Secondary phaselag computation
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Abstract
The success of using electronic positioning systems depends on a reasonable precise knowledge of the speed of propagation of the electromagnetic wave. In those systems utilizing low frequency radio waves, the ground wave becomes very dominant and therefore the speed of propagation is affected by the electrical characteristic of the ground path. For a homogeneous smooth earth model, this characteristic is mainly determined by the conductivity and dielectric constant (permittivity) of the ground, both of which gives rise to the complicated problem of secondary phaselag. Using two existing programs developed by Brunavs and Gray, based on Johler’s model to compute the secondary phaselag, a study on the method of computation and the behaviour of secondary phaselag with distance, conductivity and permittivity at 100KHz frequency is carried out here. The results of this study are then used to modify these programs for better efficiency.
The above method of computation has been found to be very complicated and time consuming. Brunavs had developed an approximate formula using coefficients to compute total phaselag at 100KHz frequency. However, the range of conductivity and permittivity in his tabulated coefficients is limited. This report expands Brunavs’ work on the approximate formula so that it can be used for a wider range of conductivity and permittivity. An attempt is also made to fit the coefficients with another approximate formula so that Interpolation can be made easily. Finally the results of this extension work are used to developed a computer program to computer total phaselag at 100KHz frequency using the approximate formula over a conductivity range of 0.00001 to 5.5 siemens/metre and permittivity range of 3.0 to 80.0 esu respectively, which in most cases agree with the results using the Johler model to within 5.0m, for distance of 2 to 20000Km.