Optimization of through-the-Earth radio communications via mine overburden conductivity estimation

Abstract

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Electromagnetic Wave Propagation in Biaxially Anisotropic Media With Azimuthal Symmetry for Modeling Wireless Telemetry in Deep Oil Well

“…Similarly, from the duality principle, if the source is now a magnetic current loop, J m has only a φ-component and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) gives…”

“…2.2 is presented a directional well using the soil and rocks as a propagation medium for wireless telemetry. These systems provide trough the earth (TTE) telemetry, and they employ electromagnetic waves to establish a communication link between the underground sub-soil and the surface [17][18][19][20][21][22]. TTE systems generally employ magnetic induction at low frequency (below 30 kHz), and therefore, they provide a very low bandwidth.…”

“…When the transmission antenna is a filament electric current loop placed at ρ = ρ and z = z , then J e in (3-19) can be described as in (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) with (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) where I e (φ) is the electric current distribution in the azimuthal direction and δ(·) is the Dirac delta. Then, the projection of (3-18) ontoî φ results in (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)…”

“…A more simplified scenario occurs, however, when the current distribution I e (φ) is uniform and azimuthally independent. This azimuthally symmetric scenario (without φ variations, i.e., ∂/∂φ = 0), allows to reduce (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) to a second-order partial differential equation in terms of only E φ , i.e.,…”

“…a function that only depends on E φ with J e,φ described by (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) for a uniform and azimuthally independent current distribution. Then, substituting into the previous equation yields…”