1887
Volume 45, Issue 3
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

[

The two-dimensional self-consistent impedance method was used to calculate the electromagnetic surface impedance above subsurface structures at very low frequencies. The technique has been applied to the analysis of a coal seam with various structural anomalies and line of oxidation. This improved technique allows in-field inverse modelling of surface impedance data.

,

The two-dimensional self-consistent impedance method is used to calculate the electromagnetic surface impedance above subsurface structures at very low frequencies. The method was derived from Faraday’s and Ampere’s Laws and results in a linear matrix equation where the right hand side of the equation corresponds to the source field introduced into the model as a fixed magnetic value. An air layer above the earth’s surface is included to allow the scattered magnetic field to be calculated at the surface. The source field is applied above the earth’s surface as a Dirichlet boundary condition, and a Neumann boundary condition is applied to all other boundaries in the solution space. The left hand side of the linear equation corresponds to the impedance matrix determined by discretising the solution space into two-dimensional rectangular pixels or cells bounded by lumped impedance elements, with values determined by the electromagnetic properties of the local media and the size of the pixel in the model. The resulting sparse matrix offers the flexibility of cells of any shape or size. Due to the large matrix dimensions, an iterative solver with a preconditioning technique was used to improve the speed, size and convergence of the solution. The efficient forward modelling has been applied to the analysis of a coal seam with various structural anomalies and line of oxidation along a line defined by 500 m with 0.5 m resolution. This improved technique allows in-field inverse modelling of surface impedance data. This paper reports several likely coal-seam scenarios relevant to surface mining operations.

]
Loading

Article metrics loading...

/content/journals/10.1071/EG12072
2014-09-01
2026-01-22
Loading full text...

Full text loading...

References

  1. Benzi M. 2002 Preconditioning techniques for large linear systems: a survey: Journal of Computational Physics 182 418 477 10.1006/jcph.2002.7176
    https://doi.org/10.1006/jcph.2002.7176 [Google Scholar]
  2. Cagniard L. 1953 Basic theory of the magnetotelluric method of geophysical prospecting: Geophysics 18 605 635 10.1190/1.1437915
    https://doi.org/10.1190/1.1437915 [Google Scholar]
  3. Chan, T. F., and Van der Vorst, H. A., 1997, Approximate and incomplete factorizations, in D. E. Keyes, A. Sameh, and V. Venkatakrishnan, eds., Parallel Numerical Algorithms: Springer, ICASE/LaRC Interdisciplinary Series in Science and Engineering 4, 167–202.
  4. Collet, L. S., and Jensen, O. G., 1982, Geophysical applications of surface wave impedance measurements: Geological Survey Canada.
  5. Elman H. C. 1986 A stability analysis of incomplete LU factorizations: Mathematics of Computation 47 191 217
    [Google Scholar]
  6. Espinosa, H. G., and Thiel, D. V., 2012, Efficient forward modelling of electromagnetic surface impedance for coal seam assessment: Proceedings of the 22nd International Geophysical Conference and Exhibition, Australian Society of Exploration Geophysicists, Brisbane, 1–4.
  7. Espinosa H. G. Heldring A. Tamayo J. M. Rius J. M. Mosig J. R. 2006 Multilevel field interpolation algorithm for large PEC objects: EuCAP Antennas and Propagation 1 5
    [Google Scholar]
  8. Gandhi O. P. DeFord J. F. Kanai H. 1984 Impedance method for calculation of power deposition patterns in magnetically induced hyperthermia: IEEE Transactions on Bio-Medical Engineering BME-31 644 651 10.1109/TBME.1984.325314
    https://doi.org/10.1109/TBME.1984.325314 [Google Scholar]
  9. James D. A. Thiel D. V. 1997 Modelling eddy currents in unbounded structures using the impedance method: Applied Computational Electromagnetics Society Journal 12 43 49
    [Google Scholar]
  10. James D. A. O’Keefe S. G. Thiel D. V. 1999 Eddy current modeling using the impedance method for surface impedance profiling: IEEE Transactions on Magnetics 35 1107 1110 10.1109/20.767140
    https://doi.org/10.1109/20.767140 [Google Scholar]
  11. Mogensen G. T. Espinosa H. G. Thiel D. V. 2014 Surface impedance mapping using sferics: IEEE Transactions on Geoscience and Remote Sensing 52 2074 2080 10.1109/TGRS.2013.2257801
    https://doi.org/10.1109/TGRS.2013.2257801 [Google Scholar]
  12. Porstendorfer, G., 1975, Principles of magnetotelluric prospecting: Gebruder Borntraeger.
  13. Rankin D. 1962 The magnetotelluric effect on a dike: Geophysics 27 666 676 10.1190/1.1439077
    https://doi.org/10.1190/1.1439077 [Google Scholar]
  14. Saad, Y., 2003, Iterative methods for sparse linear systems (2nd edition): Siam.
  15. Saad Y. Schultz M. 1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems: SIAM Journal on Scientific and Statistical Computing 7 856 869 10.1137/0907058
    https://doi.org/10.1137/0907058 [Google Scholar]
  16. Silvester P. Haslam C. R. S. 1972 Magnetotelluric modeling by the finite element method: Geophysical Prospecting 20 872 891 10.1111/j.1365‑2478.1972.tb00672.x
    https://doi.org/10.1111/j.1365-2478.1972.tb00672.x [Google Scholar]
  17. Thiel D. V. 1988 A surface impedance mapping technique based on radiation from discrete lightning strokes: Geoexploration 25 163 172 10.1016/0016‑7142(88)90011‑7
    https://doi.org/10.1016/0016-7142(88)90011-7 [Google Scholar]
  18. Thiel D. V. 1990 Surface-impedance changes in the vicinity of an abrupt lateral boundary at the earth’s surface: IEEE Transactions on Geoscience and Remote Sensing 28 500 502 10.1109/TGRS.1990.572930
    https://doi.org/10.1109/TGRS.1990.572930 [Google Scholar]
  19. Thiel D. V. Mittra R. 1997 Surface impedance modeling using the finite-difference time-domain method: IEEE Transactions on Geoscience and Remote Sensing 35 1350 1356 10.1109/36.628800
    https://doi.org/10.1109/36.628800 [Google Scholar]
  20. Thiel D. V. Mittra R. 2001 A self-consistent method for electromagnetic surface impedance modeling: Radio Science 36 31 43 10.1029/1999RS002312
    https://doi.org/10.1029/1999RS002312 [Google Scholar]
  21. Tikhonov A. N. 1950 On determining electrical characteristics of the deep layers of the earth’s crust: Soviet Mathematics Doklady 2 295 297
    [Google Scholar]
  22. Ting S. C. Hohmann G. W. 1981 Integral equation modeling of three-dimensional magnetotelluric response: Geophysics 46 182 197 10.1190/1.1441188
    https://doi.org/10.1190/1.1441188 [Google Scholar]
  23. Wait, J. R., 1970, Electromagnetic waves in stratified media (2nd edition): Pergamon
/content/journals/10.1071/EG12072
Loading
/content/journals/10.1071/EG12072
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error