This paper presents an insight into the transient behavior of a vertical log-periodic dipole antenna (LPDA) above a lossy ground and over a perfectly conducting half space. Mathematically, the problem is formulated in the Laplace domain by a singularity expansion representation of the solution of an electric field integral equation using a Sommerfeld integral kernel. The influence of the feeding network and of the mutual coupling of the elements as well as the influence of the element thickness on the natural resonances of the LPDA is studied. The modes of the antenna elements are presented and the current in frequency and time domain is computed for free space. Dependent on the ground parameters and the antenna height, we show the resonance migration in the complex frequency plane and determine the appropriate modes. Starting with the free space current distribution, we compute the transient far fields of the vertical LPDA over ground for various ground parameters and antenna heights.