Anisotropic media, mode matching methods, stratified media, well logging tools


In this paper we present an efficient mode-matching technique to analyze tilted-coil antennas in anisotropic geophysical formations. In this problem, a number of coil antennas with arbitrary relative tilt angle with respect to the symmetry axis are used to radiate electromagnetic fields in a cylindrically layered medium comprised of a metallic mandrel, a borehole, and a surrounding layered Earth formation. This configuration corresponds to that of directional well-logging tools used in oil and gas exploration. Our technique combines closed-form solutions for the Maxwell's Equations in uniaxially anisotropic and radially-stratified cylindrical coordinates with the generalized scattering matrix (GSM) at each axial discontinuity based on the mode-matching technique. The field from the transmitter tilted-coil source is represented by a set of modal coefficients which, after computation using GSM matrices, are used to compute the transimpedances. We present validation results which show that our technique can efficiently model directional well-logging tools used for oil and gas exploration.


[1] Y.-K. Hue and F. Teixeira, “FDTD simulation of MWD electromagnetic tools in large-contrast geophysical
formations,” IEEE Trans. Magn., vol. 40, pp. 1456–1459, Mar. 2004.
[2] Y.-K. Hue, “Analysis of electromagnetic well-logging tools,” Ph.D. dissertation, The Ohio State University, Columbus,
[3] H. O. Lee and F. L. Teixeira, “Cylindrical FDTD analysis of LWD tools through anisotropic dipping-layered earth
media,” IEEE Trans. Geosci. Remote Sens., vol. 45, pp. 383–388, 2007.
[4] M. S. Novo, L. C. da Silva, and F. L. Teixeira, “Three-dimensional finite-volume analysis of directional resistivity
logging sensors,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 3, pp. 1151–1158, Mar. 2010.
[5] ——, “A comparative analysis of krylov solvers for three-dimensional simulations of borehole sensors,” IEEE Geosci.
Remote Sens. Lett.,vol. 8, no. 1, pp. 98–102, Jan. 2011.
[6] J. Lovell and W. Chew, “Response of a point source in a multicylindrically layered medium,” IEEE Trans. Geosci.
Remote Sens., vol. 25, pp. 850–858, Nov. 1987.
[7] T. Hagiwara et al., “Effects of mandrel, borehole, and invasion for tilt-coil antennas,” in SPE 78th Ann. Tech. Conf.
Exhibit., 5–8 Oct. 2003.
[8] Y.-K. Hue and F. L. Teixeira, “Analysis of tilted-coil eccentric borehole antennas in cylindrical multilayered formations
for well-logging applications,” IEEE Trans. Ant. Prop., vol. 54, pp. 1058–1064, 2006.
[9] G. S. Liu, F. L. Teixeira, and G. J. Zhang, “Analysis of directional logging tools in anisotropic and multieccentric
cylindrically-layered earth formations,” IEEE Trans. Antennas Propag., vol. 60, pp. 318–327, Jan. 2012.
[10] H. Wang, P. So, S. Yang, W. J. R. Hoefer, and H. Du, “Numerical modeling of multicomponent induction well-logging
tools in the cylindrically stratified anisotropic media,” IEEE Trans. Geosci. Remote Sens., vol. 46, no. 4, pp. 1134–
1147, Apr. 2008.
[11] W. C. Chew et al., “Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities,” Geophys., vol.
49, pp. 1586–1595, 1984.
[12] Q.-H. Liu, “Electromagnetic field generated by an off-axis source in a cylindrically layered medium with an arbitrary
number of horizontal discontinuities,” Geophys., vol. 58, pp. 616–625, 1993.
[13] W. C. Chew, Waves and Fields in Inhomogeneous Media. New York, NY: IEEE Press, 1995.
[14] Y.-K. Hue and F. Teixeira, “Numerical mode-matching method for tilted-coil antennas in cylindrically layered
anisotropic media with multiple horizontal beds,” IEEE Trans. Geosci. Remote Sens., vol. 45, pp. 2451–2462, 2007.
[15] H. Moon, B. Donderici, F. L. Teixeira, “Stable evaluation of Green's functions in cylindrically stratified regions with
uniaxial anisotropic layers,” J. Comp. Phys., vol. 325, pp. 174–200, 2016.
[16] G. S. Rosa, J. R. Bergmann, and F. L. Teixeira, “A robust mode-matching algorithm for the analysis of triaxial welllogging tools in anisotropic geophysical formations,” IEEE Trans. Geosci Remote Sens., submitted, 2016.
[17] L. M. Delves and J. N. Lyness, “A numerical method for locating the zeros of an analytic function,” Mathematics of
Computation, vol. 21, no. 100, pp. 543–560, Oct. 1967.
[18] J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th ed. New York, NY, USA: McGrawHill,
[19] G. S. Rosa and J. R. Bergmann, “Pseudo-analytical modeling for the electromagnetic propagation in stratified
cylindrical structures,” IEEE Antennas Wireless Propag. Lett., vol. 15, pp. 344–347, 2016.
[20] W. C. Chew and W. H. Weedon, “A 3D perfectly matched medium from modified Maxwell’s equations with stretched
coordinates,” Microw. Opt. Tech. Lett., vol. 7, pp. 599–604, 1994.
[21] F. L. Teixeira and W. C. Chew, “Complex space approach to perfectly matched layers: a review and some new
developments,” Int. J. Num. Model., vol. 13, pp. 441–455, 2000.
[22] P. Bienstman et al., “Analysis of cylindrical waveguide discontinuities using vectorial eigenmodes and perfectly
matched layers,” IEEE Trans. Microw. Theory Techn., vol. 49, pp. 349–354, Feb. 2001.
[23] P. Bienstman and R. Baets, “Advanced boundary conditions for eigenmode expansion models,” Optical and Quantum
Electronics, vol. 34, no. 5, pp. 523–540, May. 2002.
[24] R. F. Harrington, Time-harmonic electromagnetic fields. New York, NY, USA: McGraw-Hill, 1961.
[25] V. H. Rumsey, “Reaction concept in electromagnetic theory,” Phys. Rev., vol. 94, pp. 1483–1491, Jun. 1954.
[26] K. Zaki, S.-W. Chen, and C. Chen, “Modeling discontinuities in dielectric-loaded waveguides,” IEEE Trans. Microw.
Theory Techn., vol. 36, no. 12, pp. 1804–1810, Dec. 1988.
[27] D. M. Pozar, Microwave Engineering, 3rd ed. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2005.
[28] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical
Tables. New York, NY, USA: Dover Publications, 1964.




How to Cite

PSEUDO-ANALYTICAL MODELING OF TILTED-COIL ANTENNAS IN ANISOTROPIC GEOPHYSICAL FORMATIONS. (2017). Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), 16(1), 284–296.



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