Doppler shift formulas for waves in the ionosphere
Abstract
Ray techniques are used to examine the range of validity of the Doppler shift formula Δƒ = (ƒ_{T}/c) dP/dt where ƒ_{T} is the transmitter frequency and P the phase path. The simple formula may be used when the time scale of changes in the medium and transmitter and receiver positions is sufficiently large. However, it may fail for quite moderate rates of change. For a moving transmitter a more accurate analysis shows that there may be additional solutions, associated with the complex and "faster than light" Doppler effects, which it does not predict. Spacetime rays are used to obtain formulas valid in the case where the time scale of the changes, though still large in comparison to the reciprocal of the wave frequency, is not large compared with the time characterizing the wave propagation from transmitter to receiver.
 Publication:

Radio Science
 Pub Date:
 July 1976
 DOI:
 10.1029/RS011i007p00621
 Bibcode:
 1976RaSc...11..621B
 Keywords:

 Doppler Effect;
 Ionospheric Propagation;
 Ray Tracing;
 Cerenkov Radiation;
 Spatial Distribution;
 Time Dependence;
 Transit Time;
 Wave Propagation