We present a new method for interpreting electromagnetic (EM) data usi
ng ray tomography. Direct application of ray tomography to low-frequen
cy EM data is difficult because of the diffusive nature of the field.
Diffusive EM fields can, however, be mathematically transformed to wav
efields defined in a time-like variable. The transform uniquely relate
s a field satisfying a diffusion equation in time, or in frequency, to
an integral of the corresponding wavefield. If the corresponding wave
fields 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 we
re first transformed to wavefields. The typical window of the time-dom
ain data required for the transform is 1.5 decades. Traveltimes from a
source to the receivers were estimated from the reconstructed wavefie
lds. Time-domain data with a Gaussian noise of 3 percent gave a travel
time resolution of better than one percent. For the tomographic invers
ion, the cross-section between the transmitter and receiver boreholes
is divided into a number of rectangular elements, and a continuous slo
wness is assigned to each of these elements. A functional is formulate
d by invoking Fermat's principle for the traveltime data. Imposing a s
tationary condition on the functional gives an iterative procedure for
the slowness model. Rays are allowed to bend smoothly within each cel
l. Incorporating smoothly bending rays is extremely important when the
velocity contrast is large. A model with a conductivity contrast of t
en (10) has been successfully imaged in 120 iterations with 5 CPU hour
s on a SUN SPARCstation 2.