We present an imaging scheme for mapping cross-hole electrical conductivity using nonlinear traveltime tomography. Data used are peak arrival time estimates based on an approximate wavefield transform of the synthetic frequency-domain electromagnetic (EM) field. Direct transformation of frequency-domain EM fields to wavefields is known to be an ill-posed problem because the kernel of integral transform is highly damped. In this study, instead of solving such an unstable problem, we approximate the wavefield in the transformed domain via a ray series expansion. If reflected and refracted energy is weak compared to that of direct wave, picking of the peak arrival time may be reduced to estimating the coefficients of the leading term in the ray series expansion. This simplification is valid when the conductivity contrast between background medium and the target anomalous body is small. The first three terms in the expansion are identical to the closed-form solution for the vertical magnetic field caused by a vertical magnetic dipole source in a homogeneous whole-space. An adaptive simulated annealing scheme is used to estimate the coefficients of ray series. For a whole-space, exact traveltime can be extracted using only four frequency samples in our approach, whereas the direct numerical wavefield transform needed at least ten frequencies to construct a reasonable waveform. Nonlinear traveltime tomography using thusly-extracted peak arrivals from synthetic data shows a reasonable image of the conductivity structure between boreholes.