An Appraisal of Numerical Approaches for a VED Over the Earth or Ocean

The numerical solution of the classical Sommerfeld problem is thoroughly discussed in this work. In particular, the computation of the vertical electric field excited by a vertical electric dipole (VED) is taken as a paradigm to discuss some different approaches that have been proposed in the literature (with some new variations included). A detailed study is carried out on the pros and cons of each method as well as their range of numerical efficiency in terms of frequency, ground losses, height of the dipole, and distance to the observation point. We finally propose a numerical implementation of the steepest descent method as a good overall method in terms of accuracy, computational efficiency, and extended range of validity. Asymptotic closed-form expressions for the far-field region are also provided.