We present a new method for interpreting electromagnetic (EM) data using ray tomography. Direct application of ray tomography to low-frequency EM data is difficult because of the diffusive nature of the field. Diffusive EM fields can, however, be mathematically transformed to wavefields defined in a time-like variable. The transform uniquely relates a field satisfying a diffusion equation in time, or in frequency, to an integral of the corresponding wavefield. If the corresponding wavefields can be computed from low-frequency EM data, one should be able to interpret these data using techniques developed for the wavefields.To test the idea, numerically calculated transient magnetic fields were first transformed to wavefields. The typical window of the time-domain data required for the transform is 1.5 decades. Traveltimes from a source to the receivers were estimated from the reconstructed wavefields. Time-domain data with a Gaussian noise of 3 percent gave a traveltime resolution of better than one percent.For the tomographic inversion, the cross-section between the transmitter and receiver boreholes is divided into a number of rectangular elements, and a continuous slowness is assigned to each of these elements. A functional is formulated by invoking Fermat's principle for the traveltime data. Imposing a stationary condition on the functional gives an iterative procedure for the slowness model. Rays are allowed to bend smoothly within each cell. Incorporating smoothly bending rays is extremely important when the velocity contrast is large. A model with a conductivity contrast of ten (10) has been successfully imaged in 120 iterations with 5 CPU hours on a SUN SPARCstation 2.