Mathematical Geosciences

, Volume 40, Issue 7, pp 813–829 | Cite as

Group Time Delay in the Reflection of P-Polarized Electromagnetic Plane Waves at a Stratigraphic Interface

  • Fu-Ping LiuEmail author
  • Rui-Zhong Li
  • Jin-yao Li
  • Hui-Guo Chen
  • Chang-Chun Yang


The group time delay (GTD) formulae of quasi-total reflection of inhomogeneous P-polarized electromagnetic waves (P-PEW, whose electric field parallels to the plane of incidence), caused by the Goos–Hänchen effect, is derived by the phase shift of the wave. A numerical example where the frequency equals to 1 GHz is given. The curves of calculating results show that there are three discontinuous points at the critical angle of phase shift vector, the critical angle of attenuation vector and 90. When the angle of incidence is equal to one of these three angles, the GTD will become infinite, and the electromagnetic wave will propagate along the interface. The GTD will be very large, when the angle of incidence is close to one of these three angles. The results indicate that there is an important relationship between the two critical angles and the conductivity and permittivity of the two strata, and that the GTD has an important relationship with the angle of incidence. These results can be used to determine the lithology of the strata and to delimit the interfaces of strata more effectively. It is suggested that this research may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.


P-polarized electromagnetic wave Quasi total reflection Conductive medium Group time delay Phase shift 


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Copyright information

© International Association for Mathematical Geology 2008

Authors and Affiliations

  • Fu-Ping Liu
    • 1
    • 2
    Email author
  • Rui-Zhong Li
    • 3
  • Jin-yao Li
    • 1
  • Hui-Guo Chen
    • 2
  • Chang-Chun Yang
    • 2
  1. 1.Department of Basic ScienceBeijing Institute of Graphic CommunicationBeijingChina
  2. 2.Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina
  3. 3.Economics & Development Research InstituteSINOPECBeijingChina

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