Computation of the field radiated by a FM transmitter by means of ordinary kriging

The maintenance of frequency modulation (FM) broadcasting sites is one of the activities of TDF to guarantee the availability of broadcasting services for its clients. As it is not always possible to stop the broadcasting due to the large number of listeners, TDF has to guarantee the safety of workplaces with respect to the limits of exposure to electromagnetic fields inside the mast near the antenna. Exposure limits are defined in the European Directive for workers (see [1]). Today, TDF carries out measurements with broadband fieldmeter to identify areas above the action level in terms of electric field limit, but for precise measurements, three axes probing with selective measurements are carried out, frequency by frequency, inside the workplace. Hence, the magnitude of the electric field in the zone is obtained either by a broadband fieldmeter which is moved manually along a vertical axis or by a selective three axes probing with a lot of punctual measurements to have a spatial sampling of the field in the volume of interest. Regrettably, in practice, measurements take a long time because of the difficult situation of measurement points, the closeness of metallic structures and a lack of place inside the mast. Consequently, the number of sampling points is generally too limited to assess the exposure. The challenge is not only to assess the field level anywhere inside the volume of interest, without any additional measurements, but also to know the uncertainty associated to the assessed value. By comparing these results to the limit value, one can conclude on the safety of the volume. As a simple interpolation of the measured values does not yield the associated uncertainty, we examine in this paper how ordinary kriging can be an effective tool to take up this challenge. The paper is organized as follows: in Section 2, we recall the main theoretical results concerning the ordinary kriging and, particularly, the variogram. In Section 3, we explain why numerical simulation is used as a help in the implemented process and we present a description of the FM transmitter numerical model. In Section 4, we detail the computations of bidimensional variograms that concern the distribution of electric field in restricted planes of the spatial coordinates system. In Section 5, we detail the construction of three-dimensional variograms that are necessary for the computation of fields over volumes. Finally, some concluding remarks are given in Section 6.