Calculation of electromagnetic propagation constant for a buried cable

The current and fields supported by the buried cable are assumed to have an axial dependence of the exponential form having a wave propagation constant. Thus, it is first required to determine the characteristic modes of propagation for the geometry, from which the resulting fields at the earth´s surface can then be calculated. The solution of the problem is facilitated by solving the wave equation in each region (air and earth halfspaces and internal to the cable) and then satisfying the boundary conditions at their interfaces. Under the thin-wire approximation continuity of only the axial component of the electric field E, at the cable surface is expressed as the multiplication of the excited source current and the surface impedance including propagation constant. The values of the propagation constants can be calculated numerically by solving for the zeros of the mode equation using Newton´s method. In this paper, the propagation constant is sought using an analytical type of bi-directional method for the convenience of calculation and that exploration of calculation process is graphically described. This process method to find a propagation constant has no discrepancy with other trial method and can be applied for a cable with an insulating coat or bare state.