Transient fields of a vertical electric dipole on an M-layered dielectric medium

A simple and explicit derivation for the vertical electric dipole excited by a short pulse current and located above a layered dielectric medium is derived in an analytical form using the Cagniard-de-Hoop method. The fields are expressed as the convolution of the exciting current with the layered medium response. This response is obtained directly from the integral representation for the magnetic fields in frequency-domain and is expressed as a finite integral. A modified Cagniard method is then used to derive closed-form expressions for the vertical dipole anywhere above a multilayered medium. The method is used to perform numerical calculations of the magnetic fields for applications to georadar operating on layered media.

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