Full-waveform inversion is a powerful data-fitting technique that is used for velocity-model building in seismic exploration. The inversion approach exploits the sensitivity of long-offset, wide-aperture, low-frequency data to the P-wave velocity properties in the subsurface. In the geologically complex land context in which different lithologies interleave and create large elastic property contrasts, acoustic waveform inversion is challenged due to the elastic nature of the data. The large elastic property contrasts create mode conversions. At low-to-intermediate frequencies, due to tuning/interference effects, the changes in the amplitudes of the different events affect amplitude and phase of the waveforms. We found that elastic waveform inversion of the long-offset, wide-aperture, low-frequency data leads to better retrieval of the compressional velocity model than the acoustic inversion and it is more stable. To obtain a good resolution in the shallow part of the model in an efficient manner, we have developed a two-stage inversion workflow that combines offset and frequency continuation. We have evaluated the relevance of this workflow with a challenging data set from South Oman.