Information about the nature of the low-temperature anomalies and in particular the properties of the tunneling systems in silica and lithium silica glasses are revealed via computer simulations. The potential energy landscape of these systems is systematically explored for adjacent pairs of local minima which may act as double-well potentials (DWPs) at low temperatures. Three different types of DWPs are distinguished, related to perfectly coordinated silica, intrinsic silica defects, and extrinsic defects. Their properties such as the spatial extension and the dipole moment are characterized in detail. Furthermore, the absolute number of tunneling systems, that is, symmetric DWPs, is estimated. The results are compared with dielectric echo, specific heat, and acoustic experiments on Suprasil I and Suprasil W. A semiquantitative agreement for all relevant features is obtained.