Wave hop theory of long distance propagation of low-frequency radio waves

The idea that long radio waves propagating between th e earth and ionosphere via di screte hops ean be extended far into the shadow region by evalu ating a series of complex in tegrals is exploit ed in t hi s paper. I llustrative calcu lations of LF and VLF hops and total fields are shown as a function of distance. The second and higher hops show a p seudo-Brewst er angle just before the caust ic and attenuate like ground waves in the shadow region.