The tunneling ionization of deep impurity centers induced by high-intensity terahertz radiation is investigated in the frequency range of transition between the quasi-static and the high frequency regime. A drastic enhancement of the terahertz tunneling ionization of deep impurities in semiconductors has been observed in the high frequency limit of (omega) (tau) <<T 1 ((omega) is electric field frequency and (tau) is the tunneling time). For a given constant tunneling rate an increase of frequency by a factor of seven leads to a drop of the required electric field strength by three orders of magnitude. In the opposite limit of (omega) (tau) <<T 1 within a broad range of intensity, frequency and temperature, the terahertz electric field of the radiation acts like a static field. The ionization can be described as phonon-assisted tunneling in which carrier emission is accompanied by defect tunneling in configuration space and electron tunneling in the electric field of the radiation. At high intensities the ionization is caused by the direct tunneling without involving phonons. Phonon assisted tunneling in high frequency as well as static electric fields is suggested as a method for the characterization of deep impurities in semiconductors. It is shown that an analysis of the field and temperature dependences of the ionization probability allows to obtain defect parameters like tunneling times, the Huang-Rhys factor as well as the basic structure of the defect adiabatic potentials.