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Progress in Electromagnetics Research by J. A. Kong

By J. A. Kong

This significant new quantity is the 1st in a sequence that would record on advances and purposes within the smooth improvement of electromagnetics. This sequence will function a world discussion board for the ebook of state-of-the-art overview articles on new theories, methodologies and computational strategies, and interpretations of either theoretical and experimental effects. The sequence' extensive scope covers the spectrum of comparable subject matters from electrostatics to optical frequencies and past. It constitutes a useful reference for scientists and engineers within the electromagnetics career and may act as a resource of latest subject matters for researchers in electromagnetics. this primary quantity contains papers on electromagnetics as utilized to complicated resistivity of the earth, clinical remedies, distant sensing, and extra.

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Thus a ω r E (ju>) =I(jw)dsp (jw)/2Tr for p = pi and θ = 0 (15) Now, in the presence of the inhomogeneity, we can write E (ju>) =I(jw)dsp (jw)/2rr for ^ j ^ P i and l? = 0 (16) 3 r 1 r a 2 s In other words, the apparent complex resistivity for the configuration indicated is an effective parameter that is normalized by the homoge­ neous medium parameter. In a functional sense, we can write ΡαΟ ) ω = Pa [Ριυ )>Ρ2ϋ )] ω ω (17) for a specific configuration of the source dipole and receiving circuit.

1 d. Apparent Resistivity When the medium is inhomogeneous, we need to revise our ap­ proach. To illustrate the problem, consider the situation shown in Fig. 1. 1 Current element source i n h o m o g e n e o u s region (1) in pres­ ence of target region ( 2 ) . 1. e. where p^ij^) — Ρι{ί )\· For example, in the homogeneous case, we might deal with the radial field E (ju>) at θ = 0 . Thus a ω r E (ju>) =I(jw)dsp (jw)/2Tr for p = pi and θ = 0 (15) Now, in the presence of the inhomogeneity, we can write E (ju>) =I(jw)dsp (jw)/2rr for ^ j ^ P i and l?

We discuss this aspect of the problem below. x 2 2 2 k α 2 2 e. C. or zero frequency solutions are a convenient reference. (Wl ft(»)[i + where δι, δ and δ can be regarded as dispersion functions which vanish as ω —• 0 . We now employ a MacLaurin series expansion so that in effect 2 α 1 N=0 ' s Pl°l-£ d Ο χ s Γ P2°2-Z Pi OP2 d Pa(pup ) 2 + RN (38) where R is a suitably defined remainder term [Sokolnikoff 1939]. It is to be noted that the derivatives in (38) involve only DC resistivities. To be explicit, we should note that N 7Γ= Opi U m 6i-*0 9(ρι(1 + δι)) (39) 1.

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