Refinement in the Reflection Properties of Electromagnetic Waves at a Stratigraphic Interface

The travel time of electromagnetic waves in conductive strata has a quantitative relation to the conductivity, permittivity, and permeability of the strata. Using these parameters, geologists can determine the lithology of rocks. But current logging and exploration methods take the time between incidence and reflection as zero and do not take into account the effect of the lateral shift delay when the electromagnetic wave is reflected on the interface of strata. In this article, the lateral shift delay will be considered and a more accurate relationship between petrophysics and electromagnetic wave travel time will be derived. The lateral shift delay of quasi-total reflection of inhomogeneous s-polarized electromagnetic waves (whose electric field is perpendicular to the incident plane) caused by the Goos–Hänchen effect is derived using the phase shift of the wave. The result fits both low and high frequency electromagnetic waves. But for geologists, the most valuable frequency range is between 106 and 109 Hz (1 MHz–1 GHz, wavelengths between 0.1 and 100 m). A numerical example where the frequency equals to 1 GHz. shows three discontinuous points at the critical angle of phase shift, the critical angle of attenuation and 90∘. When the incident angle equals one of these three angles, the lateral shift delay will become infinite. That is, the electromagnetic wave will propagate along the interface. Even when the incident angle is close to one of them, the lateral shift delay is very large. The results also indicate that the two critical angles have an important relation to conductivity and permittivity of the two strata, and that the lateral shift delay has a relation to the incident angle. These results can be used to determine the lithology of the strata and to divide the strata more effectively. It is suggested that this approach may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.