Investigation of electromagnetic fields in the arctic zone with uneven ice cover

Abstract. Numerical investigation of electromagnetic waves propagating near an ice cover with hummocks of different height has been carried out. Half-wave vibrators, melted into ice at the depth of about 20 sm, were used as an antenna. Transmitted signal frequencies were from 10 to 30 MHz. A mathematical model for amplitude spatial distribution of electromagnetic wave source, placed inside an ice cover with hummocks, was developed. The results of numerical study show that, when antenna is inside hummocks, the signal is amplified. Experimental investigations show good agreement with the theoretical model.


Mathematical model
We consider the following problem. We are to estimate the field of electromagnetic wave point sources placed in the ice layer of uneven form ( Fig. 1) [1][2][3]. The following medium characteristics are known: magnetic and dielectric permeability of mediums; power applied to the radiating antenna; signal frequency. We introduce generalized angular coordinates for φ = 0: U1n = k0·sin(α ± αn); U2n = k0·cos(α ± αn); k0 = 2π/λ. Point M can be located in the air, ice layer or water. To estimate by "directed" Green's functions, we consider the effect of each plane of ice relief on the resulting field. Radiation point source is located at M0 point with the coordinates x0 and y0. The resulting field at the selected point M with the coordinates x and y is equal to the sum of "directed" Green's functions E0 (n) (x0n,y0n), estimated from all the planes of ice relief.
"Directed" Green's function of the waves radiated by a point source is written as where F0 n (U0n) is the diagram function: "Directed" Green's function of the reflected waves has the from where V is the interface reflection coefficient determined by the formulas: for the reflection from upper interface; for the reflection from lower interface; Z1, Z2, Z3 -air, ice and water impedans.
"Directed" Greens' function for the waves, which transmitted through the interface, is where W is the coefficient of transmission though the interface: Resulting field amplitude at M is determined by the sum of "directed" Green's functions As an example, applying formula (4) we estimate the field from one point source for the several frequencies.

Aims and tasks of the experimental investigations
The aim of the experiment is to measure amplitudes of the signals with the frequencies of 10 MHz, 15 MHz, 28,5 MHz in the ice layer.
In the course of the experiment, the antennas were arranged as follows (Fig. 5)

Fig. 5. Antennas arrangement
In Fig. 5, xi is the receiving antenna coordinate, radiating antenna is installed at point 0 (origin of coordinates), d is the ice layer thickness.
The measuring bench is operating as follows: 1. The radiostation (block 1) forms an electric signal with required parameters. 2. A signal from the radiostation (block 1) goes to a tuner (block 2), the device for matching the radiostation and the antennas. From the tuner (block 2) output, the signal is sent to the radiating antenna (block 3).
3. The signal is received by the antenna (block 4), then it goes to the receiving radiostation (block 6) through the tuner (block 5). The power applied to the radiating antenna is 30-35 W. Wave propagation is affected by medium boundaries, ice layer thickness and distribution of solid and fluid phases in it.
The investigations were carried out in Novik bay (Fig. 7) located on the territory of Russkiy Island.

Results of experimental investigations
It is clear from Fig. 2 -Fig. 4 and Fig. 6 -Fig. 8

Conclusions
We have developed a valid mathematical model to investigate electromagnetic wave fields in the air and in the ice layer. The experimental investigation of electromagnetic wave propagation in the ice layer with hummocks show good agreement with theoretical calculations.