Complex Impedance Boundary Research Articles

Three-layer matching system for a complex-impedance boundary

Three-layer matching system for a complex-impedance boundary

Propagation of VLF Waves Past a Coastline

The fundamental solution for VLF waves propagating past a shoreline in the earth‐ionosphere duct is obtained in terms of an infinite series using the Wiener‐Hopf methods. The effects of the land, sea, and ionosphere are given in terms of complex impedance boundary conditions. As a result, each mode in the series is progressively damped. At low frequencies and distances far from the shoreline where a single mode dominates, reflection and transmission coefficients are obtained. When the ionospheric impedance is small and when the source and receiver are sufficiently elevated, the effect of the shoreline is not observable. However, when either the source or receiver is near the earth, the portion of the wave reflected is proportional to the difference of sea and land impedances. At slightly higher frequencies, there exists an annular region about the shoreline where two modes propagate over the sea while, due to heavy damping, only one mode propagates over the land. The resulting increase of the field strength as the receiver passes from land, seaward is the “recovery effect.”