The wave equation traveltime inversion (WT) method is adapted to the reconstruction of a dielectric distribution from traveltime radar data. A gradient optimization algorithm is used and the gradient function is computed from finite-difference solutions to the 2-D Maxwell's equations. The key advantage of the radar WT method over conventional ray tracing radar tomography is that it accounts for scattering and diffusion effects in the data and works well in both resistive and moderately conductive rocks. This technique is successfully applied to both synthetic and real radar data. Comparisons with a ray tracing (RT) tomography scheme show that the radar WT method is more robust and accurate than the RT method when rock conductivity is larger than .002 s/m. The WT and RT methods are about equally effective when conductivity is less than or equal to .001 s/m. The disadvantage of the WT scheme is that it generally demands an order of magnitude more computational time than the RT method.