive and fictitious wave fields. The diffusive Maxwell’s equations are transformed and solved in a so-called fictitious wave domain. This scheme allows larger time steps than conventional FDTD methods, allows including air layers, and allows simulating topography. The need for initial field calculations is avoided by including an electric current source in the governing equations. This also avoids a traditional assumption of a flat earth surface in TEM modeling. We test the accuracy of the electromagnetic fields’ responses using our method with the spectral differential difference (SLDM) solutions. The results show good agreement even under the existence of air layers and topography in the model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Ascher U M, Petzold L R. (1998). Computer methods for ordinary differential equations and differential-algebraic equations (Vol. 61). Siam.

  • Asten, M. W. (1987). Full transmitter waveform transient electromagnetic modeling and inversion for soundings over coal measures. Geophysics, 52(3), 279–288.

    Article  Google Scholar 

  • Börner, R.-U., Ernst, O. G., & Güttel, S. (2015). Three-dimensional transient electromagnetic modelling using rational Krylov methods. Geophysical Journal International, 202(3), 2025–2043.

    Article  Google Scholar 

  • Börner, R.-U., Ernst, O. G., & Spitzer, K. (2008). Fast 3D simulation of transient electromagnetic fields by model reduction in the frequency domain using Krylov subspace projection. Geophysical Journal International, 173, 766–780.

    Article  Google Scholar 

  • Chongo, M., Christiansen, A. V., Tembo, A., et al. (2015). Airborne and ground-based transient electromagnetic mapping of groundwater salinity in the Machile-Zambezi Basin, southwestern Zambia. Near Surface Geophysics., 13(4), 383–395.

    Google Scholar 

  • Christiansen, A. V., Auken, E., & Sørensen, K. (2009). The transient electromagnetic method Groundwater Geophysics (pp. 179–226). Berlin Heidelberg: Springer.

    Book  Google Scholar 

  • Commer, M., Hoversten, G. M., & Um, E. S. (2015). Transient-electromagnetic finite-difference time-domain earth modeling over steel infrastructure. Geophysics, 80(2), E147–E162.

    Article  Google Scholar 

  • Commer, M., & Newman, G. (2004). A parallel finite-difference approach for 3D transient electromagnetic modeling with galvanic sources. Geophysics, 69(5), 1192–1202.

    Article  Google Scholar 

  • Commer M, Newman G. (2006). An accelerated time domain finite difference simulation scheme for three-dimensional transient electromagnetic modeling using geometric multigrid concepts. Radio Science, 41(3).

  • Constable S. (2010). Ten years of marine CSEM for hydrocarbon exploration. Geophysics, 75 (5), 75A67–75A81.

  • Danielsen, J. E., Auken, E., Jørgensen, F., Søndergaard, V., & Sørensen, K. I. (2003). The application of the transient electromagnetic method in hydrogeophysical surveys. Journal of Applied Geophysics, 53(4), 181–198.

    Article  Google Scholar 

  • de Hoop, A. T. (1996). A general correspondence principle for time-domain electromagnetic wave and diffusion fields. Geophysical Journal International, 127, 757–761.

    Article  Google Scholar 

  • de la Kethulle de Ryhove, S., & Mittet, R. (2014). 3D marine magnetotelluric modeling and inversion with the finite-difference time-domain method. Geophysics, 79(6), E269–E286.

    Article  Google Scholar 

  • Druskin, V. L., & Knizhnerman, L. A. (1988). Spectral differential-difference method for numeric solution of three-dimensional nonstationary problems of electric prospecting. Izv. Earth Physics, 24(8), 641–648.

    Google Scholar 

  • Druskin, V., & Knizhnerman, L. (1994). Spectral approach to solving three-dimensional Maxwell’s diffusion equations in the time and frequency domains. Radio Science-Washington, 29, 937.

    Article  Google Scholar 

  • Druskin, V., Knizhnerman, L., & Lee, P. (1999). New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry. Geophysics, 64(3), 701–706.

    Article  Google Scholar 

  • Druskin, V., Knizhnerman, L., & Zaslavsky, M. (2009). Solution of large scale evolutionary problems using rational krylov subspaces with optimized shifts. Siam Journal on Scientific Computing, 31(5), 3760–3780.

