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Wave propagation characteristics of a single-core coaxial cable and a pipe enclosed cable are presented in this paper. For any underground cables, there exists a propagation mode of which the attenuation is very large and the velocity is very low. In the pipe enclosed cable case, propagati on modes within the pipe are almost the same whether the pipe thickness is finite or infinite. When the pipe thickness is finite, there exists a propagation mode between the pipe and earth which distinguishes the finite thickness case from the infinite thickness case. Voltage and currents transformation matrices are, in general, significantly frequency-dependent excepting the case of symmetrical arrangements of polyphase cables.
Akihiro Ametani (1980) studied this question.