The Quasi Total Reflected Lateral Shift of Inhomogeneous P‐Polarized Electromagnetic Wave on the Interface of Conductive Media

Abstract

Using the phase shift of reflection coefficient at the interface between two conductive media, we derive the lateral shift of quasi total reflection of inhomogeneous P-polarized electromagnetic wave (whose electric field parallels to the incident plane), and draw the curves of lateral shift with respect to the incident angle. The results show that there are three discontinuous points at the critical angle of phase constant, the critical angle of attenuation constant and 90 • . When the incident angle approaches to one of the three angles, the lateral shift becomes very large. When the incident angle equals to one of them, the lateral shift becomes infinite, i.e. the electromagnetic wave propagates along the interface. In other incident angle the lateral shift has the same order of magnitude as the wavelength. After accounting the lateral shift effect, we discuss the measuring error of electromagnetic wave logging caused by the lateral shift effect, and give a method of computing the measuring error.

The research progress on lateral shift of reflected electromagnetic wave at the interface of two conductive media

“…(1) also shows the converting of refracted electromagnetic wave between the homogeneous wave (the direction of β is consistent with the direction of α [14] ) and inhomogeneous wave (the direction of α is inconsistent with the direction of β ) at the interface of two conductive media [16][17][18][19][20] . If the electromagnetic wave strikes a multi-layer medium as shown in Figure 3 [22] (five conductive layers, the interfaces are Г 1 , Г 2 , Г 3 and Г 4 as noted), by eq.…”

“…By the phase shift and the phase constant of reflected wave [1][2][3][16][17][18] , the lateral shift of reflected wave can be derived from the following formula:…”

“…Here n is the unit normal vector of the reflection interface; α 1 , β 1 , α y , β r , α 2 and β 2 are the phase shift vectors and amplitude attenuation vectors of incident, reflected and refracted wave, respectively; ψ 1 , ϕ 1 , ψ r , ϕ r , ψ 2 and ϕ 2 are the angles between n and α 1 , β 1 , α r , β r , α 2 , β 2 , respectively. On the interface of two conductive media, α 1 , β 1 , α 2 and β 2 satisfy the following formulas [14−16] : ψ ϕ = , which is a constant [17][18][19][20][21][22] . Thus, both ψ 2 and ϕ 2 can be expressed by a variant ψ 1 or ϕ 1 .…”

“…In recent years, Liu et al [16][17][18][19][20][21] have ever explored theoretically the lateral shift of reflected electromagnetic wave at the interface of two conductive media, especially for the purpose of electromagnetic wave logging. They provided the analytic formulae for the quasi-total reflection wave lateral shift, and analyzed the error brought by the lateral shift of P-polarized electromagnetic wave (P-PEW, whose electric field was parallel to the plane of incidence).…”

Analytical solution of electromagnetic field generated by induction logging tool in a fan-ring slot of drill collar while drilling

“…In addition, in logging, the current in the emission coils causes vortex flows both in the drill collar and in the stratum, and the vortex flow in the drill collar also causes vortex flows in the stratum, so the vortex flow in the stratum is generated commonly by both the primary vortex flow caused by the current in the emission coils and the secondary vortex flow caused by the vortex flow in drill collar. All the vortex flows would generate induced electromotive force in the receiving coils [19][20][21][22][23][24] , therefore, the signals received by the receiving coils come from the induction signals generated commonly by both the stratum and the drill collar. For this new type logging system while drilling, the theoretic method of computing field distribution is not yet available at present.…”