A Comprehensive Study of Subsurface Propagation from Horizontal Electric Dipoles

Spatial attenuation rates of interfacial waves: Field and numerical tests of Sommerfeld theory using ground-penetrating radar pulses

“…We used a mirror image source for Tx to simulate the down-up-over mode in our numerical integration of the Sommerfeld solutions. radial attenuation rate becomes even closer to the α = 1 case at 37 MHz and at less than about 20λ o , as it would for increasing σ (King et al, 1980). Experimental verification of the Sommerfeld theory is not extensive, probably because it is so well established theoretically for the FR, in which it has been verified only with continuous waves and vertical polarization.…”

“…Within the IR regime geometric attenuation can be near 1/R dependency, but the range where it transitions, and how, to the FR is not clear. King et al (1980) state that they evaluated the complete integral solutions of Banos, with a complex dielectric k substituted for the simpler one Banos used based only on conductivity. They state that, above about 10 MHz, the solutions for each regime overlap with those for the neighboring regimes.…”

“…Reformulations (Banos, 1966;Norton, 1936Norton, , 1937 have been applied at higher frequencies to homogeneous and layered earth with complex permittivity, ε* (Annan, 1973;King et al, 1980;Wait, 1951), and for antennas at any height above or below the surface. On the surface of dielectric earth and in the direction normal to the antenna axis, the solutions are simple, exact and well known theoretically for E ϕ (Annan, 1973;Wait, 1951), but only approximations to integral solutions exist for E ρ in the direction parallel to the antenna axis (Banos, 1966;King et al, 1980). Following Banos (1966) and King et al (1980), above about 10 MHz geometric attenuation rates within several ranges, R, from a transmitting antenna may be characterized by a 1/R α function.…”

“…On the surface of dielectric earth and in the direction normal to the antenna axis, the solutions are simple, exact and well known theoretically for E ϕ (Annan, 1973;Wait, 1951), but only approximations to integral solutions exist for E ρ in the direction parallel to the antenna axis (Banos, 1966;King et al, 1980). Following Banos (1966) and King et al (1980), above about 10 MHz geometric attenuation rates within several ranges, R, from a transmitting antenna may be characterized by a 1/R α function. Within only one to two free space wavelengths (λ o ; λ = λ o / √ε′ is the in situ wavelength), defined as the "near range" (NR), E ϕ and E ρ are predicted to transition from α = 3 to α ≤ 2 dependency.…”

“…1a), but were not treated by Banos (1966); lossy ground would provide only NR solutions. We are interested in the IR because most GPR systems have cable lengths that limit antenna separation to about 100 m; only greater ranges have been investigated numerically (King et al, 1980).…”