    Article  Google Scholar 

  • Druskin, V., Knizhnermann, L. (2000). User’s guide for the program complex to compute 3D nonstationary electromagnetic fields in inhomogenous conductive media.

  • Druskin, V., Lieberman, C., & Zaslavsky, M. (2010). On adaptive choice of shifts in rational Krylov subspace reduction of evolutionary problems. Siam Journal on Scientific Computing, 32(5), 2485–2496.

    Article  Google Scholar 

  • Druskin, V., Remis, R., & Zaslavsky, M. (2014). An extended krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains. Journal of Computational Physics, 272(5), 608–618.

    Article  Google Scholar 

  • Du Fort, E., & Frankel, S. P. (1953). Stability conditions in the numerical treatment of parabolic differential equations. Mathematical Tables and Other Aids to Computation, 7(43), 135–152.

    Article  Google Scholar 

  • Fitterman, D. V., & Stewart, M. T. (1986). Transient electromagnetic sounding for groundwater. Geophysics, 51(4), 995–1005.

    Article  Google Scholar 

  • Goldman, M., Gilad, D., Ronen, A., & Melloul, A. (1991). Mapping of seawater intrusion into the coastal aquifer of Israel by the time domain electromagnetic method. Geoexploration, 28(2), 153–174.

    Article  Google Scholar 

  • Goldman, M. M., & Stoyer, C. H. (1983). Finite-difference calculations of the transient field of an axially symmetric earth for vertical magnetic dipole excitation. Geophysics, 48(7), 953–963.

    Article  Google Scholar 

  • Grant, F. S., West G.F. (1965). Introduction to the electrical methods. Interpretation Theory in Applied Geophysics, (McGraw-Hill. New York). pp. 385–401.

  • Haber E, Ascher U, Oldenburg D W. (2002). 3D forward modelling of time domain electromagnetic data. In 2002 SEG Annual Meeting. Society of Exploration Geophysicists.

  • Hördt, A., & Müller, M. (2000). Understanding LOTEM data from mountainous terrain. Geophysics, 65(4), 1113–1123.

    Article  Google Scholar 

  • Knight, J. H., & Raiche, A. P. (1982). Transient electromagnetic calculations using the Gaver–Stehfest inverse Laplace transform method. Geophysics, 47, 47–50.

    Article  Google Scholar 

  • Knizhnerman, L., Druskin, V., & Zaslavsky, M. (2009). On optimal convergence rate of the rational krylov subspace reduction for electromagnetic problems in unbounded domains. Siam Journal on Numerical Analysis, 47(2), 953–971.

    Article  Google Scholar 

  • Kunetz, G. (1972). Processing and interpretation of magnetotelluric soundings. Geophysics, 37, 1005–1021.

    Article  Google Scholar 

  • Lavrent’ev, M. M., Rornanov, V. G., Shishatskii, S. P. (1980). Ill-posed problems of mathematical physics and analysis (in Russian): Nauka.

  • Lee, K. H., Liu, G., & Morrison, H. F. (1989). A new approach to modeling the electromagnetic response of conductive media. Geophysics, 54(9), 1180–1192.

    Article  Google Scholar 

  • Li, H., Xue, G. Q., Zhou, N. N., & Chen, W. Y. (2015). Appraisal of an array TEM method in detecting a mined-out area beneath a conductive layer. Pure and Applied Geophysics, 172(10), 2917–2929.

    Article  Google Scholar 

  • Li, J. H., Zhu, Z. Q., Liu, S. C., & Zeng, S. H. (2011). 3D numerical simulation for the transient electromagnetic field excited by the central loop based on the vector finite-element method. Journal of Geophysics and Engineering, 8(4), 560.

    Article  Google Scholar 

  • Maaø, F. A. (2007). Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems. Geophysics, 72(2), A19–A23.

    Article  Google Scholar 

  • Mills, T., Hoekstra, P., Blohm, M., & Evans, L. (1988). Time domain electromagnetic soundings for mapping sea-water intrusion in Monterey County, California. Ground Water, 26(6), 771–782.

