The effect of waveguide dispersion on VLF timing systems

It is shown that VLF timing and navigation systems, which use two or more frequencies to resolve cycle ambiguities, may be in error when the propagation mechanism is dispersive. The error arises if the difference between group and phase velocity in such cases is neglected. At 10 kHz the error on a path 10 000 km long, for a reasonable daytime model of the earth-ionosphere waveguide, may be as much as 400
\mu
s for the first-order mode. If the second-order mode is dominant as it may be at night the error will be greatly increased.