Vol. 43
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
The Equivalence of Inclined Uniaxial and Biaxial Electrical Anisotropy in Inhomogeneous Two-Dimensional Media for Homogeneous TM-Type Plane Wave Propagation Problems
By
, Vol. 43, 143-162, 2003
Abstract
For a homogeneous TM-type wave propagating in a two-dimensional half space with both vertical and horizontal inhomogeneities, where the TM-type wave is aligned with one of the elements of the conductivity tensor, it is shown using exact solutions to boundary value problems that the shearing term in the homogeneous Helmholtz equation for inclined uniaxial anisotropic media unequivocally vanishes and solutions need only be sought to the homogeneous Helmholtz equation for fundamental biaxial anisotropic media. This implies that those problems posed with an inclined uniaxial conductivity tensor can be identically stated with a fundamental biaxial conductivity tensor, provided that the conductivity values are the reciprocal of the diagonal terms from the Euler rotated resistivity tensor. The applications of this for numerical methods of solving arbitrary two-dimensional problems for a homogeneous TM-type wave is that they need only to approximate the homogeneous Helmholtz equation and neglect the corresponding shearing term.
Citation
, "The Equivalence of Inclined Uniaxial and Biaxial Electrical Anisotropy in Inhomogeneous Two-Dimensional Media for Homogeneous TM-Type Plane Wave Propagation Problems," , Vol. 43, 143-162, 2003.
doi:10.2528/PIER03021202
http://www.jpier.org/PIER/pier.php?paper=0302122
References

1. Clemmow, P. C., "Radio propagation over a flat earth across a boundary separating two different media," Phil. Trans. Royal Soc. Lond. A, Vol. 246, 1-55, 1953.

2. d'Erceville, I. and G. Kunetz, "The effect of a fault on the earth's natural electromagnetic field," Geophysics, Vol. 27, 651-665, 1962.
doi:10.1190/1.1439075

3. Jones, F. W. and A. T. Price, "The perturbations of alternating geomagnetic field by conductivity anomalies," Geophys. J. R. Astron. Soc., Vol. 20, 317-334, 1970.

4. Koschlakov, G. V., "Effect of vertical contact on measured magneto-telluric response'' Geolog. Geofiz.," Geolog. Geofiz., Vol. 11, 119-122, 1970.

5. Obukhov, G. G., "Magneto-telluric field of a horizontally inhomogeneous medium underlayed by an ideal conducting basement," Izv. Akad. Nauk SSSR Fizika Zemli, No. 4, 89-94, 1969.

6. Rankin, D., "The magneto-telluric effect of a dike," Geophysics, Vol. 27, 666-676, 1962.
doi:10.1190/1.1439077

7. Robertson, R. C., "The E-polarization response of a twodimensional heterogeneous layer modeled by two thin sheets," IEEE Trans. Geosci. Remote Sensing, Vol. 27, 369-374, 1989.
doi:10.1109/36.29556

8. Sampaio, E. E. S. and D. Dias, "Electromagnetic profiling interpretation across vertical faults and dikes," Geophys. Prosp., Vol. 49, 107-119, 2001.
doi:10.1046/j.1365-2478.2001.00240.x

9. Sampaio, E. E. S. and J. T. Fokkema, "Scattering of monochromatic acoustic and electromagnetic plane waves by two quarter spaces," J. Geophys. Res., Vol. 97, 1953-1963, 1992.

10. Truemann, R., "Electromagnetic induction in inhomogeneous media (E-polarization)," Acta Geodaet. Mont. Acad. Sci. Hung., Vol. 5, 61-67, 1970.

11. Wait, J. R. and K P. Spies, "Magneto-telluric fields for a segmented overburden," J. Geomagn. Geoelec., Vol. 26, 449-458, 1974.

12. Weaver, J. T., "A discussion on the 'fault' and 'dike' problems in magnetotelluric theory," Geophysics, Vol. 28, 1386-1398, 1963.
doi:10.1190/1.1439212

13. Weaver, J. T., "The electromagnetic field within a discontinuous conductor with reference to geomagnetic pulsations near a coastline," Can. J. Phys., Vol. 41, 484-495, 1963.

14. Weaver, J. T., B. V. Le Quang, and G. Fischer, "A comparison of analytical and numerical results for two-dimensional control model in electromagnetic induction-I: B-polarization calculations," Geophys. J. R. astron. Soc., Vol. 87, 263-277, 1985.

15. Weaver, J. T., B. V. Le Quang, and G. Fischer, "A comparison of analytical and numerical results for a 2-D control model in electromagnetic induction-II: E-polarization calculations," Geophys. J. Roy. Astron. Soc., Vol. 87, 917-948, 1986.

16. Dmitriev, V. I. and E. V. Zakharov, "Method for calculating the magnetotelluric field over an inclined contact," Phys. Solid Earth, Vol. 6, 719-723, 1970.

17. Geyer, R. G., "The effect of a dipping contact on the behaviour of the electromagnetic field," Geophysics, Vol. 37, 337-350, 1972.
doi:10.1190/1.1440263

18. Reddy, I. K. and D. Rankin, "Magnetotelluric response of a twodimensional sloping contact by the finite element method," Pure App. Geophys., Vol. 105, 847-857, 1973.
doi:10.1007/BF00875833

19. Obukhov, G. G., "Magneto-telluric field in horizontal inhomogeneous anisotropic medium," Izv. Akad. Nauk SSSR Fizika Zemli, No. 4, 106-112, 1969.

20. Grubert, D., An extension of the classical solution from d'Erceville and Kunetz to anisotropic resistivity, 12'th Workshop on Electromagnetic Induction in the Earth, 8-13, 1994.

21. Zhdanov, M. S., I. M. Varenstov, J. T. Weaver, N. G. Golubev, and V. A. Krylov, "Method for modelling electromagnetic fields. Results from COMMEMI — the international project on the comparison of modelling methods for electromagnetic induction," J. App. Geophys., Vol. 37, 133-271, 1997.
doi:10.1016/S0926-9851(97)00013-X

22. Pek, J. and F. A. M. Santos, "Magnetotelluric inversion for anisotropic conductivities," presented at 19'th DGG Colloquy 'Electromagnetic Depth Investigations', 1-5, 2001.

23. Chetaev, D. N., "The determination of the anisotropy coefficient and the angle of inclination of a homogeneous anisotropic medium, by measuring the impedance of the natural electromagnetic field," Bull. Acad. Sci. USSR Geophys. Ser., No. 4, 407-408, 1960.