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By Abbot C. G.

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That is, 1mk2x = 1mk2z = 1m 8 2 = O. 6) Because of translational invariance in the x- and y-directions, the reflected and transmitted (or refracted) fields are also plane waves. 7) z ~ o. 8) and E{r(r) == El(r) = El(O)eikl·r = El(O)ei(k1:cx+klzz)j The corresponding components of the magnetic field are similar. 10) The boundary conditions require the continuity of the tangential components of the electric and magnetic fields across the boundary at z = O. 11) This relation is of fundamental importance and actually has a generality that far transcends the special conditions in this section, as explained in later sections of this chapter.

The low frequencies of such natural fields allow them to penetrate deeply into the earth where they induce eddy currents with amplitudes and distributions that are directly related to the magnitude and distribution of the conductivity. , by line sources (Vanyan 1967, p. 127) located above the earth's surface. This means that measurements and calculations of incident fields on and in the earth are at points effectively under the source currents. With these currents of the order of 80 to 100 km high, the field incident on the earth is approximated by a spherical or locally plane wave.

1. 1) where the direct field is . 2) Here, A is proportional to the intensity of the line source and rl = [(z d)2 + p2Jl/2. 4) fr == fer = N2 cos e + (N2 - sin 2 6)1/2 1. 1. Path of lateral wave from line source (after Tamir). 5) for H-polarization. 7) for H-polarization. The distances L1 and L2 in Region 1 and L in Region 2 are shown in Fig. 1. When the critical angle of incidence is small, Be rv 0, L1 rv d, L2 rv z, and L rv p. 7) for the line source shows that they are entirely comparable. The 1/ p2 dependence for an outgoing spherical wave corresponds to the 1/L 3 / 2 dependence for an outgoing cylindrical wave.

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