By Ronold W.P. King, Margaret Owens, Tai T. Wu
The propagation of waves alongside and around the boundary among media with varied attribute velocities is far extra advanced while the resource is on or close to the boundary than while it truly is far-off and the incident waves are airplane. Examples of waves generated by way of localized resources close to a boundary are the electromagnetic waves from the currents in a dipole at the floor of the earth and the seismic waves from a slip occasion in a fault within the earth's crust just like the San Andreas fault in California. either contain a kind of floor wave that's referred to as a lateral wave in electro magnetics and a head wave in seismology. because the are analogous and the latter is extra simply visualized, it truly is comfortably used right here to introduce and describe this crucial form of floor wave utilizing the information of Y. Ben Zion and P. Malin ("San Andreas Fault sector Head Waves close to Parkfield, CA," technological know-how 251, 1592-1594, 29 March 1991).
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Additional info for Lateral Electromagnetic Waves: Theory and Applications to Communications, Geophysical Exploration, and Remote Sensing
Example text
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.