We presented a practical approach to tomographic full-waveform inversion where the computational cost is significantly reduced. This was achieved by first breaking the model into a background component and a perturbation component, and then by restricting the offset axis of the background component to zero subsurface offset only. Breaking the model into two components assumes the data contain primary only. However, we managed to maintain the simultaneous inversion of different wavelengths of the model by mixing the gradients of the two components in Fourier domain using a high-pass and a low-pass filters. The synthetic examples show remarkable results even when the initial model had large errors. More sophisticated mixing schemes need to be further investigated.