Mutual Impedance of Grounded Wires for Horizontally Stratified Two-Layer Earth

HE general formula for the mutual impedance of wires embedded in a conducting medium and lying in one of two parallel planes of discontinuity in the conductivity with displacement currents neglected is of the following form: Z Si = The integrations are extended in the double integral over the two wires 5 and s extending between points A, B, and a, b, respectively, whose elements dS and ds are separated by distance r and include the angle e between their directions. Q(f) and P(r) are functions of the frequency, the conductivities, and of the separation b between the planes of discontinuity in the conductivities as well as of r. For wires on the surface of a horizontally stratified earth having conductivities Xi and X 2 at depths less than or greater than b, respectively, Q(r) and P{r) are given b y : * A preliminary report of some of the results of this paper has been given in a letter to the E d i t o r of the Physical Review, Vol. 37, No. 10, pp. 1369-1370 ( M a y 15, 1931). 162 MUTUAL IMPEDANCE OF GROUNDED WIRES 163 Q(r j = , | j 4ai 2(w A[aiX2 + + "2X1 a2 )(i + ~ 2)e- 2ba> -- o:2Xi)e_26a»]J X («iX2 J0 (ru)du, P(r)