Waveform inversion can be treated in theory with a variety of non-linear inverse methods. One feasible approach that has achieved some recent success is the frequency-domain implementation to seismic refraction data examples. A key common factor in these examples is the emphasis on the optimization of models that correctly predict the early (transmitted) arrival waveforms from large offset data . Due to the similarity to other tomographic schemes, we refer to this approach as Waveform Tomography".

Wide angle, refracted arrivals observed at large offsets are generally ignored in the conventional reflection processing scheme used in seismic exploration. However, large offset data are very sensitive to velocities, and waveform tomography provides a way to unravel the complexities of the refracted arrivals in order to yield well constrained velocity models. In contrast, the CMP reflection survey is less sensitive to the macro variations in seismic velocity.

Ultimately surveys should be specifically designed for waveform tomography . Such designs will need to recognize the importance of the refracted wavefield and the equal importance of low frequencies.