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It is shown t hat t he fi eld strength according to mode theory and ray theory in t he VLF ba nd are derivable from the same expression of t he original vector potential, and t he r esult of one t heory is the a nalytic continuation of t he other one in another range of convergence. In fact, both ranges of convergence overlap . E t imates of t hese ranges are made an d an example shows t hat within t his overlapping r egion (between di stances of 300 and 2,000 km ) both t heories g ive t he same result. Using this fact calculations of frequ en cy spectra a re possible whi ch in t he case of a white noise dipole show some similar features to measured frequency spectra of ligh t ning disch arges.

Comparison between mode theory and ray theory of VLF propagation