    Article  Google Scholar 

  • Mittet, R. (2010). High-order finite-difference simulations of marine CSEM surveys using a correspondence principle for wave and diffusion fields. Geophysics, 75(1), F33–F50.

    Article  Google Scholar 

  • Mulder, W. A., Wirianto, M., & Slob, E. C. (2007). Time-domain modeling of electromagnetic diffusion with a frequency-domain code. Geophysics, 73(1), F1–F8.

    Article  Google Scholar 

  • Newman, G. A., Hohmann, G. W., & Anderson, W. L. (1986). Transient electromagnetic response of a three-dimensional body in a layered earth. Geophysics, 51(8), 1608–1627.

    Article  Google Scholar 

  • Oristaglio, M. L., & Hohmann, G. W. (1984). Diffusion of electromagnetic fields into a two-dimensional earth: a finite-difference approach. Geophysics, 49(7), 870–894.

    Article  Google Scholar 

  • Roden, J. A., & Gedney, S. D. (2000). Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media. Microwave and Optical Technology Letters, 27(5), 334–338.

    Article  Google Scholar 

  • Shantsev, D. V., & Maaø, F. A. (2015). Rigorous interpolation near tilted interfaces in 3-D finite-difference EM modelling. Geophysical Journal International, 200(2), 745–757.

    Article  Google Scholar 

  • Taflove, A., Hagness, S. C. (1995). Computational electrodynamics: the finite-difference time-domain method. Norwood, 2nd Edition, (MA: Artech House).

  • Wang, T., & Hohmann, G. W. (1993). A finite-difference time-domain solution for three-dimensional electromagnetic modeling. Geophysics, 58(6), 797–809.

    Article  Google Scholar 

  • Xu, Y. C., Lin, J., Li, S. Y., Zhang, X. S., Wang, Y., & Ji, Y. J. (2012). Calculation of full-waveform airborne electromagnetic response with three-dimension finite-difference solution in time-domain. Chinese Journal of Geophysics, 55(6), 2105–2114.

    Article  Google Scholar 

  • Xue, G. Q., Qin, K. Z., Li, X., Qi, Z. P., & Zhou, N. N. (2011). Discovery and TEM detection to a large-scale porphyry molybdenum deposit in Tibet. Progress in Geophysics, 26(3), 954–960.

    Google Scholar 

  • Yang, D., & Oldenburg, D. W. (2012). Three-dimensional inversion of airborne time-domain electromagnetic data with applications to a porphyry deposit. Geophysics, 77(2), B23–B34.

    Article  Google Scholar 

  • Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation, 14(3), 302–307.

    Article  Google Scholar 

  • Zhdanov M S. (2010). Electromagnetic geophysics: Notes from the past and the road ahead. Geophysics, 75 (5), 75A49-75A66.

Download references

Acknowledgements

The authors would like to express great gratitude to Leonid Knizhnerman (Central Geophysical Expedition) for providing access to the SLDM code. They wish to thank Gary Egbert for his invaluable suggestions and discussions. This work is supported by the Development of Key Instruments of Deep Exploration (ZDYZ2012-1-03) and the National Natural Science Foundation of China (NSFC) under the Grants 41174095.

Author information

Authors and Affiliations

  1. College of Electrical Engineering and Instrumentation, Jilin University, Changchun, 130026, China

    Yanju Ji & Yanpu Hu

  2. Key Laboratory of Earth Information Detection Instruments, Ministry of Education, Jilin University, Changchun, 130026, China

    Yanju Ji

  3. College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, 104 CEOAS Admin Bldg, Corvallis, OR, 97331-5503, USA

    Naoto Imamura

Authors
  1. Yanju Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanpu Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Naoto Imamura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanpu Hu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ji, Y., Hu, Y. & Imamura, N. Three-Dimensional Transient Electromagnetic Modeling Based on Fictitious Wave Domain Methods. Pure Appl. Geophys. 174, 2077–2088 (2017). https://doi.org/10.1007/s00024-017-1528-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-017-1528-8

Keywords

Search

Navigation