The phase variation of very-low-frequency waves propagated over long distances

The proposed use of very-low-frequency waves (10¿20 kc/s) for navigational aids of the phase-comparison type has led to the study of the phase variations of these waves when propagated over distances up to 6000km. The particular aspect of this study described in the paper is the relative phase variations over a pair of adjacent paths. Measurements have been made of the variations in the phase difference between the signals received from a single transmitter at two spaced receiving stations. The two principal transmitters used were Varberg, Sweden, on a frequency of 17.2kc/s and at a range of 1000 km, and Annapolis, United States, on 15.5 kc/s at a range of 6000km. Receiver base-lines, up to 280 km in length, were situated in England and oriented both transverse to, and along, the direction of propagation. The observations were made at various seasons, and the results show the extent of the systematic diurnal changes and the random fluctuations: the former were of the order of 30° at the shorter range and 5° at the longer, and the latter had standard deviations at both ranges of the order of 4° in the day-time and 10° at night. It is shown that the magnitude of the random phase fluctuations can be calculated from measurements of the corresponding amplitude fluctuations. In this way data on phase fluctuations at night at intermediate ranges and for receiver spacings up to 2000km have been obtained. The relationship between the receiver separation and the correlation between fluctuations on two paths has been examined, and it is shown how the results of the phase measurements may be applied to other receiver arrangements.